FlatCAM/camlib.py

############################################################
# FlatCAM: 2D Post-processing for Manufacturing            #
# http://flatcam.org                                       #
# Author: Juan Pablo Caram (c)                             #
# Date: 2/5/2014                                           #
# MIT Licence                                              #
############################################################
#from __future__ import division
from scipy import optimize
import traceback

from numpy import arctan2, Inf, array, sqrt, pi, ceil, sin, cos, dot, float32, \
    transpose
from numpy.linalg import solve, norm
from matplotlib.figure import Figure
import re

import collections
import numpy as np
import matplotlib
#import matplotlib.pyplot as plt
#from scipy.spatial import Delaunay, KDTree

from rtree import index as rtindex

# See: http://toblerity.org/shapely/manual.html
from shapely.geometry import Polygon, LineString, Point, LinearRing
from shapely.geometry import MultiPoint, MultiPolygon
from shapely.geometry import box as shply_box
from shapely.ops import cascaded_union
import shapely.affinity as affinity
from shapely.wkt import loads as sloads
from shapely.wkt import dumps as sdumps
from shapely.geometry.base import BaseGeometry

# Used for solid polygons in Matplotlib
from descartes.patch import PolygonPatch

import simplejson as json
# TODO: Commented for FlatCAM packaging with cx_freeze
from matplotlib.pyplot import plot, subplot

import logging

log = logging.getLogger('base2')
log.setLevel(logging.DEBUG)
#log.setLevel(logging.WARNING)
#log.setLevel(logging.INFO)
formatter = logging.Formatter('[%(levelname)s] %(message)s')
handler = logging.StreamHandler()
handler.setFormatter(formatter)
log.addHandler(handler)


class ParseError(Exception):
    pass


class Geometry(object):
    """
    Base geometry class.
    """

    defaults = {
        "init_units": 'in'
    }

    def __init__(self):
        # Units (in or mm)
        self.units = Geometry.defaults["init_units"]
        
        # Final geometry: MultiPolygon or list (of geometry constructs)
        self.solid_geometry = None

        # Attributes to be included in serialization
        self.ser_attrs = ['units', 'solid_geometry']

        # Flattened geometry (list of paths only)
        self.flat_geometry = []

    def add_circle(self, origin, radius):
        """
        Adds a circle to the object.

        :param origin: Center of the circle.
        :param radius: Radius of the circle.
        :return: None
        """
        # TODO: Decide what solid_geometry is supposed to be and how we append to it.

        if self.solid_geometry is None:
            self.solid_geometry = []

        if type(self.solid_geometry) is list:
            self.solid_geometry.append(Point(origin).buffer(radius))
            return

        try:
            self.solid_geometry = self.solid_geometry.union(Point(origin).buffer(radius))
        except:
            #print "Failed to run union on polygons."
            log.error("Failed to run union on polygons.")
            raise

    def add_polygon(self, points):
        """
        Adds a polygon to the object (by union)

        :param points: The vertices of the polygon.
        :return: None
        """
        if self.solid_geometry is None:
            self.solid_geometry = []

        if type(self.solid_geometry) is list:
            self.solid_geometry.append(Polygon(points))
            return

        try:
            self.solid_geometry = self.solid_geometry.union(Polygon(points))
        except:
            #print "Failed to run union on polygons."
            log.error("Failed to run union on polygons.")
            raise

    def bounds(self):
        """
        Returns coordinates of rectangular bounds
        of geometry: (xmin, ymin, xmax, ymax).
        """
        log.debug("Geometry->bounds()")
        if self.solid_geometry is None:
            log.debug("solid_geometry is None")
            return 0, 0, 0, 0

        if type(self.solid_geometry) is list:
            # TODO: This can be done faster. See comment from Shapely mailing lists.
            if len(self.solid_geometry) == 0:
                log.debug('solid_geometry is empty []')
                return 0, 0, 0, 0
            return cascaded_union(self.solid_geometry).bounds
        else:
            return self.solid_geometry.bounds

    def find_polygon(self, point, geoset=None):
        """
        Find an object that object.contains(Point(point)) in
        poly, which can can be iterable, contain iterable of, or
        be itself an implementer of .contains().

        :param poly: See description
        :return: Polygon containing point or None.
        """

        if geoset is None:
            geoset = self.solid_geometry

        try:  # Iterable
            for sub_geo in geoset:
                p = self.find_polygon(point, geoset=sub_geo)
                if p is not None:
                    return p

        except TypeError:  # Non-iterable

            try:  # Implements .contains()
                if geoset.contains(Point(point)):
                    return geoset

            except AttributeError:  # Does not implement .contains()
                return None

        return None

    def flatten(self, geometry=None, reset=True, pathonly=False):
        """
        Creates a list of non-iterable linear geometry objects.
        Polygons are expanded into its exterior and interiors if specified.

        Results are placed in self.flat_geoemtry

        :param geometry: Shapely type or list or list of list of such.
        :param reset: Clears the contents of self.flat_geometry.
        :param pathonly: Expands polygons into linear elements.
        """

        if geometry is None:
            geometry = self.solid_geometry

        if reset:
            self.flat_geometry = []

        ## If iterable, expand recursively.
        try:
            for geo in geometry:
                self.flatten(geometry=geo,
                             reset=False,
                             pathonly=pathonly)

        ## Not iterable, do the actual indexing and add.
        except TypeError:
            if pathonly and type(geometry) == Polygon:
                self.flat_geometry.append(geometry.exterior)
                self.flatten(geometry=geometry.interiors,
                             reset=False,
                             pathonly=True)
            else:
                self.flat_geometry.append(geometry)

        return self.flat_geometry

    # def make2Dstorage(self):
    #
    #     self.flatten()
    #
    #     def get_pts(o):
    #         pts = []
    #         if type(o) == Polygon:
    #             g = o.exterior
    #             pts += list(g.coords)
    #             for i in o.interiors:
    #                 pts += list(i.coords)
    #         else:
    #             pts += list(o.coords)
    #         return pts
    #
    #     storage = FlatCAMRTreeStorage()
    #     storage.get_points = get_pts
    #     for shape in self.flat_geometry:
    #         storage.insert(shape)
    #     return storage

    # def flatten_to_paths(self, geometry=None, reset=True):
    #     """
    #     Creates a list of non-iterable linear geometry elements and
    #     indexes them in rtree.
    #
    #     :param geometry: Iterable geometry
    #     :param reset: Wether to clear (True) or append (False) to self.flat_geometry
    #     :return: self.flat_geometry, self.flat_geometry_rtree
    #     """
    #
    #     if geometry is None:
    #         geometry = self.solid_geometry
    #
    #     if reset:
    #         self.flat_geometry = []
    #
    #     ## If iterable, expand recursively.
    #     try:
    #         for geo in geometry:
    #             self.flatten_to_paths(geometry=geo, reset=False)
    #
    #     ## Not iterable, do the actual indexing and add.
    #     except TypeError:
    #         if type(geometry) == Polygon:
    #             g = geometry.exterior
    #             self.flat_geometry.append(g)
    #
    #             ## Add first and last points of the path to the index.
    #             self.flat_geometry_rtree.insert(len(self.flat_geometry) - 1, g.coords[0])
    #             self.flat_geometry_rtree.insert(len(self.flat_geometry) - 1, g.coords[-1])
    #
    #             for interior in geometry.interiors:
    #                 g = interior
    #                 self.flat_geometry.append(g)
    #                 self.flat_geometry_rtree.insert(len(self.flat_geometry) - 1, g.coords[0])
    #                 self.flat_geometry_rtree.insert(len(self.flat_geometry) - 1, g.coords[-1])
    #         else:
    #             g = geometry
    #             self.flat_geometry.append(g)
    #             self.flat_geometry_rtree.insert(len(self.flat_geometry) - 1, g.coords[0])
    #             self.flat_geometry_rtree.insert(len(self.flat_geometry) - 1, g.coords[-1])
    #
    #     return self.flat_geometry, self.flat_geometry_rtree

    def isolation_geometry(self, offset):
        """
        Creates contours around geometry at a given
        offset distance.

        :param offset: Offset distance.
        :type offset: float
        :return: The buffered geometry.
        :rtype: Shapely.MultiPolygon or Shapely.Polygon
        """
        return self.solid_geometry.buffer(offset)

    def is_empty(self):
        if self.solid_geometry is None:
            return True

        if type(self.solid_geometry) is list and len(self.solid_geometry) == 0:
            return True

        return False

    def size(self):
        """
        Returns (width, height) of rectangular
        bounds of geometry.
        """
        if self.solid_geometry is None:
            log.warning("Solid_geometry not computed yet.")
            return 0
        bounds = self.bounds()
        return bounds[2] - bounds[0], bounds[3] - bounds[1]
        
    def get_empty_area(self, boundary=None):
        """
        Returns the complement of self.solid_geometry within
        the given boundary polygon. If not specified, it defaults to
        the rectangular bounding box of self.solid_geometry.
        """
        if boundary is None:
            boundary = self.solid_geometry.envelope
        return boundary.difference(self.solid_geometry)
        
    @staticmethod
    def clear_polygon(polygon, tooldia, overlap=0.15):
        """
        Creates geometry inside a polygon for a tool to cover
        the whole area.

        This algorithm shrinks the edges of the polygon and takes
        the resulting edges as toolpaths.

        :param polygon: Polygon to clear.
        :param tooldia: Diameter of the tool.
        :param overlap: Overlap of toolpasses.
        :return:
        """

        assert type(polygon) == Polygon

        ## The toolpaths
        # Index first and last points in paths
        def get_pts(o):
            return [o.coords[0], o.coords[-1]]
        geoms = FlatCAMRTreeStorage()
        geoms.get_points = get_pts

        # Can only result in a Polygon or MultiPolygon
        current = polygon.buffer(-tooldia / 2.0)

        # current can be a MultiPolygon
        try:
            for p in current:
                geoms.insert(p.exterior)
                for i in p.interiors:
                    geoms.insert(i)

        # Not a Multipolygon. Must be a Polygon
        except TypeError:
            geoms.insert(current.exterior)
            for i in current.interiors:
                geoms.insert(i)

        while True:

            # Can only result in a Polygon or MultiPolygon
            current = current.buffer(-tooldia * (1 - overlap))
            if current.area > 0:

                # current can be a MultiPolygon
                try:
                    for p in current:
                        geoms.insert(p.exterior)
                        for i in p.interiors:
                            geoms.insert(i)

                # Not a Multipolygon. Must be a Polygon
                except TypeError:
                    geoms.insert(current.exterior)
                    for i in current.interiors:
                        geoms.insert(i)
            else:
                break

        # Optimization: Reduce lifts
        log.debug("Reducing tool lifts...")
        geoms = Geometry.paint_connect(geoms, polygon, tooldia)

        return geoms

    @staticmethod
    def clear_polygon2(polygon, tooldia, seedpoint=None, overlap=0.15):
        """
        Creates geometry inside a polygon for a tool to cover
        the whole area.

        This algorithm starts with a seed point inside the polygon
        and draws circles around it. Arcs inside the polygons are
        valid cuts. Finalizes by cutting around the inside edge of
        the polygon.

        :param polygon: Shapely.geometry.Polygon
        :param tooldia: Diameter of the tool
        :param seedpoint: Shapely.geometry.Point or None
        :param overlap: Tool fraction overlap bewteen passes
        :return: List of toolpaths covering polygon.
        """

        # Current buffer radius
        radius = tooldia / 2 * (1 - overlap)

        ## The toolpaths
        # Index first and last points in paths
        def get_pts(o):
            return [o.coords[0], o.coords[-1]]
        geoms = FlatCAMRTreeStorage()
        geoms.get_points = get_pts

        # Path margin
        path_margin = polygon.buffer(-tooldia / 2)

        # Estimate good seedpoint if not provided.
        if seedpoint is None:
            seedpoint = path_margin.representative_point()

        # Grow from seed until outside the box. The polygons will
        # never have an interior, so take the exterior LinearRing.
        while 1:
            path = Point(seedpoint).buffer(radius).exterior
            path = path.intersection(path_margin)

            # Touches polygon?
            if path.is_empty:
                break
            else:
                #geoms.append(path)
                #geoms.insert(path)
                # path can be a collection of paths.
                try:
                    for p in path:
                        geoms.insert(p)
                except TypeError:
                    geoms.insert(path)

            radius += tooldia * (1 - overlap)

        # Clean inside edges of the original polygon
        outer_edges = [x.exterior for x in autolist(polygon.buffer(-tooldia / 2))]
        inner_edges = []
        for x in autolist(polygon.buffer(-tooldia / 2)):  # Over resulting polygons
            for y in x.interiors:  # Over interiors of each polygon
                inner_edges.append(y)
        #geoms += outer_edges + inner_edges
        for g in outer_edges + inner_edges:
            geoms.insert(g)

        # Optimization connect touching paths
        # log.debug("Connecting paths...")
        # geoms = Geometry.path_connect(geoms)

        # Optimization: Reduce lifts
        log.debug("Reducing tool lifts...")
        geoms = Geometry.paint_connect(geoms, polygon, tooldia)

        return geoms

    def scale(self, factor):
        """
        Scales all of the object's geometry by a given factor. Override
        this method.
        :param factor: Number by which to scale.
        :type factor: float
        :return: None
        :rtype: None
        """
        return

    def offset(self, vect):
        """
        Offset the geometry by the given vector. Override this method.

        :param vect: (x, y) vector by which to offset the object.
        :type vect: tuple
        :return: None
        """
        return

    @staticmethod
    def paint_connect(storage, boundary, tooldia, max_walk=None):
        """
        Connects paths that results in a connection segment that is
        within the paint area. This avoids unnecessary tool lifting.

        :param storage: Geometry to be optimized.
        :type storage: FlatCAMRTreeStorage
        :param boundary: Polygon defining the limits of the paintable area.
        :type boundary: Polygon
        :param max_walk: Maximum allowable distance without lifting tool.
        :type max_walk: float or None
        :return: Optimized geometry.
        :rtype: FlatCAMRTreeStorage
        """

        # If max_walk is not specified, the maximum allowed is
        # 10 times the tool diameter
        max_walk = max_walk or 10 * tooldia

        # Assuming geolist is a flat list of flat elements

        ## Index first and last points in paths
        def get_pts(o):
            return [o.coords[0], o.coords[-1]]

        # storage = FlatCAMRTreeStorage()
        # storage.get_points = get_pts
        #
        # for shape in geolist:
        #     if shape is not None:  # TODO: This shouldn't have happened.
        #         # Make LlinearRings into linestrings otherwise
        #         # When chaining the coordinates path is messed up.
        #         storage.insert(LineString(shape))
        #         #storage.insert(shape)

        ## Iterate over geometry paths getting the nearest each time.
        #optimized_paths = []
        optimized_paths = FlatCAMRTreeStorage()
        optimized_paths.get_points = get_pts
        path_count = 0
        current_pt = (0, 0)
        pt, geo = storage.nearest(current_pt)
        storage.remove(geo)
        geo = LineString(geo)
        current_pt = geo.coords[-1]
        try:
            while True:
                path_count += 1
                #log.debug("Path %d" % path_count)

                pt, candidate = storage.nearest(current_pt)
                storage.remove(candidate)
                candidate = LineString(candidate)

                # If last point in geometry is the nearest
                # then reverse coordinates.
                if list(pt) == list(candidate.coords[-1]):
                    candidate.coords = list(candidate.coords)[::-1]

                # Straight line from current_pt to pt.
                # Is the toolpath inside the geometry?
                walk_path = LineString([current_pt, pt])
                walk_cut = walk_path.buffer(tooldia / 2)

                if walk_cut.within(boundary) and walk_path.length < max_walk:
                    #log.debug("Walk to path #%d is inside. Joining." % path_count)

                    # Completely inside. Append...
                    geo.coords = list(geo.coords) + list(candidate.coords)
                    # try:
                    #     last = optimized_paths[-1]
                    #     last.coords = list(last.coords) + list(geo.coords)
                    # except IndexError:
                    #     optimized_paths.append(geo)

                else:

                    # Have to lift tool. End path.
                    #log.debug("Path #%d not within boundary. Next." % path_count)
                    #optimized_paths.append(geo)
                    optimized_paths.insert(geo)
                    geo = candidate

                current_pt = geo.coords[-1]

                # Next
                #pt, geo = storage.nearest(current_pt)

        except StopIteration:  # Nothing left in storage.
            #pass
            optimized_paths.insert(geo)

        return optimized_paths

    @staticmethod
    def path_connect(storage, origin=(0, 0)):
        """

        :return: None
        """

        log.debug("path_connect()")

        ## Index first and last points in paths
        def get_pts(o):
            return [o.coords[0], o.coords[-1]]
        #
        # storage = FlatCAMRTreeStorage()
        # storage.get_points = get_pts
        #
        # for shape in pathlist:
        #     if shape is not None:  # TODO: This shouldn't have happened.
        #         storage.insert(shape)

        path_count = 0
        pt, geo = storage.nearest(origin)
        storage.remove(geo)
        #optimized_geometry = [geo]
        optimized_geometry = FlatCAMRTreeStorage()
        optimized_geometry.get_points = get_pts
        #optimized_geometry.insert(geo)
        try:
            while True:
                path_count += 1

                #print "geo is", geo

                _, left = storage.nearest(geo.coords[0])
                #print "left is", left

                # If left touches geo, remove left from original
                # storage and append to geo.
                if type(left) == LineString:
                    if left.coords[0] == geo.coords[0]:
                        storage.remove(left)
                        geo.coords = list(geo.coords)[::-1] + list(left.coords)
                        continue

                    if left.coords[-1] == geo.coords[0]:
                        storage.remove(left)
                        geo.coords = list(left.coords) + list(geo.coords)
                        continue

                    if left.coords[0] == geo.coords[-1]:
                        storage.remove(left)
                        geo.coords = list(geo.coords) + list(left.coords)
                        continue

                    if left.coords[-1] == geo.coords[-1]:
                        storage.remove(left)
                        geo.coords = list(geo.coords) + list(left.coords)[::-1]
                        continue

                _, right = storage.nearest(geo.coords[-1])
                #print "right is", right

                # If right touches geo, remove left from original
                # storage and append to geo.
                if type(right) == LineString:
                    if right.coords[0] == geo.coords[-1]:
                        storage.remove(right)
                        geo.coords = list(geo.coords) + list(right.coords)
                        continue

                    if right.coords[-1] == geo.coords[-1]:
                        storage.remove(right)
                        geo.coords = list(geo.coords) + list(right.coords)[::-1]
                        continue

                    if right.coords[0] == geo.coords[0]:
                        storage.remove(right)
                        geo.coords = list(geo.coords)[::-1] + list(right.coords)
                        continue

                    if right.coords[-1] == geo.coords[0]:
                        storage.remove(right)
                        geo.coords = list(left.coords) + list(geo.coords)
                        continue

                # right is either a LinearRing or it does not connect
                # to geo (nothing left to connect to geo), so we continue
                # with right as geo.
                storage.remove(right)

                if type(right) == LinearRing:
                    optimized_geometry.insert(right)
                else:
                    # Cannot exteng geo any further. Put it away.
                    optimized_geometry.insert(geo)

                    # Continue with right.
                    geo = right

        except StopIteration:  # Nothing found in storage.
            optimized_geometry.insert(geo)

        #print path_count
        log.debug("path_count = %d" % path_count)

        return optimized_geometry

    def convert_units(self, units):
        """
        Converts the units of the object to ``units`` by scaling all
        the geometry appropriately. This call ``scale()``. Don't call
        it again in descendents.

        :param units: "IN" or "MM"
        :type units: str
        :return: Scaling factor resulting from unit change.
        :rtype: float
        """
        log.debug("Geometry.convert_units()")

        if units.upper() == self.units.upper():
            return 1.0

        if units.upper() == "MM":
            factor = 25.4
        elif units.upper() == "IN":
            factor = 1 / 25.4
        else:
            log.error("Unsupported units: %s" % str(units))
            return 1.0

        self.units = units
        self.scale(factor)
        return factor

    def to_dict(self):
        """
        Returns a respresentation of the object as a dictionary.
        Attributes to include are listed in ``self.ser_attrs``.

        :return: A dictionary-encoded copy of the object.
        :rtype: dict
        """
        d = {}
        for attr in self.ser_attrs:
            d[attr] = getattr(self, attr)
        return d

    def from_dict(self, d):
        """
        Sets object's attributes from a dictionary.
        Attributes to include are listed in ``self.ser_attrs``.
        This method will look only for only and all the
        attributes in ``self.ser_attrs``. They must all
        be present. Use only for deserializing saved
        objects.

        :param d: Dictionary of attributes to set in the object.
        :type d: dict
        :return: None
        """
        for attr in self.ser_attrs:
            setattr(self, attr, d[attr])

    def union(self):
        """
        Runs a cascaded union on the list of objects in
        solid_geometry.

        :return: None
        """
        self.solid_geometry = [cascaded_union(self.solid_geometry)]


class ApertureMacro:
    """
    Syntax of aperture macros.

    <AM command>:           AM<Aperture macro name>*<Macro content>
    <Macro content>:        {{<Variable definition>*}{<Primitive>*}}
    <Variable definition>:  $K=<Arithmetic expression>
    <Primitive>:            <Primitive code>,<Modifier>{,<Modifier>}|<Comment>
    <Modifier>:             $M|< Arithmetic expression>
    <Comment>:              0 <Text>
    """

    ## Regular expressions
    am1_re = re.compile(r'^%AM([^\*]+)\*(.+)?(%)?$')
    am2_re = re.compile(r'(.*)%$')
    amcomm_re = re.compile(r'^0(.*)')
    amprim_re = re.compile(r'^[1-9].*')
    amvar_re = re.compile(r'^\$([0-9a-zA-z]+)=(.*)')

    def __init__(self, name=None):
        self.name = name
        self.raw = ""

        ## These below are recomputed for every aperture
        ## definition, in other words, are temporary variables.
        self.primitives = []
        self.locvars = {}
        self.geometry = None

    def to_dict(self):
        """
        Returns the object in a serializable form. Only the name and
        raw are required.

        :return: Dictionary representing the object. JSON ready.
        :rtype: dict
        """

        return {
            'name': self.name,
            'raw': self.raw
        }

    def from_dict(self, d):
        """
        Populates the object from a serial representation created
        with ``self.to_dict()``.

        :param d: Serial representation of an ApertureMacro object.
        :return: None
        """
        for attr in ['name', 'raw']:
            setattr(self, attr, d[attr])

    def parse_content(self):
        """
        Creates numerical lists for all primitives in the aperture
        macro (in ``self.raw``) by replacing all variables by their
        values iteratively and evaluating expressions. Results
        are stored in ``self.primitives``.

        :return: None
        """
        # Cleanup
        self.raw = self.raw.replace('\n', '').replace('\r', '').strip(" *")
        self.primitives = []

        # Separate parts
        parts = self.raw.split('*')

        #### Every part in the macro ####
        for part in parts:
            ### Comments. Ignored.
            match = ApertureMacro.amcomm_re.search(part)
            if match:
                continue

            ### Variables
            # These are variables defined locally inside the macro. They can be
            # numerical constant or defind in terms of previously define
            # variables, which can be defined locally or in an aperture
            # definition. All replacements ocurr here.
            match = ApertureMacro.amvar_re.search(part)
            if match:
                var = match.group(1)
                val = match.group(2)

                # Replace variables in value
                for v in self.locvars:
                    val = re.sub(r'\$'+str(v)+r'(?![0-9a-zA-Z])', str(self.locvars[v]), val)

                # Make all others 0
                val = re.sub(r'\$[0-9a-zA-Z](?![0-9a-zA-Z])', "0", val)

                # Change x with *
                val = re.sub(r'[xX]', "*", val)

                # Eval() and store.
                self.locvars[var] = eval(val)
                continue

            ### Primitives
            # Each is an array. The first identifies the primitive, while the
            # rest depend on the primitive. All are strings representing a
            # number and may contain variable definition. The values of these
            # variables are defined in an aperture definition.
            match = ApertureMacro.amprim_re.search(part)
            if match:
                ## Replace all variables
                for v in self.locvars:
                    part = re.sub(r'\$' + str(v) + r'(?![0-9a-zA-Z])', str(self.locvars[v]), part)

                # Make all others 0
                part = re.sub(r'\$[0-9a-zA-Z](?![0-9a-zA-Z])', "0", part)

                # Change x with *
                part = re.sub(r'[xX]', "*", part)

                ## Store
                elements = part.split(",")
                self.primitives.append([eval(x) for x in elements])
                continue

            log.warning("Unknown syntax of aperture macro part: %s" % str(part))

    def append(self, data):
        """
        Appends a string to the raw macro.

        :param data: Part of the macro.
        :type data: str
        :return: None
        """
        self.raw += data

    @staticmethod
    def default2zero(n, mods):
        """
        Pads the ``mods`` list with zeros resulting in an
        list of length n.

        :param n: Length of the resulting list.
        :type n: int
        :param mods: List to be padded.
        :type mods: list
        :return: Zero-padded list.
        :rtype: list
        """
        x = [0.0] * n
        na = len(mods)
        x[0:na] = mods
        return x

    @staticmethod
    def make_circle(mods):
        """

        :param mods: (Exposure 0/1, Diameter >=0, X-coord, Y-coord)
        :return:
        """

        pol, dia, x, y = ApertureMacro.default2zero(4, mods)

        return {"pol": int(pol), "geometry": Point(x, y).buffer(dia/2)}

    @staticmethod
    def make_vectorline(mods):
        """

        :param mods: (Exposure 0/1, Line width >= 0, X-start, Y-start, X-end, Y-end,
            rotation angle around origin in degrees)
        :return:
        """
        pol, width, xs, ys, xe, ye, angle = ApertureMacro.default2zero(7, mods)

        line = LineString([(xs, ys), (xe, ye)])
        box = line.buffer(width/2, cap_style=2)
        box_rotated = affinity.rotate(box, angle, origin=(0, 0))

        return {"pol": int(pol), "geometry": box_rotated}

    @staticmethod
    def make_centerline(mods):
        """

        :param mods: (Exposure 0/1, width >=0, height >=0, x-center, y-center,
            rotation angle around origin in degrees)
        :return:
        """

        pol, width, height, x, y, angle = ApertureMacro.default2zero(6, mods)

        box = shply_box(x-width/2, y-height/2, x+width/2, y+height/2)
        box_rotated = affinity.rotate(box, angle, origin=(0, 0))

        return {"pol": int(pol), "geometry": box_rotated}

    @staticmethod
    def make_lowerleftline(mods):
        """

        :param mods: (exposure 0/1, width >=0, height >=0, x-lowerleft, y-lowerleft,
            rotation angle around origin in degrees)
        :return:
        """

        pol, width, height, x, y, angle = ApertureMacro.default2zero(6, mods)

        box = shply_box(x, y, x+width, y+height)
        box_rotated = affinity.rotate(box, angle, origin=(0, 0))

        return {"pol": int(pol), "geometry": box_rotated}

    @staticmethod
    def make_outline(mods):
        """

        :param mods:
        :return:
        """

        pol = mods[0]
        n = mods[1]
        points = [(0, 0)]*(n+1)

        for i in range(n+1):
            points[i] = mods[2*i + 2:2*i + 4]

        angle = mods[2*n + 4]

        poly = Polygon(points)
        poly_rotated = affinity.rotate(poly, angle, origin=(0, 0))

        return {"pol": int(pol), "geometry": poly_rotated}

    @staticmethod
    def make_polygon(mods):
        """
        Note: Specs indicate that rotation is only allowed if the center
        (x, y) == (0, 0). I will tolerate breaking this rule.

        :param mods: (exposure 0/1, n_verts 3<=n<=12, x-center, y-center,
            diameter of circumscribed circle >=0, rotation angle around origin)
        :return:
        """

        pol, nverts, x, y, dia, angle = ApertureMacro.default2zero(6, mods)
        points = [(0, 0)]*nverts

        for i in range(nverts):
            points[i] = (x + 0.5 * dia * cos(2*pi * i/nverts),
                         y + 0.5 * dia * sin(2*pi * i/nverts))

        poly = Polygon(points)
        poly_rotated = affinity.rotate(poly, angle, origin=(0, 0))

        return {"pol": int(pol), "geometry": poly_rotated}

    @staticmethod
    def make_moire(mods):
        """
        Note: Specs indicate that rotation is only allowed if the center
        (x, y) == (0, 0). I will tolerate breaking this rule.

        :param mods: (x-center, y-center, outer_dia_outer_ring, ring thickness,
            gap, max_rings, crosshair_thickness, crosshair_len, rotation
            angle around origin in degrees)
        :return:
        """

        x, y, dia, thickness, gap, nrings, cross_th, cross_len, angle = ApertureMacro.default2zero(9, mods)

        r = dia/2 - thickness/2
        result = Point((x, y)).buffer(r).exterior.buffer(thickness/2.0)
        ring = Point((x, y)).buffer(r).exterior.buffer(thickness/2.0)  # Need a copy!

        i = 1  # Number of rings created so far

        ## If the ring does not have an interior it means that it is
        ## a disk. Then stop.
        while len(ring.interiors) > 0 and i < nrings:
            r -= thickness + gap
            if r <= 0:
                break
            ring = Point((x, y)).buffer(r).exterior.buffer(thickness/2.0)
            result = cascaded_union([result, ring])
            i += 1

        ## Crosshair
        hor = LineString([(x - cross_len, y), (x + cross_len, y)]).buffer(cross_th/2.0, cap_style=2)
        ver = LineString([(x, y-cross_len), (x, y + cross_len)]).buffer(cross_th/2.0, cap_style=2)
        result = cascaded_union([result, hor, ver])

        return {"pol": 1, "geometry": result}

    @staticmethod
    def make_thermal(mods):
        """
        Note: Specs indicate that rotation is only allowed if the center
        (x, y) == (0, 0). I will tolerate breaking this rule.

        :param mods: [x-center, y-center, diameter-outside, diameter-inside,
            gap-thickness, rotation angle around origin]
        :return:
        """

        x, y, dout, din, t, angle = ApertureMacro.default2zero(6, mods)

        ring = Point((x, y)).buffer(dout/2.0).difference(Point((x, y)).buffer(din/2.0))
        hline = LineString([(x - dout/2.0, y), (x + dout/2.0, y)]).buffer(t/2.0, cap_style=3)
        vline = LineString([(x, y - dout/2.0), (x, y + dout/2.0)]).buffer(t/2.0, cap_style=3)
        thermal = ring.difference(hline.union(vline))

        return {"pol": 1, "geometry": thermal}

    def make_geometry(self, modifiers):
        """
        Runs the macro for the given modifiers and generates
        the corresponding geometry.

        :param modifiers: Modifiers (parameters) for this macro
        :type modifiers: list
        """

        ## Primitive makers
        makers = {
            "1": ApertureMacro.make_circle,
            "2": ApertureMacro.make_vectorline,
            "20": ApertureMacro.make_vectorline,
            "21": ApertureMacro.make_centerline,
            "22": ApertureMacro.make_lowerleftline,
            "4": ApertureMacro.make_outline,
            "5": ApertureMacro.make_polygon,
            "6": ApertureMacro.make_moire,
            "7": ApertureMacro.make_thermal
        }

        ## Store modifiers as local variables
        modifiers = modifiers or []
        modifiers = [float(m) for m in modifiers]
        self.locvars = {}
        for i in range(0, len(modifiers)):
            self.locvars[str(i+1)] = modifiers[i]

        ## Parse
        self.primitives = []  # Cleanup
        self.geometry = None
        self.parse_content()

        ## Make the geometry
        for primitive in self.primitives:
            # Make the primitive
            prim_geo = makers[str(int(primitive[0]))](primitive[1:])

            # Add it (according to polarity)
            if self.geometry is None and prim_geo['pol'] == 1:
                self.geometry = prim_geo['geometry']
                continue
            if prim_geo['pol'] == 1:
                self.geometry = self.geometry.union(prim_geo['geometry'])
                continue
            if prim_geo['pol'] == 0:
                self.geometry = self.geometry.difference(prim_geo['geometry'])
                continue

        return self.geometry


class Gerber (Geometry):
    """
    **ATTRIBUTES**

    * ``apertures`` (dict): The keys are names/identifiers of each aperture.
      The values are dictionaries key/value pairs which describe the aperture. The
      type key is always present and the rest depend on the key:

    +-----------+-----------------------------------+
    | Key       | Value                             |
    +===========+===================================+
    | type      | (str) "C", "R", "O", "P", or "AP" |
    +-----------+-----------------------------------+
    | others    | Depend on ``type``                |
    +-----------+-----------------------------------+

    * ``aperture_macros`` (dictionary): Are predefined geometrical structures
      that can be instanciated with different parameters in an aperture
      definition. See ``apertures`` above. The key is the name of the macro,
      and the macro itself, the value, is a ``Aperture_Macro`` object.

    * ``flash_geometry`` (list): List of (Shapely) geometric object resulting
      from ``flashes``. These are generated from ``flashes`` in ``do_flashes()``.

    * ``buffered_paths`` (list): List of (Shapely) polygons resulting from
      *buffering* (or thickening) the ``paths`` with the aperture. These are
      generated from ``paths`` in ``buffer_paths()``.

    **USAGE**::

        g = Gerber()
        g.parse_file(filename)
        g.create_geometry()
        do_something(s.solid_geometry)

    """

    defaults = {
        "steps_per_circle": 40
    }

    def __init__(self, steps_per_circle=None):
        """
        The constructor takes no parameters. Use ``gerber.parse_files()``
        or ``gerber.parse_lines()`` to populate the object from Gerber source.

        :return: Gerber object
        :rtype: Gerber
        """

        # Initialize parent
        Geometry.__init__(self)

        self.solid_geometry = Polygon()

        # Number format
        self.int_digits = 3
        """Number of integer digits in Gerber numbers. Used during parsing."""

        self.frac_digits = 4
        """Number of fraction digits in Gerber numbers. Used during parsing."""
        
        ## Gerber elements ##
        # Apertures {'id':{'type':chr, 
        #             ['size':float], ['width':float],
        #             ['height':float]}, ...}
        self.apertures = {}

        # Aperture Macros
        self.aperture_macros = {}

        # Attributes to be included in serialization
        # Always append to it because it carries contents
        # from Geometry.
        self.ser_attrs += ['int_digits', 'frac_digits', 'apertures',
                           'aperture_macros', 'solid_geometry']

        #### Parser patterns ####
        # FS - Format Specification
        # The format of X and Y must be the same!
        # L-omit leading zeros, T-omit trailing zeros
        # A-absolute notation, I-incremental notation
        self.fmt_re = re.compile(r'%FS([LT])([AI])X(\d)(\d)Y\d\d\*%$')

        # Mode (IN/MM)
        self.mode_re = re.compile(r'^%MO(IN|MM)\*%$')

        # Comment G04|G4
        self.comm_re = re.compile(r'^G0?4(.*)$')

        # AD - Aperture definition
        self.ad_re = re.compile(r'^%ADD(\d\d+)([a-zA-Z_$\.][a-zA-Z0-9_$\.]*)(?:,(.*))?\*%$')

        # AM - Aperture Macro
        # Beginning of macro (Ends with *%):
        #self.am_re = re.compile(r'^%AM([a-zA-Z0-9]*)\*')

        # Tool change
        # May begin with G54 but that is deprecated
        self.tool_re = re.compile(r'^(?:G54)?D(\d\d+)\*$')

        # G01... - Linear interpolation plus flashes with coordinates
        # Operation code (D0x) missing is deprecated... oh well I will support it.
        self.lin_re = re.compile(r'^(?:G0?(1))?(?=.*X(-?\d+))?(?=.*Y(-?\d+))?[XY][^DIJ]*(?:D0?([123]))?\*$')

        # Operation code alone, usually just D03 (Flash)
        self.opcode_re = re.compile(r'^D0?([123])\*$')

        # G02/3... - Circular interpolation with coordinates
        # 2-clockwise, 3-counterclockwise
        # Operation code (D0x) missing is deprecated... oh well I will support it.
        # Optional start with G02 or G03, optional end with D01 or D02 with
        # optional coordinates but at least one in any order.
        self.circ_re = re.compile(r'^(?:G0?([23]))?(?=.*X(-?\d+))?(?=.*Y(-?\d+))' +
                                  '?(?=.*I(-?\d+))?(?=.*J(-?\d+))?[XYIJ][^D]*(?:D0([12]))?\*$')

        # G01/2/3 Occurring without coordinates
        self.interp_re = re.compile(r'^(?:G0?([123]))\*')

        # Single D74 or multi D75 quadrant for circular interpolation
        self.quad_re = re.compile(r'^G7([45])\*$')

        # Region mode on
        # In region mode, D01 starts a region
        # and D02 ends it. A new region can be started again
        # with D01. All contours must be closed before
        # D02 or G37.
        self.regionon_re = re.compile(r'^G36\*$')

        # Region mode off
        # Will end a region and come off region mode.
        # All contours must be closed before D02 or G37.
        self.regionoff_re = re.compile(r'^G37\*$')

        # End of file
        self.eof_re = re.compile(r'^M02\*')

        # IP - Image polarity
        self.pol_re = re.compile(r'^%IP(POS|NEG)\*%$')

        # LP - Level polarity
        self.lpol_re = re.compile(r'^%LP([DC])\*%$')

        # Units (OBSOLETE)
        self.units_re = re.compile(r'^G7([01])\*$')

        # Absolute/Relative G90/1 (OBSOLETE)
        self.absrel_re = re.compile(r'^G9([01])\*$')

        # Aperture macros
        self.am1_re = re.compile(r'^%AM([^\*]+)\*([^%]+)?(%)?$')
        self.am2_re = re.compile(r'(.*)%$')

        # How to discretize a circle.
        self.steps_per_circ = steps_per_circle or Gerber.defaults['steps_per_circle']

    def scale(self, factor):
        """
        Scales the objects' geometry on the XY plane by a given factor.
        These are:

        * ``buffered_paths``
        * ``flash_geometry``
        * ``solid_geometry``
        * ``regions``

        NOTE:
        Does not modify the data used to create these elements. If these
        are recreated, the scaling will be lost. This behavior was modified
        because of the complexity reached in this class.

        :param factor: Number by which to scale.
        :type factor: float
        :rtype : None
        """

        ## solid_geometry ???
        #  It's a cascaded union of objects.
        self.solid_geometry = affinity.scale(self.solid_geometry, factor,
                                             factor, origin=(0, 0))

        # # Now buffered_paths, flash_geometry and solid_geometry
        # self.create_geometry()

    def offset(self, vect):
        """
        Offsets the objects' geometry on the XY plane by a given vector.
        These are:

        * ``buffered_paths``
        * ``flash_geometry``
        * ``solid_geometry``
        * ``regions``

        NOTE:
        Does not modify the data used to create these elements. If these
        are recreated, the scaling will be lost. This behavior was modified
        because of the complexity reached in this class.

        :param vect: (x, y) offset vector.
        :type vect: tuple
        :return: None
        """

        dx, dy = vect

        ## Solid geometry
        self.solid_geometry = affinity.translate(self.solid_geometry, xoff=dx, yoff=dy)

    def mirror(self, axis, point):
        """
        Mirrors the object around a specified axis passign through
        the given point. What is affected:

        * ``buffered_paths``
        * ``flash_geometry``
        * ``solid_geometry``
        * ``regions``

        NOTE:
        Does not modify the data used to create these elements. If these
        are recreated, the scaling will be lost. This behavior was modified
        because of the complexity reached in this class.

        :param axis: "X" or "Y" indicates around which axis to mirror.
        :type axis: str
        :param point: [x, y] point belonging to the mirror axis.
        :type point: list
        :return: None
        """

        px, py = point
        xscale, yscale = {"X": (1.0, -1.0), "Y": (-1.0, 1.0)}[axis]

        ## solid_geometry ???
        #  It's a cascaded union of objects.
        self.solid_geometry = affinity.scale(self.solid_geometry,
                                             xscale, yscale, origin=(px, py))

    def aperture_parse(self, apertureId, apertureType, apParameters):
        """
        Parse gerber aperture definition into dictionary of apertures.
        The following kinds and their attributes are supported:

        * *Circular (C)*: size (float)
        * *Rectangle (R)*: width (float), height (float)
        * *Obround (O)*: width (float), height (float).
        * *Polygon (P)*: diameter(float), vertices(int), [rotation(float)]
        * *Aperture Macro (AM)*: macro (ApertureMacro), modifiers (list)

        :param apertureId: Id of the aperture being defined.
        :param apertureType: Type of the aperture.
        :param apParameters: Parameters of the aperture.
        :type apertureId: str
        :type apertureType: str
        :type apParameters: str
        :return: Identifier of the aperture.
        :rtype: str
        """

        # Found some Gerber with a leading zero in the aperture id and the
        # referenced it without the zero, so this is a hack to handle that.
        apid = str(int(apertureId))

        try:  # Could be empty for aperture macros
            paramList = apParameters.split('X')
        except:
            paramList = None

        if apertureType == "C":  # Circle, example: %ADD11C,0.1*%
            self.apertures[apid] = {"type": "C",
                                    "size": float(paramList[0])}
            return apid
        
        if apertureType == "R":  # Rectangle, example: %ADD15R,0.05X0.12*%
            self.apertures[apid] = {"type": "R",
                                    "width": float(paramList[0]),
                                    "height": float(paramList[1]),
                                    "size": sqrt(float(paramList[0])**2 + float(paramList[1])**2)}  # Hack
            return apid

        if apertureType == "O":  # Obround
            self.apertures[apid] = {"type": "O",
                                    "width": float(paramList[0]),
                                    "height": float(paramList[1]),
                                    "size": sqrt(float(paramList[0])**2 + float(paramList[1])**2)}  # Hack
            return apid
        
        if apertureType == "P":  # Polygon (regular)
            self.apertures[apid] = {"type": "P",
                                    "diam": float(paramList[0]),
                                    "nVertices": int(paramList[1]),
                                    "size": float(paramList[0])}  # Hack
            if len(paramList) >= 3:
                self.apertures[apid]["rotation"] = float(paramList[2])
            return apid

        if apertureType in self.aperture_macros:
            self.apertures[apid] = {"type": "AM",
                                    "macro": self.aperture_macros[apertureType],
                                    "modifiers": paramList}
            return apid

        log.warning("Aperture not implemented: %s" % str(apertureType))
        return None
        
    def parse_file(self, filename, follow=False):
        """
        Calls Gerber.parse_lines() with array of lines
        read from the given file.

        :param filename: Gerber file to parse.
        :type filename: str
        :param follow: If true, will not create polygons, just lines
            following the gerber path.
        :type follow: bool
        :return: None
        """
        gfile = open(filename, 'r')
        gstr = gfile.readlines()
        gfile.close()
        self.parse_lines(gstr, follow=follow)

    #@profile
    def parse_lines(self, glines, follow=False):
        """
        Main Gerber parser. Reads Gerber and populates ``self.paths``, ``self.apertures``,
        ``self.flashes``, ``self.regions`` and ``self.units``.

        :param glines: Gerber code as list of strings, each element being
            one line of the source file.
        :type glines: list
        :param follow: If true, will not create polygons, just lines
            following the gerber path.
        :type follow: bool
        :return: None
        :rtype: None
        """

        # Coordinates of the current path, each is [x, y]
        path = []

        # Polygons are stored here until there is a change in polarity.
        # Only then they are combined via cascaded_union and added or
        # subtracted from solid_geometry. This is ~100 times faster than
        # applyng a union for every new polygon.
        poly_buffer = []

        last_path_aperture = None
        current_aperture = None

        # 1,2 or 3 from "G01", "G02" or "G03"
        current_interpolation_mode = None

        # 1 or 2 from "D01" or "D02"
        # Note this is to support deprecated Gerber not putting
        # an operation code at the end of every coordinate line.
        current_operation_code = None

        # Current coordinates
        current_x = None
        current_y = None

        # Absolute or Relative/Incremental coordinates
        # Not implemented
        absolute = True

        # How to interpret circular interpolation: SINGLE or MULTI
        quadrant_mode = None

        # Indicates we are parsing an aperture macro
        current_macro = None

        # Indicates the current polarity: D-Dark, C-Clear
        current_polarity = 'D'

        # If a region is being defined
        making_region = False

        #### Parsing starts here ####
        line_num = 0
        gline = ""
        try:
            for gline in glines:
                line_num += 1

                ### Cleanup
                gline = gline.strip(' \r\n')

                #log.debug("%3s %s" % (line_num, gline))

                ### Aperture Macros
                # Having this at the beggining will slow things down
                # but macros can have complicated statements than could
                # be caught by other patterns.
                if current_macro is None:  # No macro started yet
                    match = self.am1_re.search(gline)
                    # Start macro if match, else not an AM, carry on.
                    if match:
                        log.info("Starting macro. Line %d: %s" % (line_num, gline))
                        current_macro = match.group(1)
                        self.aperture_macros[current_macro] = ApertureMacro(name=current_macro)
                        if match.group(2):  # Append
                            self.aperture_macros[current_macro].append(match.group(2))
                        if match.group(3):  # Finish macro
                            #self.aperture_macros[current_macro].parse_content()
                            current_macro = None
                            log.info("Macro complete in 1 line.")
                        continue
                else:  # Continue macro
                    log.info("Continuing macro. Line %d." % line_num)
                    match = self.am2_re.search(gline)
                    if match:  # Finish macro
                        log.info("End of macro. Line %d." % line_num)
                        self.aperture_macros[current_macro].append(match.group(1))
                        #self.aperture_macros[current_macro].parse_content()
                        current_macro = None
                    else:  # Append
                        self.aperture_macros[current_macro].append(gline)
                    continue

                ### G01 - Linear interpolation plus flashes
                # Operation code (D0x) missing is deprecated... oh well I will support it.
                # REGEX: r'^(?:G0?(1))?(?:X(-?\d+))?(?:Y(-?\d+))?(?:D0([123]))?\*$'
                match = self.lin_re.search(gline)
                if match:
                    # Dxx alone?
                    # if match.group(1) is None and match.group(2) is None and match.group(3) is None:
                    #     try:
                    #         current_operation_code = int(match.group(4))
                    #     except:
                    #         pass  # A line with just * will match too.
                    #     continue
                    # NOTE: Letting it continue allows it to react to the
                    #       operation code.

                    # Parse coordinates
                    if match.group(2) is not None:
                        current_x = parse_gerber_number(match.group(2), self.frac_digits)
                    if match.group(3) is not None:
                        current_y = parse_gerber_number(match.group(3), self.frac_digits)

                    # Parse operation code
                    if match.group(4) is not None:
                        current_operation_code = int(match.group(4))

                    # Pen down: add segment
                    if current_operation_code == 1:
                        path.append([current_x, current_y])
                        last_path_aperture = current_aperture

                    elif current_operation_code == 2:
                        if len(path) > 1:

                            ## --- BUFFERED ---
                            if making_region:
                                geo = Polygon(path)
                            else:
                                if last_path_aperture is None:
                                    log.warning("No aperture defined for curent path. (%d)" % line_num)
                                width = self.apertures[last_path_aperture]["size"]  # TODO: WARNING this should fail!
                                #log.debug("Line %d: Setting aperture to %s before buffering." % (line_num, last_path_aperture))
                                if follow:
                                    geo = LineString(path)
                                else:
                                    geo = LineString(path).buffer(width / 2)
                            poly_buffer.append(geo)

                        path = [[current_x, current_y]]  # Start new path

                    # Flash
                    elif current_operation_code == 3:

                        # --- BUFFERED ---
                        flash = Gerber.create_flash_geometry(Point([current_x, current_y]),
                                                             self.apertures[current_aperture])
                        poly_buffer.append(flash)

                    continue

                ### G02/3 - Circular interpolation
                # 2-clockwise, 3-counterclockwise
                match = self.circ_re.search(gline)
                if match:
                    arcdir = [None, None, "cw", "ccw"]

                    mode, x, y, i, j, d = match.groups()
                    try:
                        x = parse_gerber_number(x, self.frac_digits)
                    except:
                        x = current_x
                    try:
                        y = parse_gerber_number(y, self.frac_digits)
                    except:
                        y = current_y
                    try:
                        i = parse_gerber_number(i, self.frac_digits)
                    except:
                        i = 0
                    try:
                        j = parse_gerber_number(j, self.frac_digits)
                    except:
                        j = 0

                    if quadrant_mode is None:
                        log.error("Found arc without preceding quadrant specification G74 or G75. (%d)" % line_num)
                        log.error(gline)
                        continue

                    if mode is None and current_interpolation_mode not in [2, 3]:
                        log.error("Found arc without circular interpolation mode defined. (%d)" % line_num)
                        log.error(gline)
                        continue
                    elif mode is not None:
                        current_interpolation_mode = int(mode)

                    # Set operation code if provided
                    if d is not None:
                        current_operation_code = int(d)

                    # Nothing created! Pen Up.
                    if current_operation_code == 2:
                        log.warning("Arc with D2. (%d)" % line_num)
                        if len(path) > 1:
                            if last_path_aperture is None:
                                log.warning("No aperture defined for curent path. (%d)" % line_num)

                            # --- BUFFERED ---
                            width = self.apertures[last_path_aperture]["size"]
                            buffered = LineString(path).buffer(width / 2)
                            poly_buffer.append(buffered)

                        current_x = x
                        current_y = y
                        path = [[current_x, current_y]]  # Start new path
                        continue

                    # Flash should not happen here
                    if current_operation_code == 3:
                        log.error("Trying to flash within arc. (%d)" % line_num)
                        continue

                    if quadrant_mode == 'MULTI':
                        center = [i + current_x, j + current_y]
                        radius = sqrt(i ** 2 + j ** 2)
                        start = arctan2(-j, -i)  # Start angle
                        # Numerical errors might prevent start == stop therefore
                        # we check ahead of time. This should result in a
                        # 360 degree arc.
                        if current_x == x and current_y == y:
                            stop = start
                        else:
                            stop = arctan2(-center[1] + y, -center[0] + x)  # Stop angle

                        this_arc = arc(center, radius, start, stop,
                                       arcdir[current_interpolation_mode],
                                       self.steps_per_circ)

                        # Last point in path is current point
                        current_x = this_arc[-1][0]
                        current_y = this_arc[-1][1]

                        # Append
                        path += this_arc

                        last_path_aperture = current_aperture

                        continue

                    if quadrant_mode == 'SINGLE':

                        center_candidates = [
                            [i + current_x, j + current_y],
                            [-i + current_x, j + current_y],
                            [i + current_x, -j + current_y],
                            [-i + current_x, -j + current_y]
                        ]

                        valid = False
                        log.debug("I: %f  J: %f" % (i, j))
                        for center in center_candidates:
                            radius = sqrt(i ** 2 + j ** 2)

                            # Make sure radius to start is the same as radius to end.
                            radius2 = sqrt((center[0] - x) ** 2 + (center[1] - y) ** 2)
                            if radius2 < radius * 0.95 or radius2 > radius * 1.05:
                                continue  # Not a valid center.

                            # Correct i and j and continue as with multi-quadrant.
                            i = center[0] - current_x
                            j = center[1] - current_y

                            start = arctan2(-j, -i)  # Start angle
                            stop = arctan2(-center[1] + y, -center[0] + x)  # Stop angle
                            angle = abs(arc_angle(start, stop, arcdir[current_interpolation_mode]))
                            log.debug("ARC START: %f, %f  CENTER: %f, %f  STOP: %f, %f" %
                                      (current_x, current_y, center[0], center[1], x, y))
                            log.debug("START Ang: %f, STOP Ang: %f, DIR: %s, ABS: %.12f <= %.12f: %s" %
                                      (start * 180 / pi, stop * 180 / pi, arcdir[current_interpolation_mode],
                                       angle * 180 / pi, pi / 2 * 180 / pi, angle <= (pi + 1e-6) / 2))

                            if angle <= (pi + 1e-6) / 2:
                                log.debug("########## ACCEPTING ARC ############")
                                this_arc = arc(center, radius, start, stop,
                                               arcdir[current_interpolation_mode],
                                               self.steps_per_circ)
                                current_x = this_arc[-1][0]
                                current_y = this_arc[-1][1]
                                path += this_arc
                                last_path_aperture = current_aperture
                                valid = True
                                break

                        if valid:
                            continue
                        else:
                            log.warning("Invalid arc in line %d." % line_num)

                ### Operation code alone
                # Operation code alone, usually just D03 (Flash)
                # self.opcode_re = re.compile(r'^D0?([123])\*$')
                match = self.opcode_re.search(gline)
                if match:
                    current_operation_code = int(match.group(1))
                    if current_operation_code == 3:

                        ## --- Buffered ---
                        try:
                            log.debug("Bare op-code %d." % current_operation_code)
                            # flash = Gerber.create_flash_geometry(Point(path[-1]),
                            #                                      self.apertures[current_aperture])
                            flash = Gerber.create_flash_geometry(Point(current_x, current_y),
                                                                 self.apertures[current_aperture])
                            poly_buffer.append(flash)
                        except IndexError:
                            log.warning("Line %d: %s -> Nothing there to flash!" % (line_num, gline))

                    continue

                ### G74/75* - Single or multiple quadrant arcs
                match = self.quad_re.search(gline)
                if match:
                    if match.group(1) == '4':
                        quadrant_mode = 'SINGLE'
                    else:
                        quadrant_mode = 'MULTI'
                    continue

                ### G36* - Begin region
                if self.regionon_re.search(gline):
                    if len(path) > 1:
                        # Take care of what is left in the path

                        ## --- Buffered ---
                        width = self.apertures[last_path_aperture]["size"]
                        geo = LineString(path).buffer(width/2)
                        poly_buffer.append(geo)

                        path = [path[-1]]

                    making_region = True
                    continue

                ### G37* - End region
                if self.regionoff_re.search(gline):
                    making_region = False

                    # Only one path defines region?
                    # This can happen if D02 happened before G37 and
                    # is not and error.
                    if len(path) < 3:
                        # print "ERROR: Path contains less than 3 points:"
                        # print path
                        # print "Line (%d): " % line_num, gline
                        # path = []
                        #path = [[current_x, current_y]]
                        continue

                    # For regions we may ignore an aperture that is None
                    # self.regions.append({"polygon": Polygon(path),
                    #                      "aperture": last_path_aperture})

                    # --- Buffered ---
                    region = Polygon(path)
                    if not region.is_valid:
                        region = region.buffer(0)
                    poly_buffer.append(region)

                    path = [[current_x, current_y]]  # Start new path
                    continue

                ### Aperture definitions %ADD...
                match = self.ad_re.search(gline)
                if match:
                    log.info("Found aperture definition. Line %d: %s" % (line_num, gline))
                    self.aperture_parse(match.group(1), match.group(2), match.group(3))
                    continue

                ### G01/2/3* - Interpolation mode change
                # Can occur along with coordinates and operation code but
                # sometimes by itself (handled here).
                # Example: G01*
                match = self.interp_re.search(gline)
                if match:
                    current_interpolation_mode = int(match.group(1))
                    continue

                ### Tool/aperture change
                # Example: D12*
                match = self.tool_re.search(gline)
                if match:
                    current_aperture = match.group(1)
                    log.debug("Line %d: Aperture change to (%s)" % (line_num, match.group(1)))
                    log.debug(self.apertures[current_aperture])

                    # Take care of the current path with the previous tool
                    if len(path) > 1:
                        # --- Buffered ----
                        width = self.apertures[last_path_aperture]["size"]
                        geo = LineString(path).buffer(width / 2)
                        poly_buffer.append(geo)
                        path = [path[-1]]

                    continue

                ### Polarity change
                # Example: %LPD*% or %LPC*%
                # If polarity changes, creates geometry from current
                # buffer, then adds or subtracts accordingly.
                match = self.lpol_re.search(gline)
                if match:
                    if len(path) > 1 and current_polarity != match.group(1):

                        # --- Buffered ----
                        width = self.apertures[last_path_aperture]["size"]
                        geo = LineString(path).buffer(width / 2)
                        poly_buffer.append(geo)

                        path = [path[-1]]

                    # --- Apply buffer ---
                    # If added for testing of bug #83
                    # TODO: Remove when bug fixed
                    if len(poly_buffer) > 0:
                        if current_polarity == 'D':
                            self.solid_geometry = self.solid_geometry.union(cascaded_union(poly_buffer))
                        else:
                            self.solid_geometry = self.solid_geometry.difference(cascaded_union(poly_buffer))
                        poly_buffer = []

                    current_polarity = match.group(1)
                    continue

                ### Number format
                # Example: %FSLAX24Y24*%
                # TODO: This is ignoring most of the format. Implement the rest.
                match = self.fmt_re.search(gline)
                if match:
                    absolute = {'A': True, 'I': False}
                    self.int_digits = int(match.group(3))
                    self.frac_digits = int(match.group(4))
                    continue

                ### Mode (IN/MM)
                # Example: %MOIN*%
                match = self.mode_re.search(gline)
                if match:
                    #self.units = match.group(1)

                    # Changed for issue #80
                    self.convert_units(match.group(1))
                    continue

                ### Units (G70/1) OBSOLETE
                match = self.units_re.search(gline)
                if match:
                    #self.units = {'0': 'IN', '1': 'MM'}[match.group(1)]

                    # Changed for issue #80
                    self.convert_units({'0': 'IN', '1': 'MM'}[match.group(1)])
                    continue

                ### Absolute/relative coordinates G90/1 OBSOLETE
                match = self.absrel_re.search(gline)
                if match:
                    absolute = {'0': True, '1': False}[match.group(1)]
                    continue

                #### Ignored lines
                ## Comments
                match = self.comm_re.search(gline)
                if match:
                    continue

                ## EOF
                match = self.eof_re.search(gline)
                if match:
                    continue

                ### Line did not match any pattern. Warn user.
                log.warning("Line ignored (%d): %s" % (line_num, gline))

            if len(path) > 1:
                # EOF, create shapely LineString if something still in path

                ## --- Buffered ---
                width = self.apertures[last_path_aperture]["size"]
                geo = LineString(path).buffer(width / 2)
                poly_buffer.append(geo)

            # --- Apply buffer ---
            log.warn("Joining %d polygons." % len(poly_buffer))
            if current_polarity == 'D':
                self.solid_geometry = self.solid_geometry.union(cascaded_union(poly_buffer))
            else:
                self.solid_geometry = self.solid_geometry.difference(cascaded_union(poly_buffer))

        except Exception, err:
            #print traceback.format_exc()
            log.error("PARSING FAILED. Line %d: %s" % (line_num, gline))
            raise ParseError("%s\nLine %d: %s" % (repr(err), line_num, gline))

    @staticmethod
    def create_flash_geometry(location, aperture):

        log.debug('Flashing @%s, Aperture: %s' % (location, aperture))

        if type(location) == list:
            location = Point(location)

        if aperture['type'] == 'C':  # Circles
            return location.buffer(aperture['size'] / 2)

        if aperture['type'] == 'R':  # Rectangles
            loc = location.coords[0]
            width = aperture['width']
            height = aperture['height']
            minx = loc[0] - width / 2
            maxx = loc[0] + width / 2
            miny = loc[1] - height / 2
            maxy = loc[1] + height / 2
            return shply_box(minx, miny, maxx, maxy)

        if aperture['type'] == 'O':  # Obround
            loc = location.coords[0]
            width = aperture['width']
            height = aperture['height']
            if width > height:
                p1 = Point(loc[0] + 0.5 * (width - height), loc[1])
                p2 = Point(loc[0] - 0.5 * (width - height), loc[1])
                c1 = p1.buffer(height * 0.5)
                c2 = p2.buffer(height * 0.5)
            else:
                p1 = Point(loc[0], loc[1] + 0.5 * (height - width))
                p2 = Point(loc[0], loc[1] - 0.5 * (height - width))
                c1 = p1.buffer(width * 0.5)
                c2 = p2.buffer(width * 0.5)
            return cascaded_union([c1, c2]).convex_hull

        if aperture['type'] == 'P':  # Regular polygon
            loc = location.coords[0]
            diam = aperture['diam']
            n_vertices = aperture['nVertices']
            points = []
            for i in range(0, n_vertices):
                x = loc[0] + diam * (cos(2 * pi * i / n_vertices))
                y = loc[1] + diam * (sin(2 * pi * i / n_vertices))
                points.append((x, y))
            ply = Polygon(points)
            if 'rotation' in aperture:
                ply = affinity.rotate(ply, aperture['rotation'])
            return ply

        if aperture['type'] == 'AM':  # Aperture Macro
            loc = location.coords[0]
            flash_geo = aperture['macro'].make_geometry(aperture['modifiers'])
            return affinity.translate(flash_geo, xoff=loc[0], yoff=loc[1])

        return None
    
    def create_geometry(self):
        """
        Geometry from a Gerber file is made up entirely of polygons.
        Every stroke (linear or circular) has an aperture which gives
        it thickness. Additionally, aperture strokes have non-zero area,
        and regions naturally do as well.

        :rtype : None
        :return: None
        """

        # self.buffer_paths()
        #
        # self.fix_regions()
        #
        # self.do_flashes()
        #
        # self.solid_geometry = cascaded_union(self.buffered_paths +
        #                                      [poly['polygon'] for poly in self.regions] +
        #                                      self.flash_geometry)

    def get_bounding_box(self, margin=0.0, rounded=False):
        """
        Creates and returns a rectangular polygon bounding at a distance of
        margin from the object's ``solid_geometry``. If margin > 0, the polygon
        can optionally have rounded corners of radius equal to margin.

        :param margin: Distance to enlarge the rectangular bounding
         box in both positive and negative, x and y axes.
        :type margin: float
        :param rounded: Wether or not to have rounded corners.
        :type rounded: bool
        :return: The bounding box.
        :rtype: Shapely.Polygon
        """

        bbox = self.solid_geometry.envelope.buffer(margin)
        if not rounded:
            bbox = bbox.envelope
        return bbox


class Excellon(Geometry):
    """
    *ATTRIBUTES*

    * ``tools`` (dict): The key is the tool name and the value is
      a dictionary specifying the tool:

    ================  ====================================
    Key               Value
    ================  ====================================
    C                 Diameter of the tool
    Others            Not supported (Ignored).
    ================  ====================================

    * ``drills`` (list): Each is a dictionary:

    ================  ====================================
    Key               Value
    ================  ====================================
    point             (Shapely.Point) Where to drill
    tool              (str) A key in ``tools``
    ================  ====================================
    """

    defaults = {
        "zeros": "L"
    }

    def __init__(self, zeros=None):
        """
        The constructor takes no parameters.

        :return: Excellon object.
        :rtype: Excellon
        """

        Geometry.__init__(self)
        
        self.tools = {}
        
        self.drills = []

        ## IN|MM -> Units are inherited from Geometry
        #self.units = units

        # Trailing "T" or leading "L" (default)
        #self.zeros = "T"
        self.zeros = zeros or self.defaults["zeros"]

        # Attributes to be included in serialization
        # Always append to it because it carries contents
        # from Geometry.
        self.ser_attrs += ['tools', 'drills', 'zeros']

        #### Patterns ####
        # Regex basics:
        # ^ - beginning
        # $ - end
        # *: 0 or more, +: 1 or more, ?: 0 or 1

        # M48 - Beggining of Part Program Header
        self.hbegin_re = re.compile(r'^M48$')

        # M95 or % - End of Part Program Header
        # NOTE: % has different meaning in the body
        self.hend_re = re.compile(r'^(?:M95|%)$')

        # FMAT Excellon format
        # Ignored in the parser
        #self.fmat_re = re.compile(r'^FMAT,([12])$')

        # Number format and units
        # INCH uses 6 digits
        # METRIC uses 5/6
        self.units_re = re.compile(r'^(INCH|METRIC)(?:,([TL])Z)?$')

        # Tool definition/parameters (?= is look-ahead
        # NOTE: This might be an overkill!
        # self.toolset_re = re.compile(r'^T(0?\d|\d\d)(?=.*C(\d*\.?\d*))?' +
        #                              r'(?=.*F(\d*\.?\d*))?(?=.*S(\d*\.?\d*))?' +
        #                              r'(?=.*B(\d*\.?\d*))?(?=.*H(\d*\.?\d*))?' +
        #                              r'(?=.*Z([-\+]?\d*\.?\d*))?[CFSBHT]')
        self.toolset_re = re.compile(r'^T(\d+)(?=.*C(\d*\.?\d*))?' +
                                     r'(?=.*F(\d*\.?\d*))?(?=.*S(\d*\.?\d*))?' +
                                     r'(?=.*B(\d*\.?\d*))?(?=.*H(\d*\.?\d*))?' +
                                     r'(?=.*Z([-\+]?\d*\.?\d*))?[CFSBHT]')

        # Tool select
        # Can have additional data after tool number but
        # is ignored if present in the header.
        # Warning: This will match toolset_re too.
        # self.toolsel_re = re.compile(r'^T((?:\d\d)|(?:\d))')
        self.toolsel_re = re.compile(r'^T(\d+)')

        # Comment
        self.comm_re = re.compile(r'^;(.*)$')

        # Absolute/Incremental G90/G91
        self.absinc_re = re.compile(r'^G9([01])$')

        # Modes of operation
        # 1-linear, 2-circCW, 3-cirCCW, 4-vardwell, 5-Drill
        self.modes_re = re.compile(r'^G0([012345])')

        # Measuring mode
        # 1-metric, 2-inch
        self.meas_re = re.compile(r'^M7([12])$')

        # Coordinates
        #self.xcoord_re = re.compile(r'^X(\d*\.?\d*)(?:Y\d*\.?\d*)?$')
        #self.ycoord_re = re.compile(r'^(?:X\d*\.?\d*)?Y(\d*\.?\d*)$')
        self.coordsperiod_re = re.compile(r'(?=.*X([-\+]?\d*\.\d*))?(?=.*Y([-\+]?\d*\.\d*))?[XY]')
        self.coordsnoperiod_re = re.compile(r'(?!.*\.)(?=.*X([-\+]?\d*))?(?=.*Y([-\+]?\d*))?[XY]')

        # R - Repeat hole (# times, X offset, Y offset)
        self.rep_re = re.compile(r'^R(\d+)(?=.*[XY])+(?:X([-\+]?\d*\.?\d*))?(?:Y([-\+]?\d*\.?\d*))?$')

        # Various stop/pause commands
        self.stop_re = re.compile(r'^((G04)|(M09)|(M06)|(M00)|(M30))')

        # Parse coordinates
        self.leadingzeros_re = re.compile(r'^[-\+]?(0*)(\d*)')
        
    def parse_file(self, filename):
        """
        Reads the specified file as array of lines as
        passes it to ``parse_lines()``.

        :param filename: The file to be read and parsed.
        :type filename: str
        :return: None
        """
        efile = open(filename, 'r')
        estr = efile.readlines()
        efile.close()
        self.parse_lines(estr)

    def parse_lines(self, elines):
        """
        Main Excellon parser.

        :param elines: List of strings, each being a line of Excellon code.
        :type elines: list
        :return: None
        """

        # State variables
        current_tool = ""
        in_header = False
        current_x = None
        current_y = None

        #### Parsing starts here ####
        line_num = 0  # Line number
        eline = ""
        try:
            for eline in elines:
                line_num += 1
                #log.debug("%3d %s" % (line_num, str(eline)))

                ### Cleanup lines
                eline = eline.strip(' \r\n')

                ## Header Begin (M48) ##
                if self.hbegin_re.search(eline):
                    in_header = True
                    continue

                ## Header End ##
                if self.hend_re.search(eline):
                    in_header = False
                    continue

                ## Alternative units format M71/M72
                # Supposed to be just in the body (yes, the body)
                # but some put it in the header (PADS for example).
                # Will detect anywhere. Occurrence will change the
                # object's units.
                match = self.meas_re.match(eline)
                if match:
                    #self.units = {"1": "MM", "2": "IN"}[match.group(1)]

                    # Modified for issue #80
                    self.convert_units({"1": "MM", "2": "IN"}[match.group(1)])
                    log.debug("  Units: %s" % self.units)
                    continue

                #### Body ####
                if not in_header:

                    ## Tool change ##
                    match = self.toolsel_re.search(eline)
                    if match:
                        current_tool = str(int(match.group(1)))
                        log.debug("Tool change: %s" % current_tool)
                        continue

                    ## Coordinates without period ##
                    match = self.coordsnoperiod_re.search(eline)
                    if match:
                        try:
                            #x = float(match.group(1))/10000
                            x = self.parse_number(match.group(1))
                            current_x = x
                        except TypeError:
                            x = current_x

                        try:
                            #y = float(match.group(2))/10000
                            y = self.parse_number(match.group(2))
                            current_y = y
                        except TypeError:
                            y = current_y

                        if x is None or y is None:
                            log.error("Missing coordinates")
                            continue

                        self.drills.append({'point': Point((x, y)), 'tool': current_tool})
                        log.debug("{:15} {:8} {:8}".format(eline, x, y))
                        continue

                    ## Coordinates with period: Use literally. ##
                    match = self.coordsperiod_re.search(eline)
                    if match:
                        try:
                            x = float(match.group(1))
                            current_x = x
                        except TypeError:
                            x = current_x

                        try:
                            y = float(match.group(2))
                            current_y = y
                        except TypeError:
                            y = current_y

                        if x is None or y is None:
                            log.error("Missing coordinates")
                            continue

                        self.drills.append({'point': Point((x, y)), 'tool': current_tool})
                        log.debug("{:15} {:8} {:8}".format(eline, x, y))
                        continue

                #### Header ####
                if in_header:

                    ## Tool definitions ##
                    match = self.toolset_re.search(eline)
                    if match:

                        name = str(int(match.group(1)))
                        spec = {
                            "C": float(match.group(2)),
                            # "F": float(match.group(3)),
                            # "S": float(match.group(4)),
                            # "B": float(match.group(5)),
                            # "H": float(match.group(6)),
                            # "Z": float(match.group(7))
                        }
                        self.tools[name] = spec
                        log.debug("  Tool definition: %s %s" % (name, spec))
                        continue

                    ## Units and number format ##
                    match = self.units_re.match(eline)
                    if match:
                        self.zeros = match.group(2) or self.zeros  # "T" or "L". Might be empty

                        #self.units = {"INCH": "IN", "METRIC": "MM"}[match.group(1)]

                        # Modified for issue #80
                        self.convert_units({"INCH": "IN", "METRIC": "MM"}[match.group(1)])
                        log.debug("  Units/Format: %s %s" % (self.units, self.zeros))
                        continue

                log.warning("Line ignored: %s" % eline)

            log.info("Zeros: %s, Units %s." % (self.zeros, self.units))

        except Exception as e:
            log.error("PARSING FAILED. Line %d: %s" % (line_num, eline))
            raise
        
    def parse_number(self, number_str):
        """
        Parses coordinate numbers without period.

        :param number_str: String representing the numerical value.
        :type number_str: str
        :return: Floating point representation of the number
        :rtype: foat
        """
        if self.zeros == "L":
            # With leading zeros, when you type in a coordinate,
            # the leading zeros must always be included.  Trailing zeros
            # are unneeded and may be left off. The CNC-7 will automatically add them.
            # r'^[-\+]?(0*)(\d*)'
            # 6 digits are divided by 10^4
            # If less than size digits, they are automatically added,
            # 5 digits then are divided by 10^3 and so on.
            match = self.leadingzeros_re.search(number_str)
            if self.units.lower() == "in":
                return float(number_str) / \
                    (10 ** (len(match.group(1)) + len(match.group(2)) - 2))
            else:
                return float(number_str) / \
                    (10 ** (len(match.group(1)) + len(match.group(2)) - 3))

        else:  # Trailing
            # You must show all zeros to the right of the number and can omit
            # all zeros to the left of the number. The CNC-7 will count the number
            # of digits you typed and automatically fill in the missing zeros.
            if self.units.lower() == "in":  # Inches is 00.0000
                return float(number_str) / 10000
            else:
                return float(number_str) / 1000  # Metric is 000.000

    def create_geometry(self):
        """
        Creates circles of the tool diameter at every point
        specified in ``self.drills``.

        :return: None
        """
        self.solid_geometry = []

        for drill in self.drills:
            #poly = drill['point'].buffer(self.tools[drill['tool']]["C"]/2.0)
            tooldia = self.tools[drill['tool']]['C']
            poly = drill['point'].buffer(tooldia / 2.0)
            self.solid_geometry.append(poly)

    def scale(self, factor):
        """
        Scales geometry on the XY plane in the object by a given factor.
        Tool sizes, feedrates an Z-plane dimensions are untouched.

        :param factor: Number by which to scale the object.
        :type factor: float
        :return: None
        :rtype: NOne
        """

        # Drills
        for drill in self.drills:
            drill['point'] = affinity.scale(drill['point'], factor, factor, origin=(0, 0))

        self.create_geometry()

    def offset(self, vect):
        """
        Offsets geometry on the XY plane in the object by a given vector.

        :param vect: (x, y) offset vector.
        :type vect: tuple
        :return: None
        """

        dx, dy = vect

        # Drills
        for drill in self.drills:
            drill['point'] = affinity.translate(drill['point'], xoff=dx, yoff=dy)

        # Recreate geometry
        self.create_geometry()

    def mirror(self, axis, point):
        """

        :param axis: "X" or "Y" indicates around which axis to mirror.
        :type axis: str
        :param point: [x, y] point belonging to the mirror axis.
        :type point: list
        :return: None
        """

        px, py = point
        xscale, yscale = {"X": (1.0, -1.0), "Y": (-1.0, 1.0)}[axis]

        # Modify data
        for drill in self.drills:
            drill['point'] = affinity.scale(drill['point'], xscale, yscale, origin=(px, py))

        # Recreate geometry
        self.create_geometry()

    def convert_units(self, units):
        factor = Geometry.convert_units(self, units)

        # Tools
        for tname in self.tools:
            self.tools[tname]["C"] *= factor

        self.create_geometry()

        return factor


class CNCjob(Geometry):
    """
    Represents work to be done by a CNC machine.

    *ATTRIBUTES*

    * ``gcode_parsed`` (list): Each is a dictionary:

    =====================  =========================================
    Key                    Value
    =====================  =========================================
    geom                   (Shapely.LineString) Tool path (XY plane)
    kind                   (string) "AB", A is "T" (travel) or
                           "C" (cut). B is "F" (fast) or "S" (slow).
    =====================  =========================================
    """

    defaults = {
        "zdownrate": None,
        "coordinate_format": "X%.4fY%.4f"
    }

    def __init__(self, units="in", kind="generic", z_move=0.1,
                 feedrate=3.0, z_cut=-0.002, tooldia=0.0, zdownrate=None):

        Geometry.__init__(self)
        self.kind = kind
        self.units = units
        self.z_cut = z_cut
        self.z_move = z_move
        self.feedrate = feedrate
        self.tooldia = tooldia
        self.unitcode = {"IN": "G20", "MM": "G21"}
        self.pausecode = "G04 P1"
        self.feedminutecode = "G94"
        self.absolutecode = "G90"
        self.gcode = ""
        self.input_geometry_bounds = None
        self.gcode_parsed = None
        self.steps_per_circ = 20  # Used when parsing G-code arcs
        if zdownrate is not None:
            self.zdownrate = float(zdownrate)
        elif CNCjob.defaults["zdownrate"] is not None:
            self.zdownrate = float(CNCjob.defaults["zdownrate"])
        else:
            self.zdownrate = None

        # Attributes to be included in serialization
        # Always append to it because it carries contents
        # from Geometry.
        self.ser_attrs += ['kind', 'z_cut', 'z_move', 'feedrate', 'tooldia',
                           'gcode', 'input_geometry_bounds', 'gcode_parsed',
                           'steps_per_circ']

    def convert_units(self, units):
        factor = Geometry.convert_units(self, units)
        log.debug("CNCjob.convert_units()")

        self.z_cut *= factor
        self.z_move *= factor
        self.feedrate *= factor
        self.tooldia *= factor

        return factor

    def generate_from_excellon_by_tool(self, exobj, tools="all",
                                       toolchange=False, toolchangez=0.1):
        """
        Creates gcode for this object from an Excellon object
        for the specified tools.

        :param exobj: Excellon object to process
        :type exobj: Excellon
        :param tools: Comma separated tool names
        :type: tools: str
        :return: None
        :rtype: None
        """

        log.debug("Creating CNC Job from Excellon...")

        # Tools
        if tools == "all":
            tools = [tool for tool in exobj.tools]
        else:
            tools = [x.strip() for x in tools.split(",")]
            tools = filter(lambda i: i in exobj.tools, tools)
        log.debug("Tools are: %s" % str(tools))

        # Points (Group by tool)
        points = {}
        for drill in exobj.drills:
            if drill['tool'] in tools:
                try:
                    points[drill['tool']].append(drill['point'])
                except KeyError:
                    points[drill['tool']] = [drill['point']]

        #log.debug("Found %d drills." % len(points))
        self.gcode = []

        # Basic G-Code macros
        t = "G00 " + CNCjob.defaults["coordinate_format"] + "\n"
        down = "G01 Z%.4f\n" % self.z_cut
        up = "G01 Z%.4f\n" % self.z_move

        # Initialization
        gcode = self.unitcode[self.units.upper()] + "\n"
        gcode += self.absolutecode + "\n"
        gcode += self.feedminutecode + "\n"
        gcode += "F%.2f\n" % self.feedrate
        gcode += "G00 Z%.4f\n" % self.z_move  # Move to travel height
        gcode += "M03\n"  # Spindle start
        gcode += self.pausecode + "\n"

        for tool in points:
            if toolchange:
                gcode += "G00 Z%.4f\n" % toolchangez
                gcode += "T%d\n" % int(tool)  # Indicate tool slot (for automatic tool changer)
                gcode += "M5\n"  # Spindle Stop
                gcode += "M6\n"  # Tool change
                gcode += "(MSG, Change to tool dia=%.4f)\n" % exobj.tools[tool]["C"]
                gcode += "M0\n"  # Temporary machine stop
                gcode += "M3\n"  # Spindle on clockwise
            for point in points[tool]:
                x, y = point.coords.xy
                gcode += t % (x[0], y[0])
                gcode += down + up

        gcode += t % (0, 0)
        gcode += "M05\n"  # Spindle stop

        self.gcode = gcode

    def generate_from_geometry_2(self, geometry, append=True, tooldia=None, tolerance=0):
        """
        Second algorithm to generate from Geometry.

        ALgorithm description:
        ----------------------
        Uses RTree to find the nearest path to follow.

        :param geometry:
        :param append:
        :param tooldia:
        :param tolerance:
        :return: None
        """
        assert isinstance(geometry, Geometry)
        log.debug("generate_from_geometry_2()")

        ## Flatten the geometry
        # Only linear elements (no polygons) remain.
        flat_geometry = geometry.flatten(pathonly=True)
        log.debug("%d paths" % len(flat_geometry))

        ## Index first and last points in paths
        # What points to index.
        def get_pts(o):
            return [o.coords[0], o.coords[-1]]

        # Create the indexed storage.
        storage = FlatCAMRTreeStorage()
        storage.get_points = get_pts

        # Store the geometry
        log.debug("Indexing geometry before generating G-Code...")
        for shape in flat_geometry:
            if shape is not None:  # TODO: This shouldn't have happened.
                storage.insert(shape)

        if tooldia is not None:
            self.tooldia = tooldia

        # self.input_geometry_bounds = geometry.bounds()

        if not append:
            self.gcode = ""

        # Initial G-Code
        self.gcode = self.unitcode[self.units.upper()] + "\n"
        self.gcode += self.absolutecode + "\n"
        self.gcode += self.feedminutecode + "\n"
        self.gcode += "F%.2f\n" % self.feedrate
        self.gcode += "G00 Z%.4f\n" % self.z_move  # Move (up) to travel height
        self.gcode += "M03\n"  # Spindle start
        self.gcode += self.pausecode + "\n"

        ## Iterate over geometry paths getting the nearest each time.
        log.debug("Starting G-Code...")
        path_count = 0
        current_pt = (0, 0)
        pt, geo = storage.nearest(current_pt)
        try:
            while True:
                path_count += 1
                #print "Current: ", "(%.3f, %.3f)" % current_pt

                # Remove before modifying, otherwise
                # deletion will fail.
                storage.remove(geo)

                # If last point in geometry is the nearest
                # then reverse coordinates.
                if list(pt) == list(geo.coords[-1]):
                    geo.coords = list(geo.coords)[::-1]

                # G-code
                # Note: self.linear2gcode() and self.point2gcode() will
                # lower and raise the tool every time.
                if type(geo) == LineString or type(geo) == LinearRing:
                    self.gcode += self.linear2gcode(geo, tolerance=tolerance)
                elif type(geo) == Point:
                    self.gcode += self.point2gcode(geo)
                else:
                    log.warning("G-code generation not implemented for %s" % (str(type(geo))))

                # Delete from index, update current location and continue.
                #rti.delete(hits[0], geo.coords[0])
                #rti.delete(hits[0], geo.coords[-1])

                current_pt = geo.coords[-1]

                # Next
                pt, geo = storage.nearest(current_pt)

        except StopIteration:  # Nothing found in storage.
            pass

        log.debug("%s paths traced." % path_count)

        # Finish
        self.gcode += "G00 Z%.4f\n" % self.z_move  # Stop cutting
        self.gcode += "G00 X0Y0\n"
        self.gcode += "M05\n"  # Spindle stop

    def pre_parse(self, gtext):
        """
        Separates parts of the G-Code text into a list of dictionaries.
        Used by ``self.gcode_parse()``.

        :param gtext: A single string with g-code
        """

        # Units: G20-inches, G21-mm
        units_re = re.compile(r'^G2([01])')

        # TODO: This has to be re-done
        gcmds = []
        lines = gtext.split("\n")  # TODO: This is probably a lot of work!
        for line in lines:
            # Clean up
            line = line.strip()

            # Remove comments
            # NOTE: Limited to 1 bracket pair
            op = line.find("(")
            cl = line.find(")")
            #if op > -1 and  cl > op:
            if cl > op > -1:
                #comment = line[op+1:cl]
                line = line[:op] + line[(cl+1):]

            # Units
            match = units_re.match(line)
            if match:
                self.units = {'0': "IN", '1': "MM"}[match.group(1)]

            # Parse GCode
            # 0   4       12
            # G01 X-0.007 Y-0.057
            # --> codes_idx = [0, 4, 12]
            codes = "NMGXYZIJFP"
            codes_idx = []
            i = 0
            for ch in line:
                if ch in codes:
                    codes_idx.append(i)
                i += 1
            n_codes = len(codes_idx)
            if n_codes == 0:
                continue

            # Separate codes in line
            parts = []
            for p in range(n_codes - 1):
                parts.append(line[codes_idx[p]:codes_idx[p+1]].strip())
            parts.append(line[codes_idx[-1]:].strip())

            # Separate codes from values
            cmds = {}
            for part in parts:
                cmds[part[0]] = float(part[1:])
            gcmds.append(cmds)
        return gcmds

    def gcode_parse(self):
        """
        G-Code parser (from self.gcode). Generates dictionary with
        single-segment LineString's and "kind" indicating cut or travel,
        fast or feedrate speed.
        """

        kind = ["C", "F"]  # T=travel, C=cut, F=fast, S=slow

        # Results go here
        geometry = []        
        
        # TODO: Merge into single parser?
        gobjs = self.pre_parse(self.gcode)
        
        # Last known instruction
        current = {'X': 0.0, 'Y': 0.0, 'Z': 0.0, 'G': 0}

        # Current path: temporary storage until tool is
        # lifted or lowered.
        path = [(0, 0)]

        # Process every instruction
        for gobj in gobjs:

            ## Changing height
            if 'Z' in gobj:
                if ('X' in gobj or 'Y' in gobj) and gobj['Z'] != current['Z']:
                    log.warning("Non-orthogonal motion: From %s" % str(current))
                    log.warning("  To: %s" % str(gobj))
                current['Z'] = gobj['Z']
                # Store the path into geometry and reset path
                if len(path) > 1:
                    geometry.append({"geom": LineString(path),
                                     "kind": kind})
                    path = [path[-1]]  # Start with the last point of last path.

            if 'G' in gobj:
                current['G'] = int(gobj['G'])
                
            if 'X' in gobj or 'Y' in gobj:
                
                if 'X' in gobj:
                    x = gobj['X']
                else:
                    x = current['X']
                
                if 'Y' in gobj:
                    y = gobj['Y']
                else:
                    y = current['Y']

                kind = ["C", "F"]  # T=travel, C=cut, F=fast, S=slow

                if current['Z'] > 0:
                    kind[0] = 'T'
                if current['G'] > 0:
                    kind[1] = 'S'
                   
                arcdir = [None, None, "cw", "ccw"]
                if current['G'] in [0, 1]:  # line
                    path.append((x, y))

                if current['G'] in [2, 3]:  # arc
                    center = [gobj['I'] + current['X'], gobj['J'] + current['Y']]
                    radius = sqrt(gobj['I']**2 + gobj['J']**2)
                    start = arctan2(-gobj['J'], -gobj['I'])
                    stop = arctan2(-center[1]+y, -center[0]+x)
                    path += arc(center, radius, start, stop,
                                arcdir[current['G']],
                                self.steps_per_circ)

            # Update current instruction
            for code in gobj:
                current[code] = gobj[code]

        # There might not be a change in height at the
        # end, therefore, see here too if there is
        # a final path.
        if len(path) > 1:
            geometry.append({"geom": LineString(path),
                             "kind": kind})

        self.gcode_parsed = geometry
        return geometry

    # def plot(self, tooldia=None, dpi=75, margin=0.1,
    #          color={"T": ["#F0E24D", "#B5AB3A"], "C": ["#5E6CFF", "#4650BD"]},
    #          alpha={"T": 0.3, "C": 1.0}):
    #     """
    #     Creates a Matplotlib figure with a plot of the
    #     G-code job.
    #     """
    #     if tooldia is None:
    #         tooldia = self.tooldia
    #
    #     fig = Figure(dpi=dpi)
    #     ax = fig.add_subplot(111)
    #     ax.set_aspect(1)
    #     xmin, ymin, xmax, ymax = self.input_geometry_bounds
    #     ax.set_xlim(xmin-margin, xmax+margin)
    #     ax.set_ylim(ymin-margin, ymax+margin)
    #
    #     if tooldia == 0:
    #         for geo in self.gcode_parsed:
    #             linespec = '--'
    #             linecolor = color[geo['kind'][0]][1]
    #             if geo['kind'][0] == 'C':
    #                 linespec = 'k-'
    #             x, y = geo['geom'].coords.xy
    #             ax.plot(x, y, linespec, color=linecolor)
    #     else:
    #         for geo in self.gcode_parsed:
    #             poly = geo['geom'].buffer(tooldia/2.0)
    #             patch = PolygonPatch(poly, facecolor=color[geo['kind'][0]][0],
    #                                  edgecolor=color[geo['kind'][0]][1],
    #                                  alpha=alpha[geo['kind'][0]], zorder=2)
    #             ax.add_patch(patch)
    #
    #     return fig
        
    def plot2(self, axes, tooldia=None, dpi=75, margin=0.1,
              color={"T": ["#F0E24D", "#B5AB3A"], "C": ["#5E6CFF", "#4650BD"]},
              alpha={"T": 0.3, "C": 1.0}, tool_tolerance=0.0005):
        """
        Plots the G-code job onto the given axes.

        :param axes: Matplotlib axes on which to plot.
        :param tooldia: Tool diameter.
        :param dpi: Not used!
        :param margin: Not used!
        :param color: Color specification.
        :param alpha: Transparency specification.
        :param tool_tolerance: Tolerance when drawing the toolshape.
        :return: None
        """
        path_num = 0

        if tooldia is None:
            tooldia = self.tooldia
        
        if tooldia == 0:
            for geo in self.gcode_parsed:
                linespec = '--'
                linecolor = color[geo['kind'][0]][1]
                if geo['kind'][0] == 'C':
                    linespec = 'k-'
                x, y = geo['geom'].coords.xy
                axes.plot(x, y, linespec, color=linecolor)
        else:
            for geo in self.gcode_parsed:
                path_num += 1
                axes.annotate(str(path_num), xy=geo['geom'].coords[0],
                              xycoords='data')

                poly = geo['geom'].buffer(tooldia / 2.0).simplify(tool_tolerance)
                patch = PolygonPatch(poly, facecolor=color[geo['kind'][0]][0],
                                     edgecolor=color[geo['kind'][0]][1],
                                     alpha=alpha[geo['kind'][0]], zorder=2)
                axes.add_patch(patch)
        
    def create_geometry(self):
        # TODO: This takes forever. Too much data?
        self.solid_geometry = cascaded_union([geo['geom'] for geo in self.gcode_parsed])

    def linear2gcode(self, linear, tolerance=0):
        """
        Generates G-code to cut along the linear feature.

        :param linear: The path to cut along.
        :type: Shapely.LinearRing or Shapely.Linear String
        :param tolerance: All points in the simplified object will be within the
            tolerance distance of the original geometry.
        :type tolerance: float
        :return: G-code to cut alon the linear feature.
        :rtype: str
        """

        if tolerance > 0:
            target_linear = linear.simplify(tolerance)
        else:
            target_linear = linear

        gcode = ""
        #t = "G0%d X%.4fY%.4f\n"
        t = "G0%d " + CNCjob.defaults["coordinate_format"] + "\n"
        path = list(target_linear.coords)
        gcode += t % (0, path[0][0], path[0][1])  # Move to first point

        if self.zdownrate is not None:
            gcode += "F%.2f\n" % self.zdownrate
            gcode += "G01 Z%.4f\n" % self.z_cut       # Start cutting
            gcode += "F%.2f\n" % self.feedrate
        else:
            gcode += "G01 Z%.4f\n" % self.z_cut       # Start cutting

        for pt in path[1:]:
            gcode += t % (1, pt[0], pt[1])    # Linear motion to point
        gcode += "G00 Z%.4f\n" % self.z_move  # Stop cutting
        return gcode

    def point2gcode(self, point):
        gcode = ""
        #t = "G0%d X%.4fY%.4f\n"
        t = "G0%d " + CNCjob.defaults["coordinate_format"] + "\n"
        path = list(point.coords)
        gcode += t % (0, path[0][0], path[0][1])  # Move to first point

        if self.zdownrate is not None:
            gcode += "F%.2f\n" % self.zdownrate
            gcode += "G01 Z%.4f\n" % self.z_cut       # Start cutting
            gcode += "F%.2f\n" % self.feedrate
        else:
            gcode += "G01 Z%.4f\n" % self.z_cut       # Start cutting

        gcode += "G00 Z%.4f\n" % self.z_move      # Stop cutting
        return gcode

    def scale(self, factor):
        """
        Scales all the geometry on the XY plane in the object by the
        given factor. Tool sizes, feedrates, or Z-axis dimensions are
        not altered.

        :param factor: Number by which to scale the object.
        :type factor: float
        :return: None
        :rtype: None
        """

        for g in self.gcode_parsed:
            g['geom'] = affinity.scale(g['geom'], factor, factor, origin=(0, 0))

        self.create_geometry()

    def offset(self, vect):
        """
        Offsets all the geometry on the XY plane in the object by the
        given vector.

        :param vect: (x, y) offset vector.
        :type vect: tuple
        :return: None
        """
        dx, dy = vect

        for g in self.gcode_parsed:
            g['geom'] = affinity.translate(g['geom'], xoff=dx, yoff=dy)

        self.create_geometry()


# def get_bounds(geometry_set):
#     xmin = Inf
#     ymin = Inf
#     xmax = -Inf
#     ymax = -Inf
#
#     #print "Getting bounds of:", str(geometry_set)
#     for gs in geometry_set:
#         try:
#             gxmin, gymin, gxmax, gymax = geometry_set[gs].bounds()
#             xmin = min([xmin, gxmin])
#             ymin = min([ymin, gymin])
#             xmax = max([xmax, gxmax])
#             ymax = max([ymax, gymax])
#         except:
#             print "DEV WARNING: Tried to get bounds of empty geometry."
#
#     return [xmin, ymin, xmax, ymax]

def get_bounds(geometry_list):
    xmin = Inf
    ymin = Inf
    xmax = -Inf
    ymax = -Inf

    #print "Getting bounds of:", str(geometry_set)
    for gs in geometry_list:
        try:
            gxmin, gymin, gxmax, gymax = gs.bounds()
            xmin = min([xmin, gxmin])
            ymin = min([ymin, gymin])
            xmax = max([xmax, gxmax])
            ymax = max([ymax, gymax])
        except:
            log.warning("DEVELOPMENT: Tried to get bounds of empty geometry.")

    return [xmin, ymin, xmax, ymax]


def arc(center, radius, start, stop, direction, steps_per_circ):
    """
    Creates a list of point along the specified arc.

    :param center: Coordinates of the center [x, y]
    :type center: list
    :param radius: Radius of the arc.
    :type radius: float
    :param start: Starting angle in radians
    :type start: float
    :param stop: End angle in radians
    :type stop: float
    :param direction: Orientation of the arc, "CW" or "CCW"
    :type direction: string
    :param steps_per_circ: Number of straight line segments to
        represent a circle.
    :type steps_per_circ: int
    :return: The desired arc, as list of tuples
    :rtype: list
    """
    # TODO: Resolution should be established by maximum error from the exact arc.

    da_sign = {"cw": -1.0, "ccw": 1.0}
    points = []
    if direction == "ccw" and stop <= start:
        stop += 2 * pi
    if direction == "cw" and stop >= start:
        stop -= 2 * pi
    
    angle = abs(stop - start)
        
    #angle = stop-start
    steps = max([int(ceil(angle / (2 * pi) * steps_per_circ)), 2])
    delta_angle = da_sign[direction] * angle * 1.0 / steps
    for i in range(steps + 1):
        theta = start + delta_angle * i
        points.append((center[0] + radius * cos(theta), center[1] + radius * sin(theta)))
    return points


def arc2(p1, p2, center, direction, steps_per_circ):
    r = sqrt((center[0] - p1[0]) ** 2 + (center[1] - p1[1]) ** 2)
    start = arctan2(p1[1] - center[1], p1[0] - center[0])
    stop = arctan2(p2[1] - center[1], p2[0] - center[0])
    return arc(center, r, start, stop, direction, steps_per_circ)


def arc_angle(start, stop, direction):
    if direction == "ccw" and stop <= start:
        stop += 2 * pi
    if direction == "cw" and stop >= start:
        stop -= 2 * pi

    angle = abs(stop - start)
    return angle


# def find_polygon(poly, point):
#     """
#     Find an object that object.contains(Point(point)) in
#     poly, which can can be iterable, contain iterable of, or
#     be itself an implementer of .contains().
#
#     :param poly: See description
#     :return: Polygon containing point or None.
#     """
#
#     if poly is None:
#         return None
#
#     try:
#         for sub_poly in poly:
#             p = find_polygon(sub_poly, point)
#             if p is not None:
#                 return p
#     except TypeError:
#         try:
#             if poly.contains(Point(point)):
#                 return poly
#         except AttributeError:
#             return None
#
#     return None


def to_dict(obj):
    """
    Makes the following types into serializable form:

    * ApertureMacro
    * BaseGeometry

    :param obj: Shapely geometry.
    :type obj: BaseGeometry
    :return: Dictionary with serializable form if ``obj`` was
        BaseGeometry or ApertureMacro, otherwise returns ``obj``.
    """
    if isinstance(obj, ApertureMacro):
        return {
            "__class__": "ApertureMacro",
            "__inst__": obj.to_dict()
        }
    if isinstance(obj, BaseGeometry):
        return {
            "__class__": "Shply",
            "__inst__": sdumps(obj)
        }
    return obj


def dict2obj(d):
    """
    Default deserializer.

    :param d:  Serializable dictionary representation of an object
        to be reconstructed.
    :return: Reconstructed object.
    """
    if '__class__' in d and '__inst__' in d:
        if d['__class__'] == "Shply":
            return sloads(d['__inst__'])
        if d['__class__'] == "ApertureMacro":
            am = ApertureMacro()
            am.from_dict(d['__inst__'])
            return am
        return d
    else:
        return d


def plotg(geo, solid_poly=False, color="black"):
    try:
        _ = iter(geo)
    except:
        geo = [geo]

    for g in geo:
        if type(g) == Polygon:
            if solid_poly:
                patch = PolygonPatch(g,
                                     facecolor="#BBF268",
                                     edgecolor="#006E20",
                                     alpha=0.75,
                                     zorder=2)
                ax = subplot(111)
                ax.add_patch(patch)
            else:
                x, y = g.exterior.coords.xy
                plot(x, y, color=color)
                for ints in g.interiors:
                    x, y = ints.coords.xy
                    plot(x, y, color=color)
                continue

        if type(g) == LineString or type(g) == LinearRing:
            x, y = g.coords.xy
            plot(x, y, color=color)
            continue

        if type(g) == Point:
            x, y = g.coords.xy
            plot(x, y, 'o')
            continue

        try:
            _ = iter(g)
            plotg(g, color=color)
        except:
            log.error("Cannot plot: " + str(type(g)))
            continue


def parse_gerber_number(strnumber, frac_digits):
    """
    Parse a single number of Gerber coordinates.

    :param strnumber: String containing a number in decimal digits
    from a coordinate data block, possibly with a leading sign.
    :type strnumber: str
    :param frac_digits: Number of digits used for the fractional
    part of the number
    :type frac_digits: int
    :return: The number in floating point.
    :rtype: float
    """
    return int(strnumber) * (10 ** (-frac_digits))


# def voronoi(P):
#     """
#     Returns a list of all edges of the voronoi diagram for the given input points.
#     """
#     delauny = Delaunay(P)
#     triangles = delauny.points[delauny.vertices]
#
#     circum_centers = np.array([triangle_csc(tri) for tri in triangles])
#     long_lines_endpoints = []
#
#     lineIndices = []
#     for i, triangle in enumerate(triangles):
#         circum_center = circum_centers[i]
#         for j, neighbor in enumerate(delauny.neighbors[i]):
#             if neighbor != -1:
#                 lineIndices.append((i, neighbor))
#             else:
#                 ps = triangle[(j+1)%3] - triangle[(j-1)%3]
#                 ps = np.array((ps[1], -ps[0]))
#
#                 middle = (triangle[(j+1)%3] + triangle[(j-1)%3]) * 0.5
#                 di = middle - triangle[j]
#
#                 ps /= np.linalg.norm(ps)
#                 di /= np.linalg.norm(di)
#
#                 if np.dot(di, ps) < 0.0:
#                     ps *= -1000.0
#                 else:
#                     ps *= 1000.0
#
#                 long_lines_endpoints.append(circum_center + ps)
#                 lineIndices.append((i, len(circum_centers) + len(long_lines_endpoints)-1))
#
#     vertices = np.vstack((circum_centers, long_lines_endpoints))
#
#     # filter out any duplicate lines
#     lineIndicesSorted = np.sort(lineIndices) # make (1,2) and (2,1) both (1,2)
#     lineIndicesTupled = [tuple(row) for row in lineIndicesSorted]
#     lineIndicesUnique = np.unique(lineIndicesTupled)
#
#     return vertices, lineIndicesUnique
#
#
# def triangle_csc(pts):
#     rows, cols = pts.shape
#
#     A = np.bmat([[2 * np.dot(pts, pts.T), np.ones((rows, 1))],
#                  [np.ones((1, rows)), np.zeros((1, 1))]])
#
#     b = np.hstack((np.sum(pts * pts, axis=1), np.ones((1))))
#     x = np.linalg.solve(A,b)
#     bary_coords = x[:-1]
#     return np.sum(pts * np.tile(bary_coords.reshape((pts.shape[0], 1)), (1, pts.shape[1])), axis=0)
#
#
# def voronoi_cell_lines(points, vertices, lineIndices):
#     """
#     Returns a mapping from a voronoi cell to its edges.
#
#     :param points: shape (m,2)
#     :param vertices: shape (n,2)
#     :param lineIndices: shape (o,2)
#     :rtype: dict point index -> list of shape (n,2) with vertex indices
#     """
#     kd = KDTree(points)
#
#     cells = collections.defaultdict(list)
#     for i1, i2 in lineIndices:
#         v1, v2 = vertices[i1], vertices[i2]
#         mid = (v1+v2)/2
#         _, (p1Idx, p2Idx) = kd.query(mid, 2)
#         cells[p1Idx].append((i1, i2))
#         cells[p2Idx].append((i1, i2))
#
#     return cells
#
#
# def voronoi_edges2polygons(cells):
#     """
#     Transforms cell edges into polygons.
#
#     :param cells: as returned from voronoi_cell_lines
#     :rtype: dict point index -> list of vertex indices which form a polygon
#     """
#
#     # first, close the outer cells
#     for pIdx, lineIndices_ in cells.items():
#         dangling_lines = []
#         for i1, i2 in lineIndices_:
#             connections = filter(lambda (i1_, i2_): (i1, i2) != (i1_, i2_) and (i1 == i1_ or i1 == i2_ or i2 == i1_ or i2 == i2_), lineIndices_)
#             assert 1 <= len(connections) <= 2
#             if len(connections) == 1:
#                 dangling_lines.append((i1, i2))
#         assert len(dangling_lines) in [0, 2]
#         if len(dangling_lines) == 2:
#             (i11, i12), (i21, i22) = dangling_lines
#
#             # determine which line ends are unconnected
#             connected = filter(lambda (i1,i2): (i1,i2) != (i11,i12) and (i1 == i11 or i2 == i11), lineIndices_)
#             i11Unconnected = len(connected) == 0
#
#             connected = filter(lambda (i1,i2): (i1,i2) != (i21,i22) and (i1 == i21 or i2 == i21), lineIndices_)
#             i21Unconnected = len(connected) == 0
#
#             startIdx = i11 if i11Unconnected else i12
#             endIdx = i21 if i21Unconnected else i22
#
#             cells[pIdx].append((startIdx, endIdx))
#
#     # then, form polygons by storing vertex indices in (counter-)clockwise order
#     polys = dict()
#     for pIdx, lineIndices_ in cells.items():
#         # get a directed graph which contains both directions and arbitrarily follow one of both
#         directedGraph = lineIndices_ + [(i2, i1) for (i1, i2) in lineIndices_]
#         directedGraphMap = collections.defaultdict(list)
#         for (i1, i2) in directedGraph:
#             directedGraphMap[i1].append(i2)
#         orderedEdges = []
#         currentEdge = directedGraph[0]
#         while len(orderedEdges) < len(lineIndices_):
#             i1 = currentEdge[1]
#             i2 = directedGraphMap[i1][0] if directedGraphMap[i1][0] != currentEdge[0] else directedGraphMap[i1][1]
#             nextEdge = (i1, i2)
#             orderedEdges.append(nextEdge)
#             currentEdge = nextEdge
#
#         polys[pIdx] = [i1 for (i1, i2) in orderedEdges]
#
#     return polys
#
#
# def voronoi_polygons(points):
#     """
#     Returns the voronoi polygon for each input point.
#
#     :param points: shape (n,2)
#     :rtype: list of n polygons where each polygon is an array of vertices
#     """
#     vertices, lineIndices = voronoi(points)
#     cells = voronoi_cell_lines(points, vertices, lineIndices)
#     polys = voronoi_edges2polygons(cells)
#     polylist = []
#     for i in xrange(len(points)):
#         poly = vertices[np.asarray(polys[i])]
#         polylist.append(poly)
#     return polylist
#
#
# class Zprofile:
#     def __init__(self):
#
#         # data contains lists of [x, y, z]
#         self.data = []
#
#         # Computed voronoi polygons (shapely)
#         self.polygons = []
#         pass
#
#     def plot_polygons(self):
#         axes = plt.subplot(1, 1, 1)
#
#         plt.axis([-0.05, 1.05, -0.05, 1.05])
#
#         for poly in self.polygons:
#             p = PolygonPatch(poly, facecolor=np.random.rand(3, 1), alpha=0.3)
#             axes.add_patch(p)
#
#     def init_from_csv(self, filename):
#         pass
#
#     def init_from_string(self, zpstring):
#         pass
#
#     def init_from_list(self, zplist):
#         self.data = zplist
#
#     def generate_polygons(self):
#         self.polygons = [Polygon(p) for p in voronoi_polygons(array([[x[0], x[1]] for x in self.data]))]
#
#     def normalize(self, origin):
#         pass
#
#     def paste(self, path):
#         """
#         Return a list of dictionaries containing the parts of the original
#         path and their z-axis offset.
#         """
#
#         # At most one region/polygon will contain the path
#         containing = [i for i in range(len(self.polygons)) if self.polygons[i].contains(path)]
#
#         if len(containing) > 0:
#             return [{"path": path, "z": self.data[containing[0]][2]}]
#
#         # All region indexes that intersect with the path
#         crossing = [i for i in range(len(self.polygons)) if self.polygons[i].intersects(path)]
#
#         return [{"path": path.intersection(self.polygons[i]),
#                  "z": self.data[i][2]} for i in crossing]


def autolist(obj):
    try:
        _ = iter(obj)
        return obj
    except TypeError:
        return [obj]


def three_point_circle(p1, p2, p3):
    """
    Computes the center and radius of a circle from
    3 points on its circumference.

    :param p1: Point 1
    :param p2: Point 2
    :param p3: Point 3
    :return: center, radius
    """
    # Midpoints
    a1 = (p1 + p2) / 2.0
    a2 = (p2 + p3) / 2.0

    # Normals
    b1 = dot((p2 - p1), array([[0, -1], [1, 0]], dtype=float32))
    b2 = dot((p3 - p2), array([[0, 1], [-1, 0]], dtype=float32))

    # Params
    T = solve(transpose(array([-b1, b2])), a1 - a2)

    # Center
    center = a1 + b1 * T[0]

    # Radius
    radius = norm(center - p1)

    return center, radius, T[0]


def distance(pt1, pt2):
    return sqrt((pt1[0] - pt2[0]) ** 2 + (pt1[1] - pt2[1]) ** 2)


class FlatCAMRTree(object):

    def __init__(self):
        # Python RTree Index
        self.rti = rtindex.Index()

        ## Track object-point relationship
        # Each is list of points in object.
        self.obj2points = []

        # Index is index in rtree, value is index of
        # object in obj2points.
        self.points2obj = []

        self.get_points = lambda go: go.coords

    def grow_obj2points(self, idx):
        if len(self.obj2points) > idx:
            # len == 2, idx == 1, ok.
            return
        else:
            # len == 2, idx == 2, need 1 more.
            # range(2, 3)
            for i in range(len(self.obj2points), idx + 1):
                self.obj2points.append([])

    def insert(self, objid, obj):
        self.grow_obj2points(objid)
        self.obj2points[objid] = []

        for pt in self.get_points(obj):
            self.rti.insert(len(self.points2obj), (pt[0], pt[1], pt[0], pt[1]), obj=objid)
            self.obj2points[objid].append(len(self.points2obj))
            self.points2obj.append(objid)

    def remove_obj(self, objid, obj):
        # Use all ptids to delete from index
        for i, pt in enumerate(self.get_points(obj)):
            self.rti.delete(self.obj2points[objid][i], (pt[0], pt[1], pt[0], pt[1]))

    def nearest(self, pt):
        return self.rti.nearest(pt, objects=True).next()


class FlatCAMRTreeStorage(FlatCAMRTree):
    def __init__(self):
        super(FlatCAMRTreeStorage, self).__init__()

        self.objects = []

        # Optimization attempt!
        self.indexes = {}

    def insert(self, obj):
        self.objects.append(obj)
        idx = len(self.objects) - 1
        self.indexes[obj] = idx
        super(FlatCAMRTreeStorage, self).insert(idx, obj)

    #@profile
    def remove(self, obj):
        # Get index in list
        # TODO: This is extremely expensive
        #objidx = self.objects.index(obj)
        objidx = self.indexes[obj]

        # Remove from list
        self.objects[objidx] = None

        # Remove from index
        self.remove_obj(objidx, obj)

    def get_objects(self):
        return (o for o in self.objects if o is not None)

    def nearest(self, pt):
        """
        Returns the nearest matching points and the object
        it belongs to.

        :param pt: Query point.
        :return: (match_x, match_y), Object owner of
          matching point.
        :rtype: tuple
        """
        tidx = super(FlatCAMRTreeStorage, self).nearest(pt)
        return (tidx.bbox[0], tidx.bbox[1]), self.objects[tidx.object]


# class myO:
#     def __init__(self, coords):
#         self.coords = coords
#
#
# def test_rti():
#
#     o1 = myO([(0, 0), (0, 1), (1, 1)])
#     o2 = myO([(2, 0), (2, 1), (2, 1)])
#     o3 = myO([(2, 0), (2, 1), (3, 1)])
#
#     os = [o1, o2]
#
#     idx = FlatCAMRTree()
#
#     for o in range(len(os)):
#         idx.insert(o, os[o])
#
#     print [x.bbox for x in idx.rti.nearest((0, 0), num_results=20, objects=True)]
#
#     idx.remove_obj(0, o1)
#
#     print [x.bbox for x in idx.rti.nearest((0, 0), num_results=20, objects=True)]
#
#     idx.remove_obj(1, o2)
#
#     print [x.bbox for x in idx.rti.nearest((0, 0), num_results=20, objects=True)]
#
#
# def test_rtis():
#
#     o1 = myO([(0, 0), (0, 1), (1, 1)])
#     o2 = myO([(2, 0), (2, 1), (2, 1)])
#     o3 = myO([(2, 0), (2, 1), (3, 1)])
#
#     os = [o1, o2]
#
#     idx = FlatCAMRTreeStorage()
#
#     for o in range(len(os)):
#         idx.insert(os[o])
#
#     #os = None
#     #o1 = None
#     #o2 = None
#
#     print [x.bbox for x in idx.rti.nearest((0, 0), num_results=20, objects=True)]
#
#     idx.remove(idx.nearest((2,0))[1])
#
#     print [x.bbox for x in idx.rti.nearest((0, 0), num_results=20, objects=True)]
#
#     idx.remove(idx.nearest((0,0))[1])
#
#     print [x.bbox for x in idx.rti.nearest((0, 0), num_results=20, objects=True)]