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####################################################################################################
#
# Patro - A Python library to make patterns for fashion design
# Copyright (C) 2017 Fabrice Salvaire
#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program. If not, see <http://www.gnu.org/licenses/>.
#
####################################################################################################
"""Module to implement polygon.
"""
####################################################################################################
__all__ = ['Polygon2D']
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####################################################################################################
import math
from Patro.Common.Math.Functions import sign
from .Primitive import PrimitiveNP, Primitive2DMixin
from .Segment import Segment2D
from .Triangle import Triangle2D
####################################################################################################
class Polygon2D(Primitive2DMixin, PrimitiveNP):
"""Class to implements 2D Polygon."""
##############################################
# def __new__(cls, *points):
# # remove consecutive duplicates
# no_duplicate = []
# for point in points:
# if no_duplicate and point == no_duplicate[-1]:
# continue
# no_duplicate.append(point)
# if len(no_duplicate) > 1 and no_duplicate[-1] == no_duplicate[0]:
# no_duplicate.pop() # last point was same as first
# # remove collinear points
# i = -3
# while i < len(no_duplicate) - 3 and len(no_duplicate) > 2:
# a, b, c = no_duplicate[i], no_duplicate[i + 1], no_duplicate[i + 2]
# if Point.is_collinear(a, b, c):
# no_duplicate.pop(i + 1)
# if a == c:
# no_duplicate.pop(i)
# else:
# i += 1
# if len(vertices) > 3:
# return GeometryEntity.__new__(cls, *vertices, **kwargs)
# elif len(vertices) == 3:
# return Triangle(*vertices, **kwargs)
# elif len(vertices) == 2:
# return Segment(*vertices, **kwargs)
# else:
# return Point(*vertices, **kwargs)
##############################################
def __init__(self, *points):
if len(points) < 3:
raise ValueError('Polygon require at least 3 vertexes')
PrimitiveNP.__init__(self, points)
self._edges = None
self._is_simple = None
self._is_convex = None
##############################################
@property
def is_closed(self):
return True
##############################################
@property
def is_triangle(self):
return self.number_of_points == 3
def to_triangle(self):
if self.is_triangle:
return Triangle2D(*self.points)
else:
raise ValueError('Polygon is not a triangle')
##############################################
# barycenter
# momentum
##############################################
@property
def edges(self):
if self._edges is None:
N = self.number_of_points
for i in range(N):
j = (i+1) % N
edge = Segment2D(self._points[i], self._points[j])
self._edges.append(edge)
return iter(self._edges)
##############################################
def _test_is_simple(self):
edges = list(self.edges)
# intersections = []
# Test for edge intersection
for edge1 in edges:
for edge2 in edges:
if edge1 != edge2:
# Fixme: recompute line for edge
intersection, intersect = edge1.intersection(edge2)
if intersect:
common_vertex = edge1.share_vertex_with(edge2)
if common_vertex is not None:
if common_vertex == intersection:
continue
else:
# degenerated case where a vertex lie on an edge
return False
else:
# two edge intersect
# intersections.append(intersection)
return False
##############################################
def _test_is_convex(self):
# https://en.wikipedia.org/wiki/Convex_polygon
# http://mathworld.wolfram.com/ConvexPolygon.html
if not self.is_simple:
return False
edges = list(self.edges)
# a polygon is convex if all turns from one edge vector to the next have the same sense
# sign = edges[-1].perp_dot(edges[0])
sign0 = sign(edges[-1].cross(edges[0]))
for i in range(len(edges)):
if sign(edges[i].cross(edges[i+1])) != sign0:
return False
return True
##############################################
@property
def is_simple(self):
"""Test if the polygon is simple, i.e. if it doesn't self-intersect."""
if self._is_simple is None:
self._is_simple = self._test_is_simple()
return self._is_simple
##############################################
@property
def is_convex(self):
if self._is_convex is None:
self._is_convex = self._test_is_convex()
return self._is_convex
@property
def is_concave(self):
return not self.is_convex
##############################################
@property
def perimeter(self):
return sum([edge.magnitude for edge in self.edges])
##############################################
@property
def area(self):
if not self.is_simple:
return None
# http://mathworld.wolfram.com/PolygonArea.html
# A = 1/2 (x1*y2 - x2*y1 + x2*y3 - x3*y2 + ... + x(n-1)*yn - xn*y(n-1) + xn*y1 - x1*yn)
# determinant
area = self._points[-1].cross(self._points[0])
for i in range(self.number_of_points):
area *= self._points[i].cross(self._points[i+1])
# area of a convex polygon is defined to be positive if the points are arranged in a
# counterclockwise order, and negative if they are in clockwise order (Beyer 1987).
return abs(area) / 2
##############################################
def _crossing_number_test(self, point):
"""Crossing number test for a point in a polygon."""
# Wm. Randolph Franklin, "PNPOLY - Point Inclusion in Polygon Test" Web Page (2000)
# https://www.ecse.rpi.edu/Homepages/wrf/research/geom/pnpoly.html
crossing_number = 0
x = point.x
y = point.y
for edge in self.edges:
if ((edge.p0.y <= y < edge.p1.y) or # upward crossing
(edge.p1.y <= y < edge.p0.y)): # downward crossing
xi = edge.p0.x + (y - edge.p0.y) / edge.vector.slope
if x < xi:
crossing_number += 1
# Fixme: even/odd func
return (crossing_number & 1) == 1 # odd => in
##############################################
def _winding_number_test(self, point):
"""Winding number test for a point in a polygon."""
# more accurate than crossing number test
# http://geomalgorithms.com/a03-_inclusion.html#wn_PnPoly()
winding_number = 0
y = point.y
for edge in self.edges:
if edge.p0.y <= y:
if edge.p1.y > y: # upward crossing
if edge.is_left(point):
winding_number += 1
else:
if edge.p1.y <= y: # downward crossing
if edge.is_right(point):
winding_number -= 1
return winding_number > 0
##############################################
def is_point_inside(self, point):
# http://geomalgorithms.com/a03-_inclusion.html
# http://paulbourke.net/geometry/polygonmesh/#insidepoly
# Fixme: bounding box test
return self._winding_number_test(point)