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1c75a2dc1c
poly2tri/python/framework/triangulator.pyx
zzzzrrr 1c75a2dc1c ported Scala classes
2009-11-12 14:52:23 -05:00

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Cython
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#
# Poly2Tri
# Copyright (c) 2009, Mason Green
# http://code.google.com/p/poly2tri/
#
# All rights reserved.
#
# Redistribution and use in source and binary forms, with or without modification,
# are permitted provided that the following conditions are met:
#
# Redistributions of source code must retain the above copyright notice,
# self list of conditions and the following disclaimer.
# Redistributions in binary form must reproduce the above copyright notice,
# self list of conditions and the following disclaimer in the documentation
# and/or other materials provided with the distribution.
# Neither the name of Poly2Tri nor the names of its contributors may be
# used to endorse or promote products derived from self software without specific
# prior written permission.
#
# THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
# "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
# LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
# A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR
# CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
# EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
# PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
# PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
# LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
# NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
# SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
#
from math import floor
###
### Based on Raimund Seidel'e paper "A simple and fast incremental randomized
### algorithm for computing trapezoidal decompositions and for triangulating polygons"
### (Ported from poly2tri)
cdef extern from 'math.h':
double cos(double)
double sin(double)
double sqrt(double)
cdef list merge_sort(list l):
cdef list lleft, lright
cdef int p1, p2, p
if len(l)>1 :
lleft = merge_sort(l[:len(l)/2])
lright = merge_sort(l[len(l)/2:])
#do merge here
p1,p2,p = 0,0,0
while p1<len(lleft) and p2<len(lright):
if lleft[p1][0] < lright[p2][0]:
l[p]=lleft[p1]
p+=1
p1+=1
else:
l[p]=lright[p2]
p+=1
p2+=1
if p1<len(lleft):l[p:]=lleft[p1:]
elif p2<len(lright):l[p:]=lright[p2:]
else : print "internal error"
return l
cdef class Point:
cdef float x, y
next = None
prev = None
edge = None
edges = []
property x:
def __get__(self): return self.x
property y:
def __get__(self): return self.y
def __init__(self, float x, float y):
self.x = x
self.y = y
def __sub__(self, other):
if isinstance(other, Point):
return Point(self.x - other.x, self.y - other.y)
else:
return Point(self.x - other, self.y - other)
def __add__(self, other):
if isinstance(other, Point):
return Point(self.x + other.x, self.y + other.y)
else:
return Point(self.x + other, self.y + other)
def __mul__(self, float f):
return Point(self.x * f, self.y * f)
def __div__(self, float a):
return Point(self.x / a, self.y / a)
def cross(self, Point p):
return self.x * p.y - self.y * p.x
def dot(self, Point p):
return self.x * p.x + self.y * p.y
def length(self):
return sqrt(self.x * self.x + self.y * self.y)
def normalize(self):
return self / self.length()
def less(self, Point p):
return self.x < p.x
'''
# Sort along y axis
def greater(self, p):
if y < p.y:
return True
elif y > p.y:
return False
else:
if x < p.x:
return True
else:
return False
'''
def not_equal(self, p):
return not (p.x == self.x and p.y == self.y)
def clone(self):
return Point(self.x, self.y)
cdef class Edge:
cdef Point p, q
cdef bool above, below
cdef float slope, b
mpoints = []
def __init__(self, Point p, Point q):
self.p = p
self.q = q
self.slope = (q.y - p.y)/(q.x - p.x)
self.b = p.y - (p.x * self.slope)
property p:
def __get__(self): return self.p
property q:
def __get__(self): return self.q
property above:
def __get__(self): return self.above
property below:
def __get__(self): return self.below
cdef bool is_above(self, Point point):
return (floor(point.y) < floor(self.slope * point.x + self.b))
cdef bool is_below(self, Point point):
return (floor(point.y) > floor(self.slope * point.x + self.b))
cdef float intersect(self, Point c, Point d):
cdef float a1, a2, a3, a4, t
cdef Point a, b
a = self.p
b = self.q
a1 = self.signed_area(a, b, d)
a2 = self.signed_area(a, b, c)
if a1 != 0 and a2 != 0 and (a1 * a2) < 0:
a3 = self.signed_area(c, d, a)
a4 = a3 + a2 - a1
if a3 * a4 < 0:
t = a3 / (a3 - a4)
return a + ((b - a) * t)
return 0.0
cdef float signed_area(self, Point a, Point b, Point c):
return (a.x - c.x) * (b.y - c.y) - (a.y - c.y) * (b.x - c.x)
cdef Point line_intersect(Edge e, float x):
cdef float y = e.slope * x + e.b
return Point(x, y)
cdef class Trapezoid:
cdef:
Point lpoint, rpoint
Edge top, bottom
Trapezoid upper_left, lower_left
Trapezoid upper_right, lower_right
bool inside
sink = None
def __init__(self, Point lpoint, Point rpoint, Edge top, Edge bottom):
self.lpoint = lpoint
self.rpoint = rpoint
self.top = top
self.bottom = bottom
self.upper_left = None
self.upper_right = None
self.lower_left = None
self.lower_right = None
self.inside = True
property upper_left:
def __get__(self): return self.upper_left
def __set__(self, Trapezoid other): self.upper_left = other
property upper_right:
def __get__(self): return self.upper_right
def __set__(self, Trapezoid other): self.upper_right = other
property lower_left:
def __get__(self): return self.lower_left
def __set__(self, Trapezoid other): self.lower_left = other
property lower_right:
def __get__(self): return self.lower_right
def __set__(self, Trapezoid other): self.lower_right = other
def update_left(self, Trapezoid ul, Trapezoid ll):
self.upper_left = ul
self.lower_left = ll
if ul != None: ul.upper_right = self
if ll != None: ll.lower_right = self
def update_right(self, Trapezoid ur, Trapezoid lr):
self.upper_right = ur
self.lower_right = lr
if ur != None: ur.upper_left = self
if lr != None: lr.lower_left = self
def update_left_right(self, Trapezoid ul, Trapezoid ll, Trapezoid ur, Trapezoid lr):
self.upper_left = ul
self.lower_left = ll
self.upper_right = ur
self.lower_right = lr
if ul != None: ul.upper_right = self
if ll != None: ll.lower_right = self
if ur != None: ur.upper_left = self
if lr != None: lr.lower_left = self
def trim_neighbors(self):
if self.inside:
self.inside = False
if self.upper_left != None: self.upper_left.trim_neighbors()
if self.lower_left != None: self.lower_left.trim_neighbors()
if self.upper_right != None: self.upper_right.trim_neighbors()
if self.lower_right != None: self.lower_right.trim_neighbors()
def contains(self, Point point):
return (point.x > self.lpoint.x and point.x < self.rpoint.x and
self.top.is_above(point) and self.bottom.is_below(point))
def vertices(self):
cdef list verts = []
verts.append(line_intersect(self.top, self.lpoint.x))
verts.append(line_intersect(self.bottom, self.lpoint.x))
verts.append(line_intersect(self.bottom, self.rpoint.x))
verts.append(line_intersect(self.top, self.rpoint.x))
return verts
def add_points(self):
if self.lpoint != self.bottom.p:
self.bottom.mpoints.append(self.lpoint.clone)
if self.rpoint != self.bottom.q:
self.bottom.mpoints.append(self.rpoint.clone)
if self.lpoint != self.top.p:
self.top.mpoints.append(self.lpoint.clone)
if self.rpoint != self.top.q:
self.top.mpoints.append(self.rpoint.clone)
class TrapezoidalMap:
map = {}
margin = 50
bcross = None
tcross = None
def clear(self):
self.bcross = None
self.tcross = None
def case1(self, t, e):
trapezoids = [None, None, None, None]
trapezoids.append(Trapezoid(t.lpoint, e.p, t.top, t.bottom))
trapezoids.append(Trapezoid(e.p, e.q, t.top, e))
trapezoids.append(Trapezoid(e.p, e.q, e, t.bottom))
trapezoids.append(Trapezoid(e.q, t.rpoint, t.top, t.bottom))
trapezoids[0].update_left(t.upper_left, t.lower_left)
trapezoids[1].update_left_right(trapezoids[0], None, trapezoids[3], None)
trapezoids[2].update_left_right(None, trapezoids[0], None, trapezoids[3])
trapezoids[3].update_right(t.upper_right, t.lower_right)
return trapezoids
def case2(self, t, e):
rp = e.q if e.q.x == t.rpoint.x else t.rpoint
trapezoids = [None, None, None]
trapezoids.append(Trapezoid(t.lpoint, e.p, t.top, t.bottom))
trapezoids.append(Trapezoid(e.p, rp, t.top, e))
trapezoids.append(Trapezoid(e.p, rp, e, t.bottom))
trapezoids[0].update_left(t.upper_left, t.lower_left)
trapezoids[1].update_left_right(trapezoids[0], None, t.upper_right, None)
trapezoids[2].update_left_right(None, trapezoids[0], None, t.lower_right)
self.bcross = t.bottom
self.tcross = t.top
e.above = trapezoids[1]
e.below = trapezoids[2]
return trapezoids
def case3(self, t, e):
lp = e.p if e.p.x == t.lpoint.x else t.lpoint
rp = e.q if e.q.x == t.rpoint.x else t.rpoint
trapezoids = [None, None]
if self.tcross is t.top:
trapezoids[0] = t.upper_left
trapezoids[0].update_right(t.upper_right, None)
trapezoids[0].rpoint = rp
else:
trapezoids[0] = Trapezoid(lp, rp, t.top, e)
trapezoids[0].update_left_right(t.upper_left, e.above, t.upper_right, None)
if self.bcross is t.bottom:
trapezoids[1] = t.lower_left
trapezoids[1].update_right(None, t.lower_right)
trapezoids[1].rpoint = rp
else:
trapezoids[1] = Trapezoid(lp, rp, e, t.bottom)
trapezoids[1].update_left_right(e.below, t.lower_left, None, t.lower_right)
self.bcross = t.bottom
self.tcross = t.top
e.above = trapezoids[0]
e.below = trapezoids[1]
return trapezoids
def case4(self, t, e):
lp = e.p if e.p.x == t.lpoint.x else t.lpoint
trapezoids = [None, None, None]
if self.tcross is t.top:
trapezoids[0] = t.upper_left
trapezoids[0].rpoint = e.q
else:
trapezoids[0] = Trapezoid(lp, e.q, t.top, e)
trapezoids[0].update_left(t.upper_left, e.above)
if self.bcross is t.bottom:
trapezoids[1] = t.lower_left
trapezoids[1].rpoint = e.q
else:
trapezoids[1] = Trapezoid(lp, e.q, e, t.bottom)
trapezoids[1].update_left(e.below, t.lower_left)
trapezoids[2] = Trapezoid(e.q, t.rpoint, t.top, t.bottom)
trapezoids[2].update_left_right(trapezoids[0], trapezoids[1], t.upper_right, t.lower_right)
return trapezoids
def bounding_box(self, edges):
margin = self.margin
max = edges[0].p + margin
min = edges[0].q - margin
for e in edges:
if e.p.x > max.x: max = Point(e.p.x + margin, max.y)
if e.p.y > max.y: max = Point(max.x, e.p.y + margin)
if e.q.x > max.x: max = Point(e.q.x + margin, max.y)
if e.q.y > max.y: max = Point(max.x, e.q.y + margin)
if e.p.x < min.x: min = Point(e.p.x - margin, min.y)
if e.p.y < min.y: min = Point(min.x, e.p.y - margin)
if e.q.x < min.x: min = Point(e.q.x - margin, min.y)
if e.q.y < min.y: min = Point(min.x, e.q.y - margin)
top = Edge(Point(min.x, max.y), Point(max.x, max.y))
bottom = Edge(Point(min.x, min.y), Point(max.x, min.y))
left = bottom.p
right = top.q
return Trapezoid(left, right, top, bottom)
class Node:
parent_list = []
def __init__(self, left, right):
self.left = left
self.right = right
if left is not None:
left.parent_list.append(self)
if right is not None:
right.parent_list.append(self)
def replace(self, node):
for parent in node.parent_list:
if parent.left is node:
parent.left = self
else:
parent.right = self
self.parent_list.append(parent)
class Sink(Node):
def __new__(cls, trapezoid):
if trapezoid.sink is not None:
return trapezoid.sink
else:
return Sink(trapezoid)
def __init__(self, trapezoid):
Node.__init__(self, None, None)
trapezoid.sink = self
def locate(self, e):
return self
class XNode(Node):
def __init__(self, point, lchild, rchild):
Node.__init__(self, lchild, rchild)
self.point = point
self.lchild = lchild
self.rchild = rchild
def locate(self, e):
if e.p.x >= self.point.x:
return self.right.locate(e)
else:
return self.left.locate(e)
class YNode(Node):
def __init__(self, edge, lchild, rchild):
Node.__init__(self, lchild, rchild)
self.edge = edge
self.lchild = lchild
self.rchild = rchild
def locate(self, e):
if self.edge.is_above(e.p):
return self.right.locate(e)
elif self.edge.is_below(e.p):
return self.left.locate(e)
else:
if e.slope < self.edge.slope:
return self.right.locate(e)
else:
return self.left.locate(e)
class QueryGraph:
head = None
def __init__(self, head):
self.head = head
def locate(self, e):
return self.head.locate(e).trapezoid
def follow_segment(self, e):
trapezoids = [self.locate(e)]
j = 0
while(e.q.x > trapezoids[j].right_point.x):
if e > trapezoids[j].right_point:
trapezoids.append(trapezoids[j].upper_right)
else:
trapezoids .append(trapezoids[j].lower_right)
j += 1
return trapezoids
def replace(self, sink, node):
if not sink.parent_list:
self.head = node
else:
node.replace(sink)
def case1(self, sink, e, tlist):
yNode = YNode(e, Sink(tlist[1]), Sink(tlist[2]))
qNode = XNode(e.q, yNode, Sink(tlist[3]))
pNode = XNode(e.p, Sink(tlist[0]), qNode)
self.replace(sink, pNode)
def case2(self, sink, e, tlist):
yNode = YNode(e, Sink(tlist[1]), Sink(tlist[2]))
pNode = XNode(e.p, Sink(tlist[0]), yNode)
self.replace(sink, pNode)
def case3(self, sink, e, tlist):
yNode = YNode(e, Sink(tlist[0]), Sink(tlist[1]))
self.replace(sink, yNode)
def case4(self, sink, e, tlist):
yNode = YNode(e, Sink(tlist[0]), Sink(tlist[1]))
qNode = XNode(e.q, yNode, Sink(tlist[2]))
self.replace(sink, qNode)
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