This commit is contained in:
zzzzrrr 2009-11-17 14:21:30 -05:00
parent 048bd0740e
commit bdcfc0eb04
4 changed files with 896 additions and 254 deletions

View File

@ -5,13 +5,10 @@ from math import pi as PI
from gl cimport * from gl cimport *
#from triangulator import Point
include "triangulator.pyx"
cdef extern from 'math.h': cdef extern from 'math.h':
double cos(double) double cos(double)
double sin(double) double sin(double)
double sqrt(double)
SEGMENTS = 25 SEGMENTS = 25
INCREMENT = 2.0 * PI / SEGMENTS INCREMENT = 2.0 * PI / SEGMENTS
@ -61,11 +58,6 @@ from glfw cimport *
import sys import sys
cdef extern from 'math.h':
double cos(double)
double sin(double)
double sqrt(double)
# Keyboard callback wrapper # Keyboard callback wrapper
kbd_callback_method = None kbd_callback_method = None
@ -78,9 +70,6 @@ cdef class Game:
title = "Poly2Tri" title = "Poly2Tri"
def __init__(self, window_width, window_height): def __init__(self, window_width, window_height):
points = [Point(100,100), Point(-100,100), Point(-100,-100), Point(100,-100)]
seidel = Triangulator(points)
glfwInit() glfwInit()

View File

@ -43,145 +43,9 @@ cdef extern from 'math.h':
double floor(double) double floor(double)
double sqrt(double) double sqrt(double)
class Triangulator: class Point:
def __init__(self, points):
self.polygons = []
self.edge_list = self.init_edges(points)
self.trapezoids = []
self.trapezoidal_map = TrapezoidalMap()
bounding_box = self.trapezoidal_map.bounding_box(self.edge_list)
self.query_graph = QueryGraph(Sink(bounding_box))
self.xmono_poly = []
self.process()
def trapezoidMap(self):
return self.trapezoidal_map.map
# Build the trapezoidal map and query graph def __cinit__(self, float x, float y):
def process(self):
for e in self.edge_list:
traps = self.query_graph.follow_edge(e)
for t in traps:
try:
self.trapezoidal_map.map.remove(t)
except:
pass
for t in traps:
tlist = []
cp = t.contains(e.p)
cq = t.contains(e.q)
if cp and cq:
tlist = self.trapezoidal_map.case1(t, e)
self.query_graph.case1(t.sink, e, tlist)
elif cp and not cq:
tlist = self.trapezoidal_map.case2(t, e)
self.query_graph.case2(t.sink, e, tlist)
elif not cp and not cq:
tlist = self.trapezoidal_map.case3(t, e)
self.query_graph.case3(t.sink, e, tlist)
else:
tlist = self.trapezoidal_map.case4(t, e)
self.query_graph.case4(t.sink, e, tlist)
# Add new trapezoids to map
for t in tlist:
self.trapezoidal_map.map.append(t)
self.trapezoidal_map.clear()
# Mark outside trapezoids
for t in self.trapezoidal_map.map:
self.mark_outside(t)
# Collect interior trapezoids
for t in self.trapezoidal_map.map:
if t.inside():
self.trapezoids.append(t)
t.add_points()
self.create_mountains()
def mono_polies(self):
polies = []
for x in self.xmono_poly:
polies.append(x.monoPoly)
return polies
def create_mountains(self):
for s in self.edge_list:
if len(s.mpoints) > 0:
mountain = MonotoneMountain()
k = merge_sort(s.mpoints)
points = [s.p] + k + [s.q]
for p in points:
mountain.append(p)
mountain.process()
for t in mountain.triangles:
self.polygons.append(t)
self.xmono_poly.append(mountain)
def mark_outside(self, t):
if t.top is self.bounding_box.top or t.bottom is self.bounding_box.bottom:
t.trimNeighbors()
def init_edges(self, points):
edges = []
for i in range(len(points)-1):
edges.append(Edge(points[i], points[i+1]))
edges.append(Edge(points[0], points[-1]))
return self.order_edges(edges)
def order_edges(self, edges):
segs = []
for s in edges:
p = self.shearTransform(s.p)
q = self.shearTransform(s.q)
if p.x > q.x: segs.append(Edge(q, p))
elif p.x < q.x: segs.append(Edge(p, q))
shuffle(segs)
return segs
def shearTransform(self, point):
return Point(point.x + 1e-4 * point.y, point.y)
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:])
p1, p2, p = 0, 0, 0
while p1<len(lleft) and p2<len(lright):
if lleft[p1].x < lright[p2].x:
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.x = x
self.y = y self.y = y
@ -203,10 +67,10 @@ cdef class Point:
def __div__(self, float a): def __div__(self, float a):
return Point(self.x / a, self.y / a) return Point(self.x / a, self.y / a)
def cross(self, Point p): def cross(self, p):
return self.x * p.y - self.y * p.x return self.x * p.y - self.y * p.x
def dot(self, Point p): def dot(self, p):
return self.x * p.x + self.y * p.y return self.x * p.x + self.y * p.y
def length(self): def length(self):
@ -215,38 +79,22 @@ cdef class Point:
def normalize(self): def normalize(self):
return self / self.length() return self / self.length()
def less(self, Point p): def less(self, p):
return self.x < p.x 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): def not_equal(self, p):
return not (p.x == self.x and p.y == self.y) return not (p.x == self.x and p.y == self.y)
def clone(self): def clone(self):
return Point(self.x, self.y) return Point(self.x, self.y)
cdef class Edge:
cdef Point p, q cdef class Edge:
cdef bool above, below
cdef float slope, b
cdef object above, below
cdef float slope, b
mpoints = [] mpoints = []
def __init__(self, Point p, Point q): def __cinit__(self, p, q):
self.p = p self.p = p
self.q = q self.q = q
self.slope = (q.y - p.y)/(q.x - p.x) self.slope = (q.y - p.y)/(q.x - p.x)
@ -264,12 +112,12 @@ cdef class Edge:
property below: property below:
def __get__(self): return self.below def __get__(self): return self.below
cdef bool is_above(self, Point point): cdef bool is_above(self, point):
return (floor(point.y) < floor(self.slope * point.x + self.b)) return (floor(point.y) < floor(self.slope * point.x + self.b))
cdef bool is_below(self, Point point): cdef bool is_below(self, point):
return (floor(point.y) > floor(self.slope * point.x + self.b)) return (floor(point.y) > floor(self.slope * point.x + self.b))
cdef float intersect(self, Point c, Point d): cdef float intersect(self, c, d):
cdef float a1, a2, a3, a4, t cdef float a1, a2, a3, a4, t
cdef Point a, b cdef Point a, b
a = self.p a = self.p
@ -284,24 +132,18 @@ cdef class Edge:
return a + ((b - a) * t) return a + ((b - a) * t)
return 0.0 return 0.0
cdef float signed_area(self, Point a, Point b, Point c): cdef float signed_area(self, a, b, c):
return (a.x - c.x) * (b.y - c.y) - (a.y - c.y) * (b.x - c.x) 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 class Trapezoid:
cdef: cdef Edge top, bottom
Point left_point, right_point cdef Trapezoid upper_left, lower_left
Edge top, bottom cdef Trapezoid upper_right, lower_right
Trapezoid upper_left, lower_left cdef object sink
Trapezoid upper_right, lower_right cdef bool inside
bool inside
object sink
def __init__(self, Point left_point, Point right_point, Edge top, Edge bottom): def __cinit__(self, left_point, right_point, Edge top, Edge bottom):
self.left_point = left_point self.left_point = left_point
self.right_point = right_point self.right_point = right_point
self.top = top self.top = top
@ -313,6 +155,9 @@ cdef class Trapezoid:
self.inside = True self.inside = True
self.sink = None self.sink = None
property inside:
def __get__(self): return self.inside
property top: property top:
def __get__(self): return self.top def __get__(self): return self.top
@ -321,9 +166,11 @@ cdef class Trapezoid:
property left_point: property left_point:
def __get__(self): return self.left_point def __get__(self): return self.left_point
def __set__(self, lp): self.left_point = lp
property right_point: property right_point:
def __get__(self): return self.right_point def __get__(self): return self.right_point
def __set__(self, rp): self.right_point = rp
property sink: property sink:
def __get__(self): return self.sink def __get__(self): return self.sink
@ -375,7 +222,7 @@ cdef class Trapezoid:
if self.upper_right != None: self.upper_right.trim_neighbors() if self.upper_right != None: self.upper_right.trim_neighbors()
if self.lower_right != None: self.lower_right.trim_neighbors() if self.lower_right != None: self.lower_right.trim_neighbors()
def contains(self, Point point): def contains(self, point):
return (point.x > self.left_point.x and point.x < self.right_point.x and return (point.x > self.left_point.x and point.x < self.right_point.x and
self.top.is_above(point) and self.bottom.is_below(point)) self.top.is_above(point) and self.bottom.is_below(point))
@ -397,6 +244,140 @@ cdef class Trapezoid:
if self.right_point != self.top.q: if self.right_point != self.top.q:
self.top.mpoints.append(self.right_point.clone) self.top.mpoints.append(self.right_point.clone)
cdef Point line_intersect(Edge e, float x):
cdef float y = e.slope * x + e.b
return Point(x, y)
class Triangulator:
def __init__(self, poly_line):
self.polygons = []
self.edge_list = self.init_edges(poly_line)
self.trapezoids = []
self.trapezoidal_map = TrapezoidalMap()
self.bounding_box = self.trapezoidal_map.bounding_box(self.edge_list)
self.query_graph = QueryGraph(isink(self.bounding_box))
self.xmono_poly = []
self.process()
def trapezoidMap(self):
return self.trapezoidal_map.map
# Build the trapezoidal map and query graph
def process(self):
for e in self.edge_list:
traps = self.query_graph.follow_edge(e)
for t in traps:
try:
self.trapezoidal_map.map.remove(t)
except:
pass
for t in traps:
tlist = []
cp = t.contains(e.p)
cq = t.contains(e.q)
if cp and cq:
tlist = self.trapezoidal_map.case1(t, e)
self.query_graph.case1(t.sink, e, tlist)
elif cp and not cq:
tlist = self.trapezoidal_map.case2(t, e)
self.query_graph.case2(t.sink, e, tlist)
elif not cp and not cq:
tlist = self.trapezoidal_map.case3(t, e)
self.query_graph.case3(t.sink, e, tlist)
else:
tlist = self.trapezoidal_map.case4(t, e)
self.query_graph.case4(t.sink, e, tlist)
# Add new trapezoids to map
for t in tlist:
self.trapezoidal_map.map.append(t)
self.trapezoidal_map.clear()
# Mark outside trapezoids
for t in self.trapezoidal_map.map:
self.mark_outside(t)
# Collect interior trapezoids
for t in self.trapezoidal_map.map:
if t.inside:
self.trapezoids.append(t)
t.add_points()
self.create_mountains()
def mono_polies(self):
polies = []
for x in self.xmono_poly:
polies.append(x.monoPoly)
return polies
def create_mountains(self):
for s in self.edge_list:
if len(s.mpoints) > 0:
mountain = MonotoneMountain()
print s.mpoints
k = merge_sort(s.mpoints)
points = [s.p] + k + [s.q]
for p in points:
mountain.append(p)
mountain.process()
for t in mountain.triangles:
self.polygons.append(t)
self.xmono_poly.append(mountain)
def mark_outside(self, t):
if t.top is self.bounding_box.top or t.bottom is self.bounding_box.bottom:
t.trim_neighbors()
def init_edges(self, points):
edges = []
for i in range(len(points)-1):
p = Point(points[i][0], points[i][1])
q = Point(points[i+1][0], points[i+1][1])
edges.append(Edge(p, q))
p = Point(points[0][0], points[0][1])
q = Point(points[-1][0], points[-1][1])
edges.append(Edge(p, q))
return self.order_edges(edges)
def order_edges(self, edges):
segs = []
for s in edges:
p = self.shearTransform(s.p)
q = self.shearTransform(s.q)
if p.x > q.x:
segs.append(Edge(q, p))
elif p.x < q.x:
segs.append(Edge(p, q))
shuffle(segs)
return segs
def shearTransform(self, point):
return Point(point.x + 1e-4 * point.y, point.y)
cdef list merge_sort(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:])
p1, p2, p = 0, 0, 0
while p1<len(lleft) and p2<len(lright):
if lleft[p1].x < lright[p2].x:
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
class TrapezoidalMap: class TrapezoidalMap:
map = [] map = []
@ -408,7 +389,7 @@ class TrapezoidalMap:
self.bcross = None self.bcross = None
self.tcross = None self.tcross = None
def case1(self, t, e): def case1(self, Trapezoid t, Edge e):
trapezoids = [] trapezoids = []
trapezoids.append(Trapezoid(t.left_point, e.p, t.top, t.bottom)) trapezoids.append(Trapezoid(t.left_point, e.p, t.top, t.bottom))
trapezoids.append(Trapezoid(e.p, e.q, t.top, e)) trapezoids.append(Trapezoid(e.p, e.q, t.top, e))
@ -420,7 +401,7 @@ class TrapezoidalMap:
trapezoids[3].update_right(t.upper_right, t.lower_right) trapezoids[3].update_right(t.upper_right, t.lower_right)
return trapezoids return trapezoids
def case2(self, t, e): def case2(self, Trapezoid t, Edge e):
rp = e.q if e.q.x == t.right_point.x else t.right_point rp = e.q if e.q.x == t.right_point.x else t.right_point
trapezoids = [] trapezoids = []
trapezoids.append(Trapezoid(t.left_point, e.p, t.top, t.bottom)) trapezoids.append(Trapezoid(t.left_point, e.p, t.top, t.bottom))
@ -435,7 +416,7 @@ class TrapezoidalMap:
e.below = trapezoids[2] e.below = trapezoids[2]
return trapezoids return trapezoids
def case3(self, t, e): def case3(self, Trapezoid t, Edge e):
lp = e.p if e.p.x == t.left_point.x else t.left_point lp = e.p if e.p.x == t.left_point.x else t.left_point
rp = e.q if e.q.x == t.right_point.x else t.right_point rp = e.q if e.q.x == t.right_point.x else t.right_point
trapezoids = [] trapezoids = []
@ -459,7 +440,7 @@ class TrapezoidalMap:
e.below = trapezoids[1] e.below = trapezoids[1]
return trapezoids return trapezoids
def case4(self, t, e): def case4(self, Trapezoid t, Edge e):
lp = e.p if e.p.x == t.left_point.x else t.left_point lp = e.p if e.p.x == t.left_point.x else t.left_point
trapezoids = [] trapezoids = []
if self.tcross is t.top: if self.tcross is t.top:
@ -498,61 +479,81 @@ class TrapezoidalMap:
right = top.q right = top.q
return Trapezoid(left, right, top, bottom) return Trapezoid(left, right, top, bottom)
class Node: cdef class Node:
parent_list = [] cdef Node left, right
cdef object parent_list
def __init__(self, left, right): def __init__(self, Node left, Node right):
self.parent_list = []
self.left = left self.left = left
self.right = right self.right = right
if left != None: left.parent_list.append(self) if left != None:
if right != None: right.parent_list.append(self) left.parent_list.append(self)
if right != None:
def replace(self, node): right.parent_list.append(self)
property left:
def __get__(self): return self.left
def __set__(self, Node left): self.left = left
property right:
def __get__(self): return self.right
def __set__(self, Node right): self.right = right
property parent_list:
def __get__(self): return self.parent_list
def replace(self, Node node):
for parent in node.parent_list: for parent in node.parent_list:
if parent.left is node: if parent.left is node:
parent.left = self parent.left = self
else: else:
parent.right = self parent.right = self
self.parent_list.append(parent) self.parent_list += node.parent_list
class Sink(Node): cdef class Sink(Node):
def __new__(cls, trapezoid): cdef Trapezoid trapezoid
if trapezoid.sink != None:
return trapezoid.sink
return Sink(trapezoid)
def __init__(self, trapezoid): def __init__(self, trapezoid):
self.trapezoid = trapezoid self.trapezoid = trapezoid
Node.__init__(self, None, None) super(Sink, self).__init__(None, None)
trapezoid.sink = self trapezoid.sink = self
property trapezoid:
def __get__(self): return self.trapezoid
def locate(self, e): def locate(self, e):
return self return self
class XNode(Node):
def __init__(self, point, lchild, rchild): cdef Sink isink(Trapezoid trapezoid):
Node.__init__(self, lchild, rchild) if trapezoid.sink != None:
self.point = point return trapezoid.sink
self.lchild = lchild return Sink(trapezoid)
self.rchild = rchild
def locate(self, e): cdef class XNode(Node):
cdef Point point
def __init__(self, Point point, Node lchild, Node rchild):
super(XNode, self).__init__(lchild, rchild)
self.point = point
def locate(self, Edge e):
if e.p.x >= self.point.x: if e.p.x >= self.point.x:
return self.right.locate(e) return self.right.locate(e)
return self.left.locate(e) return self.left.locate(e)
class YNode(Node): cdef class YNode(Node):
def __init__(self, edge, lchild, rchild): cdef Edge edge
Node.__init__(self, lchild, rchild)
def __init__(self, Edge edge, Node lchild, Node rchild):
super(YNode, self).__init__(lchild, rchild)
self.edge = edge self.edge = edge
self.lchild = lchild
self.rchild = rchild
def locate(self, e): def locate(self, Edge e):
if self.edge.is_above(e.p): if self.edge.is_above(e.p):
return self.right.locate(e) return self.right.locate(e)
elif self.edge.is_below(e.p): elif self.edge.is_below(e.p):
@ -560,53 +561,54 @@ class YNode(Node):
else: else:
if e.slope < self.edge.slope: if e.slope < self.edge.slope:
return self.right.locate(e) return self.right.locate(e)
return self.left.locate(e) else:
return self.left.locate(e)
class QueryGraph: cdef class QueryGraph:
head = None cdef Node head
def __init__(self, head): def __init__(self, Node head):
self.head = head self.head = head
def locate(self, e): def locate(self, Edge e):
return self.head.locate(e).trapezoid return self.head.locate(e).trapezoid
def follow_edge(self, e): def follow_edge(self, Edge e):
trapezoids = [self.locate(e)] trapezoids = [self.locate(e)]
j = 0 cdef int j = 0
while(e.q.x > trapezoids[j].right_point.x): while(e.q.x > trapezoids[j].right_point.x):
if e > trapezoids[j].right_point: if e.is_above(trapezoids[j].right_point):
trapezoids.append(trapezoids[j].upper_right) trapezoids.append(trapezoids[j].upper_right)
else: else:
trapezoids .append(trapezoids[j].lower_right) trapezoids.append(trapezoids[j].lower_right)
j += 1 j += 1
return trapezoids return trapezoids
def replace(self, sink, node): def replace(self, Sink sink, Node node):
if not sink.parent_list: if not sink.parent_list:
self.head = node self.head = node
else: else:
node.replace(sink) node.replace(sink)
def case1(self, sink, e, tlist): def case1(self, Sink sink, Edge e, tlist):
yNode = YNode(e, Sink(tlist[1]), Sink(tlist[2])) cdef Node yNode = YNode(e, isink(tlist[1]), isink(tlist[2]))
qNode = XNode(e.q, yNode, Sink(tlist[3])) cdef Node qNode = XNode(e.q, yNode, isink(tlist[3]))
pNode = XNode(e.p, Sink(tlist[0]), qNode) cdef Node pNode = XNode(e.p, isink(tlist[0]), qNode)
self.replace(sink, pNode) self.replace(sink, pNode)
def case2(self, sink, e, tlist): def case2(self, Sink sink, Edge e, tlist):
yNode = YNode(e, Sink(tlist[1]), Sink(tlist[2])) yNode = YNode(e, isink(tlist[1]), isink(tlist[2]))
pNode = XNode(e.p, Sink(tlist[0]), yNode) pNode = XNode(e.p, isink(tlist[0]), yNode)
self.replace(sink, pNode) self.replace(sink, pNode)
def case3(self, sink, e, tlist): def case3(self, Sink sink, Edge e, tlist):
yNode = YNode(e, Sink(tlist[0]), Sink(tlist[1])) yNode = YNode(e, isink(tlist[0]), isink(tlist[1]))
self.replace(sink, yNode) self.replace(sink, yNode)
def case4(self, sink, e, tlist): def case4(self, Sink sink, Edge e, tlist):
yNode = YNode(e, Sink(tlist[0]), Sink(tlist[1])) yNode = YNode(e, isink(tlist[0]), isink(tlist[1]))
qNode = XNode(e.q, yNode, Sink(tlist[2])) qNode = XNode(e.q, yNode, isink(tlist[2]))
self.replace(sink, qNode) self.replace(sink, qNode)
cdef float PI_SLOP = 3.1 cdef float PI_SLOP = 3.1
@ -624,7 +626,8 @@ cdef class MonotoneMountain:
def __init__(self): def __init__(self):
self.size = 0 self.size = 0
self.tail, self.head = None self.tail = None
self.head = None
self.positive = False self.positive = False
self.convex_points = [] self.convex_points = []
self.mono_poly = [] self.mono_poly = []

View File

@ -1,20 +1,48 @@
#!/usr/bin/env python2.6 #!/usr/bin/env python2.6
from framework import Game from framework import Game, draw_polygon, reset_zoom
from seidel import Triangulator
class Poly2Tri(Game): class Poly2Tri(Game):
#Screen size #Screen size
screen_size = 800.0, 600.0 screen_size = 800.0, 600.0
def __init__(self): def __init__(self):
super(Poly2Tri, self).__init__(*self.screen_size) super(Poly2Tri, self).__init__(*self.screen_size)
# Load point set
file_name = "../data/star.dat"
points = self.load_points(file_name)
# Triangulate
t1 = self.time
seidel = Triangulator(points)
self.triangles = seidel.triangles()
dt = self.time - t1
print "time = %f , num triangles = %d" % (dt, len(self.triangles))
self.main_loop() self.main_loop()
def update(self): def update(self):
pass pass
def render(self): def render(self):
pass reset_zoom(1.0, (0,0), self.screen_size)
red = 255, 0, 0
for t in self.triangles:
draw_polygon(t, red)
def load_points(self, file_name):
infile = open(file_name, "r")
points = []
while infile:
line = infile.readline()
s = line.split()
if len(s) == 0:
break
points.append((float(s[0]), float(s[1])))
return points
if __name__ == '__main__': if __name__ == '__main__':
demo = Poly2Tri() demo = Poly2Tri()

622
python/seidel.py Normal file
View File

@ -0,0 +1,622 @@
#
# 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 random import shuffle
from math import atan2, 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)
class Point(object):
def __init__(self, x, y):
self.x = x
self.y = y
self.next, self.prev = None, None
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, f):
return Point(self.x * f, self.y * f)
def __div__(self, a):
return Point(self.x / a, self.y / a)
def cross(self, p):
return self.x * p.y - self.y * p.x
def dot(self, 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, p):
return self.x < p.x
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)
class Edge(object):
mpoints = []
above, below = None, None
def __init__(self, p, q):
self.p = p
self.q = q
self.slope = 0.0 if (q.x - p.x) == 0 else (q.y - p.y)/(q.x - p.x)
self.b = p.y - (p.x * self.slope)
def is_above(self, point):
return (floor(point.y) < floor(self.slope * point.x + self.b))
def is_below(self, point):
return (floor(point.y) > floor(self.slope * point.x + self.b))
def intersect(self, c, d):
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
def signed_area(self, a, b, c):
return (a.x - c.x) * (b.y - c.y) - (a.y - c.y) * (b.x - c.x)
class Trapezoid(object):
def __init__(self, left_point, right_point, top, bottom):
self.left_point = left_point
self.right_point = right_point
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
self.sink = None
def update_left(self, ul, 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, ur, 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, ul, ll, ur, 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):
return (point.x > self.left_point.x and point.x < self.right_point.x and
self.top.is_above(point) and self.bottom.is_below(point))
def vertices(self):
verts = []
verts.append(line_intersect(self.top, self.left_point.x))
verts.append(line_intersect(self.bottom, self.left_point.x))
verts.append(line_intersect(self.bottom, self.right_point.x))
verts.append(line_intersect(self.top, self.right_point.x))
return verts
def add_points(self):
if self.left_point != self.bottom.p:
self.bottom.mpoints.append(self.left_point.clone())
if self.right_point != self.bottom.q:
self.bottom.mpoints.append(self.right_point.clone())
if self.left_point != self.top.p:
self.top.mpoints.append(self.left_point.clone())
if self.right_point != self.top.q:
self.top.mpoints.append(self.right_point.clone())
def line_intersect(edge, x):
y = edge.slope * x + edge.b
return Point(x, y)
class Triangulator(object):
def __init__(self, poly_line):
self.polygons = []
self.edge_list = self.init_edges(poly_line)
self.trapezoids = []
self.trapezoidal_map = TrapezoidalMap()
self.bounding_box = self.trapezoidal_map.bounding_box(self.edge_list)
self.query_graph = QueryGraph(isink(self.bounding_box))
self.xmono_poly = []
self.process()
def triangles(self):
triangles = []
for p in self.polygons:
verts = []
for v in p:
verts.append((v.x, v.y))
triangles.append(verts)
return triangles
def trapezoid_map(self):
return self.trapezoidal_map.map
# Build the trapezoidal map and query graph
def process(self):
for edge in self.edge_list:
traps = self.query_graph.follow_edge(edge)
for t in traps:
try:
self.trapezoidal_map.map.remove(t)
except:
pass
for t in traps:
cp = t.contains(edge.p)
cq = t.contains(edge.q)
if cp and cq:
tlist = self.trapezoidal_map.case1(t, edge)
self.query_graph.case1(t.sink, edge, tlist)
elif cp and not cq:
tlist = self.trapezoidal_map.case2(t, edge)
self.query_graph.case2(t.sink, edge, tlist)
elif not cp and not cq:
tlist = self.trapezoidal_map.case3(t, edge)
self.query_graph.case3(t.sink, edge, tlist)
else:
tlist = self.trapezoidal_map.case4(t, edge)
self.query_graph.case4(t.sink, edge, tlist)
# Add new trapezoids to map
for t in tlist:
self.trapezoidal_map.map.append(t)
self.trapezoidal_map.clear()
# Mark outside trapezoids
for t in self.trapezoidal_map.map:
self.mark_outside(t)
# Collect interior trapezoids
for t in self.trapezoidal_map.map:
if t.inside:
self.trapezoids.append(t)
t.add_points()
# Generate the triangles
self.create_mountains()
def mono_polies(self):
polies = []
for x in self.xmono_poly:
polies.append(x.monoPoly)
return polies
def create_mountains(self):
for edge in self.edge_list:
if len(edge.mpoints) > 0:
mountain = MonotoneMountain()
k = merge_sort(edge.mpoints)
points = [edge.p] + k + [edge.q]
for p in points:
mountain.add(p)
mountain.process()
for t in mountain.triangles:
self.polygons.append(t)
self.xmono_poly.append(mountain)
def mark_outside(self, t):
if t.top is self.bounding_box.top or t.bottom is self.bounding_box.bottom:
t.trim_neighbors()
def init_edges(self, points):
edges = []
for i in range(len(points)-1):
p = Point(points[i][0], points[i][1])
q = Point(points[i+1][0], points[i+1][1])
edges.append(Edge(p, q))
p = Point(points[0][0], points[0][1])
q = Point(points[-1][0], points[-1][1])
edges.append(Edge(p, q))
return self.order_edges(edges)
def order_edges(self, edge_list):
edges = []
for e in edge_list:
p = self.shear_transform(e.p)
q = self.shear_transform(e.q)
if p.x > q.x:
edges.append(Edge(q, p))
elif p.x < q.x:
edges.append(Edge(p, q))
shuffle(edges)
return edges
def shear_transform(self, point):
return Point(point.x + 1e-4 * point.y, point.y)
def merge_sort(l):
if len(l)>1 :
lleft = merge_sort(l[:len(l)/2])
lright = merge_sort(l[len(l)/2:])
p1, p2, p = 0, 0, 0
while p1<len(lleft) and p2<len(lright):
if lleft[p1].x < lright[p2].x:
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
class TrapezoidalMap(object):
map = []
margin = 50
bcross = None
tcross = None
def clear(self):
self.bcross = None
self.tcross = None
map = []
def case1(self, trapezoid, edge):
t = trapezoid; e = edge
trapezoids = []
trapezoids.append(Trapezoid(t.left_point, 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.right_point, 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, trapezoid, edge):
t = trapezoid; e = edge
rp = e.q if e.q.x == t.right_point.x else t.right_point
trapezoids = []
trapezoids.append(Trapezoid(t.left_point, 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, trapezoid, edge):
t = trapezoid; e = edge
lp = e.p if e.p.x == t.left_point.x else t.left_point
rp = e.q if e.q.x == t.right_point.x else t.right_point
trapezoids = []
if self.tcross is t.top:
trapezoids.append(t.upper_left)
trapezoids[0].update_right(t.upper_right, None)
trapezoids[0].right_point = rp
else:
trapezoids.append(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.append(t.lower_left)
trapezoids[1].update_right(None, t.lower_right)
trapezoids[1].right_point = rp
else:
trapezoids.append(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, trapezoid, edge):
t = trapezoid; e = edge
lp = e.p if e.p.x == t.left_point.x else t.left_point
trapezoids = []
if self.tcross is t.top:
trapezoids.append(t.upper_left)
trapezoids[0].right_point = e.q
else:
trapezoids.append(Trapezoid(lp, e.q, t.top, e))
trapezoids[0].update_left(t.upper_left, e.above)
if self.bcross is t.bottom:
trapezoids.append(t.lower_left)
trapezoids[1].right_point = e.q
else:
trapezoids.append(Trapezoid(lp, e.q, e, t.bottom))
trapezoids[1].update_left(e.below, t.lower_left)
trapezoids.append(Trapezoid(e.q, t.right_point, 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 edge in edges:
if edge.p.x > max.x: max = Point(edge.p.x + margin, max.y)
if edge.p.y > max.y: max = Point(max.x, edge.p.y + margin)
if edge.q.x > max.x: max = Point(edge.q.x + margin, max.y)
if edge.q.y > max.y: max = Point(max.x, edge.q.y + margin)
if edge.p.x < min.x: min = Point(edge.p.x - margin, min.y)
if edge.p.y < min.y: min = Point(min.x, edge.p.y - margin)
if edge.q.x < min.x: min = Point(edge.q.x - margin, min.y)
if edge.q.y < min.y: min = Point(min.x, edge.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(object):
def __init__(self, left, right):
self.parent_list = []
self.left = left
self.right = right
if left != None:
left.parent_list.append(self)
if right != 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 += node.parent_list
class Sink(Node):
def __init__(self, trapezoid):
super(Sink, self).__init__(None, None)
self.trapezoid = trapezoid
trapezoid.sink = self
def locate(self, edge):
return self
def isink(trapezoid):
if trapezoid.sink != None:
return trapezoid.sink
return Sink(trapezoid)
class XNode(Node):
def __init__(self, point, lchild, rchild):
super(XNode, self).__init__(lchild, rchild)
self.point = point
def locate(self, edge):
if edge.p.x >= self.point.x:
return self.right.locate(edge)
return self.left.locate(edge)
class YNode(Node):
def __init__(self, edge, lchild, rchild):
super(YNode, self).__init__(lchild, rchild)
self.edge = edge
def locate(self, edge):
if self.edge.is_above(edge.p):
return self.right.locate(edge)
elif self.edge.is_below(edge.p):
return self.left.locate(edge)
else:
if edge.slope < self.edge.slope:
return self.right.locate(edge)
else:
return self.left.locate(edge)
class QueryGraph:
def __init__(self, head):
self.head = head
def locate(self, edge):
return self.head.locate(edge).trapezoid
def follow_edge(self, edge):
trapezoids = [self.locate(edge)]
j = 0
while(edge.q.x > trapezoids[j].right_point.x):
if edge.is_above(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, edge, tlist):
yNode = YNode(edge, isink(tlist[1]), isink(tlist[2]))
qNode = XNode(edge.q, yNode, isink(tlist[3]))
pNode = XNode(edge.p, isink(tlist[0]), qNode)
self.replace(sink, pNode)
def case2(self, sink, edge, tlist):
yNode = YNode(edge, isink(tlist[1]), isink(tlist[2]))
pNode = XNode(edge.p, isink(tlist[0]), yNode)
self.replace(sink, pNode)
def case3(self, sink, edge, tlist):
yNode = YNode(edge, isink(tlist[0]), isink(tlist[1]))
self.replace(sink, yNode)
def case4(self, sink, edge, tlist):
yNode = YNode(edge, isink(tlist[0]), isink(tlist[1]))
qNode = XNode(edge.q, yNode, isink(tlist[2]))
self.replace(sink, qNode)
PI_SLOP = 3.1
class MonotoneMountain:
def __init__(self):
self.size = 0
self.tail = None
self.head = None
self.positive = False
self.convex_points = []
self.mono_poly = []
self.triangles = []
self.convex_polies = []
def add(self, point):
if self.size == 0:
self.head = point
self.size += 1
elif self.size == 1:
if point.not_equal(self.head):
self.tail = point
self.tail.prev = self.head
self.head.next = self.tail
self.size += 1
else:
if point.not_equal(self.tail):
self.tail.next = point
point.prev = self.tail
self.tail = point
self.size += 1
def remove(self, point):
next = point.next
prev = point.prev
point.prev.next = next
point.next.prev = prev
self.size -= 1
def process(self):
self.positive = self.angle_sign()
self.gen_mono_poly()
p = self.head.next
while p is not self.tail:
a = self.angle(p)
if a >= PI_SLOP or a <= -PI_SLOP:
self.remove(p)
elif self.is_convex(p):
self.convex_points.append(p)
p = p.next
self.triangulate()
def triangulate(self):
while len(self.convex_points) > 0:
ear = self.convex_points.pop(0)
a = ear.prev
b = ear
c = ear.next
triangle = [a, b, c]
self.triangles.append(triangle)
self.remove(ear)
if self.valid(a): self.convex_points.append(a)
if self.valid(c): self.convex_points.append(c)
assert(self.size <= 3, "Triangulation bug, please report")
def valid(self, p):
return p != self.head and p != self.tail and self.is_convex(p)
def gen_mono_poly(self):
p = self.head
while(p != None):
self.mono_poly.append(p)
p = p.next
def angle(self, p):
a = p.next - p
b = p.prev - p
return atan2(a.cross(b), a.dot(b))
def angle_sign(self):
a = self.head.next - self.head
b = self.tail - self.head
return atan2(a.cross(b), a.dot(b)) >= 0
def is_convex(self, p):
if self.positive != (self.angle(p) >= 0): return False
return True