merge

python/bc.sh

@@ -1,5 +1,4 @@
 #!/bin/sh
 touch framework/framework.pyx
-rm framework/*.c
 rm -rf build
 python setup.py build_ext -i

python/framework/framework.pyx

@@ -5,6 +5,7 @@ from math import pi as PI
 
 from gl cimport *
 include "polydecomp.pxi"
+include "seidel.pxi"
 
 cdef extern from 'math.h':
     double cos(double)

python/framework/polydecomp.pxi

@@ -1,10 +1,13 @@
 ##
 ## Ported from PolyDeomp by Mark Bayazit 
-## http://mnbayazit.com/406/credit
+## http://mnbayazit.com/406/bayazit
 ##
 from sys import float_info
 
-def makeCCW(list poly):
+cdef extern from 'predicates.h':
+    double orient2d(double *pa, double *pb, double *pc)
+    
+def make_ccw(list poly):
     cdef int br = 0
     # find bottom right point
     for i from 1 <= i < len(poly):
@@ -48,8 +51,8 @@ cpdef list decompose_poly(list poly, list polys):
 
             # if there are no vertices to connect to, choose a point in the middle
             if lower_index == (upper_index + 1) % len(poly):
-                p[0] = (lowerInt[0] + upperInt[0]) / 2
+                p[0] = (lowerInt[0] + upperInt[0]) * 0.5
-                p[1] = (lowerInt[1] + upperInt[1]) / 2
+                p[1] = (lowerInt[1] + upperInt[1]) * 0.5
 
                 if i < upper_index:
                     lower_poly.extend(poly[i:upper_index+1])
@@ -99,26 +102,19 @@ cpdef list decompose_poly(list poly, list polys):
             else:
                 decompose_poly(upper_poly, polys)
                 decompose_poly(lower_poly, polys)
-            
             return
 
     polys.append(poly)
     
 cdef list intersection(list p1, list p2, list q1, list q2):
-    cdef list i = []
+    cdef double pqx, pqy, bax, bay, t
-    cdef float a1, b1, c1, a2, b2, c2, det
+    pqx = p1[0] - p2[0]
-    a1 = p2[1] - p1[1]
+    pqy = p1[1] - p2[1]
-    b1 = p1[0] - p2[0]
+    t = pqy*(q1[0]-p2[0]) - pqx*(q1[1]-p2[1])
-    c1 = a1 * p1[0] + b1 * p1[1]
+    t /= pqx*(q2[1]-q1[1]) - pqy*(q2[0]-q1[0])
-    a2 = q2[1] - q1[1]
+    bax = t*(q2[0]-q1[0]) + q1[0]
-    b2 = q1[0] - q2[0]
+    bay = t*(q2[1]-q1[1]) + q1[1]
-    c2 = a2 * q1[0] + b2 * q1[1]
+    return [bax, bay]
-    det = a1 * b2 - a2 * b1
-    if not eq(det, 0): 
-        # lines are not parallel
-        i.append((b2 * c1 - b1 * c2) / det)
-        i.append((a1 * c2 - a2 * c1) / det)
-    return i
 
 cdef bool eq(float a, float b):
     return abs(a - b) <= 1e-8
@@ -130,16 +126,28 @@ cdef float area(list a, list b, list c):
     return (((b[0] - a[0])*(c[1] - a[1]))-((c[0] - a[0])*(b[1] - a[1])))
 
 cdef bool left(list a, list b, list c):
-    return area(a, b, c) > 0
+    cdef double *x = [a[0], a[1]]
+    cdef double *y = [b[0], b[1]]
+    cdef double *z = [c[0], c[1]]
+    return orient2d(x, y, z) > 0.0
 
 cdef bool leftOn(list a, list b, list c):
-    return area(a, b, c) >= 0
+    cdef double *x = [a[0], a[1]]
+    cdef double *y = [b[0], b[1]]
+    cdef double *z = [c[0], c[1]]
+    return orient2d(x, y, z) >= 0.0
 
 cdef bool right(list a, list b, list c):
-    return area(a, b, c) < 0
+    cdef double *x = [a[0], a[1]]
+    cdef double *y = [b[0], b[1]]
+    cdef double *z = [c[0], c[1]]
+    return orient2d(x, y, z) < 0.0
 
 cdef bool rightOn(list a, list b, list c):
-    return area(a, b, c) <= 0
+    cdef double *x = [a[0], a[1]]
+    cdef double *y = [b[0], b[1]]
+    cdef double *z = [c[0], c[1]]
+    return orient2d(x, y, z) <= 0.0
 
 cdef float sqdist(list a, list b):
     cdef float dx = b[0] - a[0]

python/framework/predicates.h

@@ -0,0 +1,4 @@
+double orient2d(pa, pb, pc);
+double *pa;
+double *pb;
+double *pc;

python/framework/seidel.pxi

@@ -0,0 +1,636 @@
+#
+# 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
+
+##
+## Based on Raimund Seidel'e paper "A simple and fast incremental randomized
+## algorithm for computing trapezoidal decompositions and for triangulating polygons"
+## (Ported from poly2tri)
+##
+
+# Shear transform. May effect numerical robustness
+SHEAR = 1e-6
+
+cdef extern from 'math.h':
+    double atan2(double, double)
+    
+cdef extern from 'predicates.h':
+    double orient2d(double *pa, double *pb, double *pc)
+    
+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 neq(self, other):
+        return other.x != self.x or other.y != self.y
+        
+    def clone(self):
+        return Point(self.x, self.y)
+
+class Edge(object):
+    
+    def __init__(self, p, 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)
+        self.above, self.below = None, None
+        self.mpoints = []
+        self.mpoints.append(p)
+        self.mpoints.append(q)
+    
+    ##
+    ## NOTE Rounding accuracy significantly effects numerical robustness!!!
+    ##
+    
+    def is_above(self, point):
+        cdef double *a = [self.p.x, self.p.y]
+        cdef double *b = [self.q.x, self.q.y]
+        cdef double *c = [point.x, point.y]
+        return orient2d(a, b, c) < 0
+        
+    def is_below(self, point):
+        cdef double *a = [self.p.x, self.p.y]
+        cdef double *b = [self.q.x, self.q.y]
+        cdef double *c = [point.x, point.y]
+        return orient2d(a, b, c) > 0
+
+    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 != 0.0 and a2 != 0.0 and (a1 * a2) < 0.0:
+            a3 = self.signed_area(c, d, a)
+            a4 = a3 + a2 - a1
+            if a3 * a4 < 0.0:
+                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
+        self.key = hash(self)
+        
+    def update_left(self, ul, ll):
+        self.upper_left = ul
+        if ul != None: ul.upper_right = self
+        self.lower_left = ll
+        if ll != None: ll.lower_right = self
+          
+    def update_right(self, ur, lr):
+        self.upper_right = ur
+        if ur != None: ur.upper_left = self
+        self.lower_right = lr
+        if lr != None: lr.lower_left = self 
+          
+    def update_left_right(self, ul, ll, ur, lr):
+        self.upper_left = ul
+        if ul != None: ul.upper_right = self
+        self.lower_left = ll
+        if ll != None: ll.lower_right = self
+        self.upper_right = ur
+        if ur != None: ur.upper_left = self
+        self.lower_right = lr
+        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):
+        v1 = line_intersect(self.top, self.left_point.x)
+        v2 = line_intersect(self.bottom, self.left_point.x)
+        v3 = line_intersect(self.bottom, self.right_point.x)
+        v4 = line_intersect(self.top, self.right_point.x)
+        return v1, v2, v3, v4
+  
+    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 x, y
+    
+class Triangulator(object):
+     
+    def __init__(self, poly_line):
+        assert len(poly_line) > 3, "Number of points must be > 3"
+        self.polygons = []
+        self.trapezoids = []
+        self.xmono_poly = []
+        self.edge_list = self.init_edges(poly_line)
+        self.trapezoidal_map = TrapezoidalMap()
+        self.bounding_box = self.trapezoidal_map.bounding_box(self.edge_list)
+        self.query_graph = QueryGraph(isink(self.bounding_box))
+            
+        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:
+                # Remove old trapezods
+                del self.trapezoidal_map.map[t.key]
+                # Bisect old trapezoids and create new
+                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[t.key] = t
+            self.trapezoidal_map.clear()
+                    
+        # Mark outside trapezoids w/ depth-first search
+        for k, t in self.trapezoidal_map.map.items():
+            self.mark_outside(t)
+            
+        # Collect interior trapezoids
+        for k, t in self.trapezoidal_map.map.items():
+            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) > 2:
+                mountain = MonotoneMountain()
+                points = merge_sort(edge.mpoints)
+                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):
+        edge_list = []
+        size = len(points)
+        for i in range(size):
+            j = i + 1 if i < size-1 else 0
+            p = points[i][0], points[i][1]
+            q = points[j][0], points[j][1]
+            edge_list.append((p, q))
+        return self.order_edges(edge_list)
+  
+    def order_edges(self, edge_list):
+        edges = []
+        for e in edge_list:
+            p = shear_transform(e[0])
+            q = shear_transform(e[1])
+            if p.x > q.x: 
+                edges.append(Edge(q, p))
+            else: 
+                edges.append(Edge(p, q))
+        # Randomized incremental algorithm
+        shuffle(edges)
+        return edges
+
+def shear_transform(point):
+    return Point(point[0] + SHEAR * point[1], point[1])
+ 
+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):
+
+    def __init__(self):
+        self.map = {}
+        self.margin = 50.0
+        self.bcross = None
+        self.tcross = None
+
+    def clear(self):
+        self.bcross = None
+        self.tcross = None
+        
+    def case1(self, t, e):
+        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, t, e):
+        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, t, e):
+        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, t, e):
+        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 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 = top.p
+        right = top.q
+        trap = Trapezoid(left, right, top, bottom)
+        self.map[trap.key] = trap
+        return trap
+        
+class Node(object):
+
+    def __init__(self, lchild, rchild):
+        self.parent_list = []
+        self.lchild = lchild
+        self.rchild = rchild
+        if lchild != None: 
+            lchild.parent_list.append(self)
+        if rchild != None: 
+            rchild.parent_list.append(self)
+        
+    def replace(self, node):
+        for parent in node.parent_list:
+            if parent.lchild is node: 
+                parent.lchild = self
+            else: 
+                parent.rchild = 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 is None: 
+        return Sink(trapezoid)
+    return trapezoid.sink
+    
+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.rchild.locate(edge)
+        return self.lchild.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.rchild.locate(edge)
+        if self.edge.is_below(edge.p): 
+            return self.lchild.locate(edge)
+        if edge.slope < self.edge.slope: 
+            return self.rchild.locate(edge)
+        return self.lchild.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)]
+        while(edge.q.x > trapezoids[-1].right_point.x):
+            if edge.is_above(trapezoids[-1].right_point):
+                trapezoids.append(trapezoids[-1].upper_right)
+            else:
+                trapezoids.append(trapezoids[-1].lower_right)
+        return trapezoids
+  
+    def replace(self, sink, node):
+        if sink.parent_list:
+            node.replace(sink)
+        else:
+            self.head = node
+
+    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 is 0: 
+            self.head = point
+            self.size = 1
+        elif self.size is 1:
+            if point.neq(self.head):
+                self.tail = point
+                self.tail.prev = self.head
+                self.head.next = self.tail
+                self.size = 2
+        else:
+            if point.neq(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 != self.tail:
+            a = self.angle(p)
+            if a >= PI_SLOP or a <= -PI_SLOP or a == 0: 
+                self.remove(p)
+            elif self.is_convex(p): 
+                self.convex_points.append(p)
+            p = p.next
+        self.triangulate()
+
+    def triangulate(self):
+        while self.convex_points:
+            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  

python/poly2tri.py

@@ -1,7 +1,5 @@
 #!/usr/bin/env python2.6
-from framework import Game, draw_polygon, reset_zoom, draw_line, decompose_poly, makeCCW
+from framework import Game, draw_polygon, reset_zoom, draw_line, decompose_poly, make_ccw, Triangulator
-
-from seidel import Triangulator
 
 class Poly2Tri(Game):
 
@@ -22,6 +20,92 @@ class Poly2Tri(Game):
         [192.89701,377.80796],[177.18272,402.27225],[172.36129,413.87939],[169.14701,430.48653],[168.61129,458.52225],
         [168.61129,492.80796]]
     
+    test = [[235.04275999999999, 739.07534999999996], [218.13066000000001, 719.73902999999996], 
+            [218.15215000000001, 709.96821], [218.17362, 700.19740000000002], [243.15215000000001, 685.27858000000003], 
+            [268.13065, 670.35974999999996], [268.13065, 660.81429000000003], [268.13065, 651.26882999999998],
+            [314.55921999999998, 651.26882999999998], [360.98779000000002, 651.26882999999998], 
+            [360.98683999999997, 666.44740000000002], [360.98046561000007, 669.27438118000009], 
+            [360.96234088000011,672.68539864000013], [360.93345946999995, 676.58895225999993], 
+            [360.89481504000003, 680.89354191999996], [360.84740125000002, 685.50766749999991], 
+            [360.79221175999999, 690.33982888000003], [360.73024022999999, 695.29852593999999], 
+            [360.66248032000004, 700.29225856000005], [360.58992569000003, 705.22952662000012],          
+            [360.51357000000002, 710.01882999999998], [360.04131999999998, 738.41168000000005],
+            [310.51454999999999, 738.41168000000005], [260.98779999999999, 738.41168000000005], 
+            [260.98779999999999, 748.41168000000005], [260.98779999999999, 758.41168000000005], 
+            [256.47133000000002, 758.41168000000005], [251.95484999999999, 758.41168000000005]]
+    
+    test2 = [[101.25, 1006.8145], [-0.0, 869.65629999999999], [0.012800000000000001, 630.57820000000004], 
+		[0.025600000000000001, 391.5], [13.7628, 385.74239999999998], [20.536000000000001, 382.96260000000001], 
+		[26.871200000000002, 380.49279999999999],[32.864100000000001, 378.30540000000002], 
+		[38.610700000000001, 376.37279999999998], [44.206600000000002, 374.66730000000001], 
+		[49.747799999999998, 373.16129999999998], [55.329900000000002, 371.82709999999997], 
+		[61.0488, 370.63720000000001],[67.000299999999996, 369.56400000000002], [73.280299999999997, 368.5797], 
+		[77.521299999999997, 368.07459999999998], [82.578500000000005, 367.66539999999998], 
+		[88.263199999999998, 367.35390000000001], [94.386899999999997, 367.14170000000001], 
+		[100.7611, 367.0308], [107.1972, 367.02269999999999], [113.5067, 367.11930000000001], 
+		[119.5009, 367.32229999999998], [124.9913, 367.63339999999999], [129.7894, 368.05450000000002], 
+		[136.77860000000001, 368.94200000000001], [143.9999, 370.10390000000001], [151.3793, 371.52069999999998], 
+		[158.84270000000001, 373.17270000000002], [166.3159, 375.04050000000001], [173.72499999999999, 377.10449999999997], 
+		[180.9957, 379.34500000000003], [188.0539, 381.74250000000001], [194.82570000000001, 384.27749999999997], 
+		[201.23679999999999, 386.93029999999999], [212.5, 391.83980000000003], [212.08760000000001, 550.41989999999998], 
+		[211.67509999999999, 709.0], [274.00200000000001, 709.0], [336.3288, 709.0], [335.66520000000003, 636.25], 
+		[335.55739999999997, 623.91790000000003], [335.45409999999998, 611.09199999999998], [335.3569, 598.0163], 
+		[335.267, 584.93499999999995], [335.18599999999998, 572.09220000000005], [335.11540000000002, 559.73199999999997], 
+		[335.0566, 548.09860000000003], [335.0111, 537.43600000000004], [334.98039999999997, 527.98839999999996], 
+		[334.96589999999998, 520.0], [334.93029999999999, 476.5], [264.0222, 418.0], [193.114, 359.5], 
+		[193.05699999999999, 295.4984], [193.0, 231.49680000000001], [308.7516, 115.7484], [424.50319999999999, 0.0], 
+		[430.71390000000002, -0.0], [436.9246, -0.0], [458.9753, 20.0], [481.02589999999998, 40.0], 
+		[558.38530000000003, 40.0], [635.74469999999997, 40.0], [660.50120000000004, 19.9588], 
+		[685.25779999999997, -0.082400000000000001], [692.0471, 0.20880000000000001], 
+		[698.8365, 0.5], [809.42550000000006, 115.9161], [920.01459999999997, 231.3321], [919.75729999999999, 295.3526], 
+		[919.5, 359.37310000000002], [850.31790000000001, 416.4366], [781.13589999999999, 473.5], 
+		[781.06790000000001, 593.7577], [781.0, 714.0154], [842.25, 713.7577], [903.5, 713.5], [903.5, 552.5], [903.5, 391.5],
+		[915.5, 386.2894], [925.01319999999998, 382.34390000000002], [934.29579999999999, 378.88010000000003], 
+		[943.42060000000004, 375.8827], [952.46050000000002,373.33629999999999], [961.48839999999996, 371.22570000000002], 
+		[970.57719999999995, 369.53559999999999], [979.79989999999998, 368.25069999999999], 
+		[989.22929999999997, 367.35570000000001], [998.9384, 366.83539999999999], [1009.0, 366.67430000000002], 
+		[1018.876, 366.87939999999998], [1028.7419, 367.4649], [1038.5688, 368.42529999999999], 
+		[1048.3277, 369.75490000000002], [1057.9897000000001, 371.44799999999998], [1067.5259000000001, 373.49900000000002],
+		[1076.9074000000001, 375.90219999999999], [1086.1052, 378.65210000000002], [1095.0904, 381.74290000000002],
+		[1103.8340000000001, 385.16899999999998], [1105.4327000000001, 385.83539999999999], 
+		[1107.0215000000001, 386.49689999999998], [1108.5744999999999, 387.1429], [1110.0654999999999, 387.76240000000001], 
+		[1111.4684, 388.34469999999999], [1112.7573, 388.87900000000002], [1113.9059, 389.3544], 
+		[1114.8883000000001, 389.76010000000002], [1115.6784, 390.08530000000002], [1116.25, 390.3193], 
+		[1119.0, 391.43849999999998], [1118.9577999999999, 633.4692], [1118.9155000000001, 875.5],[1016.0895, 1009.5], 
+		[913.26340000000005, 1143.5], [908.63170000000002, 1143.8047999999999], [904.0, 1144.1096], [904.0, 993.0548], 
+		[904.0, 842.0], [842.5, 842.0], [781.0, 842.0], [781.0, 918.5], [781.0, 995.0], [758.5, 995.0], 
+		[753.20910000000003, 995.00739999999996], [748.79459999999995, 995.03269999999998], 
+		[745.18129999999996, 995.08109999999999], [742.29399999999998, 995.15729999999996], 
+		[740.05730000000005, 995.26639999999998], [738.39599999999996, 995.41330000000005],
+		[737.23490000000004, 995.60289999999998], [736.49869999999999, 995.84010000000001], 
+		[736.11210000000005, 996.13], [736.0, 996.47739999999999], [736.09749999999997, 996.82140000000004], 
+		[736.42740000000003, 997.11329999999998], [737.04610000000002, 997.3587], [738.01009999999997, 997.56290000000001], 
+		[739.37559999999996, 997.73140000000001], [741.19910000000004, 997.86959999999999], [743.53679999999997, 997.9828], 
+		[746.44510000000002, 998.07659999999998], [749.98040000000003,998.15629999999999], 
+		[754.19910000000004, 998.22739999999999], [772.39829999999995, 998.5], [823.72850000000005, 1071.0], 
+		[875.05859999999996, 1143.5], [558.86419999999998, 1143.7516000000001], [507.74619999999999, 1143.787], 
+		[459.17950000000002, 1143.8106], [413.82889999999998, 1143.8226], [372.35939999999999, 1143.8232], 
+		[335.43560000000002, 1143.8130000000001], [303.7226, 1143.7919999999999], [277.88499999999999, 1143.7606000000001], 
+		[258.58789999999999, 1143.7192], [246.49590000000001, 1143.6679999999999], [242.2739, 1143.6072999999999], 
+		[244.95830000000001, 1139.4844000000001], [252.41210000000001, 1128.4439], [263.45999999999998, 1112.2019], 
+		[276.92660000000001, 1092.4740999999999], [291.63650000000001, 1070.9766], [306.41430000000003, 1049.4251999999999], 
+		[320.0847, 1029.5360000000001], [331.47219999999999, 1013.0247000000001], [339.4015, 1001.6074], 
+		[342.69729999999998, 997.0], [342.98259999999999, 996.91470000000004], [343.6619, 996.82510000000002], 
+		[344.70080000000002, 996.7328], [346.06450000000001, 996.63959999999997], [347.71870000000001, 996.54729999999995], 
+		[349.62880000000001, 996.45770000000005], [351.76029999999997, 996.37249999999995], 
+		[354.07859999999999, 996.29349999999999], [356.54919999999998, 996.22249999999997], [359.1377, 996.16110000000003], 
+		[363.04469999999998, 996.07169999999996], [366.26229999999998, 995.97929999999997], 
+		[368.85410000000002, 995.87580000000003], [370.88319999999999, 995.75319999999999], 
+		[372.41320000000002, 995.60320000000002], [373.50729999999999,995.41790000000003], 
+		[374.22899999999998, 995.18920000000003], [374.64159999999998, 994.90880000000004], 
+		[374.80860000000001, 994.56889999999999], [374.79329999999999, 994.16110000000003], 
+		[374.63619999999997, 993.7568], [374.2833, 993.4194], [373.65809999999999, 993.14160000000004], 
+		[372.6841, 992.91570000000002], [371.28500000000003, 992.73419999999999], [369.3843, 992.58960000000002], 
+		[366.90559999999999, 992.47429999999997], [363.77249999999998, 992.38059999999996], 
+		[359.90839999999997, 992.30119999999999], [355.2371, 992.22839999999997], [336.0, 991.95680000000004], 
+		[336.0, 914.97839999999997], [336.0, 838.0], [274.0, 838.0], [212.0, 838.0], [212.0, 991.0], [212.0, 1144.0], 
+		[207.25, 1143.9864], [202.5, 1143.9727]]
+
     def __init__(self):
         super(Poly2Tri, self).__init__(*self.screen_size)       
         
@@ -43,12 +127,12 @@ class Poly2Tri(Game):
         for p in self.dude:
             p[0] -= 75
         
-        makeCCW(self.dude)
+        make_ccw(self.dude)
-        self.dude_poly = []
+        self.decomp_poly = []
         t1 = self.time
-        decompose_poly(self.dude, self.dude_poly)
+        decompose_poly(self.dude, self.decomp_poly)
         dt = (self.time - t1) * 1000.0
-        print "time (ms) = %f  , num polies = %d" % (dt, len(self.dude_poly))
+        print "time (ms) = %f  , num polies = %d" % (dt, len(self.decomp_poly))
         
         self.main_loop()
         
@@ -56,14 +140,14 @@ class Poly2Tri(Game):
         pass
         
     def render(self):
-        reset_zoom(2.1, (300, 450), self.screen_size)
+        reset_zoom(2.0, (300, 450), self.screen_size)
         red = 255, 0, 0
         yellow = 255, 255, 0
         green = 0, 255, 0
         for t in self.triangles:
             draw_polygon(t, red)
         
-        for p in self.dude_poly:
+        for p in self.decomp_poly:
             draw_polygon(p, red)
                 
         '''
@@ -77,8 +161,6 @@ class Poly2Tri(Game):
             p2 = e.q.x, e.q.y
             draw_line(p1, p2, green)
         
-        #draw_polygon(self.points, green)
-        
         
     def load_points(self, file_name):
         infile = open(file_name, "r")
@@ -91,8 +173,5 @@ class Poly2Tri(Game):
             points.append((float(s[0]), float(s[1])))
         return points
         
-spam = (544.80998999999997, 579.86046999999996), (544.80998999999997, 450.57477), (594.09569999999997, 450.57477), (643.38142000000005, 450.57477), (643.38142000000005, 525.26486999999997), (643.38142000000005, 599.95487000000003), (603.67391999999995, 654.55056999999999), (563.96655999999996, 709.14621999999997), (554.38819999999998, 709.14621999999997), (544.80998999999997, 709.14621999999997)
-eggs = [474.80999000000003, 555.15656999999999], [474.80999000000003, 530.87086999999997], [509.09570000000002, 530.87086999999997], [543.38142000000005, 530.87086999999997], [543.38142000000005, 555.15656999999999], [543.38142000000005, 579.44227000000001], [509.09570000000002, 579.44227000000001], [474.80999000000003, 579.44227000000001]   
-
 if __name__ == '__main__':
     demo = Poly2Tri()

python/setup.py

@@ -9,7 +9,7 @@ from Cython.Distutils import build_ext
 
 version = '0.1'
 
-sourcefiles = ['framework/framework.pyx']
+sourcefiles = ['framework/framework.pyx', 'framework/predicates.c']
 
 # Platform-dependent submodules