mirror of https://github.com/jhasse/poly2tri.git
seidel
This commit is contained in:
zzzzrrr
parent
048bd0740e
commit
bdcfc0eb04
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@ -5,13 +5,10 @@ from math import pi as PI
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from gl cimport *
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#from triangulator import Point
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include "triangulator.pyx"
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cdef extern from 'math.h':
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double cos(double)
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double sin(double)
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double sqrt(double)
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SEGMENTS = 25
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INCREMENT = 2.0 * PI / SEGMENTS
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@ -61,11 +58,6 @@ from glfw cimport *
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import sys
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cdef extern from 'math.h':
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double cos(double)
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double sin(double)
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double sqrt(double)
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# Keyboard callback wrapper
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kbd_callback_method = None
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@ -78,9 +70,6 @@ cdef class Game:
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title = "Poly2Tri"
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def __init__(self, window_width, window_height):
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points = [Point(100,100), Point(-100,100), Point(-100,-100), Point(100,-100)]
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seidel = Triangulator(points)
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glfwInit()
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@ -43,145 +43,9 @@ cdef extern from 'math.h':
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double floor(double)
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double sqrt(double)
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class Triangulator:
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def __init__(self, points):
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self.polygons = []
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self.edge_list = self.init_edges(points)
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self.trapezoids = []
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self.trapezoidal_map = TrapezoidalMap()
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bounding_box = self.trapezoidal_map.bounding_box(self.edge_list)
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self.query_graph = QueryGraph(Sink(bounding_box))
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self.xmono_poly = []
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self.process()
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def trapezoidMap(self):
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return self.trapezoidal_map.map
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class Point:
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# Build the trapezoidal map and query graph
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def process(self):
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for e in self.edge_list:
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traps = self.query_graph.follow_edge(e)
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for t in traps:
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try:
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self.trapezoidal_map.map.remove(t)
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except:
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pass
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for t in traps:
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tlist = []
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cp = t.contains(e.p)
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cq = t.contains(e.q)
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if cp and cq:
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tlist = self.trapezoidal_map.case1(t, e)
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self.query_graph.case1(t.sink, e, tlist)
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elif cp and not cq:
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tlist = self.trapezoidal_map.case2(t, e)
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self.query_graph.case2(t.sink, e, tlist)
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elif not cp and not cq:
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tlist = self.trapezoidal_map.case3(t, e)
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self.query_graph.case3(t.sink, e, tlist)
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else:
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tlist = self.trapezoidal_map.case4(t, e)
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self.query_graph.case4(t.sink, e, tlist)
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# Add new trapezoids to map
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for t in tlist:
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self.trapezoidal_map.map.append(t)
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self.trapezoidal_map.clear()
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# Mark outside trapezoids
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for t in self.trapezoidal_map.map:
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self.mark_outside(t)
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# Collect interior trapezoids
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for t in self.trapezoidal_map.map:
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if t.inside():
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self.trapezoids.append(t)
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t.add_points()
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self.create_mountains()
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def mono_polies(self):
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polies = []
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for x in self.xmono_poly:
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polies.append(x.monoPoly)
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return polies
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def create_mountains(self):
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for s in self.edge_list:
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if len(s.mpoints) > 0:
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mountain = MonotoneMountain()
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k = merge_sort(s.mpoints)
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points = [s.p] + k + [s.q]
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for p in points:
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mountain.append(p)
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mountain.process()
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for t in mountain.triangles:
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self.polygons.append(t)
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self.xmono_poly.append(mountain)
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def mark_outside(self, t):
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if t.top is self.bounding_box.top or t.bottom is self.bounding_box.bottom:
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t.trimNeighbors()
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def init_edges(self, points):
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edges = []
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for i in range(len(points)-1):
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edges.append(Edge(points[i], points[i+1]))
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edges.append(Edge(points[0], points[-1]))
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return self.order_edges(edges)
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def order_edges(self, edges):
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segs = []
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for s in edges:
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p = self.shearTransform(s.p)
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q = self.shearTransform(s.q)
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if p.x > q.x: segs.append(Edge(q, p))
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elif p.x < q.x: segs.append(Edge(p, q))
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shuffle(segs)
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return segs
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def shearTransform(self, point):
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return Point(point.x + 1e-4 * point.y, point.y)
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cdef list merge_sort(list l):
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cdef list lleft, lright
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cdef int p1, p2, p
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if len(l)>1 :
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lleft = merge_sort(l[:len(l)/2])
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lright = merge_sort(l[len(l)/2:])
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p1, p2, p = 0, 0, 0
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while p1<len(lleft) and p2<len(lright):
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if lleft[p1].x < lright[p2].x:
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l[p]=lleft[p1]
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p+=1
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p1+=1
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else:
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l[p]=lright[p2]
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p+=1
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p2+=1
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if p1<len(lleft):l[p:]=lleft[p1:]
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elif p2<len(lright):l[p:]=lright[p2:]
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else : print "internal error"
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return l
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cdef class Point:
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cdef float x, y
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next = None
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prev = None
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edge = None
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edges = []
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property x:
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def __get__(self): return self.x
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property y:
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def __get__(self): return self.y
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def __init__(self, float x, float y):
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def __cinit__(self, float x, float y):
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self.x = x
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self.y = y
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@ -203,10 +67,10 @@ cdef class Point:
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def __div__(self, float a):
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return Point(self.x / a, self.y / a)
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def cross(self, Point p):
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def cross(self, p):
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return self.x * p.y - self.y * p.x
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def dot(self, Point p):
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def dot(self, p):
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return self.x * p.x + self.y * p.y
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def length(self):
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@ -215,38 +79,22 @@ cdef class Point:
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def normalize(self):
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return self / self.length()
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def less(self, Point p):
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def less(self, p):
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return self.x < p.x
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'''
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# Sort along y axis
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def greater(self, p):
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if y < p.y:
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return True
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elif y > p.y:
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return False
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else:
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if x < p.x:
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return True
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else:
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return False
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'''
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def not_equal(self, p):
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return not (p.x == self.x and p.y == self.y)
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def clone(self):
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return Point(self.x, self.y)
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cdef class Edge:
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cdef Point p, q
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cdef bool above, below
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cdef float slope, b
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cdef class Edge:
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cdef object above, below
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cdef float slope, b
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mpoints = []
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def __init__(self, Point p, Point q):
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def __cinit__(self, p, q):
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self.p = p
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self.q = q
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self.slope = (q.y - p.y)/(q.x - p.x)
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@ -264,12 +112,12 @@ cdef class Edge:
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property below:
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def __get__(self): return self.below
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cdef bool is_above(self, Point point):
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cdef bool is_above(self, point):
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return (floor(point.y) < floor(self.slope * point.x + self.b))
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cdef bool is_below(self, Point point):
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cdef bool is_below(self, point):
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return (floor(point.y) > floor(self.slope * point.x + self.b))
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cdef float intersect(self, Point c, Point d):
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cdef float intersect(self, c, d):
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cdef float a1, a2, a3, a4, t
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cdef Point a, b
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a = self.p
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@ -284,24 +132,18 @@ cdef class Edge:
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return a + ((b - a) * t)
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return 0.0
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cdef float signed_area(self, Point a, Point b, Point c):
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cdef float signed_area(self, a, b, c):
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return (a.x - c.x) * (b.y - c.y) - (a.y - c.y) * (b.x - c.x)
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cdef Point line_intersect(Edge e, float x):
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cdef float y = e.slope * x + e.b
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return Point(x, y)
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cdef class Trapezoid:
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cdef:
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Point left_point, right_point
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Edge top, bottom
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Trapezoid upper_left, lower_left
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Trapezoid upper_right, lower_right
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bool inside
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object sink
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cdef Edge top, bottom
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cdef Trapezoid upper_left, lower_left
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cdef Trapezoid upper_right, lower_right
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cdef object sink
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cdef bool inside
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def __init__(self, Point left_point, Point right_point, Edge top, Edge bottom):
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def __cinit__(self, left_point, right_point, Edge top, Edge bottom):
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self.left_point = left_point
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self.right_point = right_point
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self.top = top
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self.inside = True
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self.sink = None
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property inside:
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def __get__(self): return self.inside
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property top:
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def __get__(self): return self.top
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@ -321,9 +166,11 @@ cdef class Trapezoid:
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property left_point:
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def __get__(self): return self.left_point
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def __set__(self, lp): self.left_point = lp
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property right_point:
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def __get__(self): return self.right_point
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def __set__(self, rp): self.right_point = rp
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property sink:
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def __get__(self): return self.sink
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@ -375,7 +222,7 @@ cdef class Trapezoid:
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if self.upper_right != None: self.upper_right.trim_neighbors()
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if self.lower_right != None: self.lower_right.trim_neighbors()
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def contains(self, Point point):
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def contains(self, point):
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return (point.x > self.left_point.x and point.x < self.right_point.x and
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self.top.is_above(point) and self.bottom.is_below(point))
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@ -397,6 +244,140 @@ cdef class Trapezoid:
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if self.right_point != self.top.q:
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self.top.mpoints.append(self.right_point.clone)
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cdef Point line_intersect(Edge e, float x):
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cdef float y = e.slope * x + e.b
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return Point(x, y)
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class Triangulator:
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def __init__(self, poly_line):
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self.polygons = []
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self.edge_list = self.init_edges(poly_line)
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self.trapezoids = []
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self.trapezoidal_map = TrapezoidalMap()
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self.bounding_box = self.trapezoidal_map.bounding_box(self.edge_list)
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self.query_graph = QueryGraph(isink(self.bounding_box))
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self.xmono_poly = []
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self.process()
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def trapezoidMap(self):
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return self.trapezoidal_map.map
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# Build the trapezoidal map and query graph
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def process(self):
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for e in self.edge_list:
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traps = self.query_graph.follow_edge(e)
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for t in traps:
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try:
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self.trapezoidal_map.map.remove(t)
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except:
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pass
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for t in traps:
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tlist = []
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cp = t.contains(e.p)
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cq = t.contains(e.q)
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if cp and cq:
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tlist = self.trapezoidal_map.case1(t, e)
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self.query_graph.case1(t.sink, e, tlist)
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elif cp and not cq:
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tlist = self.trapezoidal_map.case2(t, e)
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self.query_graph.case2(t.sink, e, tlist)
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elif not cp and not cq:
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tlist = self.trapezoidal_map.case3(t, e)
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self.query_graph.case3(t.sink, e, tlist)
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else:
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tlist = self.trapezoidal_map.case4(t, e)
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self.query_graph.case4(t.sink, e, tlist)
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# Add new trapezoids to map
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for t in tlist:
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self.trapezoidal_map.map.append(t)
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self.trapezoidal_map.clear()
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# Mark outside trapezoids
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for t in self.trapezoidal_map.map:
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self.mark_outside(t)
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# Collect interior trapezoids
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for t in self.trapezoidal_map.map:
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if t.inside:
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self.trapezoids.append(t)
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t.add_points()
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self.create_mountains()
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def mono_polies(self):
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polies = []
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for x in self.xmono_poly:
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polies.append(x.monoPoly)
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return polies
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def create_mountains(self):
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for s in self.edge_list:
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if len(s.mpoints) > 0:
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mountain = MonotoneMountain()
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print s.mpoints
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k = merge_sort(s.mpoints)
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points = [s.p] + k + [s.q]
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for p in points:
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mountain.append(p)
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mountain.process()
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for t in mountain.triangles:
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self.polygons.append(t)
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self.xmono_poly.append(mountain)
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def mark_outside(self, t):
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if t.top is self.bounding_box.top or t.bottom is self.bounding_box.bottom:
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t.trim_neighbors()
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def init_edges(self, points):
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edges = []
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for i in range(len(points)-1):
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p = Point(points[i][0], points[i][1])
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q = Point(points[i+1][0], points[i+1][1])
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edges.append(Edge(p, q))
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p = Point(points[0][0], points[0][1])
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q = Point(points[-1][0], points[-1][1])
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edges.append(Edge(p, q))
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return self.order_edges(edges)
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def order_edges(self, edges):
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segs = []
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for s in edges:
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p = self.shearTransform(s.p)
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q = self.shearTransform(s.q)
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if p.x > q.x:
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segs.append(Edge(q, p))
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elif p.x < q.x:
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segs.append(Edge(p, q))
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shuffle(segs)
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return segs
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def shearTransform(self, point):
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return Point(point.x + 1e-4 * point.y, point.y)
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cdef list merge_sort(l):
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cdef list lleft, lright
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cdef int p1, p2, p
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if len(l)>1 :
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lleft = merge_sort(l[:len(l)/2])
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lright = merge_sort(l[len(l)/2:])
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p1, p2, p = 0, 0, 0
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while p1<len(lleft) and p2<len(lright):
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if lleft[p1].x < lright[p2].x:
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l[p]=lleft[p1]
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p+=1
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p1+=1
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else:
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l[p]=lright[p2]
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p+=1
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p2+=1
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if p1<len(lleft):l[p:]=lleft[p1:]
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elif p2<len(lright):l[p:]=lright[p2:]
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else : print "internal error"
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return l
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class TrapezoidalMap:
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map = []
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@ -408,7 +389,7 @@ class TrapezoidalMap:
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self.bcross = None
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self.tcross = None
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def case1(self, t, e):
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def case1(self, Trapezoid t, Edge e):
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trapezoids = []
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trapezoids.append(Trapezoid(t.left_point, e.p, t.top, t.bottom))
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trapezoids.append(Trapezoid(e.p, e.q, t.top, e))
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@ -420,7 +401,7 @@ class TrapezoidalMap:
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trapezoids[3].update_right(t.upper_right, t.lower_right)
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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
|
||||
trapezoids = []
|
||||
trapezoids.append(Trapezoid(t.left_point, e.p, t.top, t.bottom))
|
||||
|
|
@ -435,7 +416,7 @@ class TrapezoidalMap:
|
|||
e.below = trapezoids[2]
|
||||
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
|
||||
rp = e.q if e.q.x == t.right_point.x else t.right_point
|
||||
trapezoids = []
|
||||
|
|
@ -459,7 +440,7 @@ class TrapezoidalMap:
|
|||
e.below = trapezoids[1]
|
||||
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
|
||||
trapezoids = []
|
||||
if self.tcross is t.top:
|
||||
|
|
@ -498,61 +479,81 @@ class TrapezoidalMap:
|
|||
right = top.q
|
||||
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.right = right
|
||||
if left != None: left.parent_list.append(self)
|
||||
if right != None: right.parent_list.append(self)
|
||||
|
||||
def replace(self, node):
|
||||
if left != None:
|
||||
left.parent_list.append(self)
|
||||
if right != None:
|
||||
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:
|
||||
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 != None:
|
||||
return trapezoid.sink
|
||||
return Sink(trapezoid)
|
||||
|
||||
self.parent_list += node.parent_list
|
||||
|
||||
cdef class Sink(Node):
|
||||
|
||||
cdef Trapezoid trapezoid
|
||||
|
||||
def __init__(self, trapezoid):
|
||||
self.trapezoid = trapezoid
|
||||
Node.__init__(self, None, None)
|
||||
super(Sink, self).__init__(None, None)
|
||||
trapezoid.sink = self
|
||||
|
||||
property trapezoid:
|
||||
def __get__(self): return self.trapezoid
|
||||
|
||||
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
|
||||
cdef Sink isink(Trapezoid trapezoid):
|
||||
if trapezoid.sink != None:
|
||||
return trapezoid.sink
|
||||
return Sink(trapezoid)
|
||||
|
||||
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:
|
||||
return self.right.locate(e)
|
||||
return self.left.locate(e)
|
||||
|
||||
class YNode(Node):
|
||||
cdef class YNode(Node):
|
||||
|
||||
def __init__(self, edge, lchild, rchild):
|
||||
Node.__init__(self, lchild, rchild)
|
||||
cdef Edge edge
|
||||
|
||||
def __init__(self, Edge edge, Node lchild, Node rchild):
|
||||
super(YNode, self).__init__(lchild, rchild)
|
||||
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):
|
||||
return self.right.locate(e)
|
||||
elif self.edge.is_below(e.p):
|
||||
|
|
@ -560,53 +561,54 @@ class YNode(Node):
|
|||
else:
|
||||
if e.slope < self.edge.slope:
|
||||
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
|
||||
|
||||
def locate(self, e):
|
||||
def locate(self, Edge e):
|
||||
return self.head.locate(e).trapezoid
|
||||
|
||||
def follow_edge(self, e):
|
||||
def follow_edge(self, Edge e):
|
||||
trapezoids = [self.locate(e)]
|
||||
j = 0
|
||||
cdef int j = 0
|
||||
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)
|
||||
else:
|
||||
trapezoids .append(trapezoids[j].lower_right)
|
||||
trapezoids.append(trapezoids[j].lower_right)
|
||||
j += 1
|
||||
return trapezoids
|
||||
|
||||
def replace(self, sink, node):
|
||||
def replace(self, Sink sink, Node 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)
|
||||
def case1(self, Sink sink, Edge e, tlist):
|
||||
cdef Node yNode = YNode(e, isink(tlist[1]), isink(tlist[2]))
|
||||
cdef Node qNode = XNode(e.q, yNode, isink(tlist[3]))
|
||||
cdef Node pNode = XNode(e.p, isink(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)
|
||||
def case2(self, Sink sink, Edge e, tlist):
|
||||
yNode = YNode(e, isink(tlist[1]), isink(tlist[2]))
|
||||
pNode = XNode(e.p, isink(tlist[0]), yNode)
|
||||
self.replace(sink, pNode)
|
||||
|
||||
def case3(self, sink, e, tlist):
|
||||
yNode = YNode(e, Sink(tlist[0]), Sink(tlist[1]))
|
||||
def case3(self, Sink sink, Edge e, tlist):
|
||||
yNode = YNode(e, isink(tlist[0]), isink(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]))
|
||||
def case4(self, Sink sink, Edge e, tlist):
|
||||
yNode = YNode(e, isink(tlist[0]), isink(tlist[1]))
|
||||
qNode = XNode(e.q, yNode, isink(tlist[2]))
|
||||
self.replace(sink, qNode)
|
||||
|
||||
cdef float PI_SLOP = 3.1
|
||||
|
|
@ -624,7 +626,8 @@ cdef class MonotoneMountain:
|
|||
|
||||
def __init__(self):
|
||||
self.size = 0
|
||||
self.tail, self.head = None
|
||||
self.tail = None
|
||||
self.head = None
|
||||
self.positive = False
|
||||
self.convex_points = []
|
||||
self.mono_poly = []
|
||||
|
|
|
|||
|
|
@ -1,20 +1,48 @@
|
|||
#!/usr/bin/env python2.6
|
||||
from framework import Game
|
||||
|
||||
from framework import Game, draw_polygon, reset_zoom
|
||||
|
||||
from seidel import Triangulator
|
||||
|
||||
class Poly2Tri(Game):
|
||||
|
||||
#Screen size
|
||||
screen_size = 800.0, 600.0
|
||||
|
||||
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()
|
||||
|
||||
def update(self):
|
||||
pass
|
||||
|
||||
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__':
|
||||
demo = Poly2Tri()
|
||||
|
|
@ -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
|
||||
Loading…
Reference in New Issue