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ported Scala classes
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python/bc.sh
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python/bc.sh
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#!/bin/sh
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touch framework/framework.pyx
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rm framework/*.c
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rm -rf build
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python setup.py build_ext -i
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138
python/framework/framework.pyx
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138
python/framework/framework.pyx
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##
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## GL convenience layer
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##
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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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SEGMENTS = 25
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INCREMENT = 2.0 * PI / SEGMENTS
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def init_gl(width, height):
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#glEnable(GL_LINE_SMOOTH)
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glEnable(GL_BLEND)
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glBlendFunc(GL_SRC_ALPHA, GL_ONE_MINUS_SRC_ALPHA)
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glClearColor(0.0, 0.0, 0.0, 0.0)
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glHint (GL_LINE_SMOOTH_HINT, GL_NICEST)
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def reset_zoom(float zoom, center, size):
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zinv = 1.0 / zoom
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left = -size[0] * zinv
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right = size[0] * zinv
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bottom = -size[1] * zinv
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top = size[1] * zinv
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# Reset viewport
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glLoadIdentity()
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glMatrixMode(GL_PROJECTION)
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glLoadIdentity()
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# Reset ortho view
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glOrtho(left, right, bottom, top, 1, -1)
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glTranslatef(-center[0], -center[1], 0)
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glMatrixMode(GL_MODELVIEW)
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glDisable(GL_DEPTH_TEST)
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glLoadIdentity()
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# Clear the screen
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glClear(GL_COLOR_BUFFER_BIT)
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def draw_polygon(verts, color):
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r, g, b = color
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glColor3f(r, g, b)
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glBegin(GL_LINE_LOOP)
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for v in verts:
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glVertex2f(v[0], v[1])
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glEnd()
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##
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## Game engine / main loop / UI
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##
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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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cdef extern void __stdcall kbd_callback(int id, int state):
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kbd_callback_method(id, state)
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cdef class Game:
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title = "Poly2Tri"
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def __init__(self, window_width, window_height):
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p1 = Point(12, 10)
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p2 = Point(50, 47)
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print p1.cross(p2)
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glfwInit()
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# 16 bit color, no depth, alpha or stencil buffers, windowed
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if not glfwOpenWindow(window_width, window_height, 8, 8, 8, 8, 24, 0, GLFW_WINDOW):
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glfwTerminate()
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raise SystemError('Unable to create GLFW window')
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glfwEnable(GLFW_STICKY_KEYS)
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glfwSwapInterval(1) #VSync on
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def register_kbd_callback(self, f):
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global kbd_callback_method
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glfwSetKeyCallback(kbd_callback)
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kbd_callback_method = f
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def main_loop(self):
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frame_count = 1
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start_time = glfwGetTime()
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running = True
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while running:
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current_time = glfwGetTime()
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#Calculate and display FPS (frames per second)
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if (current_time - start_time) > 1 or frame_count == 0:
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frame_rate = frame_count / (current_time - start_time)
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t = self.title + " (%d FPS)" % frame_rate
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glfwSetWindowTitle(t)
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start_time = current_time
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frame_count = 0
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frame_count = frame_count + 1
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# Check if the ESC key was pressed or the window was closed
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running = ((not glfwGetKey(GLFW_KEY_ESC))
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and glfwGetWindowParam(GLFW_OPENED))
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self.update()
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self.render()
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glfwSwapBuffers()
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glfwTerminate()
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property window_title:
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def __set__(self, title): self.title = title
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property time:
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def __get__(self): return glfwGetTime()
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def __set__(self, t): glfwSetTime(t)
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496
python/framework/triangulator.pyx
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496
python/framework/triangulator.pyx
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#
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# Poly2Tri
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# Copyright (c) 2009, Mason Green
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# http://code.google.com/p/poly2tri/
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#
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# All rights reserved.
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#
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# Redistribution and use in source and binary forms, with or without modification,
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# are permitted provided that the following conditions are met:
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#
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# Redistributions of source code must retain the above copyright notice,
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# self list of conditions and the following disclaimer.
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# Redistributions in binary form must reproduce the above copyright notice,
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# self list of conditions and the following disclaimer in the documentation
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# and/or other materials provided with the distribution.
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# Neither the name of Poly2Tri nor the names of its contributors may be
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# used to endorse or promote products derived from self software without specific
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# prior written permission.
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#
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# THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
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# "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
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# LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
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# A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR
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# CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
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# EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
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# PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
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# PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
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# LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
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# NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
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# SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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#
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from math import floor
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###
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### Based on Raimund Seidel'e paper "A simple and fast incremental randomized
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### algorithm for computing trapezoidal decompositions and for triangulating polygons"
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### (Ported from poly2tri)
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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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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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#do merge here
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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][0] < lright[p2][0]:
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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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self.x = x
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self.y = y
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def __sub__(self, other):
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if isinstance(other, Point):
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return Point(self.x - other.x, self.y - other.y)
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else:
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return Point(self.x - other, self.y - other)
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def __add__(self, other):
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if isinstance(other, Point):
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return Point(self.x + other.x, self.y + other.y)
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else:
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return Point(self.x + other, self.y + other)
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def __mul__(self, float f):
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return Point(self.x * f, self.y * f)
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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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return self.x * p.y - self.y * p.x
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def dot(self, Point 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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return sqrt(self.x * self.x + self.y * self.y)
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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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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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mpoints = []
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def __init__(self, Point p, Point 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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self.b = p.y - (p.x * self.slope)
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property p:
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def __get__(self): return self.p
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property q:
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def __get__(self): return self.q
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property above:
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def __get__(self): return self.above
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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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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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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 a1, a2, a3, a4, t
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cdef Point a, b
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a = self.p
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b = self.q
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a1 = self.signed_area(a, b, d)
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a2 = self.signed_area(a, b, c)
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if a1 != 0 and a2 != 0 and (a1 * a2) < 0:
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a3 = self.signed_area(c, d, a)
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a4 = a3 + a2 - a1
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if a3 * a4 < 0:
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t = a3 / (a3 - a4)
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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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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 lpoint, rpoint
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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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sink = None
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def __init__(self, Point lpoint, Point rpoint, Edge top, Edge bottom):
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self.lpoint = lpoint
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self.rpoint = rpoint
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self.top = top
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self.bottom = bottom
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self.upper_left = None
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self.upper_right = None
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self.lower_left = None
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self.lower_right = None
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self.inside = True
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property upper_left:
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def __get__(self): return self.upper_left
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def __set__(self, Trapezoid other): self.upper_left = other
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property upper_right:
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def __get__(self): return self.upper_right
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def __set__(self, Trapezoid other): self.upper_right = other
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property lower_left:
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def __get__(self): return self.lower_left
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def __set__(self, Trapezoid other): self.lower_left = other
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property lower_right:
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def __get__(self): return self.lower_right
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def __set__(self, Trapezoid other): self.lower_right = other
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def update_left(self, Trapezoid ul, Trapezoid ll):
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self.upper_left = ul
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self.lower_left = ll
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if ul != None: ul.upper_right = self
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if ll != None: ll.lower_right = self
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def update_right(self, Trapezoid ur, Trapezoid lr):
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self.upper_right = ur
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self.lower_right = lr
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if ur != None: ur.upper_left = self
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if lr != None: lr.lower_left = self
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def update_left_right(self, Trapezoid ul, Trapezoid ll, Trapezoid ur, Trapezoid lr):
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self.upper_left = ul
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self.lower_left = ll
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self.upper_right = ur
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self.lower_right = lr
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if ul != None: ul.upper_right = self
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if ll != None: ll.lower_right = self
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if ur != None: ur.upper_left = self
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if lr != None: lr.lower_left = self
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def trim_neighbors(self):
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if self.inside:
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self.inside = False
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if self.upper_left != None: self.upper_left.trim_neighbors()
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if self.lower_left != None: self.lower_left.trim_neighbors()
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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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return (point.x > self.lpoint.x and point.x < self.rpoint.x and
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self.top.is_above(point) and self.bottom.is_below(point))
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def vertices(self):
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cdef list verts = []
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verts.append(line_intersect(self.top, self.lpoint.x))
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verts.append(line_intersect(self.bottom, self.lpoint.x))
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verts.append(line_intersect(self.bottom, self.rpoint.x))
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verts.append(line_intersect(self.top, self.rpoint.x))
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return verts
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def add_points(self):
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if self.lpoint != self.bottom.p:
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self.bottom.mpoints.append(self.lpoint.clone)
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if self.rpoint != self.bottom.q:
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self.bottom.mpoints.append(self.rpoint.clone)
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if self.lpoint != self.top.p:
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self.top.mpoints.append(self.lpoint.clone)
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if self.rpoint != self.top.q:
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self.top.mpoints.append(self.rpoint.clone)
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class TrapezoidalMap:
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map = {}
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margin = 50
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bcross = None
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tcross = None
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def clear(self):
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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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trapezoids = [None, None, None, None]
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trapezoids.append(Trapezoid(t.lpoint, e.p, t.top, t.bottom))
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trapezoids.append(Trapezoid(e.p, e.q, t.top, e))
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trapezoids.append(Trapezoid(e.p, e.q, e, t.bottom))
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trapezoids.append(Trapezoid(e.q, t.rpoint, t.top, t.bottom))
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trapezoids[0].update_left(t.upper_left, t.lower_left)
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trapezoids[1].update_left_right(trapezoids[0], None, trapezoids[3], None)
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trapezoids[2].update_left_right(None, trapezoids[0], None, trapezoids[3])
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trapezoids[3].update_right(t.upper_right, t.lower_right)
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return trapezoids
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def case2(self, t, e):
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rp = e.q if e.q.x == t.rpoint.x else t.rpoint
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trapezoids = [None, None, None]
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trapezoids.append(Trapezoid(t.lpoint, e.p, t.top, t.bottom))
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trapezoids.append(Trapezoid(e.p, rp, t.top, e))
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trapezoids.append(Trapezoid(e.p, rp, e, t.bottom))
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trapezoids[0].update_left(t.upper_left, t.lower_left)
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trapezoids[1].update_left_right(trapezoids[0], None, t.upper_right, None)
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trapezoids[2].update_left_right(None, trapezoids[0], None, t.lower_right)
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self.bcross = t.bottom
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self.tcross = t.top
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e.above = trapezoids[1]
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e.below = trapezoids[2]
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return trapezoids
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def case3(self, t, e):
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lp = e.p if e.p.x == t.lpoint.x else t.lpoint
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rp = e.q if e.q.x == t.rpoint.x else t.rpoint
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trapezoids = [None, None]
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if self.tcross is t.top:
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trapezoids[0] = t.upper_left
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trapezoids[0].update_right(t.upper_right, None)
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trapezoids[0].rpoint = rp
|
||||
else:
|
||||
trapezoids[0] = Trapezoid(lp, rp, t.top, e)
|
||||
trapezoids[0].update_left_right(t.upper_left, e.above, t.upper_right, None)
|
||||
if self.bcross is t.bottom:
|
||||
trapezoids[1] = t.lower_left
|
||||
trapezoids[1].update_right(None, t.lower_right)
|
||||
trapezoids[1].rpoint = rp
|
||||
else:
|
||||
trapezoids[1] = Trapezoid(lp, rp, e, t.bottom)
|
||||
trapezoids[1].update_left_right(e.below, t.lower_left, None, t.lower_right)
|
||||
self.bcross = t.bottom
|
||||
self.tcross = t.top
|
||||
e.above = trapezoids[0]
|
||||
e.below = trapezoids[1]
|
||||
return trapezoids
|
||||
|
||||
def case4(self, t, e):
|
||||
lp = e.p if e.p.x == t.lpoint.x else t.lpoint
|
||||
trapezoids = [None, None, None]
|
||||
if self.tcross is t.top:
|
||||
trapezoids[0] = t.upper_left
|
||||
trapezoids[0].rpoint = e.q
|
||||
else:
|
||||
trapezoids[0] = Trapezoid(lp, e.q, t.top, e)
|
||||
trapezoids[0].update_left(t.upper_left, e.above)
|
||||
if self.bcross is t.bottom:
|
||||
trapezoids[1] = t.lower_left
|
||||
trapezoids[1].rpoint = e.q
|
||||
else:
|
||||
trapezoids[1] = Trapezoid(lp, e.q, e, t.bottom)
|
||||
trapezoids[1].update_left(e.below, t.lower_left)
|
||||
trapezoids[2] = Trapezoid(e.q, t.rpoint, t.top, t.bottom)
|
||||
trapezoids[2].update_left_right(trapezoids[0], trapezoids[1], t.upper_right, t.lower_right)
|
||||
|
||||
return trapezoids
|
||||
|
||||
def bounding_box(self, edges):
|
||||
margin = self.margin
|
||||
max = edges[0].p + margin
|
||||
min = edges[0].q - margin
|
||||
for e in edges:
|
||||
if e.p.x > max.x: max = Point(e.p.x + margin, max.y)
|
||||
if e.p.y > max.y: max = Point(max.x, e.p.y + margin)
|
||||
if e.q.x > max.x: max = Point(e.q.x + margin, max.y)
|
||||
if e.q.y > max.y: max = Point(max.x, e.q.y + margin)
|
||||
if e.p.x < min.x: min = Point(e.p.x - margin, min.y)
|
||||
if e.p.y < min.y: min = Point(min.x, e.p.y - margin)
|
||||
if e.q.x < min.x: min = Point(e.q.x - margin, min.y)
|
||||
if e.q.y < min.y: min = Point(min.x, e.q.y - margin)
|
||||
top = Edge(Point(min.x, max.y), Point(max.x, max.y))
|
||||
bottom = Edge(Point(min.x, min.y), Point(max.x, min.y))
|
||||
left = bottom.p
|
||||
right = top.q
|
||||
return Trapezoid(left, right, top, bottom)
|
||||
|
||||
class Node:
|
||||
|
||||
parent_list = []
|
||||
|
||||
def __init__(self, left, right):
|
||||
self.left = left
|
||||
self.right = right
|
||||
if left is not None:
|
||||
left.parent_list.append(self)
|
||||
if right is not None:
|
||||
right.parent_list.append(self)
|
||||
|
||||
def replace(self, node):
|
||||
for parent in node.parent_list:
|
||||
if parent.left is node:
|
||||
parent.left = self
|
||||
else:
|
||||
parent.right = self
|
||||
self.parent_list.append(parent)
|
||||
|
||||
class Sink(Node):
|
||||
|
||||
def __new__(cls, trapezoid):
|
||||
if trapezoid.sink is not None:
|
||||
return trapezoid.sink
|
||||
else:
|
||||
return Sink(trapezoid)
|
||||
|
||||
def __init__(self, trapezoid):
|
||||
Node.__init__(self, None, None)
|
||||
trapezoid.sink = self
|
||||
|
||||
def locate(self, e):
|
||||
return self
|
||||
|
||||
class XNode(Node):
|
||||
|
||||
def __init__(self, point, lchild, rchild):
|
||||
Node.__init__(self, lchild, rchild)
|
||||
self.point = point
|
||||
self.lchild = lchild
|
||||
self.rchild = rchild
|
||||
|
||||
def locate(self, e):
|
||||
if e.p.x >= self.point.x:
|
||||
return self.right.locate(e)
|
||||
else:
|
||||
return self.left.locate(e)
|
||||
|
||||
class YNode(Node):
|
||||
|
||||
def __init__(self, edge, lchild, rchild):
|
||||
Node.__init__(self, lchild, rchild)
|
||||
self.edge = edge
|
||||
self.lchild = lchild
|
||||
self.rchild = rchild
|
||||
|
||||
def locate(self, e):
|
||||
if self.edge.is_above(e.p):
|
||||
return self.right.locate(e)
|
||||
elif self.edge.is_below(e.p):
|
||||
return self.left.locate(e)
|
||||
else:
|
||||
if e.slope < self.edge.slope:
|
||||
return self.right.locate(e)
|
||||
else:
|
||||
return self.left.locate(e)
|
||||
|
||||
class QueryGraph:
|
||||
|
||||
head = None
|
||||
|
||||
def __init__(self, head):
|
||||
self.head = head
|
||||
|
||||
def locate(self, e):
|
||||
return self.head.locate(e).trapezoid
|
||||
|
||||
def follow_segment(self, e):
|
||||
trapezoids = [self.locate(e)]
|
||||
j = 0
|
||||
while(e.q.x > trapezoids[j].right_point.x):
|
||||
if e > trapezoids[j].right_point:
|
||||
trapezoids.append(trapezoids[j].upper_right)
|
||||
else:
|
||||
trapezoids .append(trapezoids[j].lower_right)
|
||||
j += 1
|
||||
return trapezoids
|
||||
|
||||
def replace(self, sink, node):
|
||||
if not sink.parent_list:
|
||||
self.head = node
|
||||
else:
|
||||
node.replace(sink)
|
||||
|
||||
def case1(self, sink, e, tlist):
|
||||
yNode = YNode(e, Sink(tlist[1]), Sink(tlist[2]))
|
||||
qNode = XNode(e.q, yNode, Sink(tlist[3]))
|
||||
pNode = XNode(e.p, Sink(tlist[0]), qNode)
|
||||
self.replace(sink, pNode)
|
||||
|
||||
def case2(self, sink, e, tlist):
|
||||
yNode = YNode(e, Sink(tlist[1]), Sink(tlist[2]))
|
||||
pNode = XNode(e.p, Sink(tlist[0]), yNode)
|
||||
self.replace(sink, pNode)
|
||||
|
||||
def case3(self, sink, e, tlist):
|
||||
yNode = YNode(e, Sink(tlist[0]), Sink(tlist[1]))
|
||||
self.replace(sink, yNode)
|
||||
|
||||
def case4(self, sink, e, tlist):
|
||||
yNode = YNode(e, Sink(tlist[0]), Sink(tlist[1]))
|
||||
qNode = XNode(e.q, yNode, Sink(tlist[2]))
|
||||
self.replace(sink, qNode)
|
||||
|
||||
@ -1 +0,0 @@
|
||||
import "triangulator.pyx"
|
||||
@ -1,647 +0,0 @@
|
||||
/* 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,
|
||||
* this list of conditions and the following disclaimer.
|
||||
* * Redistributions in binary form must reproduce the above copyright notice,
|
||||
* this 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 this software without specific
|
||||
* prior written permission.
|
||||
*
|
||||
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
|
||||
* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
|
||||
* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
|
||||
* A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR
|
||||
* CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
|
||||
* EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
|
||||
* PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
|
||||
* PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
|
||||
* LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
|
||||
* NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
|
||||
* SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
|
||||
*/
|
||||
from math import floor
|
||||
|
||||
###
|
||||
### Based on Raimund Seidel's paper "A simple and fast incremental randomized
|
||||
### algorithm for computing trapezoidal decompositions and for triangulating polygons"
|
||||
### (Ported from poly2tri)
|
||||
|
||||
class Triangulator(object) {
|
||||
|
||||
def __init__(points):
|
||||
|
||||
# Convex polygon list
|
||||
self.polygons = []
|
||||
# Order and randomize the Edges
|
||||
self.EdgeList = initEdges()
|
||||
|
||||
# Initialize trapezoidal map and query structure
|
||||
self.trapezoidalMap = new TrapezoidalMap
|
||||
self.bounding_box = trapezoidalMap.bounding_box(EdgeList)
|
||||
self.queryGraph = QueryGraph(Sink.init(bounding_box))
|
||||
self.xMonoPoly = []
|
||||
|
||||
# The trapezoidal map
|
||||
self.trapezoidMap = trapezoidalMap.map
|
||||
# Trapezoid decomposition list
|
||||
self.trapezoids = []
|
||||
|
||||
self.process()
|
||||
|
||||
// Build the trapezoidal map and query graph
|
||||
def process(self):
|
||||
|
||||
i = 0
|
||||
while(i < len(EdgeList)):
|
||||
|
||||
s = EdgeList(i)
|
||||
traps = queryGraph.followEdge(s)
|
||||
|
||||
// Remove trapezoids from trapezoidal Map
|
||||
for j in range(len(traps)):
|
||||
trapezoidalMap.map -= traps(j)
|
||||
|
||||
for j in range(len(traps)):
|
||||
t = traps(j)
|
||||
tList = []
|
||||
containsP = t.contains(s.p)
|
||||
containsQ = t.contains(s.q)
|
||||
if containsP and containsQ:
|
||||
// Case 1
|
||||
tList = trapezoidalMap.case1(t,s)
|
||||
queryGraph.case1(t.sink, s, tList)
|
||||
elif containsP and !containsQ:
|
||||
// Case 2
|
||||
tList = trapezoidalMap.case2(t,s)
|
||||
queryGraph.case2(t.sink, s, tList)
|
||||
elif !containsP and !containsQ:
|
||||
// Case 3
|
||||
tList = trapezoidalMap.case3(t, s)
|
||||
queryGraph.case3(t.sink, s, tList)
|
||||
else:
|
||||
// Case 4
|
||||
tList = trapezoidalMap.case4(t, s)
|
||||
queryGraph.case4(t.sink, s, tList)
|
||||
|
||||
// Add new trapezoids to map
|
||||
for k in range(len(tList)):
|
||||
trapezoidalMap.map += tList[k]
|
||||
|
||||
trapezoidalMap.clear
|
||||
i += 1
|
||||
|
||||
for t in trapezoidalMap.map
|
||||
markOutside(t)
|
||||
|
||||
for t in trapezoidalMap.map
|
||||
if t.inside:
|
||||
trapezoids.append(t)
|
||||
t.addPoints()
|
||||
|
||||
createMountains()
|
||||
|
||||
}
|
||||
|
||||
// Monotone polygons - these are monotone mountains
|
||||
def monoPolies(self):
|
||||
polies = []
|
||||
for i in range(len(self.xMonoPoly)):
|
||||
polies.append(self.xMonoPoly(i).monoPoly)
|
||||
return polies
|
||||
|
||||
|
||||
// Build a list of x-monotone mountains
|
||||
private def createMountains {
|
||||
|
||||
var i = 0
|
||||
while(i < EdgeList.size) {
|
||||
|
||||
val s = EdgeList(i)
|
||||
|
||||
if(s.mPoints.size > 0) {
|
||||
|
||||
mountain = MonotoneMountain()
|
||||
|
||||
|
||||
if len(s.mPoints) < 10:
|
||||
k = insertSort((p1: Point, p2: Point) => p1 < p2)(s.mPoints).toList
|
||||
else
|
||||
k = msort((p1: Point, p2: Point) => p1 < p2)(s.mPoints.toList)
|
||||
|
||||
points = s.p :: k ::: List(s.q)
|
||||
|
||||
for p in points:
|
||||
mountain.add(p)
|
||||
|
||||
mountain.process()
|
||||
|
||||
// Extract the triangles into a single list
|
||||
j = 0
|
||||
while(j < mountain.triangles.size) {
|
||||
polygons += mountain.triangles(j)
|
||||
j += 1
|
||||
}
|
||||
|
||||
xMonoPoly += mountain
|
||||
}
|
||||
i += 1
|
||||
}
|
||||
}
|
||||
|
||||
// Mark the outside trapezoids surrounding the polygon
|
||||
private def markOutside(t: Trapezoid) {
|
||||
if(t.top == bounding_box.top || t.bottom == bounding_box.bottom) {
|
||||
t trimNeighbors
|
||||
}
|
||||
}
|
||||
|
||||
// Create Edges and connect end points; update edge event pointer
|
||||
private def initEdges: ArrayBuffer[Edge] = {
|
||||
var Edges = List[Edge]()
|
||||
for(i <- 0 until points.size-1)
|
||||
Edges = new Edge(points(i), points(i+1)) :: Edges
|
||||
Edges = new Edge(points.first, points.last) :: Edges
|
||||
orderEdges(Edges)
|
||||
}
|
||||
|
||||
private def orderEdges(Edges: List[Edge]) = {
|
||||
|
||||
// Ignore vertical Edges!
|
||||
val segs = new ArrayBuffer[Edge]
|
||||
for(s <- Edges) {
|
||||
val p = shearTransform(s.p)
|
||||
val q = shearTransform(s.q)
|
||||
// Point p must be to the left of point q
|
||||
if(p.x > q.x) {
|
||||
segs += new Edge(q, p)
|
||||
} else if(p.x < q.x) {
|
||||
segs += new Edge(p, q)
|
||||
}
|
||||
}
|
||||
// Randomized triangulation improves performance
|
||||
// See Seidel's paper, or O'Rourke's book, p. 57
|
||||
Random.shuffle(segs)
|
||||
segs
|
||||
}
|
||||
|
||||
// Prevents any two distinct endpoints from lying on a common vertical line, and avoiding
|
||||
// the degenerate case. See Mark de Berg et al, Chapter 6.3
|
||||
//val SHEER = 0.0001f
|
||||
def shearTransform(point: Point) = Point(point.x + 0.0001f * point.y, point.y)
|
||||
|
||||
}
|
||||
|
||||
// Doubly linked list
|
||||
class MonotoneMountain {
|
||||
|
||||
var tail, head: Point = None
|
||||
var size = 0
|
||||
|
||||
private val convexPoints = new ArrayBuffer[Point]
|
||||
// Monotone mountain points
|
||||
val monoPoly = new ArrayBuffer[Point]
|
||||
// Triangles that constitute the mountain
|
||||
val triangles = new ArrayBuffer[Array[Point]]
|
||||
// Convex polygons that constitute the mountain
|
||||
val convexPolies = new ArrayBuffer[Array[Point]]
|
||||
// Used to track which side of the line we are on
|
||||
private var positive = false
|
||||
// Almost Pi!
|
||||
private val PI_SLOP = 3.1
|
||||
|
||||
// Append a point to the list
|
||||
def +=(point: Point) {
|
||||
size match {
|
||||
case 0 =>
|
||||
head = point
|
||||
size += 1
|
||||
case 1 =>
|
||||
// Keep repeat points out of the list
|
||||
if(point ! head) {
|
||||
tail = point
|
||||
tail.prev = head
|
||||
head.next = tail
|
||||
size += 1
|
||||
}
|
||||
case _ =>
|
||||
// Keep repeat points out of the list
|
||||
if(point ! tail) {
|
||||
tail.next = point
|
||||
point.prev = tail
|
||||
tail = point
|
||||
size += 1
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
// Remove a point from the list
|
||||
def remove(point: Point) {
|
||||
val next = point.next
|
||||
val prev = point.prev
|
||||
point.prev.next = next
|
||||
point.next.prev = prev
|
||||
size -= 1
|
||||
}
|
||||
|
||||
// Partition a x-monotone mountain into triangles O(n)
|
||||
// See "Computational Geometry in C", 2nd edition, by Joseph O'Rourke, page 52
|
||||
def process {
|
||||
|
||||
// Establish the proper sign
|
||||
positive = angleSign
|
||||
// create monotone polygon - for dubug purposes
|
||||
genMonoPoly
|
||||
|
||||
// Initialize internal angles at each nonbase vertex
|
||||
// Link strictly convex vertices into a list, ignore reflex vertices
|
||||
var p = head.next
|
||||
while(p != tail) {
|
||||
val a = angle(p)
|
||||
// If the point is almost colinear with it's neighbor, remove it!
|
||||
if(a >= PI_SLOP || a <= -PI_SLOP)
|
||||
remove(p)
|
||||
else
|
||||
if(convex(p)) convexPoints += p
|
||||
p = p.next
|
||||
}
|
||||
|
||||
triangulate
|
||||
|
||||
}
|
||||
|
||||
private def triangulate {
|
||||
|
||||
while(!convexPoints.isEmpty) {
|
||||
|
||||
val ear = convexPoints.remove(0)
|
||||
val a = ear.prev
|
||||
val b = ear
|
||||
val c = ear.next
|
||||
val triangle = Array(a, b, c)
|
||||
|
||||
triangles += triangle
|
||||
|
||||
// Remove ear, update angles and convex list
|
||||
remove(ear)
|
||||
if(valid(a)) convexPoints += a
|
||||
if(valid(c)) convexPoints += c
|
||||
}
|
||||
assert(size <= 3, "Triangulation bug, please report")
|
||||
|
||||
}
|
||||
|
||||
private def valid(p: Point) = (p != head && p != tail && convex(p))
|
||||
|
||||
// Create the monotone polygon
|
||||
private def genMonoPoly {
|
||||
var p = head
|
||||
while(p != None) {
|
||||
monoPoly += p
|
||||
p = p.next
|
||||
}
|
||||
}
|
||||
|
||||
private def angle(p: Point) = {
|
||||
val a = (p.next - p)
|
||||
val b = (p.prev - p)
|
||||
Math.atan2(a cross b, a dot b)
|
||||
}
|
||||
|
||||
private def angleSign = {
|
||||
val a = (head.next - head)
|
||||
val b = (tail - head)
|
||||
(Math.atan2(a cross b, a dot b) >= 0)
|
||||
}
|
||||
|
||||
// Determines if the inslide angle is convex or reflex
|
||||
private def convex(p: Point) = {
|
||||
if(positive != (angle(p) >= 0)) false
|
||||
else true
|
||||
}
|
||||
|
||||
}
|
||||
|
||||
# Node for a Directed Acyclic graph (DAG)
|
||||
class Node(object):
|
||||
|
||||
def __init__(self, left, right):
|
||||
self.left = left
|
||||
self.right = right
|
||||
if left is not None:
|
||||
left.parentList.append(self)
|
||||
if right is not None:
|
||||
right.parentList.append(self)
|
||||
parentList = []
|
||||
|
||||
def replace(self, node):
|
||||
for parent in node.parentList:
|
||||
if(parent.left == node):
|
||||
parent.left = self
|
||||
else:
|
||||
parent.right = self
|
||||
parentList.append(parent)
|
||||
|
||||
# Directed Acyclic graph (DAG)
|
||||
# See "Computational Geometry", 3rd edition, by Mark de Berg et al, Chapter 6.2
|
||||
|
||||
class QueryGraph(var head: Node) {
|
||||
|
||||
def locate(s: Edge) = head.locate(s).trapezoid
|
||||
|
||||
def followEdge(s: Edge) = {
|
||||
|
||||
val trapezoids = new ArrayBuffer[Trapezoid]
|
||||
trapezoids += locate(s)
|
||||
var j = 0
|
||||
while(s.q.x > trapezoids(j).rightPoint.x) {
|
||||
if(s > trapezoids(j).rightPoint) {
|
||||
trapezoids += trapezoids(j).upperRight
|
||||
} else {
|
||||
trapezoids += trapezoids(j).lowerRight
|
||||
}
|
||||
j += 1
|
||||
}
|
||||
trapezoids
|
||||
}
|
||||
|
||||
def replace(sink: Sink, node: Node) {
|
||||
if(sink.parentList.size == 0) {
|
||||
head = node
|
||||
} else {
|
||||
node replace sink
|
||||
}
|
||||
}
|
||||
|
||||
def case1(sink: Sink, s: Edge, tList: Array[Trapezoid]) {
|
||||
val yNode = new YNode(s, Sink.init(tList(1)), Sink.init(tList(2)))
|
||||
val qNode = new XNode(s.q, yNode, Sink.init(tList(3)))
|
||||
val pNode = new XNode(s.p, Sink.init(tList(0)), qNode)
|
||||
replace(sink, pNode)
|
||||
}
|
||||
|
||||
def case2(sink: Sink, s: Edge, tList: Array[Trapezoid]) {
|
||||
val yNode = new YNode(s, Sink.init(tList(1)), Sink.init(tList(2)))
|
||||
val pNode = new XNode(s.p, Sink.init(tList(0)), yNode)
|
||||
replace(sink, pNode)
|
||||
}
|
||||
|
||||
def case3(sink: Sink, s: Edge, tList: Array[Trapezoid]) {
|
||||
val yNode = new YNode(s, Sink.init(tList(0)), Sink.init(tList(1)))
|
||||
replace(sink, yNode)
|
||||
}
|
||||
|
||||
def case4(sink: Sink, s: Edge, tList: Array[Trapezoid]) {
|
||||
val yNode = new YNode(s, Sink.init(tList(0)), Sink.init(tList(1)))
|
||||
val qNode = new XNode(s.q, yNode, Sink.init(tList(2)))
|
||||
replace(sink, qNode)
|
||||
}
|
||||
|
||||
}
|
||||
|
||||
class Sink(Node):
|
||||
|
||||
def __new__(cls, trapezoid):
|
||||
if trapezoid.sink is not None:
|
||||
return trapezoid.sink
|
||||
else
|
||||
return Sink(trapezoid)
|
||||
|
||||
def __init__(self, trapezoid):
|
||||
Node.__init__(self, None, None)
|
||||
trapezoid.sink = self
|
||||
|
||||
def locate(e):
|
||||
return self
|
||||
|
||||
class TrapezoidalMap(object):
|
||||
|
||||
map = {}
|
||||
margin = 50
|
||||
bcross = None
|
||||
tcross = None
|
||||
|
||||
def clear(self):
|
||||
self.bcross = None
|
||||
self.tcross = None
|
||||
|
||||
def case1(self, t, e):
|
||||
trapezoids = (None, None, None, None)
|
||||
trapezoids.append(Trapezoid(t.leftPoint, 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.rightPoint, t.top, t.bottom))
|
||||
trapezoids[0].updateLeft(t.upperLeft, t.lowerLeft)
|
||||
trapezoids[1].updateLeftRight(trapezoids[0], None, trapezoids[3], None)
|
||||
trapezoids[2].updateLeftRight(None, trapezoids[0], None, trapezoids[3])
|
||||
trapezoids[3].updateRight(t.upperRight, t.lowerRight)
|
||||
return trapezoids
|
||||
|
||||
def case2(self, t, e):
|
||||
val rp = e.q if e.q.x == t.rightPoint.x else t.rightPoint
|
||||
trapezoids = (None, None, None)
|
||||
trapezoids.append(Trapezoid(t.leftPoint, 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].updateLeft(t.upperLeft, t.lowerLeft)
|
||||
trapezoids[1].updateLeftRight(trapezoids[0], None, t.upperRight, None)
|
||||
trapezoids[2].updateLeftRight(None, trapezoids[0], None, t.lowerRight)
|
||||
self.bcross = t.bottom
|
||||
self.tcross = t.top
|
||||
e.above = trapezoids[1]
|
||||
e.below = trapezoids[2]
|
||||
return trapezoids
|
||||
|
||||
def case3(self, t, e):
|
||||
lp = s.p if s.p.x == t.leftPoint.x else t.leftPoint
|
||||
rp = s.q if s.q.x == t.rightPoint.x else t.rightPoint
|
||||
trapezoids = (None, None)
|
||||
if self.tcross is t.top:
|
||||
trapezoids[0] = t.upperLeft
|
||||
trapezoids[0].updateRight(t.upperRight, None)
|
||||
trapezoids[0].rightPoint = rp
|
||||
else:
|
||||
trapezoids[0] = Trapezoid(lp, rp, t.top, s)
|
||||
trapezoids[0].updateLeftRight(t.upperLeft, s.above, t.upperRight, None)
|
||||
if self.bcross is t.bottom:
|
||||
trapezoids[1] = t.lowerLeft
|
||||
trapezoids[1].updateRight(None, t.lowerRight)
|
||||
trapezoids[1].rightPoint = rp
|
||||
else:
|
||||
trapezoids[1] = Trapezoid(lp, rp, s, t.bottom)
|
||||
trapezoids[1].updateLeftRight(s.below, t.lowerLeft, None, t.lowerRight)
|
||||
self.bcross = t.bottom
|
||||
self.tcross = t.top
|
||||
s.above = trapezoids[0]
|
||||
s.below = trapezoids[1]
|
||||
return trapezoids
|
||||
|
||||
def case4(self, t, e):
|
||||
lp = s.p if s.p.x == t.leftPoint.x else t.leftPoint
|
||||
trapezoids = (None, None, None)
|
||||
if self.tcross is t.top:
|
||||
trapezoids[0] = t.upperLeft
|
||||
trapezoids[0].rightPoint = s.q
|
||||
else:
|
||||
trapezoids[0] = Trapezoid(lp, s.q, t.top, s)
|
||||
trapezoids[0].updateLeft(t.upperLeft, s.above)
|
||||
if self.bcross is t.bottom:
|
||||
trapezoids[1] = t.lowerLeft
|
||||
trapezoids[1].rightPoint = s.q
|
||||
else:
|
||||
trapezoids[1] = Trapezoid(lp, s.q, s, t.bottom)
|
||||
trapezoids[1].updateLeft(s.below, t.lowerLeft)
|
||||
trapezoids[2] = Trapezoid(s.q, t.rightPoint, t.top, t.bottom)
|
||||
trapezoids[2].updateLeftRight(trapezoids[0], trapezoids[1], t.upperRight, t.lowerRight)
|
||||
|
||||
return trapezoids
|
||||
|
||||
def bounding_box(self, edges):
|
||||
max = edges[0].p + margin
|
||||
min = edges[0].q - margin
|
||||
for s in edges:
|
||||
if s.p.x > max.x: max = Point(s.p.x + margin, max.y)
|
||||
if s.p.y > max.y: max = Point(max.x, s.p.y + margin)
|
||||
if s.q.x > max.x: max = Point(s.q.x+margin, max.y)
|
||||
if s.q.y > max.y: max = Point(max.x, s.q.y+margin)
|
||||
if s.p.x < min.x: min = Point(s.p.x-margin, min.y)
|
||||
if s.p.y < min.y: min = Point(min.x, s.p.y-margin)
|
||||
if s.q.x < min.x: min = Point(s.q.x-margin, min.y)
|
||||
if s.q.y < min.y: min = Point(min.x, s.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 XNode(Node):
|
||||
|
||||
def __init__(self, point, lchild, rchild):
|
||||
Node.__init__(self, lChild, rChild)
|
||||
self.point = point
|
||||
self.lchild = lchild
|
||||
self.rchild = rchils
|
||||
|
||||
def locate(self, e):
|
||||
if e.p.x >= self.point.x:
|
||||
return self.right.locate(e)
|
||||
else:
|
||||
return self.left.locate(e)
|
||||
|
||||
class YNode(Node):
|
||||
|
||||
def __init__(self, edge, lchild, rchild):
|
||||
Node.__init__(self, lChild, rChild)
|
||||
self.edge = edge
|
||||
self.lchild = lchild
|
||||
self.rchile = rchild
|
||||
|
||||
def locate(self, e):
|
||||
if edge > e.p:
|
||||
return self.right.locate(e)
|
||||
elif edge < e.p:
|
||||
return self.left.locate(e)
|
||||
else:
|
||||
if e.slope < self.edge.slope:
|
||||
return self.right.locate(e)
|
||||
else:
|
||||
return self.left.locate(e)
|
||||
|
||||
cdef class Point(object):
|
||||
|
||||
def __init__(self, x, y):
|
||||
self.x = x
|
||||
self.y = y
|
||||
next = None
|
||||
prev = None
|
||||
Edge = None
|
||||
edges = []
|
||||
|
||||
cdef __sub__(self, Point p):
|
||||
return Point(self.x - p.x, self.y - p.y)
|
||||
|
||||
cdef __sub__(self, float f):
|
||||
return Point(self.x - f, self.y - f)
|
||||
|
||||
cdef __add__(self, Point p):
|
||||
return Point(self.x + p.x, self.y + p.y)
|
||||
|
||||
cdef __add__(self, float f):
|
||||
return Point(self.x + f, self.y + f)
|
||||
|
||||
cdef __mul__(self, float f):
|
||||
return Point(self.x * f, self.y * f)
|
||||
|
||||
cdef __div__(self, float a):
|
||||
return Point(self.x / a, self.y / a)
|
||||
|
||||
cdef cross(self, Point p):
|
||||
return self.x * p.y - self.y * p.x
|
||||
|
||||
cdef dot(self, Point p):
|
||||
return self.x * p.x + self.y * p.y
|
||||
|
||||
cdef length(self):
|
||||
return math.sqrt(self.x * self.x + self.y * self.y)
|
||||
|
||||
cdef normalize(self):
|
||||
return self / length
|
||||
|
||||
cdef __lt__(self, Point p):
|
||||
return self.x < p.x
|
||||
|
||||
# Sort along y axis
|
||||
cdef >(p: Point):
|
||||
if y < p.y:
|
||||
return True
|
||||
elif y > p.y:
|
||||
return False
|
||||
else {
|
||||
if x < p.x:
|
||||
return True
|
||||
else
|
||||
return False
|
||||
|
||||
cdef !(p: Point) = !(p.x == x && p.y == y)
|
||||
cdef clone = Point(x, y)
|
||||
|
||||
|
||||
// Represents a simple polygon's edge
|
||||
// TODO: Rename this class to Edge?
|
||||
class Edge(object):
|
||||
|
||||
def __init__(self, p, q):
|
||||
self.p = p
|
||||
self.q = q
|
||||
self.above, self.below = None
|
||||
mPoints = []
|
||||
self.slope = (q.y - p.y)/(q.x - p.x)
|
||||
self.b = p.y - (p.x * self.slope)
|
||||
|
||||
def __gt__(self, point):
|
||||
return (floor(point.y) < floor(slope * point.x + b))
|
||||
def __lt__(self, point):
|
||||
return (floor(point.y) > floor(slope * point.x + b))
|
||||
|
||||
def intersect(self, c, d):
|
||||
a = self.p
|
||||
b = self.q
|
||||
a1 = _signed_area(a, b, d)
|
||||
a2 = _signed_area(a, b, c)
|
||||
if a1 != 0 and a2 != 0 and a1 * a2 < 0:
|
||||
a3 = _signed_area(c, d, a)
|
||||
a4 = a3 + a2 - a1
|
||||
if a3 * a4 < 0:
|
||||
t = a3 / (a3 - a4)
|
||||
return a + ((b - a) * t)
|
||||
|
||||
def _signed_area(self, a, b, c):
|
||||
return (a.x - c.x) * (b.y - c.y) - (a.y - c.y) * (b.x - c.x)
|
||||
2
python/p2t.sh
Normal file
2
python/p2t.sh
Normal file
@ -0,0 +1,2 @@
|
||||
#!/bin/sh
|
||||
python -O poly2tri.py
|
||||
20
python/poly2tri.py
Normal file
20
python/poly2tri.py
Normal file
@ -0,0 +1,20 @@
|
||||
#!/usr/bin/env python2.6
|
||||
from framework import Game
|
||||
|
||||
class Poly2Tri(Game):
|
||||
|
||||
#Screen size
|
||||
screen_size = 800.0, 600.0
|
||||
|
||||
def __init__(self):
|
||||
super(Poly2Tri, self).__init__(*self.screen_size)
|
||||
self.main_loop()
|
||||
|
||||
def update(self):
|
||||
pass
|
||||
|
||||
def render(self):
|
||||
pass
|
||||
|
||||
if __name__ == '__main__':
|
||||
demo = Poly2Tri()
|
||||
Loading…
Reference in New Issue
Block a user