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path: root/helpers.py
blob: 47dfbe4f2ac4ae19976700200baedec7ccc30008 (plain)
 ```1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 ``` ``````""" Physics, a 2D Physics Playground for Kids Copyright (C) 2008 Alex Levenson and Brian Jordan This program is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with this program. If not, see . """ #================================================================== # Physics.activity # Helper classes and functions # By Alex Levenson #================================================================== import math # distance calculator, pt1 and pt2 are ordred pairs def distance(pt1, pt2): return math.sqrt((pt1[0] - pt2[0]) ** 2 + (pt1[1] - pt2[1]) ** 2) # returns the angle between the line segment from pt1 --> pt2 and the x axis, from -pi to pi def getAngle(pt1,pt2): xcomp = pt2[0] - pt1[0] ycomp = pt1[1] - pt2[1] return math.atan2(ycomp, xcomp) # returns a list of ordered pairs that describe an equilteral triangle around the segment from pt1 --> pt2 def constructTriangleFromLine(p1,p2): halfHeightVector = (0.57735 * (p2[1] - p1[1]), 0.57735 * (p2[0] - p1[0])) p3 = (p1[0] + halfHeightVector[0], p1[1] - halfHeightVector[1]) p4 = (p1[0] - halfHeightVector[0], p1[1] + halfHeightVector[1]) return [p2, p3, p4] # returns the area of a polygon def polyArea(vertices): n = len(vertices) A = 0 p=n - 1 q=0 while q < n: A+=vertices[p][0] * vertices[q][1] - vertices[q][0] * vertices[p][1] p=q q += 1 return A / 2.0 #Some polygon magic, thanks to John W. Ratcliff on www.flipcode.com # returns true if pt is in triangle def insideTriangle(pt, triangle): ax = triangle[2][0] - triangle[1][0] ay = triangle[2][1] - triangle[1][1] bx = triangle[0][0] - triangle[2][0] by = triangle[0][1] - triangle[2][1] cx = triangle[1][0] - triangle[0][0] cy = triangle[1][1] - triangle[0][1] apx= pt[0] - triangle[0][0] apy= pt[1] - triangle[0][1] bpx= pt[0] - triangle[1][0] bpy= pt[1] - triangle[1][1] cpx= pt[0] - triangle[2][0] cpy= pt[1] - triangle[2][1] aCROSSbp = ax * bpy - ay * bpx cCROSSap = cx * apy - cy * apx bCROSScp = bx * cpy - by * cpx return aCROSSbp >= 0.0 and bCROSScp >= 0.0 and cCROSSap >= 0.0 def polySnip(vertices, u, v, w, n): EPSILON = 0.0000000001 Ax = vertices[u][0] Ay = vertices[u][1] Bx = vertices[v][0] By = vertices[v][1] Cx = vertices[w][0] Cy = vertices[w][1] if EPSILON > (((Bx-Ax) * (Cy - Ay)) - ((By - Ay) * (Cx - Ax))): return False for p in range(0, n): if p == u or p == v or p == w: continue Px = vertices[p][0] Py = vertices[p][1] if insideTriangle((Px, Py), ((Ax, Ay), (Bx, By), (Cx, Cy))): return False return True # decomposes a polygon into its triangles def decomposePoly(vertices): vertices = list(vertices) n = len(vertices) result = [] if(n < 3): return [] # not a poly! # force a counter-clockwise polygon if 0 >= polyArea(vertices): vertices.reverse() # remove nv-2 vertices, creating 1 triangle every time nv = n count = 2 * nv # error detection m = 0 v = nv - 1 while nv > 2: count -= 1 if 0 >= count: return [] # Error -- probably bad polygon # three consecutive vertices u = v if nv <= u: u = 0 # previous v = u + 1 if nv <= v: v = 0 # new v w = v + 1 if nv <= w: w = 0 # next if(polySnip(vertices, u, v, w, nv)): # record this triangle result.append((vertices[u], vertices[v], vertices[w])) m += 1 # remove v from remaining polygon vertices.pop(v) nv -= 1 # reset error detection count = 2 * nv return result def cast_tuple_to_int(tuple): """Cast tuple values to ints to avoid gtk+ and pygame's dislike of floats. """ return [int(i) for i in tuple] ``````