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from gem import vector |
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class SimplexVerts(object): |
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def __init__(self): |
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self.p1 = vector.Vector(2) |
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self.p2 = vector.Vector(2) |
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self.p = vector.Vector(2) |
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self.u = 1 |
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self.index1 = 0 |
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self.index2 = 0 |
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def copy(self, v): |
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self.p1 = v.p1 |
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self.p2 = v.p2 |
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self.p = v.p |
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self.u = v.u |
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self.index1 = v.index1 |
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self.index2 = v.index2 |
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class Simplex(object): |
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def __init__(self, vertices): |
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self.vertices = [] |
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self.vertices.append(vertices) |
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def __getitem__(self, key): |
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return self.vertices[key] |
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def getCount(self): |
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return len(self.vertices) |
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def add(self, vertex): |
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self.vertices.append(vertex) |
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def copy(self, s): |
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self.vertices = s.vertices |
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def remove(self, vertex): |
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index = 0 |
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for i in range(len(self.vertices)): |
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if vertex == self.vertices[i]: |
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index = i |
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#Trash the value |
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del self.vertices[index] |
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def Support(regionOne, regionTwo, direction): |
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'''Makes use of the primities. Each primitive has its own getFurthestPoint function. ''' |
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return regionOne.getFurthestPoint(direction) - regionTwo.getFurthestPoint(-direction) |
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class GJK(object): |
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def __init__(self): |
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self.direction = vector.Vector(3) |
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def intersects(self, regionOne, regionTwo): |
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# Get initial point on the Minkowski difference |
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s = Support(regionOne, regionTwo, vector.Vector(3).one()) |
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# Create the inital simplex |
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simplex = Simplex(s) |
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# Choose an initial direction towards the origin |
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self.direction = -s |
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# Choose a maximum number of iterations to avoid |
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# an infinite loop during non-convergent search. |
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maxIterations = 50 |
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for i in range(maxIterations): |
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# Get our next simplex point towards the origin |
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a = Support(regionOne, regionTwo, self.direction) |
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# If we move toward the origin and didn't pass it |
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# then we never will and there is no intersection |
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if (a.isInOppositeDirection(self.direction)): |
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return False |
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# Otherwise we add the new point to the simplex and process it. |
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simplex.add(a) |
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# Here we either find a collision or we find the closest feature of |
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# simplex to the origin, make the new simplex and update the direction |
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# to move toward the origin from that feature. |
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if self.processSimplex(simplex): |
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return True |
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# If we still couldn't find a simplex that contains the origin |
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# then we probably have an intersection |
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return True |
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def processSimplex(self, simplex): |
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'''Either finds a collision or the closest feature of the simplex to the origin, and updates the simplex and direction''' |
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if (simplex.getCount() == 2): |
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return self.processLine(simplex) |
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elif (simplex.getCount() == 3): |
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return self.processTriangle(simplex) |
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else: |
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return self.processTetrehedron(simplex) |
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def processLine(self, simplex): |
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'''Determines which Veronoi region of a tetrehedron the origin is in, utilizing the preserved winding of the simplex to eliminate certain regions''' |
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a = simplex[1] |
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b = simplex[0] |
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ab = b - a |
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aO = -a |
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if(ab.isInSameDirection(aO)): |
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#dot = ab.dot(aO) |
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#angle = math.acos(dot / ab.magnitude() * aO.magnitude()) |
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self.direction = vector.cross(vector.cross(ab, aO), ab) |
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else: |
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simplex.remove(b) |
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self.direction = aO |
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return False |
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def processTriangle(self, simplex): |
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'''Determines which Veronoi region of a tetrehedron the origin is in, utilizing the preserved winding of the simplex to eliminate certain regions''' |
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a = simplex[2] |
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b = simplex[1] |
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c = simplex[0] |
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ab = b - a |
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ac = c - a |
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abc = vector.cross(ab, ac) |
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aO = -a |
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acNormal = vector.cross(abc, ac) |
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abNormal = vector.cross(ab, abc) |
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if(acNormal.isInSameDirection(aO)): |
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if(ac.isInSameDirection(aO)): |
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simplex.remove(b) |
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self.direction = vector.cross(vector.cross(ac, aO), ac) |
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else: |
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if(ab.isInSameDirection(aO)): |
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simplex.remove(c) |
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self.direction = vector.cross(vector.cross(ab, aO), ab) |
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else: |
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simplex.remove(b) |
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simplex.remove(c) |
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self.direction = aO |
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else: |
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View Code Duplication |
if (abNormal.isInSameDirection(aO)): |
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if(ab.isInSameDirection(aO)): |
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simplex.remove(c) |
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self.direction = vector.cross(vector.cross(ab, aO), ab) |
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else: |
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simplex.remove(b) |
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simplex.remove(c) |
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self.direction = aO |
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else: |
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if(abc.isInSameDirection(aO)): |
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self.direction = vector.cross(vector.cross(abc, aO), abc) |
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else: |
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self.direction = vector.cross(vector.cross(-abc, aO), -abc) |
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return False |
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def processTetrehedron(self, simplex): |
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'''Determines which Veronoi region of a tetrehedron the origin is in, utilizing the preserved winding of the simplex to eliminate certain regions''' |
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a = simplex[3] |
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b = simplex[2] |
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c = simplex[1] |
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d = simplex[0] |
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ac = c - a |
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ad = d - a |
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ab = b - a |
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#bc = c - b |
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#bd = d - b |
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acd = vector.cross(ad, ac) |
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abd = vector.cross(ab, ad) |
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abc = vector.cross(ac, ab) |
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aO = -a |
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if (abc.isInSameDirection(aO)): |
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View Code Duplication |
if (vector.cross(abc, ac).isInSameDirection(aO)): |
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simplex.remove(b) |
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simplex.remove(d) |
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self.direction = vector.cross(vector.cross(ac, aO), ac) |
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elif(vector.cross(ab, abc).isInSameDirection(aO)): |
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simplex.remove(c) |
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simplex.remove(d) |
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self.direction = vector.cross(vector.cross(ab, aO), ab) |
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else: |
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simplex.remove(d) |
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self.direction = abc |
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elif (acd.isInSameDirection(aO)): |
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View Code Duplication |
if (vector.cross(acd, ad).isInSameDirection(aO)): |
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simplex.remove(b) |
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simplex.remove(c) |
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self.direction = vector.cross(vector.cross(ad, aO), ad) |
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elif(vector.cross(ac, acd).isInSameDirection(aO)): |
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simplex.remove(b) |
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simplex.remove(d) |
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self.direction = vector.cross(vector.cross(ac, aO), ac) |
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else: |
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simplex.remove(b) |
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self.direction = acd |
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View Code Duplication |
elif(abd.isInSameDirection(aO)): |
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if(vector.cross(abd, ab).isInSameDirection(aO)): |
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simplex.remove(b) |
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simplex.remove(d) |
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self.direction = vector.cross(vector.cross(ab, aO), ab) |
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elif(vector.cross(ab, abd).isInSameDirection(aO)): |
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simplex.remove(b) |
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simplex.remove(c) |
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self.direction = vector.cross(vector.cross(ad, aO), ad) |
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else: |
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simplex.remove(c) |
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self.direction = abd |
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else: |
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return True |
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return False |
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