146 lines
3.5 KiB
Python
146 lines
3.5 KiB
Python
from mathutils import *
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def IsSamePoint(v31, v32, limitDistance):
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if (v31 - v32).magnitude < limitDistance: return True
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return False
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class Plane:
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@staticmethod
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def XY():
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p1 = Vector((0, 0, 0))
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p2 = Vector((1, 0, 0))
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p3 = Vector((0, 1, 0))
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return Plane(p1, p2, p3)
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# plane equation: (p - position).dot(normal) = 0
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def __init__(self, P1, P2, P3):
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self.normal = (P2 - P1).cross(P3 - P1)
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self.normal.normalize()
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self.position = P1
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def CalcIntersectionPointLineSegment(self, PL1, PL2):
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DL = PL2 - PL1
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try: rvPar = ((self.position - PL1).dot(self.normal)) / (DL.dot(self.normal))
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except: return None
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return rvPar
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def CalcNormalParameter(self, vector):
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return (vector - self.position).dot(self.normal)
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def CalcProjection(self, vector):
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normalParameter = self.CalcNormalParameter(vector)
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rvv3 = vector - (self.normal * normalParameter)
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return [normalParameter, rvv3]
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# http://geomalgorithms.com/a07-_distance.html
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def CalcClosestPointLineSegments(v3P0, v3P1, v3Q0, v3Q1):
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u = v3P1 - v3P0
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v = v3Q1 - v3Q0
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w0 = v3P0 - v3Q0
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a = u.dot(u)
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b = u.dot(v)
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c = v.dot(v)
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d = u.dot(w0)
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e = v.dot(w0)
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try: parP = (b * e - c * d) / (a * c - b * b)
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except: return None
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try: parQ = (a * e - b * d) / (a * c - b * b)
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except: return None
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return [parP, parQ]
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def CalcIntersectionPointLineSegments(v3P0, v3P1, v3Q0, v3Q1, limitDistance):
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rvList = CalcClosestPointLineSegments(v3P0, v3P1, v3Q0, v3Q1)
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if rvList is None: return None
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parP = rvList[0]
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if parP < 0.0: return None
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if parP > 1.0: return None
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parQ = rvList[1]
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if parQ < 0.0: return None
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if parQ > 1.0: return None
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pointP = v3P0 + ((v3P1 - v3P0) * parP)
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pointQ = v3Q0 + ((v3Q1 - v3Q0) * parQ)
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if not IsSamePoint(pointP, pointQ, limitDistance): return None
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return [parP, parQ, pointP, pointQ]
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def CalcIntersectionPointsLineSegmentsPOV(v3P0, v3P1, v3Q0, v3Q1, v3POV):
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planeQ = Plane(v3POV, v3Q0, v3Q1)
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parP = planeQ.CalcIntersectionPointLineSegment(v3P0, v3P1)
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if parP is None: return None
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if parP < 0.0: return None
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if parP > 1.0: return None
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planeP = Plane(v3POV, v3P0, v3P1)
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parQ = planeP.CalcIntersectionPointLineSegment(v3Q0, v3Q1)
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if parQ is None: return None
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if parQ < 0.0: return None
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if parQ > 1.0: return None
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return [parP, parQ]
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def CalcIntersectionPointsLineSegmentsDIR(v3P0, v3P1, v3Q0, v3Q1, v3DIR):
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v3POV = v3Q0 + v3DIR
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planeQ = Plane(v3POV, v3Q0, v3Q1)
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parP = planeQ.CalcIntersectionPointLineSegment(v3P0, v3P1)
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if parP is None: return None
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if parP < 0.0: return None
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if parP > 1.0: return None
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v3POV = v3P0 + v3DIR
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planeP = Plane(v3POV, v3P0, v3P1)
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parQ = planeP.CalcIntersectionPointLineSegment(v3Q0, v3Q1)
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if parQ is None: return None
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if parQ < 0.0: return None
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if parQ > 1.0: return None
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return [parP, parQ]
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def CalcRotationMatrix(v3From, v3To):
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cross = v3From.cross(v3To)
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try: angle = v3From.angle(v3To)
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except: return Matrix.Identity(4)
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return Matrix.Rotation(angle, 4, cross) # normalize axis?
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def subdivide_cubic_bezier(p1, p2, p3, p4, t):
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p12 = (p2 - p1) * t + p1
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p23 = (p3 - p2) * t + p2
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p34 = (p4 - p3) * t + p3
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p123 = (p23 - p12) * t + p12
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p234 = (p34 - p23) * t + p23
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p1234 = (p234 - p123) * t + p123
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return [p12, p123, p1234, p234, p34]
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