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