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Geometry.py
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Geometry.py
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#! /usr/bin/env python
import math
class GeometryType :
none = 0
point = 1
segment = 2
triangle = 3
class Point3D:
def __init__(self,x=0,y=0,z=0):
if isinstance(x, list):
assert len(x)==3
self.coordinates = x
else:
self.coordinates = [x,y,z]
def x(self):
return self.coordinates[0]
def y(self):
return self.coordinates[1]
def z(self):
return self.coordinates[2]
def __repr__(self):
return "Point3D("+str(self.x())+","+str(self.y())+","+str(self.z())+")"
def __str__(self):
return "P("+str(self.x())+","+str(self.y())+","+str(self.z())+")"
def get(self):
return self.coordinates
def returnCopy(self):
return Point3D( self.x(), self.y(), self.z() )
def asVector3D(self):
return Vector3D( self.x(), self.y(), self.z() )
def distance(self,other):
return (other-self).length()
def average(self,other):
return Point3D( (self.x()+other.x())*0.5, (self.y()+other.y())*0.5, (self.z()+other.z())*0.5 )
def __add__(self,other):
return Point3D( self.x()+other.x(), self.y()+other.y(), self.z()+other.z() )
def __sub__(self,other):
if isinstance(other,Vector3D):
return Point3D( self.x()-other.x(), self.y()-other.y(), self.z()-other.z() )
return Vector3D( self.x()-other.x(), self.y()-other.y(), self.z()-other.z() )
def __eq__(self,other):
return self.x()==other.x() and self.y()==other.y() and self.z()==other.z()
def __ne__(self,other):
return not (self==other)
class Vector3D:
def __init__(self,x=0,y=0,z=0):
self.coordinates = [x,y,z]
def x(self):
return self.coordinates[0]
def y(self):
return self.coordinates[1]
def z(self):
return self.coordinates[2]
def __repr__(self):
return "Vector3D("+str(self.x())+","+str(self.y())+","+str(self.z())+")"
def __str__(self):
return "V("+str(self.x())+","+str(self.y())+","+str(self.z())+")"
def get(self):
return self.coordinates
def returnCopy(self):
return Vector3D( self.x(), self.y(), self.z() )
def asPoint3D(self):
return Point3D( self.x(), self.y(), self.z() )
def lengthSquared(self):
return self.x()*self.x()+self.y()*self.y()+self.z()*self.z()
def length(self):
return math.sqrt( self.lengthSquared() )
def normalized(self):
l = self.length()
if ( l > 0 ):
return Vector3D( self.x()/l, self.y()/l, self.z()/l )
return self.returnCopy()
def __neg__(self):
return Vector3D( -self.x(), -self.y(), -self.z() )
def __add__(self,other):
if isinstance(other,Point3D):
return Point3D( self.x()+other.x(), self.y()+other.y(), self.z()+other.z() )
return Vector3D( self.x()+other.x(), self.y()+other.y(), self.z()+other.z() )
def __sub__(self,other):
return Vector3D( self.x()-other.x(), self.y()-other.y(), self.z()-other.z() )
def __mul__(self,other):
if isinstance(other,Vector3D):
# dot product
return self.x()*other.x() + self.y()*other.y() + self.z()*other.z()
# scalar product
return Vector3D( self.x()*other, self.y()*other, self.z()*other )
def __rmul__(self,other):
return self*other
def __div__(self,other):
return Vector3D( self.x()/other, self.y()/other, self.z()/other )
def __xor__(self,other): # cross product
return Vector3D(
self.y()*other.z() - self.z()*other.y(),
self.z()*other.x() - self.x()*other.z(),
self.x()*other.y() - self.y()*other.x() )
def __eq__(self,other):
return self.x()==other.x() and self.y()==other.y() and self.z()==other.z()
def __ne__(self,other):
return not (self==other)
class Matrix4x4:
def __init__(self):
self.setToIdentity()
def __str__(self):
return str(self.m[0:4]) + "\n" + str(self.m[4:8]) + "\n" + str(self.m[8:12]) + "\n" + str(self.m[12:16])
def get(self):
return self.m
def returnCopy(self):
M = Matrix4x4()
M.m = list(self.m) # copy the list
return M
def setToIdentity(self):
self.m = [ 1.0, 0.0, 0.0, 0.0,
0.0, 1.0, 0.0, 0.0,
0.0, 0.0, 1.0, 0.0,
0.0, 0.0, 0.0, 1.0 ]
@staticmethod
def translation( vector3D ):
M = Matrix4x4()
M.m[ 0] = 1.0; M.m[ 4] = 0.0; M.m[ 8] = 0.0; M.m[12] = vector3D.x();
M.m[ 1] = 0.0; M.m[ 5] = 1.0; M.m[ 9] = 0.0; M.m[13] = vector3D.y();
M.m[ 2] = 0.0; M.m[ 6] = 0.0; M.m[10] = 1.0; M.m[14] = vector3D.z();
M.m[ 3] = 0.0; M.m[ 7] = 0.0; M.m[11] = 0.0; M.m[15] = 1.0;
return M
@staticmethod
def rotationAroundOrigin( angleInRadians, axisVector ):
# Note: assumes axisVector is normalized
c = math.cos( angleInRadians )
s = math.sin( angleInRadians )
one_minus_c = 1-c
M = Matrix4x4()
M.m[ 0] = c + one_minus_c * axisVector.x()*axisVector.x()
M.m[ 5] = c + one_minus_c * axisVector.y()*axisVector.y()
M.m[10] = c + one_minus_c * axisVector.z()*axisVector.z()
M.m[ 1] = M.m[ 4] = one_minus_c * axisVector.x()*axisVector.y();
M.m[ 2] = M.m[ 8] = one_minus_c * axisVector.x()*axisVector.z();
M.m[ 6] = M.m[ 9] = one_minus_c * axisVector.y()*axisVector.z();
xs = axisVector.x() * s
ys = axisVector.y() * s
zs = axisVector.z() * s
M.m[ 1] += zs; M.m[ 4] -= zs;
M.m[ 2] -= ys; M.m[ 8] += ys;
M.m[ 6] += xs; M.m[ 9] -= xs;
M.m[12] = 0.0;
M.m[13] = 0.0;
M.m[14] = 0.0;
M.m[ 3] = 0.0; M.m[ 7] = 0.0; M.m[11] = 0.0; M.m[15] = 1.0;
return M
@staticmethod
def rotation( angleInRadians, axisVector, originPoint ):
v = originPoint.asVector3D()
return Matrix4x4.translation(v) * Matrix4x4.rotationAroundOrigin(angleInRadians,axisVector) * Matrix4x4.translation(- v)
@staticmethod
def uniformScaleAroundOrigin(scaleFactor):
M = Matrix4x4()
M.m[ 0] = scaleFactor; M.m[ 4] = 0.0; M.m[ 8] = 0.0; M.m[12] = 0.0;
M.m[ 1] = 0.0; M.m[ 5] = scaleFactor; M.m[ 9] = 0.0; M.m[13] = 0.0;
M.m[ 2] = 0.0; M.m[ 6] = 0.0; M.m[10] = scaleFactor; M.m[14] = 0.0;
M.m[ 3] = 0.0; M.m[ 7] = 0.0; M.m[11] = 0.0; M.m[15] = 1.0;
return M
@staticmethod
def uniformScale( scaleFactor, originPoint ):
v = originPoint.asVector3D()
return Matrix4x4.translation(v) * Matrix4x4.uniformScaleAroundOrigin(scaleFactor) * Matrix4x4.translation(- v)
@staticmethod
def lookAt( eyePoint, targetPoint, upVector, isInverted ):
# step one: generate a rotation matrix
z = (eyePoint-targetPoint).normalized()
y = upVector
x = y ^ z # cross product
y = z ^ x # cross product
# Cross product gives area of parallelogram, which is < 1 for
# non-perpendicular unit-length vectors; so normalize x and y.
x = x.normalized()
y = y.normalized()
M = Matrix4x4()
if isInverted :
# the rotation matrix
M.m[ 0] = x.x(); M.m[ 4] = y.x(); M.m[ 8] = z.x(); M.m[12] = 0.0;
M.m[ 1] = x.y(); M.m[ 5] = y.y(); M.m[ 9] = z.y(); M.m[13] = 0.0;
M.m[ 2] = x.z(); M.m[ 6] = y.z(); M.m[10] = z.z(); M.m[14] = 0.0;
M.m[ 3] = 0.0; M.m[ 7] = 0.0; M.m[11] = 0.0; M.m[15] = 1.0;
# step two: premultiply by a translation matrix
return Matrix4x4.translation( eyePoint.asVector3D() ) * M
else:
# the rotation matrix
M.m[ 0] = x.x(); M.m[ 4] = x.y(); M.m[ 8] = x.z(); M.m[12] = 0.0;
M.m[ 1] = y.x(); M.m[ 5] = y.y(); M.m[ 9] = y.z(); M.m[13] = 0.0;
M.m[ 2] = z.x(); M.m[ 6] = z.y(); M.m[10] = z.z(); M.m[14] = 0.0;
M.m[ 3] = 0.0; M.m[ 7] = 0.0; M.m[11] = 0.0; M.m[15] = 1.0;
# step two: postmultiply by a translation matrix
return M * Matrix4x4.translation( - eyePoint.asVector3D() )
def __mul__(a,b): # note: a is really self
if isinstance(b,Matrix4x4):
M = Matrix4x4()
M.m[ 0] = a.m[ 0]*b.m[ 0] + a.m[ 4]*b.m[ 1] + a.m[ 8]*b.m[ 2] + a.m[12]*b.m[ 3];
M.m[ 1] = a.m[ 1]*b.m[ 0] + a.m[ 5]*b.m[ 1] + a.m[ 9]*b.m[ 2] + a.m[13]*b.m[ 3];
M.m[ 2] = a.m[ 2]*b.m[ 0] + a.m[ 6]*b.m[ 1] + a.m[10]*b.m[ 2] + a.m[14]*b.m[ 3];
M.m[ 3] = a.m[ 3]*b.m[ 0] + a.m[ 7]*b.m[ 1] + a.m[11]*b.m[ 2] + a.m[15]*b.m[ 3];
M.m[ 4] = a.m[ 0]*b.m[ 4] + a.m[ 4]*b.m[ 5] + a.m[ 8]*b.m[ 6] + a.m[12]*b.m[ 7];
M.m[ 5] = a.m[ 1]*b.m[ 4] + a.m[ 5]*b.m[ 5] + a.m[ 9]*b.m[ 6] + a.m[13]*b.m[ 7];
M.m[ 6] = a.m[ 2]*b.m[ 4] + a.m[ 6]*b.m[ 5] + a.m[10]*b.m[ 6] + a.m[14]*b.m[ 7];
M.m[ 7] = a.m[ 3]*b.m[ 4] + a.m[ 7]*b.m[ 5] + a.m[11]*b.m[ 6] + a.m[15]*b.m[ 7];
M.m[ 8] = a.m[ 0]*b.m[ 8] + a.m[ 4]*b.m[ 9] + a.m[ 8]*b.m[10] + a.m[12]*b.m[11];
M.m[ 9] = a.m[ 1]*b.m[ 8] + a.m[ 5]*b.m[ 9] + a.m[ 9]*b.m[10] + a.m[13]*b.m[11];
M.m[10] = a.m[ 2]*b.m[ 8] + a.m[ 6]*b.m[ 9] + a.m[10]*b.m[10] + a.m[14]*b.m[11];
M.m[11] = a.m[ 3]*b.m[ 8] + a.m[ 7]*b.m[ 9] + a.m[11]*b.m[10] + a.m[15]*b.m[11];
M.m[12] = a.m[ 0]*b.m[12] + a.m[ 4]*b.m[13] + a.m[ 8]*b.m[14] + a.m[12]*b.m[15];
M.m[13] = a.m[ 1]*b.m[12] + a.m[ 5]*b.m[13] + a.m[ 9]*b.m[14] + a.m[13]*b.m[15];
M.m[14] = a.m[ 2]*b.m[12] + a.m[ 6]*b.m[13] + a.m[10]*b.m[14] + a.m[14]*b.m[15];
M.m[15] = a.m[ 3]*b.m[12] + a.m[ 7]*b.m[13] + a.m[11]*b.m[14] + a.m[15]*b.m[15];
return M
elif isinstance(b,Vector3D):
# We treat the vector as if its (homogeneous) 4th component were zero.
return Vector3D(
a.m[ 0]*b.x() + a.m[ 4]*b.y() + a.m[ 8]*b.z(), # + a.m[12]*b.w(),
a.m[ 1]*b.x() + a.m[ 5]*b.y() + a.m[ 9]*b.z(), # + a.m[13]*b.w(),
a.m[ 2]*b.x() + a.m[ 6]*b.y() + a.m[10]*b.z() # + a.m[14]*b.w(),
# a.m[ 3]*b.x() + a.m[ 7]*b.y() + a.m[11]*b.z() + a.m[15]*b.w()
)
elif isinstance(b,Point3D):
# We treat the point as if its (homogeneous) 4th component were one.
return Point3D(
a.m[ 0]*b.x() + a.m[ 4]*b.y() + a.m[ 8]*b.z() + a.m[12],
a.m[ 1]*b.x() + a.m[ 5]*b.y() + a.m[ 9]*b.z() + a.m[13],
a.m[ 2]*b.x() + a.m[ 6]*b.y() + a.m[10]*b.z() + a.m[14]
)