def lookAt(eye, center, up):
''' Matrix 4x4 lookAt function.'''
f = (center - eye).normalize()
u = up.normalize()
s = vector.cross(f, u).normalize()
u = vector.cross(s, f)
output = [[s.vector[0], u.vector[0], -f.vector[0], 0.0],
[s.vector[1], u.vector[1], -f.vector[1], 0.0],
[s.vector[2], u.vector[2], -f.vector[2], 0.0],
[-s.dot(eye), -u.dot(eye), f.dot(eye), 1.0]]
return Matrix(4, data=output)
def lookAt(eye, center, up):
''' Matrix 4x4 lookAt function.'''
f = (center - eye).normalize()
u = up.normalize()
s = vector.cross(f, u).normalize()
u = vector.cross(s, f)
output = [[s.vector[0], u.vector[0], -f.vector[0], 0.0],
[s.vector[1], u.vector[1], -f.vector[1], 0.0],
[s.vector[2], u.vector[2], -f.vector[2], 0.0],
[-s.dot(eye), -u.dot(eye),
f.dot(eye), 1.0]]
return Matrix(4, data=output)
def fromPoints(self, a, b, c):
'''Calculate the plane from A,B,C.'''
self.a = a
self.b = b
self.c = c
self.normal = vector.cross(b - a, c - a).normalize()
self.d = self.normal.dot(self.a)
def fromCoeffs(self, a, b, c, d):
''' Create the plane from A,B,C,D. '''
self.a = a
self.b = b
self.c = c
self.d = d
self.normal = vector.cross(b - a, c - a).normalize()
def fromPoints(self, a, b, c):
"""Calculate the plane from A,B,C."""
self.a = a
self.b = b
self.c = c
self.normal = vector.cross(b - a, c - a).normalize()
self.d = self.normal.dot(self.a)
def fromCoeffs(self, a, b, c, d):
""" Create the plane from A,B,C,D. """
self.a = a
self.b = b
self.c = c
self.d = d
self.normal = vector.cross(b - a, c - a).normalize()
def processLine(self, simplex):
'''Determines which Veronoi region of a tetrehedron the origin is in, utilizing the preserved winding of the simplex to eliminate certain regions'''
a = simplex[1]
b = simplex[0]
ab = b - a
aO = -a
if(ab.isInSameDirection(aO)):
#dot = ab.dot(aO)
#angle = math.acos(dot / ab.magnitude() * aO.magnitude())
self.direction = vector.cross(vector.cross(ab, aO), ab)
else:
simplex.remove(b)
self.direction = aO
return False
def processTetrehedron(self, simplex):
'''Determines which Veronoi region of a tetrehedron the origin is in, utilizing the preserved winding of the simplex to eliminate certain regions'''
a = simplex[3]
b = simplex[2]
c = simplex[1]
d = simplex[0]
ac = c - a
ad = d - a
ab = b - a
#bc = c - b
#bd = d - b
acd = vector.cross(ad, ac)
abd = vector.cross(ab, ad)
abc = vector.cross(ac, ab)
aO = -a
if (abc.isInSameDirection(aO)):
if (vector.cross(abc, ac).isInSameDirection(aO)):
simplex.remove(b)
simplex.remove(d)
self.direction = vector.cross(vector.cross(ac, aO), ac)
elif(vector.cross(ab, abc).isInSameDirection(aO)):
simplex.remove(c)
simplex.remove(d)
self.direction = vector.cross(vector.cross(ab, aO), ab)
else:
simplex.remove(d)
self.direction = abc
elif (acd.isInSameDirection(aO)):
if (vector.cross(acd, ad).isInSameDirection(aO)):
simplex.remove(b)
simplex.remove(c)
self.direction = vector.cross(vector.cross(ad, aO), ad)
elif(vector.cross(ac, acd).isInSameDirection(aO)):
simplex.remove(b)
simplex.remove(d)
self.direction = vector.cross(vector.cross(ac, aO), ac)
else:
simplex.remove(b)
self.direction = acd
elif(abd.isInSameDirection(aO)):
if(vector.cross(abd, ab).isInSameDirection(aO)):
simplex.remove(b)
simplex.remove(d)
self.direction = vector.cross(vector.cross(ab, aO), ab)
elif(vector.cross(ab, abd).isInSameDirection(aO)):
simplex.remove(b)
simplex.remove(c)
self.direction = vector.cross(vector.cross(ad, aO), ad)
else:
simplex.remove(c)
self.direction = abd
else:
return True
return False
def processTriangle(self, simplex):
'''Determines which Veronoi region of a tetrehedron the origin is in, utilizing the preserved winding of the simplex to eliminate certain regions'''
a = simplex[2]
b = simplex[1]
c = simplex[0]
ab = b - a
ac = c - a
abc = vector.cross(ab, ac)
aO = -a
acNormal = vector.cross(abc, ac)
abNormal = vector.cross(ab, abc)
if(acNormal.isInSameDirection(aO)):
if(ac.isInSameDirection(aO)):
simplex.remove(b)
self.direction = vector.cross(vector.cross(ac, aO), ac)
else:
if(ab.isInSameDirection(aO)):
simplex.remove(c)
self.direction = vector.cross(vector.cross(ab, aO), ab)
else:
simplex.remove(b)
simplex.remove(c)
self.direction = aO
else:
if (abNormal.isInSameDirection(aO)):
if(ab.isInSameDirection(aO)):
simplex.remove(c)
self.direction = vector.cross(vector.cross(ab, aO), ab)
else:
simplex.remove(b)
simplex.remove(c)
self.direction = aO
else:
if(abc.isInSameDirection(aO)):
self.direction = vector.cross(vector.cross(abc, aO), abc)
else:
self.direction = vector.cross(vector.cross(-abc, aO), -abc)
return False
