def decompose(self):
"""Decomposes the matrix into a translation, rotation and scaling part.
Returns a tuple (translation, rotation, scaling). The
translation and scaling parts are given as vec3's, the rotation
is still given as a mat4.
"""
dummy = self.ortho()
dummy.setRow(3,_vec4(0.0, 0.0, 0.0, 1.0))
dummy.setColumn(3,_vec4(0.0, 0.0, 0.0, 1.0))
x = dummy.getColumn(0)
y = dummy.getColumn(1)
z = dummy.getColumn(2)
xl = x.length()
yl = y.length()
zl = z.length()
scale = _vec3(xl,yl,zl)
x/=xl
y/=yl
z/=zl
dummy.setColumn(0,x)
dummy.setColumn(1,y)
dummy.setColumn(2,z)
if dummy.determinant()<0.0:
dummy.setColumn(0,-x)
scale.x=-scale.x
return (_vec3(self.mlist[3], self.mlist[7], self.mlist[11]),
dummy,
scale)
def decompose(self):
"""Decomposes the matrix into a translation, rotation and scaling part.
Returns a tuple (translation, rotation, scaling). The
translation and scaling parts are given as vec3's, the rotation
is still given as a mat4.
"""
try:
dummy = self.ortho()
except ZeroDivisionError:
return (_vec3(0), mat4(1.0), _vec3(0))
dummy.setRow(3, _vec4(0.0, 0.0, 0.0, 1.0))
dummy.setColumn(3, _vec4(0.0, 0.0, 0.0, 1.0))
x = dummy.getColumn(0)
y = dummy.getColumn(1)
z = dummy.getColumn(2)
xl = x.length()
yl = y.length()
zl = z.length()
scale = _vec3(xl, yl, zl)
x /= xl
y /= yl
z /= zl
dummy.setColumn(0, x)
dummy.setColumn(1, y)
dummy.setColumn(2, z)
if dummy.determinant() < 0.0:
dummy.setColumn(0, -x)
scale.x = -scale.x
return (_vec3(self.mlist[3], self.mlist[7],
self.mlist[11]), dummy, scale)
def getColumn(self, idx):
"""Return column (as vec4)."""
m = self.mlist
if idx == 0: return _vec4(m[0], m[4], m[8], m[12])
elif idx == 1: return _vec4(m[1], m[5], m[9], m[13])
elif idx == 2: return _vec4(m[2], m[6], m[10], m[14])
elif idx == 3: return _vec4(m[3], m[7], m[11], m[15])
else:
raise IndexError, "index out of range"
def getColumn(self, idx):
"""Return column (as vec4)."""
m=self.mlist
if idx==0: return _vec4(m[0], m[4], m[8], m[12])
elif idx==1: return _vec4(m[1], m[5], m[9], m[13])
elif idx==2: return _vec4(m[2], m[6], m[10], m[14])
elif idx==3: return _vec4(m[3], m[7], m[11], m[15])
else:
raise IndexError,"index out of range"
def getColumn(self, index):
"""Return column (as vec4)."""
if type(index)==int:
m=self.mlist
if index==0: return _vec4(m[0], m[4], m[8], m[12])
elif index==1: return _vec4(m[1], m[5], m[9], m[13])
elif index==2: return _vec4(m[2], m[6], m[10], m[14])
elif index==3: return _vec4(m[3], m[7], m[11], m[15])
else:
raise IndexError("index out of range")
else:
raise TypeError("index must be integer or 2-tuple")
def getColumn(self, index):
"""Return column (as vec4)."""
if type(index) == int:
m = self.mlist
if index == 0: return _vec4(m[0], m[4], m[8], m[12])
elif index == 1: return _vec4(m[1], m[5], m[9], m[13])
elif index == 2: return _vec4(m[2], m[6], m[10], m[14])
elif index == 3: return _vec4(m[3], m[7], m[11], m[15])
else:
raise IndexError("index out of range")
else:
raise TypeError("index must be integer or 2-tuple")
def __rmul__(self, other):
T = type(other)
# scalar*mat4
if T == types.FloatType or T == types.IntType or T == types.LongType:
return mat4(map(lambda x, other=other: other * x, self.mlist))
# vec4*mat4
if isinstance(other, _vec4):
m11, m12, m13, m14, m21, m22, m23, m24, m31, m32, m33, m34, m41, m42, m43, m44 = self.mlist
return _vec4(
other.x * m11 + other.y * m21 + other.z * m31 + other.w * m41,
other.x * m12 + other.y * m22 + other.z * m32 + other.w * m42,
other.x * m13 + other.y * m23 + other.z * m33 + other.w * m43,
other.x * m14 + other.y * m24 + other.z * m34 + other.w * m44)
# vec3*mat4
if isinstance(other, _vec3):
m11, m12, m13, m14, m21, m22, m23, m24, m31, m32, m33, m34, m41, m42, m43, m44 = self.mlist
w = float(other.x * m14 + other.y * m24 + other.z * m34 + m44)
return _vec3(
other.x * m11 + other.y * m21 + other.z * m31 + m41,
other.x * m12 + other.y * m22 + other.z * m32 + m42,
other.x * m13 + other.y * m23 + other.z * m33 + m43) / w
# mat4*mat4
if isinstance(other, mat4):
return self.__mul__(other)
# unsupported
else:
raise TypeError, "unsupported operand type for *"
def __getitem__(self, key):
if type(key)==types.IntType:
if key<0 or key>3:
raise IndexError("index out of range")
m=self.mlist
if key==0: return _vec4(m[0],m[4],m[8],m[12])
elif key==1: return _vec4(m[1],m[5],m[9],m[13])
elif key==2: return _vec4(m[2],m[6],m[10],m[14])
elif key==3: return _vec4(m[3],m[7],m[11],m[15])
elif type(key)==types.TupleType:
i,j=key
if i<0 or i>3 or j<0 or j>3:
raise IndexError("index out of range")
return self.mlist[i*4+j]
else:
raise TypeError("index must be integer or 2-tuple")
def __rmul__(self, other):
T = type(other)
# scalar*mat4
if T==types.FloatType or T==types.IntType or T==types.LongType:
return mat4(map(lambda x,other=other: other*x, self.mlist))
# vec4*mat4
if isinstance(other, _vec4):
m11,m12,m13,m14,m21,m22,m23,m24,m31,m32,m33,m34,m41,m42,m43,m44 = self.mlist
return _vec4(other.x*m11 + other.y*m21 + other.z*m31 + other.w*m41,
other.x*m12 + other.y*m22 + other.z*m32 + other.w*m42,
other.x*m13 + other.y*m23 + other.z*m33 + other.w*m43,
other.x*m14 + other.y*m24 + other.z*m34 + other.w*m44)
# vec3*mat4
if isinstance(other, _vec3):
m11,m12,m13,m14,m21,m22,m23,m24,m31,m32,m33,m34,m41,m42,m43,m44 = self.mlist
w = float(other.x*m14 + other.y*m24 + other.z*m34 + m44)
return _vec3(other.x*m11 + other.y*m21 + other.z*m31 + m41,
other.x*m12 + other.y*m22 + other.z*m32 + m42,
other.x*m13 + other.y*m23 + other.z*m33 + m43)/w
# mat4*mat4
if isinstance(other, mat4):
return self.__mul__(other)
# unsupported
else:
raise TypeError("unsupported operand type for *")
def __getitem__(self, key):
if type(key) == types.IntType:
if key < 0 or key > 3:
raise IndexError("index out of range")
m = self.mlist
if key == 0: return _vec4(m[0], m[4], m[8], m[12])
elif key == 1: return _vec4(m[1], m[5], m[9], m[13])
elif key == 2: return _vec4(m[2], m[6], m[10], m[14])
elif key == 3: return _vec4(m[3], m[7], m[11], m[15])
elif type(key) == types.TupleType:
i, j = key
if i < 0 or i > 3 or j < 0 or j > 3:
raise IndexError("index out of range")
return self.mlist[i * 4 + j]
else:
raise TypeError("index must be integer or 2-tuple")
def rotateVec(self, v):
"""Return the rotated vector v.
The quaternion must be a unit quaternion.
This operation is equivalent to turning v into a quat, computing
self*v*self.conjugate() and turning the result back into a vec3.
"""
u = _vec3(v[:3])
ww = self.w * self.w
xx = self.x * self.x
yy = self.y * self.y
zz = self.z * self.z
wx = self.w * self.x
wy = self.w * self.y
wz = self.w * self.z
xy = self.x * self.y
xz = self.x * self.z
yz = self.y * self.z
u = (ww * u.x + xx * u.x - yy * u.x - zz * u.x + 2 *
((xy - wz) * u.y + (xz + wy) * u.z), ww * u.y - xx * u.y +
yy * u.y - zz * u.y + 2 * ((xy + wz) * u.x + (yz - wx) * u.z),
ww * u.z - xx * u.z - yy * u.z + zz * u.z + 2 * ((xz - wy) * u.x +
(yz + wx) * u.y))
if isinstance(v, _vec4):
return _vec4(u)
return _vec3(u)
def rotateVec(self, v):
"""Return the rotated vector v.
The quaternion must be a unit quaternion.
This operation is equivalent to turning v into a quat, computing
self*v*self.conjugate() and turning the result back into a vec3.
"""
u = _vec3(v[:3])
ww = self.w*self.w
xx = self.x*self.x
yy = self.y*self.y
zz = self.z*self.z
wx = self.w*self.x
wy = self.w*self.y
wz = self.w*self.z
xy = self.x*self.y
xz = self.x*self.z
yz = self.y*self.z
u = (ww*u.x + xx*u.x - yy*u.x - zz*u.x + 2*((xy-wz)*u.y + (xz+wy)*u.z),
ww*u.y - xx*u.y + yy*u.y - zz*u.y + 2*((xy+wz)*u.x + (yz-wx)*u.z),
ww*u.z - xx*u.z - yy*u.z + zz*u.z + 2*((xz-wy)*u.x + (yz+wx)*u.y))
if isinstance(v, _vec4):
return _vec4(u)
return _vec3(u)
def __mul__(self, other):
"""Multiplication.
>>> M=mat4(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16)
>>> print M*2.0
[ 2.0000, 4.0000, 6.0000, 8.0000]
[ 10.0000, 12.0000, 14.0000, 16.0000]
[ 18.0000, 20.0000, 22.0000, 24.0000]
[ 26.0000, 28.0000, 30.0000, 32.0000]
>>> print 2.0*M
[ 2.0000, 4.0000, 6.0000, 8.0000]
[ 10.0000, 12.0000, 14.0000, 16.0000]
[ 18.0000, 20.0000, 22.0000, 24.0000]
[ 26.0000, 28.0000, 30.0000, 32.0000]
>>> print M*M
[ 90.0000, 100.0000, 110.0000, 120.0000]
[ 202.0000, 228.0000, 254.0000, 280.0000]
[ 314.0000, 356.0000, 398.0000, 440.0000]
[ 426.0000, 484.0000, 542.0000, 600.0000]
>>> print M*_vec3(1,2,3)
(0.1765, 0.4510, 0.7255)
>>> print _vec3(1,2,3)*M
(0.7083, 0.8056, 0.9028)
"""
T = type(other)
# mat4*scalar
if T == types.FloatType or T == types.IntType or T == types.LongType:
return mat4(map(lambda x, other=other: x * other, self.mlist))
# mat4*vec3
if isinstance(other, _vec3):
m11, m12, m13, m14, m21, m22, m23, m24, m31, m32, m33, m34, m41, m42, m43, m44 = self.mlist
w = float(m41 * other.x + m42 * other.y + m43 * other.z + m44)
return _vec3(
m11 * other.x + m12 * other.y + m13 * other.z + m14,
m21 * other.x + m22 * other.y + m23 * other.z + m24,
m31 * other.x + m32 * other.y + m33 * other.z + m34) / w
# mat4*vec4
if isinstance(other, _vec4):
m11, m12, m13, m14, m21, m22, m23, m24, m31, m32, m33, m34, m41, m42, m43, m44 = self.mlist
return _vec4(
m11 * other.x + m12 * other.y + m13 * other.z + m14 * other.w,
m21 * other.x + m22 * other.y + m23 * other.z + m24 * other.w,
m31 * other.x + m32 * other.y + m33 * other.z + m34 * other.w,
m41 * other.x + m42 * other.y + m43 * other.z + m44 * other.w)
# mat4*mat4
if isinstance(other, mat4):
m11, m12, m13, m14, m21, m22, m23, m24, m31, m32, m33, m34, m41, m42, m43, m44 = self.mlist
n11, n12, n13, n14, n21, n22, n23, n24, n31, n32, n33, n34, n41, n42, n43, n44 = other.mlist
return mat4(m11 * n11 + m12 * n21 + m13 * n31 + m14 * n41,
m11 * n12 + m12 * n22 + m13 * n32 + m14 * n42,
m11 * n13 + m12 * n23 + m13 * n33 + m14 * n43,
m11 * n14 + m12 * n24 + m13 * n34 + m14 * n44,
m21 * n11 + m22 * n21 + m23 * n31 + m24 * n41,
m21 * n12 + m22 * n22 + m23 * n32 + m24 * n42,
m21 * n13 + m22 * n23 + m23 * n33 + m24 * n43,
m21 * n14 + m22 * n24 + m23 * n34 + m24 * n44,
m31 * n11 + m32 * n21 + m33 * n31 + m34 * n41,
m31 * n12 + m32 * n22 + m33 * n32 + m34 * n42,
m31 * n13 + m32 * n23 + m33 * n33 + m34 * n43,
m31 * n14 + m32 * n24 + m33 * n34 + m34 * n44,
m41 * n11 + m42 * n21 + m43 * n31 + m44 * n41,
m41 * n12 + m42 * n22 + m43 * n32 + m44 * n42,
m41 * n13 + m42 * n23 + m43 * n33 + m44 * n43,
m41 * n14 + m42 * n24 + m43 * n34 + m44 * n44)
# unsupported
else:
raise TypeError, "unsupported operand type for *"
def getDiag(self):
"""Return the diagonal."""
return _vec4(self.mlist[0], self.mlist[5], self.mlist[10], self.mlist[15])
def __mul__(self, other):
"""Multiplication.
>>> M=mat4(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16)
>>> print M*2.0
[ 2.0000, 4.0000, 6.0000, 8.0000]
[ 10.0000, 12.0000, 14.0000, 16.0000]
[ 18.0000, 20.0000, 22.0000, 24.0000]
[ 26.0000, 28.0000, 30.0000, 32.0000]
>>> print 2.0*M
[ 2.0000, 4.0000, 6.0000, 8.0000]
[ 10.0000, 12.0000, 14.0000, 16.0000]
[ 18.0000, 20.0000, 22.0000, 24.0000]
[ 26.0000, 28.0000, 30.0000, 32.0000]
>>> print M*M
[ 90.0000, 100.0000, 110.0000, 120.0000]
[ 202.0000, 228.0000, 254.0000, 280.0000]
[ 314.0000, 356.0000, 398.0000, 440.0000]
[ 426.0000, 484.0000, 542.0000, 600.0000]
>>> print M*_vec3(1,2,3)
(0.1765, 0.4510, 0.7255)
>>> print _vec3(1,2,3)*M
(0.7083, 0.8056, 0.9028)
"""
T = type(other)
# mat4*scalar
if T==types.FloatType or T==types.IntType or T==types.LongType:
return mat4(map(lambda x,other=other: x*other, self.mlist))
# mat4*vec3
if isinstance(other, _vec3):
m11,m12,m13,m14,m21,m22,m23,m24,m31,m32,m33,m34,m41,m42,m43,m44 = self.mlist
w = float(m41*other.x + m42*other.y + m43*other.z + m44)
return _vec3(m11*other.x + m12*other.y + m13*other.z + m14,
m21*other.x + m22*other.y + m23*other.z + m24,
m31*other.x + m32*other.y + m33*other.z + m34)/w
# mat4*vec4
if isinstance(other, _vec4):
m11,m12,m13,m14,m21,m22,m23,m24,m31,m32,m33,m34,m41,m42,m43,m44 = self.mlist
return _vec4(m11*other.x + m12*other.y + m13*other.z + m14*other.w,
m21*other.x + m22*other.y + m23*other.z + m24*other.w,
m31*other.x + m32*other.y + m33*other.z + m34*other.w,
m41*other.x + m42*other.y + m43*other.z + m44*other.w)
# mat4*mat4
if isinstance(other, mat4):
m11,m12,m13,m14,m21,m22,m23,m24,m31,m32,m33,m34,m41,m42,m43,m44 = self.mlist
n11,n12,n13,n14,n21,n22,n23,n24,n31,n32,n33,n34,n41,n42,n43,n44 = other.mlist
return mat4( m11*n11+m12*n21+m13*n31+m14*n41,
m11*n12+m12*n22+m13*n32+m14*n42,
m11*n13+m12*n23+m13*n33+m14*n43,
m11*n14+m12*n24+m13*n34+m14*n44,
m21*n11+m22*n21+m23*n31+m24*n41,
m21*n12+m22*n22+m23*n32+m24*n42,
m21*n13+m22*n23+m23*n33+m24*n43,
m21*n14+m22*n24+m23*n34+m24*n44,
m31*n11+m32*n21+m33*n31+m34*n41,
m31*n12+m32*n22+m33*n32+m34*n42,
m31*n13+m32*n23+m33*n33+m34*n43,
m31*n14+m32*n24+m33*n34+m34*n44,
m41*n11+m42*n21+m43*n31+m44*n41,
m41*n12+m42*n22+m43*n32+m44*n42,
m41*n13+m42*n23+m43*n33+m44*n43,
m41*n14+m42*n24+m43*n34+m44*n44)
# unsupported
else:
raise TypeError("unsupported operand type for *")
def getDiag(self):
"""Return the diagonal."""
return _vec4(self.mlist[0], self.mlist[5], self.mlist[10],
self.mlist[15])
