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 *")