void Matrix4::makeInverseTransform(const Vector3& position, const Vector3& scale, const Quaternion& orientation)
{
Vector3 invTranslate = -position;
Vector3 invScale(1 / scale.x, 1 / scale.y, 1 / scale.z);
Quaternion invRot = orientation.inverse();
invTranslate *= invScale;
invTranslate = invRot.rotate(invTranslate);
Matrix3 rot3x3, scale3x3;
rot3x3 = invRot.toRotationMatrix();
scale3x3 = Matrix3::ZERO;
scale3x3[0][0] = invScale.x;
scale3x3[1][1] = invScale.y;
scale3x3[2][2] = invScale.z;
*this = scale3x3 * rot3x3;
this->setTrans(invTranslate);
d[3][0] = 0; d[3][1] = 0; d[3][2] = 0; d[3][3] = 1;
}
//-----------------------------------------------------------------------
void Matrix4::makeInverseTransform(const Vector3& position, const Vector3& scale, const Quaternion& orientation)
{
// Invert the parameters
Vector3 invTranslate = -position;
Vector3 invScale(1 / scale.x, 1 / scale.y, 1 / scale.z);
Quaternion invRot = orientation.Inverse();
// Because we're inverting, order is translation, rotation, scale
// So make translation relative to scale & rotation
invTranslate *= invScale; // scale
invTranslate = invRot * invTranslate; // rotate
// Next, make a 3x3 rotation matrix and apply inverse scale
Matrix3 rot3x3, scale3x3;
invRot.ToRotationMatrix(rot3x3);
scale3x3 = Matrix3::ZERO;
scale3x3[0][0] = invScale.x;
scale3x3[1][1] = invScale.y;
scale3x3[2][2] = invScale.z;
// Set up final matrix with scale, rotation and translation
*this = scale3x3 * rot3x3;
this->setTrans(invTranslate);
// No projection term
m[3][0] = 0; m[3][1] = 0; m[3][2] = 0; m[3][3] = 1;
}
//-----------------------------------------------------------------------
void Matrix4::MakeInverseTransform(Vector3 position, Vector3 scale, Quaternion orientation)
{
// Invert the parameters
Vector3 invTranslate = -position;
Vector3 invScale(1 / scale.x, 1 / scale.y, 1 / scale.z);
Quaternion invRot = orientation.Inverse();
// Because we're inverting, order is translation, rotation, scale
// So make translation relative to scale & rotation
invTranslate *= invScale; // scale
invTranslate = invRot * invTranslate; // rotate
// Next, make a 3x3 rotation matrix and apply inverse scale
Matrix3^ rot3x3, ^scale3x3;
rot3x3 = invRot.ToRotationMatrix();
scale3x3 = Matrix3::ZERO;
scale3x3->m00 = invScale.x;
scale3x3->m11 = invScale.y;
scale3x3->m22 = invScale.z;
// Set up final matrix with scale, rotation and translation
*this = scale3x3 * rot3x3;
this->SetTrans(invTranslate);
// No projection term
m30 = 0; m31 = 0; m32 = 0; m33 = 1;
}
void Matrix3x4::Decompose(Vector3& translation, Quaternion& rotation, Vector3& scale) const
{
translation.x_ = m03_;
translation.y_ = m13_;
translation.z_ = m23_;
scale.x_ = sqrtf(m00_ * m00_ + m10_ * m10_ + m20_ * m20_);
scale.y_ = sqrtf(m01_ * m01_ + m11_ * m11_ + m21_ * m21_);
scale.z_ = sqrtf(m02_ * m02_ + m12_ * m12_ + m22_ * m22_);
Vector3 invScale(1.0f / scale.x_, 1.0f / scale.y_, 1.0f / scale.z_);
rotation = Quaternion(ToMatrix3().Scaled(invScale));
}
void Matrix4::makeInverseTransform(const Vector3& position, const Vector3& scale, const Quaternion& orientation)
{
Vector3 invTranslate = -position;
Vector3 invScale(1 / scale.x, 1 / scale.y, 1 / scale.z);
Quaternion invRot = orientation.getInverse();
invTranslate *= invScale;
invTranslate = invRot * invTranslate;
Matrix3 rot3x3 = invRot.ToRotationMatrix();
m[0][0] = invScale.x * rot3x3[0][0]; m[0][1] = invScale.x * rot3x3[0][1]; m[0][2] = invScale.x * rot3x3[0][2]; m[0][3] = invTranslate.x;
m[1][0] = invScale.y * rot3x3[1][0]; m[1][1] = invScale.y * rot3x3[1][1]; m[1][2] = invScale.y * rot3x3[1][2]; m[1][3] = invTranslate.y;
m[2][0] = invScale.z * rot3x3[2][0]; m[2][1] = invScale.z * rot3x3[2][1]; m[2][2] = invScale.z * rot3x3[2][2]; m[2][3] = invTranslate.z;
m[3][0] = 0; m[3][1] = 0; m[3][2] = 0; m[3][3] = 1;
}
void Matrix4::makeInverseTransform(const Vector3& position, const Vector3& scale, const Quaternion& orientation)
{
// Invert the parameters
Vector3 invTranslate = Vector3(-position.x,-position.y,-position.z);
Vector3 invScale(1 / scale.x, 1 / scale.y, 1 / scale.z);
Quaternion invRot = orientation.inverse();
// Because we're inverting, order is translation, rotation, scale
// So make translation relative to scale & rotation
invTranslate = invRot * invTranslate; // rotate
invTranslate *= invScale; // scale
// Next, make a 3x3 rotation matrix
Matrix3 rot3x3;
invRot.ToRotationMatrix(rot3x3);
// Set up final matrix with scale, rotation and translation
m[0][0] = invScale.x * rot3x3[0][0]; m[0][1] = invScale.x * rot3x3[0][1]; m[0][2] = invScale.x * rot3x3[0][2]; m[0][3] = invTranslate.x;
m[1][0] = invScale.y * rot3x3[1][0]; m[1][1] = invScale.y * rot3x3[1][1]; m[1][2] = invScale.y * rot3x3[1][2]; m[1][3] = invTranslate.y;
m[2][0] = invScale.z * rot3x3[2][0]; m[2][1] = invScale.z * rot3x3[2][1]; m[2][2] = invScale.z * rot3x3[2][2]; m[2][3] = invTranslate.z;
// No projection term
m[3][0] = 0; m[3][1] = 0; m[3][2] = 0; m[3][3] = 1;
}
//--------------------------------------
static void m_matF_x_scale_x_planeF_C(const F32* m, const F32* s, const F32* p, F32* presult)
{
// We take in a matrix, a scale factor, and a plane equation. We want to output
// the resultant normal
// We have T = m*s
// To multiply the normal, we want Inv(Tr(m*s))
// Inv(Tr(ms)) = Inv(Tr(s) * Tr(m))
// = Inv(Tr(m)) * Inv(Tr(s))
//
// Inv(Tr(s)) = Inv(s) = [ 1/x 0 0 0]
// [ 0 1/y 0 0]
// [ 0 0 1/z 0]
// [ 0 0 0 1]
//
// Since m is an affine matrix,
// Tr(m) = [ [ ] 0 ]
// [ [ R ] 0 ]
// [ [ ] 0 ]
// [ [ x y z ] 1 ]
//
// Inv(Tr(m)) = [ [ -1 ] 0 ]
// [ [ R ] 0 ]
// [ [ ] 0 ]
// [ [ A B C ] 1 ]
// Where:
//
// P = (x, y, z)
// A = -(Row(0, r) * P);
// B = -(Row(1, r) * P);
// C = -(Row(2, r) * P);
MatrixF invScale(true);
F32* pScaleElems = invScale;
pScaleElems[MatrixF::idx(0, 0)] = 1.0f / s[0];
pScaleElems[MatrixF::idx(1, 1)] = 1.0f / s[1];
pScaleElems[MatrixF::idx(2, 2)] = 1.0f / s[2];
const Point3F shear( m[MatrixF::idx(3, 0)], m[MatrixF::idx(3, 1)], m[MatrixF::idx(3, 2)] );
const Point3F row0(m[MatrixF::idx(0, 0)], m[MatrixF::idx(0, 1)], m[MatrixF::idx(0, 2)]);
const Point3F row1(m[MatrixF::idx(1, 0)], m[MatrixF::idx(1, 1)], m[MatrixF::idx(1, 2)]);
const Point3F row2(m[MatrixF::idx(2, 0)], m[MatrixF::idx(2, 1)], m[MatrixF::idx(2, 2)]);
const F32 A = -mDot(row0, shear);
const F32 B = -mDot(row1, shear);
const F32 C = -mDot(row2, shear);
MatrixF invTrMatrix(true);
F32* destMat = invTrMatrix;
destMat[MatrixF::idx(0, 0)] = m[MatrixF::idx(0, 0)];
destMat[MatrixF::idx(1, 0)] = m[MatrixF::idx(1, 0)];
destMat[MatrixF::idx(2, 0)] = m[MatrixF::idx(2, 0)];
destMat[MatrixF::idx(0, 1)] = m[MatrixF::idx(0, 1)];
destMat[MatrixF::idx(1, 1)] = m[MatrixF::idx(1, 1)];
destMat[MatrixF::idx(2, 1)] = m[MatrixF::idx(2, 1)];
destMat[MatrixF::idx(0, 2)] = m[MatrixF::idx(0, 2)];
destMat[MatrixF::idx(1, 2)] = m[MatrixF::idx(1, 2)];
destMat[MatrixF::idx(2, 2)] = m[MatrixF::idx(2, 2)];
destMat[MatrixF::idx(0, 3)] = A;
destMat[MatrixF::idx(1, 3)] = B;
destMat[MatrixF::idx(2, 3)] = C;
invTrMatrix.mul(invScale);
Point3F norm(p[0], p[1], p[2]);
Point3F point = norm * -p[3];
invTrMatrix.mulP(norm);
norm.normalize();
MatrixF temp;
memcpy(temp, m, sizeof(F32) * 16);
point.x *= s[0];
point.y *= s[1];
point.z *= s[2];
temp.mulP(point);
PlaneF resultPlane(point, norm);
presult[0] = resultPlane.x;
presult[1] = resultPlane.y;
presult[2] = resultPlane.z;
presult[3] = resultPlane.d;
}