/**
* \brief Tridiagonalizes a 3x3 matrix using a single
* Householder transformation and returns the result.
*
* Based on "Geometric Tools" by David Eberly.
*/
static inline void tred3(Matrix3x3 &m, Float *diag, Float *subd) {
Float m00 = m(0, 0), m01 = m(0, 1), m02 = m(0, 2),
m11 = m(1, 1), m12 = m(1, 2), m22 = m(2, 2);
diag[0] = m00;
subd[2] = 0;
if (std::abs(m02) > std::numeric_limits<Float>::epsilon()) {
Float length = std::sqrt(m01*m01 + m02*m02),
invLength = 1 / length;
m01 *= invLength;
m02 *= invLength;
Float q = 2*m01*m12 + m02*(m22 - m11);
diag[1] = m11 + m02*q;
diag[2] = m22 - m02*q;
subd[0] = length;
subd[1] = m12 - m01*q;
m = Matrix3x3(
1, 0, 0,
0, m01, m02,
0, m02, -m01);
} else {
/* The matrix is already tridiagonal,
return an identity transformation matrix */
diag[1] = m11;
diag[2] = m22;
subd[0] = m01;
subd[1] = m12;
m = Matrix3x3(
1, 0, 0,
0, 1, 0,
0, 0, 1);
}
}
Matrix3x3 Matrix3x3::rotation(const Vector3& axis, float angleRadians) {
float angle = -angleRadians;
return Matrix3x3(
(axis.x * axis.x) * (1 - cos(angle)) + cos(angle) , axis.x * axis.y * (1 - cos(angle)) + axis.z * sin(angle), (axis.x * axis.z) * (1 - cos(angle)) - axis.y * sin(angle),
(axis.x * axis.y) * (1 - cos(angle)) - axis.z * sin(angle), axis.y * axis.y * (1 - cos(angle)) + cos(angle) , (axis.y * axis.z) * (1 - cos(angle)) + axis.x * sin(angle),
(axis.x * axis.z) * (1 - cos(angle)) + axis.y * sin(angle), axis.y * axis.z * (1 - cos(angle)) - axis.x * sin(angle), (axis.z * axis.z) * (1 - cos(angle)) + cos(angle));
}
Matrix3x3 Quaternion::rotationMatrix3x3() const
{
Vector3 col1 = Vector3(1.0f - 2.0f * (y * y + z * z), 2.0f * (x * y + w * z), 2.0f * (x * z - w * y));
Vector3 col2 = Vector3(2.0f * (x * y - w * z), 1.0f - 2.0f * (x * x + z * z), 2.0f * (y * z + w * x));
Vector3 col3 = Vector3(2.0f * (x * z + w * y), 2.0f * (y * z - w * x), 1.0f - 2.0f * (x * x + y * y));
return Matrix3x3(col1, col2, col3);
}
Matrix3x3 Matrix3x3::CompMax(const Matrix3x3& m1,
const Matrix3x3& m2)
{
return Matrix3x3(Vector3::CompMax(m1[0], m2[0]),
Vector3::CompMax(m1[1], m2[1]),
Vector3::CompMax(m1[2], m2[2]));
}
// Return the transpose matrix
inline Matrix3x3 Matrix3x3::getTranspose() const {
// Return the transpose matrix
return Matrix3x3(mRows[0][0], mRows[1][0], mRows[2][0],
mRows[0][1], mRows[1][1], mRows[2][1],
mRows[0][2], mRows[1][2], mRows[2][2]);
}
Matrix3x3 Matrix3x3::CompPow(const Matrix3x3& base,
const Matrix3x3& exponent)
{
return Matrix3x3(Vector3::CompPow(base[0], exponent[0]),
Vector3::CompPow(base[1], exponent[1]),
Vector3::CompPow(base[2], exponent[2]));
}
Matrix3x3 Matrix3x3::operator*(const Matrix3x3& m) const
{
return Matrix3x3( (*this)[0][0]*m[0][0]
+ (*this)[1][0]*m[0][1]
+ (*this)[2][0]*m[0][2],
(*this)[0][0]*m[1][0]
+ (*this)[1][0]*m[1][1]
+ (*this)[2][0]*m[1][2],
(*this)[0][0]*m[2][0]
+ (*this)[1][0]*m[2][1]
+ (*this)[2][0]*m[2][2],
(*this)[0][1]*m[0][0]
+ (*this)[1][1]*m[0][1]
+ (*this)[2][1]*m[0][2],
(*this)[0][1]*m[1][0]
+ (*this)[1][1]*m[1][1]
+ (*this)[2][1]*m[1][2],
(*this)[0][1]*m[2][0]
+ (*this)[1][1]*m[2][1]
+ (*this)[2][1]*m[2][2],
(*this)[0][2]*m[0][0]
+ (*this)[1][2]*m[0][1]
+ (*this)[2][2]*m[0][2],
(*this)[0][2]*m[1][0]
+ (*this)[1][2]*m[1][1]
+ (*this)[2][2]*m[1][2],
(*this)[0][2]*m[2][0]
+ (*this)[1][2]*m[2][1]
+ (*this)[2][2]*m[2][2] );
}
Matrix3x3 get_unistate_mat3(const char *name)
{
int sidx = get_unistate_index(name);
if(sidx == -1) {
return Matrix3x3();
}
return get_unistate_mat3(sidx);
}
Matrix3x3 Matrix3x3::operator+( const Matrix3x3& rhs ) const
{
return Matrix3x3(
_00+rhs._00, _01+rhs._01, _02+rhs._02,
_10+rhs._10, _11+rhs._11, _12+rhs._12,
_20+rhs._20, _21+rhs._21, _22+rhs._22
);
}
Matrix3x3
matScale(double x,
double y)
{
return Matrix3x3(x, 0., 0.,
0., y, 0.,
0., 0., 1.);
}
Matrix3x3 Matrix3x3::Diagonal(const float& m00,
const float& m11,
const float& m22)
{
return Matrix3x3(m00, 0 , 0 ,
0 , m11, 0 ,
0 , 0 , m22);
}
Matrix3x3 Matrix3x3::CompClamp(const Matrix3x3& m,
const Matrix3x3& min,
const Matrix3x3& max)
{
return Matrix3x3(Vector3::CompClamp(m[0], min[0], max[0]),
Vector3::CompClamp(m[1], min[1], max[1]),
Vector3::CompClamp(m[2], min[2], max[2]));
}
// Overloaded operator for substraction
inline Matrix3x3 operator-(const Matrix3x3& matrix1, const Matrix3x3& matrix2) {
return Matrix3x3(matrix1.mRows[0][0] - matrix2.mRows[0][0], matrix1.mRows[0][1] -
matrix2.mRows[0][1], matrix1.mRows[0][2] - matrix2.mRows[0][2],
matrix1.mRows[1][0] - matrix2.mRows[1][0], matrix1.mRows[1][1] -
matrix2.mRows[1][1], matrix1.mRows[1][2] - matrix2.mRows[1][2],
matrix1.mRows[2][0] - matrix2.mRows[2][0], matrix1.mRows[2][1] -
matrix2.mRows[2][1], matrix1.mRows[2][2] - matrix2.mRows[2][2]);
}
Matrix3x3 Matrix3x3::operator-( const Matrix3x3& rhs ) const
{
return Matrix3x3(
_00-rhs._00, _01-rhs._01, _02-rhs._02,
_10-rhs._10, _11-rhs._11, _12-rhs._12,
_20-rhs._20, _21-rhs._21, _22-rhs._22
);
}
Matrix3x3
matTranslation(double x,
double y)
{
return Matrix3x3(1., 0., x,
0., 1., y,
0., 0., 1.);
}
Matrix3x3
matRotation(double rads)
{
double c = std::cos(rads);
double s = std::sin(rads);
return Matrix3x3(c, s, 0, -s, c, 0, 0, 0, 1);
}
Matrix3x3 Matrix3x3::RotationAboutY(const float& radians)
{
// do some precomputations
float c = std::cos(radians);
float s = std::sin(radians);
return Matrix3x3( c, 0, s,
0, 1, 0,
-s, 0, c);
}
Matrix3x3
matSkewXY(double skewX,
double skewY,
bool skewOrderYX)
{
return Matrix3x3(skewOrderYX ? 1. : (1. + skewX * skewY), skewX, 0.,
skewY, skewOrderYX ? (1. + skewX * skewY) : 1, 0.,
0., 0., 1.);
}
void TargetCamera::set_camera(long time)
{
set_view_matrix(get_matrix());
set_unistate("st_view_matrix3",Matrix3x3(get_matrix()));
//DEBUG
Matrix4x4 view = get_matrix();
glMatrixMode(GL_MODELVIEW);
glLoadTransposeMatrixf(view[0]);
}
Matrix3x3 Matrix3x3::Transpose() const
{
float data[9];
int cnt = 0;
for (int i = 0; i < 3; i++) {
for (int j = 0; j < 3; j++) {
data[cnt++] = data_[j][i];
}
}
return Matrix3x3(data);
}
Matrix3x3
matMul(const Matrix3x3 & m1,
const Matrix3x3 & m2)
{
return Matrix3x3(m1.a * m2.a + m1.b * m2.d + m1.c * m2.g,
m1.a * m2.b + m1.b * m2.e + m1.c * m2.h,
m1.a * m2.c + m1.b * m2.f + m1.c * m2.i,
m1.d * m2.a + m1.e * m2.d + m1.f * m2.g,
m1.d * m2.b + m1.e * m2.e + m1.f * m2.h,
m1.d * m2.c + m1.e * m2.f + m1.f * m2.i,
m1.g * m2.a + m1.h * m2.d + m1.i * m2.g,
m1.g * m2.b + m1.h * m2.e + m1.i * m2.h,
m1.g * m2.c + m1.h * m2.f + m1.i * m2.i);
}
Matrix3x3 Matrix3x3::getTranspose()
{
std::vector<float> tmp(9);
for (int i = 0; i < 3; i++)
{
tmp[3 * i] = elements[i];
tmp[3 * i + 1] = elements[i + 3];
tmp[3 * i + 2] = elements[i + 6];
}
return Matrix3x3(tmp);
}
Matrix3x3 Matrix3x3::VectorRotation(const Vector3& unitFrom,
const Vector3& unitTo)
{
// compute the unit rotation axis
Vector3 v = Vector3::CrossProduct(unitFrom, unitTo);
float e = Vector3::DotProduct(unitFrom, unitTo);
float h = 1.0f / (1.0f + e);
Vector3 hv = h*v;
// return the matrix
return Matrix3x3(e + hv[0]*v[0], hv[0]*v[1] - v[2], hv[0]*v[2] + v[1],
hv[0]*v[1] + v[2], e + hv[1]*v[1], hv[1]*v[2] - v[0],
hv[0]*v[2] - v[1], hv[1]*v[2] + v[0], e + hv[2]*v[2]);
}
a2de::Matrix3x3 Matrix3x3::operator*(const Matrix3x3& rhs) {
a2de::Vector3D r1(this->GetRowOne());
a2de::Vector3D r2(this->GetRowTwo());
a2de::Vector3D r3(this->GetRowThree());
a2de::Vector3D c1(rhs.GetColumnOne());
a2de::Vector3D c2(rhs.GetColumnTwo());
a2de::Vector3D c3(rhs.GetColumnThree());
return Matrix3x3(a2de::Vector3D::DotProduct(r1, c1), a2de::Vector3D::DotProduct(r1, c2), a2de::Vector3D::DotProduct(r1, c3),
a2de::Vector3D::DotProduct(r2, c1), a2de::Vector3D::DotProduct(r2, c2), a2de::Vector3D::DotProduct(r2, c3),
a2de::Vector3D::DotProduct(r3, c1), a2de::Vector3D::DotProduct(r3, c2), a2de::Vector3D::DotProduct(r3, c3));
}
void configure() {
PhaseFunction::configure();
m_type = EAnisotropic | ENonSymmetric;
Properties props("independent");
m_sampler = static_cast<Sampler*>(PluginManager::getInstance()->createObject(MTS_CLASS(Sampler), props));
m_sampler->configure();
if (m_stddev != -1.f) {
Float sigma1 = m_fiberDistr.sigmaT(0.f) * 2.f;
Float sigma2 = sigma1;
Float sigma3 = m_fiberDistr.sigmaT(1.f) * 2.f;
D = Matrix3x3(Vector(sigma1 * sigma1, 0, 0), Vector(0, sigma2 * sigma2, 0), Vector(0, 0, sigma3 * sigma3));
}
}
static bool
triangle_intersection(const Ray *ray,
const Point3D &p0,
const Point3D &p1,
const Point3D &p2,
double &beta,
double &gamma)
{
Vector3D v1 = p1 - p0;
Vector3D v2 = p2 - p0;
Vector3D r = ray->get_pos() - p0;
double d = Matrix3x3(v1,v2,ray->get_dir()).det();
double d1 = Matrix3x3(r,v2,ray->get_dir()).det();
beta = d1/d;
if (beta < 0)
return false;
double d2 = Matrix3x3(v1, r, ray->get_dir()).det();
gamma = d2/d;
if (gamma < 0 || (beta+gamma) >= 1)
return false;
return true;
}
Matrix3x3 Matrix3x3::Multiply(const Matrix3x3& rhs) const
{
float newMatrix[] =
{
(_elements[0] * rhs._elements[0] + _elements[3] * rhs._elements[1] + _elements[6] * rhs._elements[2]),
(_elements[1] * rhs._elements[0] + _elements[4] * rhs._elements[1] + _elements[7] * rhs._elements[2]),
(_elements[2] * rhs._elements[0] + _elements[5] * rhs._elements[1] + _elements[8] * rhs._elements[2]),
(_elements[0] * rhs._elements[3] + _elements[3] * rhs._elements[4] + _elements[6] * rhs._elements[5]),
(_elements[1] * rhs._elements[3] + _elements[4] * rhs._elements[4] + _elements[7] * rhs._elements[5]),
(_elements[2] * rhs._elements[3] + _elements[5] * rhs._elements[4] + _elements[8] * rhs._elements[5]),
(_elements[0] * rhs._elements[6] + _elements[3] * rhs._elements[7] + _elements[6] * rhs._elements[8]),
(_elements[1] * rhs._elements[6] + _elements[4] * rhs._elements[7] + _elements[7] * rhs._elements[8]),
(_elements[2] * rhs._elements[6] + _elements[5] * rhs._elements[7] + _elements[8] * rhs._elements[8])
};
return Matrix3x3(newMatrix);
}
Matrix3x3 Matrix3x3::LookAtRotation(const Vector3& eyePos,
const Vector3& targetPos,
const Vector3& unitUpVector)
{
#ifndef NDEBUG
assert(eyePos != targetPos && unitUpVector != Vector3::ZERO);
#endif
// using OpenGL2.1 SDK (gluLookAt)
Vector3 f((targetPos - eyePos).Normalize());
Vector3 s(Vector3::CrossProduct(f, unitUpVector));
Vector3 u(Vector3::CrossProduct(s, f));
return Matrix3x3(s[0], u[0], -f[0],
s[1], u[1], -f[1],
s[2], u[2], -f[2] );
}
void set_view_matrix(const Matrix4x4 &mat)
{
static int sidx = -1, sidx_transp, sidx_mat3, sidx_inv;
if(sidx == -1) {
sidx = add_unistate("st_view_matrix", ST_MATRIX4);
sidx_mat3 = add_unistate("st_view_matrix3", ST_MATRIX3);
sidx_transp = add_unistate("st_view_matrix_transpose", ST_MATRIX4);
sidx_inv = add_unistate("st_view_matrix_inverse", ST_MATRIX4);
}
set_unistate(sidx, mat);
set_unistate(sidx_mat3, Matrix3x3(mat));
set_unistate(sidx_transp, mat[0]); // by using the float* variant, we unset the transpose flag
set_unistate(sidx_inv, mat.inverse());
}
Matrix3x3 Matrix3x3::operator*( const Matrix3x3& rhs ) const
{
return Matrix3x3(
_00*rhs._00 + _01*rhs._10 + _02*rhs._20,
_00*rhs._01 + _01*rhs._11 + _02*rhs._21,
_00*rhs._02 + _01*rhs._12 + _02*rhs._22,
_10*rhs._00 + _11*rhs._10 + _12*rhs._20,
_10*rhs._01 + _11*rhs._11 + _12*rhs._21,
_10*rhs._02 + _11*rhs._12 + _12*rhs._22,
_20*rhs._00 + _21*rhs._10 + _22*rhs._20,
_20*rhs._01 + _21*rhs._11 + _22*rhs._21,
_20*rhs._02 + _21*rhs._12 + _22*rhs._22
);
}