float det3x3(float a1,float a2,float a3,
float b1,float b2,float b3,
float c1,float c2,float c3) {
return a1 * det2x2( b2, b3, c2, c3 ) -
b1 * det2x2( a2, a3, c2, c3 ) +
c1 * det2x2( a2, a3, b2, b3 );
}
static inline double det3x3(double m00, double m01, double m02,
double m10, double m11, double m12,
double m20, double m21, double m22) {
return m00 * det2x2(m11, m12, m21, m22) -
m10 * det2x2(m01, m02, m21, m22) +
m20 * det2x2(m01, m02, m11, m12);
}
static inline double det3x3(double a1, double a2, double a3,
double b1, double b2, double b3,
double c1, double c2, double c3)
{
return a1 * det2x2(b2, b3, c2, c3)
- b1 * det2x2(a2, a3, c2, c3)
+ c1 * det2x2(a2, a3, b2, b3);
}
static RtFloat det3x3(RtFloat a1, RtFloat a2, RtFloat a3,
RtFloat b1, RtFloat b2, RtFloat b3,
RtFloat c1, RtFloat c2, RtFloat c3)
{
return a1 * det2x2(b2, b3, c2, c3) -
b1 * det2x2(a2, a3, c2, c3) +
c1 * det2x2(a2, a3, b2, b3);
}
double det3x3( double a1, double a2, double a3, double b1,
double b2, double b3, double c1, double c2, double c3 )
{
double ans;
ans = a1 * det2x2( b2, b3, c2, c3 )
- b1 * det2x2( a2, a3, c2, c3 )
+ c1 * det2x2( a2, a3, b2, b3 );
return ans;
}
static void adjoint(
double out[3][3],
double in[3][3]
) {
double a1, a2, a3, b1, b2, b3, c1, c2, c3;
/* assign to individual variable names to aid */
/* selecting correct values */
a1 = in[0][0]; b1 = in[0][1]; c1 = in[0][2];
a2 = in[1][0]; b2 = in[1][1]; c2 = in[1][2];
a3 = in[2][0]; b3 = in[2][1]; c3 = in[2][2];
/* row column labeling reversed since we transpose rows & columns */
out[0][0] = det2x2(b2, b3, c2, c3);
out[1][0] = - det2x2(a2, a3, c2, c3);
out[2][0] = det2x2(a2, a3, b2, b3);
out[0][1] = - det2x2(b1, b3, c1, c3);
out[1][1] = det2x2(a1, a3, c1, c3);
out[2][1] = - det2x2(a1, a3, b1, b3);
out[0][2] = det2x2(b1, b2, c1, c2);
out[1][2] = - det2x2(a1, a2, c1, c2);
out[2][2] = det2x2(a1, a2, b1, b2);
}
static Lib3dsFloat
det3x3(
Lib3dsFloat a1, Lib3dsFloat a2, Lib3dsFloat a3,
Lib3dsFloat b1, Lib3dsFloat b2, Lib3dsFloat b3,
Lib3dsFloat c1, Lib3dsFloat c2, Lib3dsFloat c3)
{
return(
a1*det2x2(b2,b3,c2,c3)-
b1*det2x2(a2,a3,c2,c3)+
c1*det2x2(a2,a3,b2,b3)
);
}
static double sa_Det3x3(double in[3][3]) {
double a1, a2, a3, b1, b2, b3, c1, c2, c3;
double ans;
a1 = in[0][0]; b1 = in[0][1]; c1 = in[0][2];
a2 = in[1][0]; b2 = in[1][1]; c2 = in[1][2];
a3 = in[2][0]; b3 = in[2][1]; c3 = in[2][2];
ans = a1 * det2x2(b2, b3, c2, c3)
- b1 * det2x2(a2, a3, c2, c3)
+ c1 * det2x2(a2, a3, b2, b3);
return ans;
}
void DenseMatImpl::myDet(RingElem& d) const
{
if (myNumRows()==2)
{ det2x2(d, ConstMatrixView(this)); return; }
if (myNumRows()==3)
{ det3x3(d, ConstMatrixView(this)); return; }
if (IsField(myR))
{ DetByGauss(d, ConstMatrixView(this)); return; }
if (IsIntegralDomain(myR))
{ d = DetByBareiss(ConstMatrixView(this)); return; }
CoCoA_ERROR(ERR::NYI, "det for non integral domain");
}
static SkFloat3x3 invert(const SkFloat3x3& m) {
double d = det(m);
SkASSERT(SkFloatIsFinite((float)d));
double scale = 1 / d;
SkASSERT(SkFloatIsFinite((float)scale));
return {{
(float)(scale * det2x2(m, 4, 8, 5, 7)),
(float)(scale * det2x2(m, 7, 2, 8, 1)),
(float)(scale * det2x2(m, 1, 5, 2, 4)),
(float)(scale * det2x2(m, 6, 5, 8, 3)),
(float)(scale * det2x2(m, 0, 8, 2, 6)),
(float)(scale * det2x2(m, 3, 2, 5, 0)),
(float)(scale * det2x2(m, 3, 7, 4, 6)),
(float)(scale * det2x2(m, 6, 1, 7, 0)),
(float)(scale * det2x2(m, 0, 4, 1, 3)),
}};
}
std::vector<double> computeInterpolationWeights2d(const GenericPoint& thepoint,
const Container& pt_v)
{
if (pt_v.size() !=3)
{
std::cout << " Compute interpolation weights.. error.. wrong number of points: " << pt_v.size() << std::endl;
return std::vector<double>();
}
double c1[2], c2[2];
c1[0] = pt_v[1][0] - pt_v[0][0];
c1[1] = pt_v[1][1] - pt_v[0][1];
c2[0] = pt_v[2][0] - pt_v[0][0];
c2[1] = pt_v[2][1] - pt_v[0][1];
double det(det2x2(c1, c2));
if (det == 0.0)
{
throw gsse::numerical_calculation_error(":: interpolation :: 2D :: coefficients.. determinant to small.. ");
}
double rhs[2];
std::vector<double> weights(3);
rhs[0] = thepoint[0] - pt_v[0][0];
rhs[1] = thepoint[1] - pt_v[0][1];
weights[1] = det2x2(rhs, c2) / det;
weights[2] = det2x2(c1, rhs) / det;
weights[0] = 1.0 - weights[1] - weights[2];
return weights; // here .. copy constructor // think about it.. [RH]
}
// Returns the inverse of this matrix
FMMatrix33 FMMatrix33::Inverted() const
{
FMMatrix33 b;
b.m[0][0] = det2x2(m[1][1], m[1][2], m[2][1], m[2][2]);
b.m[0][1] = -det2x2(m[0][1], m[0][2], m[2][1], m[2][2]);
b.m[0][2] = det2x2(m[0][1], m[0][2], m[1][1], m[1][2]);
b.m[1][0] = -det2x2(m[1][0], m[1][2], m[2][0], m[2][2]);
b.m[1][1] = det2x2(m[0][0], m[0][2], m[2][0], m[2][2]);
b.m[1][2] = -det2x2(m[0][0], m[0][2], m[1][0], m[1][2]);
b.m[2][0] = det2x2(m[1][0], m[1][1], m[2][0], m[2][1]);
b.m[2][1] = -det2x2(m[0][0], m[0][1], m[2][0], m[2][1]);
b.m[2][2] = det2x2(m[0][0], m[0][1], m[1][0], m[1][1]);
float det = (m[0][0] * b.m[0][0]) + (m[1][0] * b.m[0][1]) + (m[2][0] * b.m[0][2]);
// We should consider throwing an exception if det < eps.
if (IsEquivalent(det, 0.0f)) det = 0.01f;
float oodet = 1.0f / det;
b.m[0][0] *= oodet;
b.m[0][1] *= oodet;
b.m[0][2] *= oodet;
b.m[1][0] *= oodet;
b.m[1][1] *= oodet;
b.m[1][2] *= oodet;
b.m[2][0] *= oodet;
b.m[2][1] *= oodet;
b.m[2][2] *= oodet;
return b;
}
static double vp(vec x, vec y, vec z) {
z[0] = det2x2(x[1], x[2], y[1], y[2]);
z[1] = det2x2(x[2], x[0], y[2], y[0]);
z[2] = det2x2(x[0], x[1], y[0], y[1]);
return sqrt(dot(z,z));
}
/*
calculate the determinent of a 3x3 matrix in the from
| a1 a2 a3 |
| b1 b2 b3 |
| c1 c2 c3 |
*/
nv_scalar det3x3(nv_scalar a1, nv_scalar a2, nv_scalar a3,
nv_scalar b1, nv_scalar b2, nv_scalar b3,
nv_scalar c1, nv_scalar c2, nv_scalar c3)
{
return a1 * det2x2(b2, b3, c2, c3) - b1 * det2x2(a2, a3, c2, c3) + c1 * det2x2(a2, a3, b2, b3);
}
inline scalar_t det3x3(scalar_t a1, scalar_t a2, scalar_t a3, scalar_t b1, scalar_t b2, scalar_t b3,
scalar_t c1, scalar_t c2, scalar_t c3)
{
return a1 * det2x2(b2, b3, c2, c3) - b1 * det2x2(a2, a3, c2, c3) + c1 * det2x2(a2, a3, b2, b3);
}
