31 #ifndef OPENVDB_MATH_MAT3_H_HAS_BEEN_INCLUDED 32 #define OPENVDB_MATH_MAT3_H_HAS_BEEN_INCLUDED 48 template<
typename T>
class Vec3;
49 template<
typename T>
class Mat4;
50 template<
typename T>
class Quat;
77 template<
typename Source>
78 Mat3(Source a, Source b, Source c,
79 Source d, Source e, Source f,
80 Source g, Source h, Source i)
82 MyBase::mm[0] = static_cast<ValueType>(a);
83 MyBase::mm[1] = static_cast<ValueType>(b);
84 MyBase::mm[2] = static_cast<ValueType>(c);
85 MyBase::mm[3] = static_cast<ValueType>(d);
86 MyBase::mm[4] = static_cast<ValueType>(e);
87 MyBase::mm[5] = static_cast<ValueType>(f);
88 MyBase::mm[6] = static_cast<ValueType>(g);
89 MyBase::mm[7] = static_cast<ValueType>(h);
90 MyBase::mm[8] = static_cast<ValueType>(i);
95 template<
typename Source>
99 this->setRows(v1, v2, v3);
101 this->setColumns(v1, v2, v3);
109 template<
typename Source>
112 MyBase::mm[0] = a[0];
113 MyBase::mm[1] = a[1];
114 MyBase::mm[2] = a[2];
115 MyBase::mm[3] = a[3];
116 MyBase::mm[4] = a[4];
117 MyBase::mm[5] = a[5];
118 MyBase::mm[6] = a[6];
119 MyBase::mm[7] = a[7];
120 MyBase::mm[8] = a[8];
126 for (
int i=0; i<3; ++i) {
127 for (
int j=0; j<3; ++j) {
128 MyBase::mm[i*3 + j] = m[i][j];
134 template<
typename Source>
137 for (
int i=0; i<3; ++i) {
138 for (
int j=0; j<3; ++j) {
139 MyBase::mm[i*3 + j] = static_cast<T>(m[i][j]);
147 for (
int i=0; i<3; ++i) {
148 for (
int j=0; j<3; ++j) {
149 MyBase::mm[i*3 + j] = m[i][j];
180 MyBase::mm[i3+0] = v[0];
181 MyBase::mm[i3+1] = v[1];
182 MyBase::mm[i3+2] = v[2];
189 return Vec3<T>((*
this)(i,0), (*
this)(i,1), (*
this)(i,2));
196 MyBase::mm[0+j] = v[0];
197 MyBase::mm[3+j] = v[1];
198 MyBase::mm[6+j] = v[2];
205 return Vec3<T>((*
this)(0,j), (*
this)(1,j), (*
this)(2,j));
213 T* operator[](
int i) {
return &(MyBase::mm[i*3]); }
216 const T*
operator[](
int i)
const {
return &(MyBase::mm[i*3]); }
229 return MyBase::mm[3*i+j];
239 return MyBase::mm[3*i+j];
245 MyBase::mm[0] = v1[0];
246 MyBase::mm[1] = v1[1];
247 MyBase::mm[2] = v1[2];
248 MyBase::mm[3] = v2[0];
249 MyBase::mm[4] = v2[1];
250 MyBase::mm[5] = v2[2];
251 MyBase::mm[6] = v3[0];
252 MyBase::mm[7] = v3[1];
253 MyBase::mm[8] = v3[2];
259 MyBase::mm[0] = v1[0];
260 MyBase::mm[1] = v2[0];
261 MyBase::mm[2] = v3[0];
262 MyBase::mm[3] = v1[1];
263 MyBase::mm[4] = v2[1];
264 MyBase::mm[5] = v3[1];
265 MyBase::mm[6] = v1[2];
266 MyBase::mm[7] = v2[2];
267 MyBase::mm[8] = v3[2];
273 MyBase::mm[0] = vdiag[0];
274 MyBase::mm[1] = vtri[0];
275 MyBase::mm[2] = vtri[1];
276 MyBase::mm[3] = vtri[0];
277 MyBase::mm[4] = vdiag[1];
278 MyBase::mm[5] = vtri[2];
279 MyBase::mm[6] = vtri[1];
280 MyBase::mm[7] = vtri[2];
281 MyBase::mm[8] = vdiag[2];
288 vdiag[0], vtri[0], vtri[1],
289 vtri[0], vdiag[1], vtri[2],
290 vtri[1], vtri[2], vdiag[2]
302 {*
this = rotation<Mat3<T> >(q);}
307 {*
this = rotation<Mat3<T> >(axis,
angle);}
338 template<
typename Source>
344 std::copy(src, (src + this->numElements()), MyBase::mm);
349 bool eq(
const Mat3 &m, T eps=1.0e-8)
const 366 -MyBase::mm[0], -MyBase::mm[1], -MyBase::mm[2],
367 -MyBase::mm[3], -MyBase::mm[4], -MyBase::mm[5],
368 -MyBase::mm[6], -MyBase::mm[7], -MyBase::mm[8]
378 template <
typename S>
381 MyBase::mm[0] *= scalar;
382 MyBase::mm[1] *= scalar;
383 MyBase::mm[2] *= scalar;
384 MyBase::mm[3] *= scalar;
385 MyBase::mm[4] *= scalar;
386 MyBase::mm[5] *= scalar;
387 MyBase::mm[6] *= scalar;
388 MyBase::mm[7] *= scalar;
389 MyBase::mm[8] *= scalar;
394 template <
typename S>
399 MyBase::mm[0] += s[0];
400 MyBase::mm[1] += s[1];
401 MyBase::mm[2] += s[2];
402 MyBase::mm[3] += s[3];
403 MyBase::mm[4] += s[4];
404 MyBase::mm[5] += s[5];
405 MyBase::mm[6] += s[6];
406 MyBase::mm[7] += s[7];
407 MyBase::mm[8] += s[8];
412 template <
typename S>
417 MyBase::mm[0] -= s[0];
418 MyBase::mm[1] -= s[1];
419 MyBase::mm[2] -= s[2];
420 MyBase::mm[3] -= s[3];
421 MyBase::mm[4] -= s[4];
422 MyBase::mm[5] -= s[5];
423 MyBase::mm[6] -= s[6];
424 MyBase::mm[7] -= s[7];
425 MyBase::mm[8] -= s[8];
430 template <
typename S>
437 MyBase::mm[0] = static_cast<T>(s0[0] * s1[0] +
440 MyBase::mm[1] = static_cast<T>(s0[0] * s1[1] +
443 MyBase::mm[2] = static_cast<T>(s0[0] * s1[2] +
447 MyBase::mm[3] = static_cast<T>(s0[3] * s1[0] +
450 MyBase::mm[4] = static_cast<T>(s0[3] * s1[1] +
453 MyBase::mm[5] = static_cast<T>(s0[3] * s1[2] +
457 MyBase::mm[6] = static_cast<T>(s0[6] * s1[0] +
460 MyBase::mm[7] = static_cast<T>(s0[6] * s1[1] +
463 MyBase::mm[8] = static_cast<T>(s0[6] * s1[2] +
474 MyBase::mm[4] * MyBase::mm[8] - MyBase::mm[5] * MyBase::mm[7],
475 MyBase::mm[5] * MyBase::mm[6] - MyBase::mm[3] * MyBase::mm[8],
476 MyBase::mm[3] * MyBase::mm[7] - MyBase::mm[4] * MyBase::mm[6],
477 MyBase::mm[2] * MyBase::mm[7] - MyBase::mm[1] * MyBase::mm[8],
478 MyBase::mm[0] * MyBase::mm[8] - MyBase::mm[2] * MyBase::mm[6],
479 MyBase::mm[1] * MyBase::mm[6] - MyBase::mm[0] * MyBase::mm[7],
480 MyBase::mm[1] * MyBase::mm[5] - MyBase::mm[2] * MyBase::mm[4],
481 MyBase::mm[2] * MyBase::mm[3] - MyBase::mm[0] * MyBase::mm[5],
482 MyBase::mm[0] * MyBase::mm[4] - MyBase::mm[1] * MyBase::mm[3]);
489 MyBase::mm[4] * MyBase::mm[8] - MyBase::mm[5] * MyBase::mm[7],
490 MyBase::mm[2] * MyBase::mm[7] - MyBase::mm[1] * MyBase::mm[8],
491 MyBase::mm[1] * MyBase::mm[5] - MyBase::mm[2] * MyBase::mm[4],
492 MyBase::mm[5] * MyBase::mm[6] - MyBase::mm[3] * MyBase::mm[8],
493 MyBase::mm[0] * MyBase::mm[8] - MyBase::mm[2] * MyBase::mm[6],
494 MyBase::mm[2] * MyBase::mm[3] - MyBase::mm[0] * MyBase::mm[5],
495 MyBase::mm[3] * MyBase::mm[7] - MyBase::mm[4] * MyBase::mm[6],
496 MyBase::mm[1] * MyBase::mm[6] - MyBase::mm[0] * MyBase::mm[7],
497 MyBase::mm[0] * MyBase::mm[4] - MyBase::mm[1] * MyBase::mm[3]);
505 MyBase::mm[0], MyBase::mm[3], MyBase::mm[6],
506 MyBase::mm[1], MyBase::mm[4], MyBase::mm[7],
507 MyBase::mm[2], MyBase::mm[5], MyBase::mm[8]);
517 const T det = inv.
mm[0]*MyBase::mm[0] + inv.
mm[1]*MyBase::mm[3] + inv.
mm[2]*MyBase::mm[6];
523 return inv * (T(1)/det);
529 const T co00 = MyBase::mm[4]*MyBase::mm[8] - MyBase::mm[5]*MyBase::mm[7];
530 const T co10 = MyBase::mm[5]*MyBase::mm[6] - MyBase::mm[3]*MyBase::mm[8];
531 const T co20 = MyBase::mm[3]*MyBase::mm[7] - MyBase::mm[4]*MyBase::mm[6];
532 return MyBase::mm[0]*co00 + MyBase::mm[1]*co10 + MyBase::mm[2]*co20;
538 return MyBase::mm[0]+MyBase::mm[4]+MyBase::mm[8];
552 template<
typename T0>
555 return static_cast< Vec3<T0> >(v * *
this);
560 template<
typename T0>
563 return static_cast< Vec3<T0> >(*
this * v);
573 ret.
mm[0] *= diag(0);
574 ret.
mm[1] *= diag(1);
575 ret.
mm[2] *= diag(2);
576 ret.
mm[3] *= diag(0);
577 ret.
mm[4] *= diag(1);
578 ret.
mm[5] *= diag(2);
579 ret.
mm[6] *= diag(0);
580 ret.
mm[7] *= diag(1);
581 ret.
mm[8] *= diag(2);
589 template <
typename T0,
typename T1>
595 for (
int i=0; i<9; ++i) {
603 template <
typename T0,
typename T1>
608 template <
typename S,
typename T>
614 template <
typename S,
typename T>
624 template <
typename T0,
typename T1>
634 template <
typename T0,
typename T1>
644 template <
typename T0,
typename T1>
654 template<
typename T,
typename MT>
660 _v[0]*m[0] + _v[1]*m[1] + _v[2]*m[2],
661 _v[0]*m[3] + _v[1]*m[4] + _v[2]*m[5],
662 _v[0]*m[6] + _v[1]*m[7] + _v[2]*m[8]);
667 template<
typename T,
typename MT>
673 _v[0]*m[0] + _v[1]*m[3] + _v[2]*m[6],
674 _v[0]*m[1] + _v[1]*m[4] + _v[2]*m[7],
675 _v[0]*m[2] + _v[1]*m[5] + _v[2]*m[8]);
680 template<
typename T,
typename MT>
690 template <
typename T>
693 return Mat3<T>(v1[0]*v2[0], v1[0]*v2[1], v1[0]*v2[2],
694 v1[1]*v2[0], v1[1]*v2[1], v1[1]*v2[2],
695 v1[2]*v2[0], v1[2]*v2[1], v1[2]*v2[2]);
702 template<
typename T,
typename T0>
712 namespace mat3_internal {
721 double cotan_of_2_theta;
723 double cosin_of_theta;
729 double Sjj_minus_Sii = D[j] - D[i];
732 tan_of_theta = Sij / Sjj_minus_Sii;
735 cotan_of_2_theta = 0.5*Sjj_minus_Sii / Sij ;
737 if (cotan_of_2_theta < 0.) {
739 -1./(sqrt(1. + cotan_of_2_theta*cotan_of_2_theta) - cotan_of_2_theta);
742 1./(sqrt(1. + cotan_of_2_theta*cotan_of_2_theta) + cotan_of_2_theta);
746 cosin_of_theta = 1./sqrt( 1. + tan_of_theta * tan_of_theta);
747 sin_of_theta = cosin_of_theta * tan_of_theta;
748 z = tan_of_theta * Sij;
752 for (
int k = 0; k < i; ++k) {
754 S(k,i) = cosin_of_theta * temp - sin_of_theta * S(k,j);
755 S(k,j)= sin_of_theta * temp + cosin_of_theta * S(k,j);
757 for (
int k = i+1; k < j; ++k) {
759 S(i,k) = cosin_of_theta * temp - sin_of_theta * S(k,j);
760 S(k,j) = sin_of_theta * temp + cosin_of_theta * S(k,j);
762 for (
int k = j+1; k < n; ++k) {
764 S(i,k) = cosin_of_theta * temp - sin_of_theta * S(j,k);
765 S(j,k) = sin_of_theta * temp + cosin_of_theta * S(j,k);
767 for (
int k = 0; k < n; ++k)
770 Q(k,i) = cosin_of_theta * temp - sin_of_theta*Q(k,j);
771 Q(k,j) = sin_of_theta * temp + cosin_of_theta*Q(k,j);
786 unsigned int MAX_ITERATIONS=250)
796 for (
int i = 0; i < n; ++i) {
800 unsigned int iterations(0);
807 for (
int i = 0; i < n; ++i) {
808 for (
int j = i+1; j < n; ++j) {
821 for (
int i = 0; i < n; ++i) {
822 for (
int j = i+1; j < n; ++j){
828 if (fabs(S(i,j)) > max_element) {
829 max_element = fabs(S(i,j));
836 }
while (iterations < MAX_ITERATIONS);
849 template<>
inline math::Mat3s zeroVal<math::Mat3s>() {
return math::Mat3s::zero(); }
850 template<>
inline math::Mat3d zeroVal<math::Mat3d>() {
return math::Mat3d::zero(); }
855 #endif // OPENVDB_MATH_MAT3_H_HAS_BEEN_INCLUDED 4x4 -matrix class.
Definition: Mat3.h:49
Mat3(Source a, Source b, Source c, Source d, Source e, Source f, Source g, Source h, Source i)
Constructor given array of elements, the ordering is in row major form:
Definition: Mat3.h:78
const Mat3< T > & operator-=(const Mat3< S > &m1)
Subtract each element of the given matrix from the corresponding element of this matrix.
Definition: Mat3.h:413
bool diagonalizeSymmetricMatrix(const Mat3< T > &input, Mat3< T > &Q, Vec3< T > &D, unsigned int MAX_ITERATIONS=250)
Use Jacobi iterations to decompose a symmetric 3x3 matrix (diagonalize and compute eigenvectors)
Definition: Mat3.h:785
bool operator==(const Mat3< T0 > &m0, const Mat3< T1 > &m1)
Equality operator, does exact floating point comparisons.
Definition: Mat3.h:590
Mat3 cofactor() const
Return the cofactor matrix of this matrix.
Definition: Mat3.h:471
const Mat3 & operator=(const Mat3< Source > &m)
Assignment operator.
Definition: Mat3.h:339
void setIdentity()
Set this matrix to identity.
Definition: Mat3.h:324
void setToRotation(const Quat< T > &q)
Set this matrix to the rotation matrix specified by the quaternion.
Definition: Mat3.h:301
#define OPENVDB_THROW(exception, message)
Definition: Exceptions.h:109
bool isExactlyEqual(const T0 &a, const T1 &b)
Return true if a is exactly equal to b.
Definition: Math.h:395
Vec3< T > row(int i) const
Get ith row, e.g. Vec3d v = m.row(1);.
Definition: Mat3.h:186
void setToRotation(const Vec3< T > &axis, T angle)
Set this matrix to the rotation specified by axis and angle.
Definition: Mat3.h:306
Mat3< typename promote< T0, T1 >::type > operator+(const Mat3< T0 > &m0, const Mat3< T1 > &m1)
Add corresponding elements of m0 and m1 and return the result.
Definition: Mat3.h:625
void setRow(int i, const Vec3< T > &v)
Set ith row to vector v.
Definition: Mat3.h:175
3x3 matrix class.
Definition: Mat3.h:55
void setCol(int j, const Vec3< T > &v)
Set jth column to vector v.
Definition: Mat3.h:193
Mat3< double > Mat3d
Definition: Mat3.h:843
Mat3< T > powLerp(const Mat3< T0 > &m1, const Mat3< T0 > &m2, T t)
Definition: Mat3.h:703
Mat3< typename promote< T0, T1 >::type > operator *(const Mat3< T0 > &m0, const Mat3< T1 > &m1)
Multiply m0 by m1 and return the resulting matrix.
Definition: Mat3.h:645
static const Mat3< T > & zero()
Predefined constant for zero matrix.
Definition: Mat3.h:165
T operator()(int i, int j) const
Definition: Mat3.h:235
const Mat3< T > & operator+=(const Mat3< S > &m1)
Add each element of the given matrix to the corresponding element of this matrix.
Definition: Mat3.h:395
T & operator()(int i, int j)
Definition: Mat3.h:225
Mat3 snapBasis(Axis axis, const Vec3< T > &direction)
Definition: Mat3.h:545
bool eq(const Mat3 &m, T eps=1.0e-8) const
Return true if this matrix is equivalent to m within a tolerance of eps.
Definition: Mat3.h:349
const T * operator[](int i) const
Definition: Mat3.h:216
Vec3< T0 > transform(const Vec3< T0 > &v) const
Definition: Mat3.h:553
void powSolve(const MatType &aA, MatType &aB, double aPower, double aTol=0.01)
Definition: Mat.h:854
bool operator!=(const Mat3< T0 > &m0, const Mat3< T1 > &m1)
Inequality operator, does exact floating point comparisons.
Definition: Mat3.h:604
Axis
Definition: Math.h:856
#define OPENVDB_VERSION_NAME
The version namespace name for this library version.
Definition: version.h:136
Mat3(const Mat3< Source > &m)
Conversion constructor.
Definition: Mat3.h:135
T mm[SIZE *SIZE]
Definition: Mat.h:192
Definition: Exceptions.h:40
void setColumns(const Vec3< T > &v1, const Vec3< T > &v2, const Vec3< T > &v3)
Set the columns of this matrix to the vectors v1, v2, v3.
Definition: Mat3.h:257
T value_type
Definition: Mat.h:56
Vec3< T > col(int j) const
Get jth column, e.g. Vec3d v = m.col(0);.
Definition: Mat3.h:202
T trace() const
Trace of matrix.
Definition: Mat3.h:536
void setSymmetric(const Vec3< T > &vdiag, const Vec3< T > &vtri)
Set diagonal and symmetric triangular components.
Definition: Mat3.h:271
const T * asPointer() const
Definition: Mat3.h:220
void setRows(const Vec3< T > &v1, const Vec3< T > &v2, const Vec3< T > &v3)
Set the rows of this matrix to the vectors v1, v2, v3.
Definition: Mat3.h:243
Mat3< T > outerProduct(const Vec3< T > &v1, const Vec3< T > &v2)
Definition: Mat3.h:691
bool isApproxEqual(const Type &a, const Type &b)
Return true if a is equal to b to within the default floating-point comparison tolerance.
Definition: Math.h:358
T * asPointer()
Definition: Mat3.h:219
Tolerance for floating-point comparison.
Definition: Math.h:117
Mat3 transpose() const
returns transpose of this
Definition: Mat3.h:502
Vec3< T0 > pretransform(const Vec3< T0 > &v) const
Definition: Mat3.h:561
MatType snapMatBasis(const MatType &source, Axis axis, const Vec3< typename MatType::value_type > &direction)
This function snaps a specific axis to a specific direction, preserving scaling.
Definition: Mat.h:783
void pivot(int i, int j, Mat3< T > &S, Vec3< T > &D, Mat3< T > &Q)
Definition: Mat3.h:716
T angle(const Vec2< T > &v1, const Vec2< T > &v2)
Definition: Vec2.h:472
Mat3< typename promote< T0, T1 >::type > operator-(const Mat3< T0 > &m0, const Mat3< T1 > &m1)
Subtract corresponding elements of m0 and m1 and return the result.
Definition: Mat3.h:635
Mat3(const Vec3< Source > &v1, const Vec3< Source > &v2, const Vec3< Source > &v3, bool rows=true)
Definition: Mat3.h:96
Mat3(const Mat< 3, T > &m)
Copy constructor.
Definition: Mat3.h:124
Mat3()
Trivial constructor, the matrix is NOT initialized.
Definition: Mat3.h:63
Mat3(Source *a)
Definition: Mat3.h:110
T det() const
Determinant of matrix.
Definition: Mat3.h:527
Mat3 timesDiagonal(const Vec3< T > &diag) const
Treat diag as a diagonal matrix and return the product of this matrix with diag (from the right).
Definition: Mat3.h:569
MatType skew(const Vec3< typename MatType::value_type > &skew)
Return a matrix as the cross product of the given vector.
Definition: Mat.h:740
static Mat3 symmetric(const Vec3< T > &vdiag, const Vec3< T > &vtri)
Return a matrix with the prescribed diagonal and symmetric triangular components.
Definition: Mat3.h:285
#define OPENVDB_USE_VERSION_NAMESPACE
Definition: version.h:188
Mat3 inverse(T tolerance=0) const
Definition: Mat3.h:513
T ValueType
Definition: Mat.h:57
void setZero()
Set this matrix to zero.
Definition: Mat3.h:310
Mat3 adjoint() const
Return the adjoint of this matrix, i.e., the transpose of its cofactor.
Definition: Mat3.h:486
Mat3(const Quat< T > &q)
Definition: Mat3.h:67
static const Mat3< T > & identity()
Predefined constant for identity matrix.
Definition: Mat3.h:155
Definition: Exceptions.h:83
void setSkew(const Vec3< T > &v)
Set the matrix as cross product of the given vector.
Definition: Mat3.h:295
Mat3(const Mat4< T > &m)
Conversion from Mat4 (copies top left)
Definition: Mat3.h:145
Mat3< T > operator-() const
Negation operator, for e.g. m1 = -m2;.
Definition: Mat3.h:363