4 #ifndef OPENVDB_MATH_MAT3_H_HAS_BEEN_INCLUDED 5 #define OPENVDB_MATH_MAT3_H_HAS_BEEN_INCLUDED 21 template<
typename T>
class Vec3;
22 template<
typename T>
class Mat4;
23 template<
typename T>
class Quat;
50 template<
typename Source>
51 Mat3(Source a, Source b, Source c,
52 Source d, Source e, Source f,
53 Source g, Source h, Source i)
55 MyBase::mm[0] = static_cast<T>(a);
56 MyBase::mm[1] = static_cast<T>(b);
57 MyBase::mm[2] = static_cast<T>(c);
58 MyBase::mm[3] = static_cast<T>(d);
59 MyBase::mm[4] = static_cast<T>(e);
60 MyBase::mm[5] = static_cast<T>(f);
61 MyBase::mm[6] = static_cast<T>(g);
62 MyBase::mm[7] = static_cast<T>(h);
63 MyBase::mm[8] = static_cast<T>(i);
68 template<
typename Source>
72 this->setRows(v1, v2, v3);
74 this->setColumns(v1, v2, v3);
82 template<
typename Source>
85 MyBase::mm[0] = static_cast<T>(a[0]);
86 MyBase::mm[1] = static_cast<T>(a[1]);
87 MyBase::mm[2] = static_cast<T>(a[2]);
88 MyBase::mm[3] = static_cast<T>(a[3]);
89 MyBase::mm[4] = static_cast<T>(a[4]);
90 MyBase::mm[5] = static_cast<T>(a[5]);
91 MyBase::mm[6] = static_cast<T>(a[6]);
92 MyBase::mm[7] = static_cast<T>(a[7]);
93 MyBase::mm[8] = static_cast<T>(a[8]);
99 for (
int i=0; i<3; ++i) {
100 for (
int j=0; j<3; ++j) {
101 MyBase::mm[i*3 + j] = m[i][j];
107 template<
typename Source>
110 for (
int i=0; i<3; ++i) {
111 for (
int j=0; j<3; ++j) {
112 MyBase::mm[i*3 + j] = static_cast<T>(m[i][j]);
120 for (
int i=0; i<3; ++i) {
121 for (
int j=0; j<3; ++j) {
122 MyBase::mm[i*3 + j] = m[i][j];
153 MyBase::mm[i3+0] = v[0];
154 MyBase::mm[i3+1] = v[1];
155 MyBase::mm[i3+2] = v[2];
162 return Vec3<T>((*
this)(i,0), (*
this)(i,1), (*
this)(i,2));
169 MyBase::mm[0+j] = v[0];
170 MyBase::mm[3+j] = v[1];
171 MyBase::mm[6+j] = v[2];
178 return Vec3<T>((*
this)(0,j), (*
this)(1,j), (*
this)(2,j));
186 T* operator[](
int i) {
return &(MyBase::mm[i*3]); }
189 const T*
operator[](
int i)
const {
return &(MyBase::mm[i*3]); }
202 return MyBase::mm[3*i+j];
212 return MyBase::mm[3*i+j];
218 MyBase::mm[0] = v1[0];
219 MyBase::mm[1] = v1[1];
220 MyBase::mm[2] = v1[2];
221 MyBase::mm[3] = v2[0];
222 MyBase::mm[4] = v2[1];
223 MyBase::mm[5] = v2[2];
224 MyBase::mm[6] = v3[0];
225 MyBase::mm[7] = v3[1];
226 MyBase::mm[8] = v3[2];
232 MyBase::mm[0] = v1[0];
233 MyBase::mm[1] = v2[0];
234 MyBase::mm[2] = v3[0];
235 MyBase::mm[3] = v1[1];
236 MyBase::mm[4] = v2[1];
237 MyBase::mm[5] = v3[1];
238 MyBase::mm[6] = v1[2];
239 MyBase::mm[7] = v2[2];
240 MyBase::mm[8] = v3[2];
246 MyBase::mm[0] = vdiag[0];
247 MyBase::mm[1] = vtri[0];
248 MyBase::mm[2] = vtri[1];
249 MyBase::mm[3] = vtri[0];
250 MyBase::mm[4] = vdiag[1];
251 MyBase::mm[5] = vtri[2];
252 MyBase::mm[6] = vtri[1];
253 MyBase::mm[7] = vtri[2];
254 MyBase::mm[8] = vdiag[2];
261 vdiag[0], vtri[0], vtri[1],
262 vtri[0], vdiag[1], vtri[2],
263 vtri[1], vtri[2], vdiag[2]
275 {*
this = rotation<Mat3<T> >(q);}
280 {*
this = rotation<Mat3<T> >(axis,
angle);}
311 template<
typename Source>
317 std::copy(src, (src + this->numElements()), MyBase::mm);
322 bool eq(
const Mat3 &m, T eps=1.0e-8)
const 339 -MyBase::mm[0], -MyBase::mm[1], -MyBase::mm[2],
340 -MyBase::mm[3], -MyBase::mm[4], -MyBase::mm[5],
341 -MyBase::mm[6], -MyBase::mm[7], -MyBase::mm[8]
351 template <
typename S>
354 MyBase::mm[0] *= scalar;
355 MyBase::mm[1] *= scalar;
356 MyBase::mm[2] *= scalar;
357 MyBase::mm[3] *= scalar;
358 MyBase::mm[4] *= scalar;
359 MyBase::mm[5] *= scalar;
360 MyBase::mm[6] *= scalar;
361 MyBase::mm[7] *= scalar;
362 MyBase::mm[8] *= scalar;
367 template <
typename S>
372 MyBase::mm[0] += s[0];
373 MyBase::mm[1] += s[1];
374 MyBase::mm[2] += s[2];
375 MyBase::mm[3] += s[3];
376 MyBase::mm[4] += s[4];
377 MyBase::mm[5] += s[5];
378 MyBase::mm[6] += s[6];
379 MyBase::mm[7] += s[7];
380 MyBase::mm[8] += s[8];
385 template <
typename S>
390 MyBase::mm[0] -= s[0];
391 MyBase::mm[1] -= s[1];
392 MyBase::mm[2] -= s[2];
393 MyBase::mm[3] -= s[3];
394 MyBase::mm[4] -= s[4];
395 MyBase::mm[5] -= s[5];
396 MyBase::mm[6] -= s[6];
397 MyBase::mm[7] -= s[7];
398 MyBase::mm[8] -= s[8];
403 template <
typename S>
410 MyBase::mm[0] = static_cast<T>(s0[0] * s1[0] +
413 MyBase::mm[1] = static_cast<T>(s0[0] * s1[1] +
416 MyBase::mm[2] = static_cast<T>(s0[0] * s1[2] +
420 MyBase::mm[3] = static_cast<T>(s0[3] * s1[0] +
423 MyBase::mm[4] = static_cast<T>(s0[3] * s1[1] +
426 MyBase::mm[5] = static_cast<T>(s0[3] * s1[2] +
430 MyBase::mm[6] = static_cast<T>(s0[6] * s1[0] +
433 MyBase::mm[7] = static_cast<T>(s0[6] * s1[1] +
436 MyBase::mm[8] = static_cast<T>(s0[6] * s1[2] +
447 MyBase::mm[4] * MyBase::mm[8] - MyBase::mm[5] * MyBase::mm[7],
448 MyBase::mm[5] * MyBase::mm[6] - MyBase::mm[3] * MyBase::mm[8],
449 MyBase::mm[3] * MyBase::mm[7] - MyBase::mm[4] * MyBase::mm[6],
450 MyBase::mm[2] * MyBase::mm[7] - MyBase::mm[1] * MyBase::mm[8],
451 MyBase::mm[0] * MyBase::mm[8] - MyBase::mm[2] * MyBase::mm[6],
452 MyBase::mm[1] * MyBase::mm[6] - MyBase::mm[0] * MyBase::mm[7],
453 MyBase::mm[1] * MyBase::mm[5] - MyBase::mm[2] * MyBase::mm[4],
454 MyBase::mm[2] * MyBase::mm[3] - MyBase::mm[0] * MyBase::mm[5],
455 MyBase::mm[0] * MyBase::mm[4] - MyBase::mm[1] * MyBase::mm[3]);
462 MyBase::mm[4] * MyBase::mm[8] - MyBase::mm[5] * MyBase::mm[7],
463 MyBase::mm[2] * MyBase::mm[7] - MyBase::mm[1] * MyBase::mm[8],
464 MyBase::mm[1] * MyBase::mm[5] - MyBase::mm[2] * MyBase::mm[4],
465 MyBase::mm[5] * MyBase::mm[6] - MyBase::mm[3] * MyBase::mm[8],
466 MyBase::mm[0] * MyBase::mm[8] - MyBase::mm[2] * MyBase::mm[6],
467 MyBase::mm[2] * MyBase::mm[3] - MyBase::mm[0] * MyBase::mm[5],
468 MyBase::mm[3] * MyBase::mm[7] - MyBase::mm[4] * MyBase::mm[6],
469 MyBase::mm[1] * MyBase::mm[6] - MyBase::mm[0] * MyBase::mm[7],
470 MyBase::mm[0] * MyBase::mm[4] - MyBase::mm[1] * MyBase::mm[3]);
478 MyBase::mm[0], MyBase::mm[3], MyBase::mm[6],
479 MyBase::mm[1], MyBase::mm[4], MyBase::mm[7],
480 MyBase::mm[2], MyBase::mm[5], MyBase::mm[8]);
490 const T det = inv.
mm[0]*MyBase::mm[0] + inv.
mm[1]*MyBase::mm[3] + inv.
mm[2]*MyBase::mm[6];
496 return inv * (T(1)/det);
502 const T co00 = MyBase::mm[4]*MyBase::mm[8] - MyBase::mm[5]*MyBase::mm[7];
503 const T co10 = MyBase::mm[5]*MyBase::mm[6] - MyBase::mm[3]*MyBase::mm[8];
504 const T co20 = MyBase::mm[3]*MyBase::mm[7] - MyBase::mm[4]*MyBase::mm[6];
505 return MyBase::mm[0]*co00 + MyBase::mm[1]*co10 + MyBase::mm[2]*co20;
511 return MyBase::mm[0]+MyBase::mm[4]+MyBase::mm[8];
525 template<
typename T0>
528 return static_cast< Vec3<T0> >(v * *
this);
533 template<
typename T0>
536 return static_cast< Vec3<T0> >(*
this * v);
546 ret.
mm[0] *= diag(0);
547 ret.
mm[1] *= diag(1);
548 ret.
mm[2] *= diag(2);
549 ret.
mm[3] *= diag(0);
550 ret.
mm[4] *= diag(1);
551 ret.
mm[5] *= diag(2);
552 ret.
mm[6] *= diag(0);
553 ret.
mm[7] *= diag(1);
554 ret.
mm[8] *= diag(2);
562 template <
typename T0,
typename T1>
568 for (
int i=0; i<9; ++i) {
576 template <
typename T0,
typename T1>
581 template <
typename S,
typename T>
587 template <
typename S,
typename T>
597 template <
typename T0,
typename T1>
607 template <
typename T0,
typename T1>
617 template <
typename T0,
typename T1>
627 template<
typename T,
typename MT>
633 _v[0]*m[0] + _v[1]*m[1] + _v[2]*m[2],
634 _v[0]*m[3] + _v[1]*m[4] + _v[2]*m[5],
635 _v[0]*m[6] + _v[1]*m[7] + _v[2]*m[8]);
640 template<
typename T,
typename MT>
646 _v[0]*m[0] + _v[1]*m[3] + _v[2]*m[6],
647 _v[0]*m[1] + _v[1]*m[4] + _v[2]*m[7],
648 _v[0]*m[2] + _v[1]*m[5] + _v[2]*m[8]);
653 template<
typename T,
typename MT>
663 template <
typename T>
666 return Mat3<T>(v1[0]*v2[0], v1[0]*v2[1], v1[0]*v2[2],
667 v1[1]*v2[0], v1[1]*v2[1], v1[1]*v2[2],
668 v1[2]*v2[0], v1[2]*v2[1], v1[2]*v2[2]);
675 template<
typename T,
typename T0>
685 namespace mat3_internal {
694 double cotan_of_2_theta;
696 double cosin_of_theta;
702 double Sjj_minus_Sii = D[j] - D[i];
705 tan_of_theta = Sij / Sjj_minus_Sii;
708 cotan_of_2_theta = 0.5*Sjj_minus_Sii / Sij ;
710 if (cotan_of_2_theta < 0.) {
712 -1./(sqrt(1. + cotan_of_2_theta*cotan_of_2_theta) - cotan_of_2_theta);
715 1./(sqrt(1. + cotan_of_2_theta*cotan_of_2_theta) + cotan_of_2_theta);
719 cosin_of_theta = 1./sqrt( 1. + tan_of_theta * tan_of_theta);
720 sin_of_theta = cosin_of_theta * tan_of_theta;
721 z = tan_of_theta * Sij;
725 for (
int k = 0; k < i; ++k) {
727 S(k,i) = cosin_of_theta * temp - sin_of_theta * S(k,j);
728 S(k,j)= sin_of_theta * temp + cosin_of_theta * S(k,j);
730 for (
int k = i+1; k < j; ++k) {
732 S(i,k) = cosin_of_theta * temp - sin_of_theta * S(k,j);
733 S(k,j) = sin_of_theta * temp + cosin_of_theta * S(k,j);
735 for (
int k = j+1; k < n; ++k) {
737 S(i,k) = cosin_of_theta * temp - sin_of_theta * S(j,k);
738 S(j,k) = sin_of_theta * temp + cosin_of_theta * S(j,k);
740 for (
int k = 0; k < n; ++k)
743 Q(k,i) = cosin_of_theta * temp - sin_of_theta*Q(k,j);
744 Q(k,j) = sin_of_theta * temp + cosin_of_theta*Q(k,j);
759 unsigned int MAX_ITERATIONS=250)
769 for (
int i = 0; i < n; ++i) {
773 unsigned int iterations(0);
780 for (
int i = 0; i < n; ++i) {
781 for (
int j = i+1; j < n; ++j) {
794 for (
int i = 0; i < n; ++i) {
795 for (
int j = i+1; j < n; ++j){
801 if (fabs(S(i,j)) > max_element) {
802 max_element = fabs(S(i,j));
809 }
while (iterations < MAX_ITERATIONS);
822 template<>
inline math::Mat3s zeroVal<math::Mat3s>() {
return math::Mat3s::zero(); }
823 template<>
inline math::Mat3d zeroVal<math::Mat3d>() {
return math::Mat3d::zero(); }
828 #endif // OPENVDB_MATH_MAT3_H_HAS_BEEN_INCLUDED Vec3< typename promote< T, MT >::type > operator*(const Vec3< T > &_v, const Mat3< MT > &_m)
Multiply _v by _m and return the resulting vector.
Definition: Mat3.h:642
Vec3< T > row(int i) const
Get ith row, e.g. Vec3d v = m.row(1);.
Definition: Mat3.h:159
void pivot(int i, int j, Mat3< T > &S, Vec3< T > &D, Mat3< T > &Q)
Definition: Mat3.h:689
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:351
Mat3(const Vec3< Source > &v1, const Vec3< Source > &v2, const Vec3< Source > &v3, bool rows=true)
Definition: Mat3.h:69
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:230
Mat3(const Mat4< T > &m)
Conversion from Mat4 (copies top left)
Definition: Mat3.h:118
T trace() const
Trace of matrix.
Definition: Mat3.h:509
Vec3< T0 > pretransform(const Vec3< T0 > &v) const
Definition: Mat3.h:534
T ValueType
Definition: Mat.h:30
MatType skew(const Vec3< typename MatType::value_type > &skew)
Return a matrix as the cross product of the given vector.
Definition: Mat.h:713
Mat3< typename promote< S, T >::type > operator*(const Mat3< T > &m, S scalar)
Multiply each element of the given matrix by scalar and return the result.
Definition: Mat3.h:588
#define OPENVDB_THROW(exception, message)
Definition: Exceptions.h:82
Mat3< double > Mat3d
Definition: Mat3.h:816
Vec3< T > col(int j) const
Get jth column, e.g. Vec3d v = m.col(0);.
Definition: Mat3.h:175
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:542
const T * asPointer() const
Definition: Mat3.h:193
T mm[SIZE *SIZE]
Definition: Mat.h:165
Mat3(const Mat< 3, T > &m)
Copy constructor.
Definition: Mat3.h:97
Axis
Definition: Math.h:849
void setIdentity()
Set this matrix to identity.
Definition: Mat3.h:297
Mat3(Source *a)
Definition: Mat3.h:83
T det() const
Determinant of matrix.
Definition: Mat3.h:500
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:216
void setToRotation(const Vec3< T > &axis, T angle)
Set this matrix to the rotation specified by axis and angle.
Definition: Mat3.h:279
Mat3< T > powLerp(const Mat3< T0 > &m1, const Mat3< T0 > &m2, T t)
Definition: Mat3.h:676
Mat3()
Trivial constructor, the matrix is NOT initialized.
Definition: Mat3.h:36
Mat3 cofactor() const
Return the cofactor matrix of this matrix.
Definition: Mat3.h:444
void setSkew(const Vec3< T > &v)
Set the matrix as cross product of the given vector.
Definition: Mat3.h:268
void setSymmetric(const Vec3< T > &vdiag, const Vec3< T > &vtri)
Set diagonal and symmetric triangular components.
Definition: Mat3.h:244
#define OPENVDB_VERSION_NAME
The version namespace name for this library version.
Definition: version.h:102
T * asPointer()
Definition: Mat3.h:192
const Mat3< T > & operator*=(S scalar)
Multiplication operator, e.g. M = scalar * M;.
Definition: Mat3.h:352
Mat3(const Quat< T > &q)
Definition: Mat3.h:40
T operator()(int i, int j) const
Definition: Mat3.h:208
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:608
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:598
const Mat3< T > & operator*=(const Mat3< S > &m1)
Multiply this matrix by the given matrix.
Definition: Mat3.h:404
4x4 -matrix class.
Definition: Mat3.h:22
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:51
Mat3< typename promote< S, T >::type > operator*(S scalar, const Mat3< T > &m)
Multiply each element of the given matrix by scalar and return the result.
Definition: Mat3.h:582
Definition: Exceptions.h:13
Definition: Exceptions.h:56
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:758
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:258
bool operator==(const Mat3< T0 > &m0, const Mat3< T1 > &m1)
Equality operator, does exact floating point comparisons.
Definition: Mat3.h:563
void setToRotation(const Quat< T > &q)
Set this matrix to the rotation matrix specified by the quaternion.
Definition: Mat3.h:274
void setCol(int j, const Vec3< T > &v)
Set jth column to vector v.
Definition: Mat3.h:166
Mat3< T > operator-() const
Negation operator, for e.g. m1 = -m2;.
Definition: Mat3.h:336
const T * operator[](int i) const
Definition: Mat3.h:189
Vec3< T0 > transform(const Vec3< T0 > &v) const
Definition: Mat3.h:526
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:386
Vec3< typename promote< T, MT >::type > operator*(const Mat3< MT > &_m, const Vec3< T > &_v)
Multiply _m by _v and return the resulting vector.
Definition: Mat3.h:629
static const Mat3< T > & zero()
Predefined constant for zero matrix.
Definition: Mat3.h:138
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:368
Tolerance for floating-point comparison.
Definition: Math.h:90
void powSolve(const MatType &aA, MatType &aB, double aPower, double aTol=0.01)
Definition: Mat.h:827
3x3 matrix class.
Definition: Mat3.h:28
Mat3 inverse(T tolerance=0) const
Definition: Mat3.h:486
Mat3(const Mat3< Source > &m)
Conversion constructor.
Definition: Mat3.h:108
void setZero()
Set this matrix to zero.
Definition: Mat3.h:283
Mat3 adjoint() const
Return the adjoint of this matrix, i.e., the transpose of its cofactor.
Definition: Mat3.h:459
static const Mat3< T > & identity()
Predefined constant for identity matrix.
Definition: Mat3.h:128
T value_type
Definition: Mat.h:29
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:618
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:756
Mat3< T > outerProduct(const Vec3< T > &v1, const Vec3< T > &v2)
Definition: Mat3.h:664
T angle(const Vec2< T > &v1, const Vec2< T > &v2)
Definition: Vec2.h:445
const Mat3 & operator=(const Mat3< Source > &m)
Assignment operator.
Definition: Mat3.h:312
Mat3 snapBasis(Axis axis, const Vec3< T > &direction)
Definition: Mat3.h:518
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:322
bool isExactlyEqual(const T0 &a, const T1 &b)
Return true if a is exactly equal to b.
Definition: Math.h:388
#define OPENVDB_USE_VERSION_NAMESPACE
Definition: version.h:154
T & operator()(int i, int j)
Definition: Mat3.h:198
void setRow(int i, const Vec3< T > &v)
Set ith row to vector v.
Definition: Mat3.h:148
Mat3 transpose() const
returns transpose of this
Definition: Mat3.h:475
bool operator!=(const Mat3< T0 > &m0, const Mat3< T1 > &m1)
Inequality operator, does exact floating point comparisons.
Definition: Mat3.h:577