4#ifndef OPENVDB_MATH_MAT4_H_HAS_BEEN_INCLUDED
5#define OPENVDB_MATH_MAT4_H_HAS_BEEN_INCLUDED
24template<
typename T>
class Vec4;
50 template<
typename Source>
53 for (
int i = 0; i < 16; i++) {
65 template<
typename Source>
66 Mat4(Source a, Source b, Source c, Source d,
67 Source e, Source f, Source g, Source h,
68 Source i, Source j, Source k, Source l,
69 Source m, Source n, Source o, Source p)
94 template<
typename Source>
106 template<
typename Source>
111 for (
int i=0; i<16; ++i) {
153 return Vec4<T>((*
this)(i,0), (*
this)(i,1), (*
this)(i,2), (*
this)(i,3));
170 return Vec4<T>((*
this)(0,j), (*
this)(1,j), (*
this)(2,j), (*
this)(3,j));
292 for (
int i = 0; i < 3; i++)
293 for (
int j=0; j < 3; j++)
301 for (
int i = 0; i < 3; i++)
302 for (
int j = 0; j < 3; j++)
322 template<
typename Source>
333 bool eq(
const Mat4 &m, T eps=1.0e-8)
const
335 for (
int i = 0; i < 16; i++) {
354 template <
typename S>
380 template <
typename S>
409 template <
typename S>
438 template <
typename S>
446 for (
int i = 0; i < 4; i++) {
448 MyBase::mm[i4+0] =
static_cast<T
>(s0[i4+0] * s1[ 0] +
453 MyBase::mm[i4+1] =
static_cast<T
>(s0[i4+0] * s1[ 1] +
458 MyBase::mm[i4+2] =
static_cast<T
>(s0[i4+0] * s1[ 2] +
463 MyBase::mm[i4+3] =
static_cast<T
>(s0[i4+0] * s1[ 3] +
508 T m0011 = m[0][0] * m[1][1];
509 T m0012 = m[0][0] * m[1][2];
510 T m0110 = m[0][1] * m[1][0];
511 T m0210 = m[0][2] * m[1][0];
512 T m0120 = m[0][1] * m[2][0];
513 T m0220 = m[0][2] * m[2][0];
515 T detA = m0011 * m[2][2] - m0012 * m[2][1] - m0110 * m[2][2]
516 + m0210 * m[2][1] + m0120 * m[1][2] - m0220 * m[1][1];
518 bool hasPerspective =
525 if (hasPerspective) {
526 det = m[0][3] * det3(m, 1,2,3, 0,2,1)
527 + m[1][3] * det3(m, 2,0,3, 0,2,1)
528 + m[2][3] * det3(m, 3,0,1, 0,2,1)
531 det = detA * m[3][3];
542 invertible = m.invert(inv, tolerance);
551 inv[0][0] = detA * ( m[1][1] * m[2][2] - m[1][2] * m[2][1]);
552 inv[0][1] = detA * (-m[0][1] * m[2][2] + m[0][2] * m[2][1]);
553 inv[0][2] = detA * ( m[0][1] * m[1][2] - m[0][2] * m[1][1]);
555 inv[1][0] = detA * (-m[1][0] * m[2][2] + m[1][2] * m[2][0]);
556 inv[1][1] = detA * ( m[0][0] * m[2][2] - m0220);
557 inv[1][2] = detA * ( m0210 - m0012);
559 inv[2][0] = detA * ( m[1][0] * m[2][1] - m[1][1] * m[2][0]);
560 inv[2][1] = detA * ( m0120 - m[0][0] * m[2][1]);
561 inv[2][2] = detA * ( m0011 - m0110);
563 if (hasPerspective) {
568 r[0] = m[3][0] * inv[0][0] + m[3][1] * inv[1][0]
569 + m[3][2] * inv[2][0];
570 r[1] = m[3][0] * inv[0][1] + m[3][1] * inv[1][1]
571 + m[3][2] * inv[2][1];
572 r[2] = m[3][0] * inv[0][2] + m[3][1] * inv[1][2]
573 + m[3][2] * inv[2][2];
576 p[0] = inv[0][0] * m[0][3] + inv[0][1] * m[1][3]
577 + inv[0][2] * m[2][3];
578 p[1] = inv[1][0] * m[0][3] + inv[1][1] * m[1][3]
579 + inv[1][2] * m[2][3];
580 p[2] = inv[2][0] * m[0][3] + inv[2][1] * m[1][3]
581 + inv[2][2] * m[2][3];
583 T h = m[3][3] - p.
dot(
Vec3<T>(m[3][0],m[3][1],m[3][2]));
594 inv[3][0] = -h * r[0];
595 inv[3][1] = -h * r[1];
596 inv[3][2] = -h * r[2];
598 inv[0][3] = -h * p[0];
599 inv[1][3] = -h * p[1];
600 inv[2][3] = -h * p[2];
606 inv[0][0] += p[0] * r[0];
607 inv[0][1] += p[0] * r[1];
608 inv[0][2] += p[0] * r[2];
609 inv[1][0] += p[1] * r[0];
610 inv[1][1] += p[1] * r[1];
611 inv[1][2] += p[1] * r[2];
612 inv[2][0] += p[2] * r[0];
613 inv[2][1] += p[2] * r[1];
614 inv[2][2] += p[2] * r[2];
618 inv[3][0] = - (m[3][0] * inv[0][0] + m[3][1] * inv[1][0]
619 + m[3][2] * inv[2][0]);
620 inv[3][1] = - (m[3][0] * inv[0][1] + m[3][1] * inv[1][1]
621 + m[3][2] * inv[2][1]);
622 inv[3][2] = - (m[3][0] * inv[0][2] + m[3][1] * inv[1][2]
623 + m[3][2] * inv[2][2]);
647 for (i = 0; i < 4; i++) {
650 for (j = 0; j < 4; j++) {
651 for (k = 0; k < 4; k++) {
652 if ((k != i) && (j != 0)) {
670 T(1), T(0), T(0), T(0),
671 T(0), T(1), T(0), T(0),
672 T(0), T(0), T(1), T(0),
673 T(v.
x()), T(v.
y()),T(v.
z()), T(1));
677 template <
typename T0>
702 template <
typename T0>
708 *
this = Tr * (*this);
713 template <
typename T0>
719 *
this = (*this) * Tr;
725 template <
typename T0>
735 template <
typename T0>
757 template <
typename T0>
800 T c =
static_cast<T
>(cos(
angle));
801 T s = -
static_cast<T
>(sin(
angle));
880 T c =
static_cast<T
>(cos(
angle));
881 T s = -
static_cast<T
>(sin(
angle));
970 int index0 =
static_cast<int>(axis0);
971 int index1 =
static_cast<int>(axis1);
985 int index0 =
static_cast<int>(axis0);
986 int index1 =
static_cast<int>(axis1);
997 template<
typename T0>
1000 return static_cast< Vec4<T0> >(v * *
this);
1004 template<
typename T0>
1007 return static_cast< Vec3<T0> >(v * *
this);
1011 template<
typename T0>
1014 return static_cast< Vec4<T0> >(*
this * v);
1018 template<
typename T0>
1021 return static_cast< Vec3<T0> >(*
this * v);
1025 template<
typename T0>
1047 template<
typename T0>
1068 template<
typename T0>
1079 bool invert(
Mat4<T> &inverse, T tolerance)
const;
1081 T det2(
const Mat4<T> &a,
int i0,
int i1,
int j0,
int j1)
const {
1084 return a.
mm[i0row+j0]*a.
mm[i1row+j1] - a.
mm[i0row+j1]*a.
mm[i1row+j0];
1087 T det3(
const Mat4<T> &a,
int i0,
int i1,
int i2,
1088 int j0,
int j1,
int j2)
const {
1090 return a.mm[i0row+j0]*det2(a, i1,i2, j1,j2) +
1091 a.mm[i0row+j1]*det2(a, i1,i2, j2,j0) +
1092 a.mm[i0row+j2]*det2(a, i1,i2, j0,j1);
1099template <
typename T0,
typename T1>
1105 for (
int i=0; i<16; ++i)
if (!
isExactlyEqual(t0[i], t1[i]))
return false;
1111template <
typename T0,
typename T1>
1116template <
typename S,
typename T>
1124template <
typename S,
typename T>
1134template<
typename T,
typename MT>
1141 _v[0]*m[0] + _v[1]*m[1] + _v[2]*m[2] + _v[3]*m[3],
1142 _v[0]*m[4] + _v[1]*m[5] + _v[2]*m[6] + _v[3]*m[7],
1143 _v[0]*m[8] + _v[1]*m[9] + _v[2]*m[10] + _v[3]*m[11],
1144 _v[0]*m[12] + _v[1]*m[13] + _v[2]*m[14] + _v[3]*m[15]);
1149template<
typename T,
typename MT>
1156 _v[0]*m[0] + _v[1]*m[4] + _v[2]*m[8] + _v[3]*m[12],
1157 _v[0]*m[1] + _v[1]*m[5] + _v[2]*m[9] + _v[3]*m[13],
1158 _v[0]*m[2] + _v[1]*m[6] + _v[2]*m[10] + _v[3]*m[14],
1159 _v[0]*m[3] + _v[1]*m[7] + _v[2]*m[11] + _v[3]*m[15]);
1164template<
typename T,
typename MT>
1170 _v[0]*m[0] + _v[1]*m[1] + _v[2]*m[2] + m[3],
1171 _v[0]*m[4] + _v[1]*m[5] + _v[2]*m[6] + m[7],
1172 _v[0]*m[8] + _v[1]*m[9] + _v[2]*m[10] + m[11]);
1177template<
typename T,
typename MT>
1183 _v[0]*m[0] + _v[1]*m[4] + _v[2]*m[8] + m[12],
1184 _v[0]*m[1] + _v[1]*m[5] + _v[2]*m[9] + m[13],
1185 _v[0]*m[2] + _v[1]*m[6] + _v[2]*m[10] + m[14]);
1190template <
typename T0,
typename T1>
1201template <
typename T0,
typename T1>
1212template <
typename T0,
typename T1>
1225template<
typename T0,
typename T1>
1229 static_cast<T1
>(m[0][0]*n[0] + m[0][1]*n[1] + m[0][2]*n[2]),
1230 static_cast<T1
>(m[1][0]*n[0] + m[1][1]*n[1] + m[1][2]*n[2]),
1231 static_cast<T1
>(m[2][0]*n[0] + m[2][1]*n[1] + m[2][2]*n[2]));
1237bool Mat4<T>::invert(Mat4<T> &inverse, T tolerance)
const
1239 Mat4<T> temp(*
this);
1240 inverse.setIdentity();
1244 for (
int i = 0; i < 4; ++i) {
1246 double max = fabs(temp[i][i]);
1248 for (
int k = i+1; k < 4; ++k) {
1249 if (fabs(temp[k][i]) > max) {
1251 max = fabs(temp[k][i]);
1255 if (isExactlyEqual(max, 0.0))
return false;
1260 for (
int k = 0; k < 4; ++k) {
1261 std::swap(temp[row][k], temp[i][k]);
1262 std::swap(inverse[row][k], inverse[i][k]);
1266 double pivot = temp[i][i];
1270 for (
int k = 0; k < 4; ++k) {
1271 temp[i][k] /=
pivot;
1272 inverse[i][k] /=
pivot;
1276 for (
int j = i+1; j < 4; ++j) {
1277 double t = temp[j][i];
1280 for (
int k = 0; k < 4; ++k) {
1281 temp[j][k] -= temp[i][k] * t;
1282 inverse[j][k] -= inverse[i][k] * t;
1289 for (
int i = 3; i > 0; --i) {
1290 for (
int j = 0; j < i; ++j) {
1291 double t = temp[j][i];
1294 for (
int k = 0; k < 4; ++k) {
1295 inverse[j][k] -= inverse[i][k]*t;
1300 return det*det >= tolerance*tolerance;
1303template <
typename T>
1308template <
typename T>
1320 for (
unsigned i = 0; i < 16; ++i, ++op, ++ip) *op =
math::Abs(*ip);
1324template<
typename Type1,
typename Type2>
1331 for (
unsigned i = 0; i < 16; ++i, ++op, ++ip) {
General-purpose arithmetic and comparison routines, most of which accept arbitrary value types (or at...
#define OPENVDB_IS_POD(Type)
Definition Math.h:56
Definition Exceptions.h:56
3x3 matrix class.
Definition Mat3.h:29
T det() const
Determinant of matrix.
Definition Mat3.h:479
4x4 -matrix class.
Definition Mat4.h:31
void postTranslate(const Vec3< T0 > &tr)
Right multiplies by the specified translation matrix, i.e. (*this) * Trans.
Definition Mat4.h:714
void preScale(const Vec3< T0 > &v)
Definition Mat4.h:736
Mat4< typename promote< T0, T1 >::type > operator+(const Mat4< T0 > &m0, const Mat4< T1 > &m1)
Add corresponding elements of m0 and m1 and return the result.
Definition Mat4.h:1192
const Mat4< T > & operator*=(const Mat4< S > &m1)
Multiply this matrix by the given matrix.
Definition Mat4.h:439
Vec3< T > getTranslation() const
Return the translation component.
Definition Mat4.h:309
Mat4(const Mat4< Source > &m)
Conversion constructor.
Definition Mat4.h:107
void preTranslate(const Vec3< T0 > &tr)
Left multiples by the specified translation, i.e. Trans * (*this)
Definition Mat4.h:703
void postRotate(Axis axis, T angle)
Right multiplies by a rotation clock-wiseabout the given axis into this matrix.
Definition Mat4.h:878
void setIdentity()
Set this matrix to identity.
Definition Mat4.h:265
Mat4< typename promote< S, T >::type > operator*(const Mat4< T > &m, S scalar)
Multiply each element of the given matrix by scalar and return the result.
Definition Mat4.h:1125
Vec4< typename promote< T, MT >::type > operator*(const Vec4< T > &_v, const Mat4< MT > &_m)
Multiply _v by _m and return the resulting vector.
Definition Mat4.h:1151
void setToRotation(const Vec3< T > &axis, T angle)
Sets the matrix to a rotation about an arbitrary axis.
Definition Mat4.h:788
void setRows(const Vec4< Real > &v1, const Vec4< Real > &v2, const Vec4< Real > &v3, const Vec4< Real > &v4)
Definition Mat4.h:194
void setZero()
Definition Mat4.h:244
void setToScale(const Vec3< T0 > &v)
Sets the matrix to a matrix that scales by v.
Definition Mat4.h:726
Mat4 inverse(T tolerance=0) const
Definition Mat4.h:485
static Mat4 translation(const Vec3d &v)
Sets the matrix to a matrix that translates by v.
Definition Mat4.h:667
void preRotate(Axis axis, T angle)
Left multiplies by a rotation clock-wiseabout the given axis into this matrix.
Definition Mat4.h:798
Mat3< T > getMat3() const
Definition Mat4.h:297
Vec4< T > col(int j) const
Get jth column, e.g. Vec4f v = m.col(0);.
Definition Mat4.h:167
static const Mat4< T > & identity()
Predefined constant for identity matrix.
Definition Mat4.h:117
bool eq(const Mat4 &m, T eps=1.0e-8) const
Return true if this matrix is equivalent to m within a tolerance of eps.
Definition Mat4.h:333
void setToShear(Axis axis0, Axis axis1, T shearby)
Sets the matrix to a shear along axis0 by a fraction of axis1.
Definition Mat4.h:960
Vec3< T0 > pretransform(const Vec3< T0 > &v) const
Transform a Vec3 by pre-multiplication, without homogenous division.
Definition Mat4.h:1019
Mat4 transpose() const
Definition Mat4.h:472
void postShear(Axis axis0, Axis axis1, T shear)
Right multiplies a shearing transformation into the matrix.
Definition Mat4.h:983
bool operator==(const Mat4< T0 > &m0, const Mat4< T1 > &m1)
Equality operator, does exact floating point comparisons.
Definition Mat4.h:1100
void setToRotation(Axis axis, T angle)
Sets the matrix to a rotation about the given axis.
Definition Mat4.h:783
void setCol(int j, const Vec4< T > &v)
Set jth column to vector v.
Definition Mat4.h:157
Vec3< typename promote< T, MT >::type > operator*(const Mat4< MT > &_m, const Vec3< T > &_v)
Multiply _m by _v and return the resulting vector.
Definition Mat4.h:1166
Vec3< typename promote< T, MT >::type > operator*(const Vec3< T > &_v, const Mat4< MT > &_m)
Multiply _v by _m and return the resulting vector.
Definition Mat4.h:1179
Vec4< T0 > transform(const Vec4< T0 > &v) const
Transform a Vec4 by post-multiplication.
Definition Mat4.h:998
void preShear(Axis axis0, Axis axis1, T shear)
Left multiplies a shearing transformation into the matrix.
Definition Mat4.h:968
void setColumns(const Vec4< Real > &v1, const Vec4< Real > &v2, const Vec4< Real > &v3, const Vec4< Real > &v4)
Definition Mat4.h:219
Mat< 4, Real > MyBase
Definition Mat4.h:36
static const Mat4< T > & zero()
Predefined constant for zero matrix.
Definition Mat4.h:128
Vec3< T0 > transform3x3(const Vec3< T0 > &v) const
Transform a Vec3 by post-multiplication, without translation.
Definition Mat4.h:1069
Mat4(const Vec4< Source > &v1, const Vec4< Source > &v2, const Vec4< Source > &v3, const Vec4< Source > &v4, bool rows=true)
Definition Mat4.h:95
void setTranslation(const Vec3< T > &t)
Definition Mat4.h:314
Vec3< T0 > pretransformH(const Vec3< T0 > &p) const
Transform a Vec3 by pre-multiplication, doing homogenous division.
Definition Mat4.h:1048
void setToRotation(const Vec3< T > &v1, const Vec3< T > &v2)
Sets the matrix to a rotation that maps v1 onto v2 about the cross product of v1 and v2.
Definition Mat4.h:792
void setToTranslation(const Vec3< T0 > &v)
Sets the matrix to a matrix that translates by v.
Definition Mat4.h:678
Real det() const
Definition Mat4.h:637
Mat4< typename promote< S, T >::type > operator*(S scalar, const Mat4< T > &m)
Multiply each element of the given matrix by scalar and return the result.
Definition Mat4.h:1117
Vec4< T > row(int i) const
Get ith row, e.g. Vec4f v = m.row(1);.
Definition Mat4.h:150
const Mat4< T > & operator+=(const Mat4< S > &m1)
Add each element of the given matrix to the corresponding element of this matrix.
Definition Mat4.h:381
Mat4< typename promote< T0, T1 >::type > operator-(const Mat4< T0 > &m0, const Mat4< T1 > &m1)
Subtract corresponding elements of m0 and m1 and return the result.
Definition Mat4.h:1203
Mat4(Source *a)
Constructor given array of elements, the ordering is in row major form:
Definition Mat4.h:51
bool operator!=(const Mat4< T0 > &m0, const Mat4< T1 > &m1)
Inequality operator, does exact floating point comparisons.
Definition Mat4.h:1112
T & operator()(int i, int j)
Definition Mat4.h:176
void setRow(int i, const Vec4< T > &v)
Set ith row to vector v.
Definition Mat4.h:139
Mat4(Source a, Source b, Source c, Source d, Source e, Source f, Source g, Source h, Source i, Source j, Source k, Source l, Source m, Source n, Source o, Source p)
Constructor given array of elements, the ordering is in row major form:
Definition Mat4.h:66
void postScale(const Vec3< T0 > &v)
Definition Mat4.h:758
Vec3< T0 > transform(const Vec3< T0 > &v) const
Transform a Vec3 by post-multiplication, without homogenous division.
Definition Mat4.h:1005
Mat4< typename promote< T0, T1 >::type > operator*(const Mat4< T0 > &m0, const Mat4< T1 > &m1)
Multiply m0 by m1 and return the resulting matrix.
Definition Mat4.h:1214
T operator()(int i, int j) const
Definition Mat4.h:186
const Mat4< T > & operator-=(const Mat4< S > &m1)
Subtract each element of the given matrix from the corresponding element of this matrix.
Definition Mat4.h:410
Vec3< T0 > transformH(const Vec3< T0 > &p) const
Transform a Vec3 by post-multiplication, doing homogenous divison.
Definition Mat4.h:1026
void setMat3(const Mat3< T > &m)
Set upper left to a Mat3.
Definition Mat4.h:290
Vec4< T0 > pretransform(const Vec4< T0 > &v) const
Transform a Vec4 by pre-multiplication.
Definition Mat4.h:1012
const Mat4 & operator=(const Mat4< Source > &m)
Assignment operator.
Definition Mat4.h:323
const Mat4< T > & operator*=(S scalar)
Multiply each element of this matrix by scalar.
Definition Mat4.h:355
Real ValueType
Definition Mat4.h:35
Vec4< typename promote< T, MT >::type > operator*(const Mat4< MT > &_m, const Vec4< T > &_v)
Multiply _m by _v and return the resulting vector.
Definition Mat4.h:1136
Real value_type
Definition Mat4.h:34
Mat4< T > operator-() const
Negation operator, for e.g. m1 = -m2;.
Definition Mat4.h:343
T mm[SIZE *SIZE]
Definition Mat.h:160
T * asPointer()
Direct access to the internal data.
Definition Mat.h:101
static unsigned numElements()
Definition Mat.h:41
T & x()
Reference to the component, e.g. v.x() = 4.5f;.
Definition Vec3.h:85
T dot(const Vec3< T > &v) const
Dot product.
Definition Vec3.h:191
T & y()
Definition Vec3.h:86
T & z()
Definition Vec3.h:87
void pivot(int i, int j, Mat3< T > &S, Vec3< T > &D, Mat3< T > &Q)
Definition Mat3.h:668
Vec3< T1 > transformNormal(const Mat4< T0 > &m, const Vec3< T1 > &n)
Definition Mat4.h:1226
bool hasTranslation(const Mat4< T > &m)
Definition Mat4.h:1309
Mat4< float > Mat4s
Definition Mat4.h:1353
bool cwiseLessThan(const Mat< SIZE, T > &m0, const Mat< SIZE, T > &m1)
Definition Mat.h:1015
Mat4d Mat4f
Definition Mat4.h:1355
bool isApproxEqual(const Type &a, const Type &b, const Type &tolerance)
Return true if a is equal to b to within the given tolerance.
Definition Math.h:406
Mat3< Type1 > cwiseAdd(const Mat3< Type1 > &m, const Type2 s)
Definition Mat3.h:806
Vec3< double > Vec3d
Definition Vec3.h:664
bool isAffine(const Mat4< T > &m)
Definition Mat4.h:1304
MatType rotation(const Quat< typename MatType::value_type > &q, typename MatType::value_type eps=static_cast< typename MatType::value_type >(1.0e-8))
Return the rotation matrix specified by the given quaternion.
Definition Mat.h:172
Coord Abs(const Coord &xyz)
Definition Coord.h:517
Mat4< double > Mat4d
Definition Mat4.h:1354
T angle(const Vec2< T > &v1, const Vec2< T > &v2)
Definition Vec2.h:446
bool isExactlyEqual(const T0 &a, const T1 &b)
Return true if a is exactly equal to b.
Definition Math.h:443
MatType shear(Axis axis0, Axis axis1, typename MatType::value_type shear)
Set the matrix to a shear along axis0 by a fraction of axis1.
Definition Mat.h:688
Axis
Definition Math.h:901
@ Z_AXIS
Definition Math.h:904
@ X_AXIS
Definition Math.h:902
@ Y_AXIS
Definition Math.h:903
bool cwiseGreaterThan(const Mat< SIZE, T > &m0, const Mat< SIZE, T > &m1)
Definition Mat.h:1029
constexpr T zeroVal()
Return the value of type T that corresponds to zero.
Definition Math.h:70
Definition Exceptions.h:13
#define OPENVDB_THROW(exception, message)
Definition Exceptions.h:74
#define OPENVDB_VERSION_NAME
The version namespace name for this library version.
Definition version.h.in:121
#define OPENVDB_USE_VERSION_NAMESPACE
Definition version.h.in:212