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>
801 T c =
static_cast<T
>(cos(
angle));
802 T s = -
static_cast<T
>(sin(
angle));
882 T c =
static_cast<T
>(cos(
angle));
883 T s = -
static_cast<T
>(sin(
angle));
971 int index0 =
static_cast<int>(axis0);
972 int index1 =
static_cast<int>(axis1);
986 int index0 =
static_cast<int>(axis0);
987 int index1 =
static_cast<int>(axis1);
998 template<
typename T0>
1001 return static_cast< Vec4<T0> >(v * *
this);
1005 template<
typename T0>
1008 return static_cast< Vec3<T0> >(v * *
this);
1012 template<
typename T0>
1015 return static_cast< Vec4<T0> >(*
this * v);
1019 template<
typename T0>
1022 return static_cast< Vec3<T0> >(*
this * v);
1026 template<
typename T0>
1048 template<
typename T0>
1069 template<
typename T0>
1080 bool invert(
Mat4<T> &inverse, T tolerance)
const;
1082 T det2(
const Mat4<T> &a,
int i0,
int i1,
int j0,
int j1)
const {
1085 return a.
mm[i0row+j0]*a.
mm[i1row+j1] - a.
mm[i0row+j1]*a.
mm[i1row+j0];
1088 T det3(
const Mat4<T> &a,
int i0,
int i1,
int i2,
1089 int j0,
int j1,
int j2)
const {
1091 return a.mm[i0row+j0]*det2(a, i1,i2, j1,j2) +
1092 a.mm[i0row+j1]*det2(a, i1,i2, j2,j0) +
1093 a.mm[i0row+j2]*det2(a, i1,i2, j0,j1);
1100template <
typename T0,
typename T1>
1106 for (
int i=0; i<16; ++i)
if (!
isExactlyEqual(t0[i], t1[i]))
return false;
1112template <
typename T0,
typename T1>
1117template <
typename S,
typename T>
1125template <
typename S,
typename T>
1135template<
typename T,
typename MT>
1142 _v[0]*m[0] + _v[1]*m[1] + _v[2]*m[2] + _v[3]*m[3],
1143 _v[0]*m[4] + _v[1]*m[5] + _v[2]*m[6] + _v[3]*m[7],
1144 _v[0]*m[8] + _v[1]*m[9] + _v[2]*m[10] + _v[3]*m[11],
1145 _v[0]*m[12] + _v[1]*m[13] + _v[2]*m[14] + _v[3]*m[15]);
1150template<
typename T,
typename MT>
1157 _v[0]*m[0] + _v[1]*m[4] + _v[2]*m[8] + _v[3]*m[12],
1158 _v[0]*m[1] + _v[1]*m[5] + _v[2]*m[9] + _v[3]*m[13],
1159 _v[0]*m[2] + _v[1]*m[6] + _v[2]*m[10] + _v[3]*m[14],
1160 _v[0]*m[3] + _v[1]*m[7] + _v[2]*m[11] + _v[3]*m[15]);
1165template<
typename T,
typename MT>
1171 _v[0]*m[0] + _v[1]*m[1] + _v[2]*m[2] + m[3],
1172 _v[0]*m[4] + _v[1]*m[5] + _v[2]*m[6] + m[7],
1173 _v[0]*m[8] + _v[1]*m[9] + _v[2]*m[10] + m[11]);
1178template<
typename T,
typename MT>
1184 _v[0]*m[0] + _v[1]*m[4] + _v[2]*m[8] + m[12],
1185 _v[0]*m[1] + _v[1]*m[5] + _v[2]*m[9] + m[13],
1186 _v[0]*m[2] + _v[1]*m[6] + _v[2]*m[10] + m[14]);
1191template <
typename T0,
typename T1>
1202template <
typename T0,
typename T1>
1213template <
typename T0,
typename T1>
1226template<
typename T0,
typename T1>
1230 static_cast<T1
>(m[0][0]*n[0] + m[0][1]*n[1] + m[0][2]*n[2]),
1231 static_cast<T1
>(m[1][0]*n[0] + m[1][1]*n[1] + m[1][2]*n[2]),
1232 static_cast<T1
>(m[2][0]*n[0] + m[2][1]*n[1] + m[2][2]*n[2]));
1238bool Mat4<T>::invert(Mat4<T> &inverse, T tolerance)
const
1240 Mat4<T> temp(*
this);
1241 inverse.setIdentity();
1245 for (
int i = 0; i < 4; ++i) {
1247 double max = fabs(temp[i][i]);
1249 for (
int k = i+1; k < 4; ++k) {
1250 if (fabs(temp[k][i]) > max) {
1252 max = fabs(temp[k][i]);
1256 if (isExactlyEqual(max, 0.0))
return false;
1261 for (
int k = 0; k < 4; ++k) {
1262 std::swap(temp[row][k], temp[i][k]);
1263 std::swap(inverse[row][k], inverse[i][k]);
1267 double pivot = temp[i][i];
1271 for (
int k = 0; k < 4; ++k) {
1272 temp[i][k] /=
pivot;
1273 inverse[i][k] /=
pivot;
1277 for (
int j = i+1; j < 4; ++j) {
1278 double t = temp[j][i];
1281 for (
int k = 0; k < 4; ++k) {
1282 temp[j][k] -= temp[i][k] * t;
1283 inverse[j][k] -= inverse[i][k] * t;
1290 for (
int i = 3; i > 0; --i) {
1291 for (
int j = 0; j < i; ++j) {
1292 double t = temp[j][i];
1295 for (
int k = 0; k < 4; ++k) {
1296 inverse[j][k] -= inverse[i][k]*t;
1301 return det*det >= tolerance*tolerance;
1304template <
typename T>
1309template <
typename T>
1321 for (
unsigned i = 0; i < 16; ++i, ++op, ++ip) *op =
math::Abs(*ip);
1325template<
typename Type1,
typename Type2>
1332 for (
unsigned i = 0; i < 16; ++i, ++op, ++ip) {
#define OPENVDB_ASSERT(X)
Definition Assert.h:41
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:1193
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:880
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:1126
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:1152
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:797
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:961
Vec3< T0 > pretransform(const Vec3< T0 > &v) const
Transform a Vec3 by pre-multiplication, without homogenous division.
Definition Mat4.h:1020
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:984
bool operator==(const Mat4< T0 > &m0, const Mat4< T1 > &m1)
Equality operator, does exact floating point comparisons.
Definition Mat4.h:1101
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:1167
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:1180
Vec4< T0 > transform(const Vec4< T0 > &v) const
Transform a Vec4 by post-multiplication.
Definition Mat4.h:999
void preShear(Axis axis0, Axis axis1, T shear)
Left multiplies a shearing transformation into the matrix.
Definition Mat4.h:969
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:1070
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:1049
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:1118
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:1204
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:1113
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:1006
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:1215
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:1027
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:1013
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:1137
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:86
T dot(const Vec3< T > &v) const
Dot product.
Definition Vec3.h:192
T & y()
Definition Vec3.h:87
T & z()
Definition Vec3.h:88
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:1227
bool hasTranslation(const Mat4< T > &m)
Definition Mat4.h:1310
Mat4< float > Mat4s
Definition Mat4.h:1354
bool cwiseLessThan(const Mat< SIZE, T > &m0, const Mat< SIZE, T > &m1)
Definition Mat.h:1015
Mat4d Mat4f
Definition Mat4.h:1356
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
Vec3< double > Vec3d
Definition Vec3.h:665
bool isAffine(const Mat4< T > &m)
Definition Mat4.h:1305
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
auto cwiseAdd(const math::Vec3< math::half > &v, const float s)
Definition Types.h:694
Coord Abs(const Coord &xyz)
Definition Coord.h:518
Mat4< double > Mat4d
Definition Mat4.h:1355
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:218