summaryrefslogtreecommitdiff
path: root/core/math/matrix3.cpp
diff options
context:
space:
mode:
Diffstat (limited to 'core/math/matrix3.cpp')
-rw-r--r--core/math/matrix3.cpp479
1 files changed, 479 insertions, 0 deletions
diff --git a/core/math/matrix3.cpp b/core/math/matrix3.cpp
new file mode 100644
index 0000000000..ff62e7786b
--- /dev/null
+++ b/core/math/matrix3.cpp
@@ -0,0 +1,479 @@
+/*************************************************************************/
+/* matrix3.cpp */
+/*************************************************************************/
+/* This file is part of: */
+/* GODOT ENGINE */
+/* http://www.godotengine.org */
+/*************************************************************************/
+/* Copyright (c) 2007-2014 Juan Linietsky, Ariel Manzur. */
+/* */
+/* Permission is hereby granted, free of charge, to any person obtaining */
+/* a copy of this software and associated documentation files (the */
+/* "Software"), to deal in the Software without restriction, including */
+/* without limitation the rights to use, copy, modify, merge, publish, */
+/* distribute, sublicense, and/or sell copies of the Software, and to */
+/* permit persons to whom the Software is furnished to do so, subject to */
+/* the following conditions: */
+/* */
+/* The above copyright notice and this permission notice shall be */
+/* included in all copies or substantial portions of the Software. */
+/* */
+/* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, */
+/* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF */
+/* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.*/
+/* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY */
+/* CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, */
+/* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE */
+/* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. */
+/*************************************************************************/
+#include "matrix3.h"
+#include "math_funcs.h"
+#include "os/copymem.h"
+
+#define cofac(row1,col1, row2, col2)\
+ (elements[row1][col1] * elements[row2][col2] - elements[row1][col2] * elements[row2][col1])
+
+void Matrix3::from_z(const Vector3& p_z) {
+
+ if (Math::abs(p_z.z) > Math_SQRT12 ) {
+
+ // choose p in y-z plane
+ real_t a = p_z[1]*p_z[1] + p_z[2]*p_z[2];
+ real_t k = 1.0/Math::sqrt(a);
+ elements[0]=Vector3(0,-p_z[2]*k,p_z[1]*k);
+ elements[1]=Vector3(a*k,-p_z[0]*elements[0][2],p_z[0]*elements[0][1]);
+ } else {
+
+ // choose p in x-y plane
+ real_t a = p_z.x*p_z.x + p_z.y*p_z.y;
+ real_t k = 1.0/Math::sqrt(a);
+ elements[0]=Vector3(-p_z.y*k,p_z.x*k,0);
+ elements[1]=Vector3(-p_z.z*elements[0].y,p_z.z*elements[0].x,a*k);
+ }
+ elements[2]=p_z;
+}
+
+void Matrix3::invert() {
+
+
+ real_t co[3]={
+ cofac(1, 1, 2, 2), cofac(1, 2, 2, 0), cofac(1, 0, 2, 1)
+ };
+ real_t det = elements[0][0] * co[0]+
+ elements[0][1] * co[1]+
+ elements[0][2] * co[2];
+
+ ERR_FAIL_COND( det == 0 );
+ real_t s = 1.0/det;
+
+ set( co[0]*s, cofac(0, 2, 2, 1) * s, cofac(0, 1, 1, 2) * s,
+ co[1]*s, cofac(0, 0, 2, 2) * s, cofac(0, 2, 1, 0) * s,
+ co[2]*s, cofac(0, 1, 2, 0) * s, cofac(0, 0, 1, 1) * s );
+
+}
+
+void Matrix3::orthonormalize() {
+
+ // Gram-Schmidt Process
+
+ Vector3 x=get_axis(0);
+ Vector3 y=get_axis(1);
+ Vector3 z=get_axis(2);
+
+ x.normalize();
+ y = (y-x*(x.dot(y)));
+ y.normalize();
+ z = (z-x*(x.dot(z))-y*(y.dot(z)));
+ z.normalize();
+
+ set_axis(0,x);
+ set_axis(1,y);
+ set_axis(2,z);
+
+}
+
+Matrix3 Matrix3::orthonormalized() const {
+
+ Matrix3 c = *this;
+ c.orthonormalize();
+ return c;
+}
+
+
+Matrix3 Matrix3::inverse() const {
+
+ Matrix3 inv=*this;
+ inv.invert();
+ return inv;
+}
+
+void Matrix3::transpose() {
+
+ SWAP(elements[0][1],elements[1][0]);
+ SWAP(elements[0][2],elements[2][0]);
+ SWAP(elements[1][2],elements[2][1]);
+}
+
+Matrix3 Matrix3::transposed() const {
+
+ Matrix3 tr=*this;
+ tr.transpose();
+ return tr;
+}
+
+void Matrix3::scale(const Vector3& p_scale) {
+
+ elements[0][0]*=p_scale.x;
+ elements[1][0]*=p_scale.x;
+ elements[2][0]*=p_scale.x;
+ elements[0][1]*=p_scale.y;
+ elements[1][1]*=p_scale.y;
+ elements[2][1]*=p_scale.y;
+ elements[0][2]*=p_scale.z;
+ elements[1][2]*=p_scale.z;
+ elements[2][2]*=p_scale.z;
+}
+
+Matrix3 Matrix3::scaled( const Vector3& p_scale ) const {
+
+ Matrix3 m = *this;
+ m.scale(p_scale);
+ return m;
+}
+
+Vector3 Matrix3::get_scale() const {
+
+ return Vector3(
+ Vector3(elements[0][0],elements[1][0],elements[2][0]).length(),
+ Vector3(elements[0][1],elements[1][1],elements[2][1]).length(),
+ Vector3(elements[0][2],elements[1][2],elements[2][2]).length()
+ );
+
+}
+void Matrix3::rotate(const Vector3& p_axis, real_t p_phi) {
+
+ *this = *this * Matrix3(p_axis, p_phi);
+}
+
+Matrix3 Matrix3::rotated(const Vector3& p_axis, real_t p_phi) const {
+
+ return *this * Matrix3(p_axis, p_phi);
+
+}
+
+Vector3 Matrix3::get_euler() const {
+
+ // rot = cy*cz -cy*sz sy
+ // cz*sx*sy+cx*sz cx*cz-sx*sy*sz -cy*sx
+ // -cx*cz*sy+sx*sz cz*sx+cx*sy*sz cx*cy
+
+ Matrix3 m = *this;
+ m.orthonormalize();
+
+ Vector3 euler;
+
+ euler.y = Math::asin(m[0][2]);
+ if ( euler.y < Math_PI*0.5) {
+ if ( euler.y > -Math_PI*0.5) {
+ euler.x = Math::atan2(-m[1][2],m[2][2]);
+ euler.z = Math::atan2(-m[0][1],m[0][0]);
+
+ } else {
+ real_t r = Math::atan2(m[1][0],m[1][1]);
+ euler.z = 0.0;
+ euler.x = euler.z - r;
+
+ }
+ } else {
+ real_t r = Math::atan2(m[0][1],m[1][1]);
+ euler.z = 0;
+ euler.x = r - euler.z;
+ }
+
+ return euler;
+
+
+}
+
+void Matrix3::set_euler(const Vector3& p_euler) {
+
+ real_t c, s;
+
+ c = Math::cos(p_euler.x);
+ s = Math::sin(p_euler.x);
+ Matrix3 xmat(1.0,0.0,0.0,0.0,c,-s,0.0,s,c);
+
+ c = Math::cos(p_euler.y);
+ s = Math::sin(p_euler.y);
+ Matrix3 ymat(c,0.0,s,0.0,1.0,0.0,-s,0.0,c);
+
+ c = Math::cos(p_euler.z);
+ s = Math::sin(p_euler.z);
+ Matrix3 zmat(c,-s,0.0,s,c,0.0,0.0,0.0,1.0);
+
+ //optimizer will optimize away all this anyway
+ *this = xmat*(ymat*zmat);
+}
+
+bool Matrix3::operator==(const Matrix3& p_matrix) const {
+
+ for (int i=0;i<3;i++) {
+ for (int j=0;j<3;j++) {
+ if (elements[i][j]!=p_matrix.elements[i][j])
+ return false;
+ }
+ }
+
+ return true;
+}
+bool Matrix3::operator!=(const Matrix3& p_matrix) const {
+
+ return (!(*this==p_matrix));
+}
+
+Matrix3::operator String() const {
+
+ String mtx;
+ for (int i=0;i<3;i++) {
+
+ for (int j=0;j<3;j++) {
+
+ if (i!=0 || j!=0)
+ mtx+=", ";
+
+ mtx+=rtos( elements[i][j] );
+ }
+ }
+
+ return mtx;
+}
+
+Matrix3::operator Quat() const {
+
+ Matrix3 m=*this;
+ m.orthonormalize();
+
+ real_t trace = m.elements[0][0] + m.elements[1][1] + m.elements[2][2];
+ real_t temp[4];
+
+ if (trace > 0.0)
+ {
+ real_t s = Math::sqrt(trace + 1.0);
+ temp[3]=(s * 0.5);
+ s = 0.5 / s;
+
+ temp[0]=((m.elements[2][1] - m.elements[1][2]) * s);
+ temp[1]=((m.elements[0][2] - m.elements[2][0]) * s);
+ temp[2]=((m.elements[1][0] - m.elements[0][1]) * s);
+ }
+ else
+ {
+ int i = m.elements[0][0] < m.elements[1][1] ?
+ (m.elements[1][1] < m.elements[2][2] ? 2 : 1) :
+ (m.elements[0][0] < m.elements[2][2] ? 2 : 0);
+ int j = (i + 1) % 3;
+ int k = (i + 2) % 3;
+
+ real_t s = Math::sqrt(m.elements[i][i] - m.elements[j][j] - m.elements[k][k] + 1.0);
+ temp[i] = s * 0.5;
+ s = 0.5 / s;
+
+ temp[3] = (m.elements[k][j] - m.elements[j][k]) * s;
+ temp[j] = (m.elements[j][i] + m.elements[i][j]) * s;
+ temp[k] = (m.elements[k][i] + m.elements[i][k]) * s;
+ }
+
+ return Quat(temp[0],temp[1],temp[2],temp[3]);
+
+}
+
+static const Matrix3 _ortho_bases[24]={
+ Matrix3(1, 0, 0, 0, 1, 0, 0, 0, 1),
+ Matrix3(0, -1, 0, 1, 0, 0, 0, 0, 1),
+ Matrix3(-1, 0, 0, 0, -1, 0, 0, 0, 1),
+ Matrix3(0, 1, 0, -1, 0, 0, 0, 0, 1),
+ Matrix3(1, 0, 0, 0, 0, -1, 0, 1, 0),
+ Matrix3(0, 0, 1, 1, 0, 0, 0, 1, 0),
+ Matrix3(-1, 0, 0, 0, 0, 1, 0, 1, 0),
+ Matrix3(0, 0, -1, -1, 0, 0, 0, 1, 0),
+ Matrix3(1, 0, 0, 0, -1, 0, 0, 0, -1),
+ Matrix3(0, 1, 0, 1, 0, 0, 0, 0, -1),
+ Matrix3(-1, 0, 0, 0, 1, 0, 0, 0, -1),
+ Matrix3(0, -1, 0, -1, 0, 0, 0, 0, -1),
+ Matrix3(1, 0, 0, 0, 0, 1, 0, -1, 0),
+ Matrix3(0, 0, -1, 1, 0, 0, 0, -1, 0),
+ Matrix3(-1, 0, 0, 0, 0, -1, 0, -1, 0),
+ Matrix3(0, 0, 1, -1, 0, 0, 0, -1, 0),
+ Matrix3(0, 0, 1, 0, 1, 0, -1, 0, 0),
+ Matrix3(0, -1, 0, 0, 0, 1, -1, 0, 0),
+ Matrix3(0, 0, -1, 0, -1, 0, -1, 0, 0),
+ Matrix3(0, 1, 0, 0, 0, -1, -1, 0, 0),
+ Matrix3(0, 0, 1, 0, -1, 0, 1, 0, 0),
+ Matrix3(0, 1, 0, 0, 0, 1, 1, 0, 0),
+ Matrix3(0, 0, -1, 0, 1, 0, 1, 0, 0),
+ Matrix3(0, -1, 0, 0, 0, -1, 1, 0, 0)
+};
+
+int Matrix3::get_orthogonal_index() const {
+
+ //could be sped up if i come up with a way
+ Matrix3 orth=*this;
+ for(int i=0;i<3;i++) {
+ for(int j=0;j<3;j++) {
+
+ float v = orth[i][j];
+ if (v>0.5)
+ v=1.0;
+ else if (v<-0.5)
+ v=-1.0;
+ else
+ v=0;
+
+ orth[i][j]=v;
+ }
+ }
+
+ for(int i=0;i<24;i++) {
+
+ if (_ortho_bases[i]==orth)
+ return i;
+
+
+ }
+
+ return 0;
+}
+
+void Matrix3::set_orthogonal_index(int p_index){
+
+ //there only exist 24 orthogonal bases in r3
+ ERR_FAIL_INDEX(p_index,24);
+
+
+ *this=_ortho_bases[p_index];
+
+}
+
+
+void Matrix3::get_axis_and_angle(Vector3 &r_axis,real_t& r_angle) const {
+
+
+ double angle,x,y,z; // variables for result
+ double epsilon = 0.01; // margin to allow for rounding errors
+ double epsilon2 = 0.1; // margin to distinguish between 0 and 180 degrees
+
+ if ( (Math::abs(elements[1][0]-elements[0][1])< epsilon)
+ && (Math::abs(elements[2][0]-elements[0][2])< epsilon)
+ && (Math::abs(elements[2][1]-elements[1][2])< epsilon)) {
+ // singularity found
+ // first check for identity matrix which must have +1 for all terms
+ // in leading diagonaland zero in other terms
+ if ((Math::abs(elements[1][0]+elements[0][1]) < epsilon2)
+ && (Math::abs(elements[2][0]+elements[0][2]) < epsilon2)
+ && (Math::abs(elements[2][1]+elements[1][2]) < epsilon2)
+ && (Math::abs(elements[0][0]+elements[1][1]+elements[2][2]-3) < epsilon2)) {
+ // this singularity is identity matrix so angle = 0
+ r_axis=Vector3(0,1,0);
+ r_angle=0;
+ return;
+ }
+ // otherwise this singularity is angle = 180
+ angle = Math_PI;
+ double xx = (elements[0][0]+1)/2;
+ double yy = (elements[1][1]+1)/2;
+ double zz = (elements[2][2]+1)/2;
+ double xy = (elements[1][0]+elements[0][1])/4;
+ double xz = (elements[2][0]+elements[0][2])/4;
+ double yz = (elements[2][1]+elements[1][2])/4;
+ if ((xx > yy) && (xx > zz)) { // elements[0][0] is the largest diagonal term
+ if (xx< epsilon) {
+ x = 0;
+ y = 0.7071;
+ z = 0.7071;
+ } else {
+ x = Math::sqrt(xx);
+ y = xy/x;
+ z = xz/x;
+ }
+ } else if (yy > zz) { // elements[1][1] is the largest diagonal term
+ if (yy< epsilon) {
+ x = 0.7071;
+ y = 0;
+ z = 0.7071;
+ } else {
+ y = Math::sqrt(yy);
+ x = xy/y;
+ z = yz/y;
+ }
+ } else { // elements[2][2] is the largest diagonal term so base result on this
+ if (zz< epsilon) {
+ x = 0.7071;
+ y = 0.7071;
+ z = 0;
+ } else {
+ z = Math::sqrt(zz);
+ x = xz/z;
+ y = yz/z;
+ }
+ }
+ r_axis=Vector3(x,y,z);
+ r_angle=angle;
+ return;
+ }
+ // as we have reached here there are no singularities so we can handle normally
+ double s = Math::sqrt((elements[1][2] - elements[2][1])*(elements[1][2] - elements[2][1])
+ +(elements[2][0] - elements[0][2])*(elements[2][0] - elements[0][2])
+ +(elements[0][1] - elements[1][0])*(elements[0][1] - elements[1][0])); // used to normalise
+ if (Math::abs(s) < 0.001) s=1;
+ // prevent divide by zero, should not happen if matrix is orthogonal and should be
+ // caught by singularity test above, but I've left it in just in case
+ angle = Math::acos(( elements[0][0] + elements[1][1] + elements[2][2] - 1)/2);
+ x = (elements[1][2] - elements[2][1])/s;
+ y = (elements[2][0] - elements[0][2])/s;
+ z = (elements[0][1] - elements[1][0])/s;
+
+ r_axis=Vector3(x,y,z);
+ r_angle=angle;
+}
+
+Matrix3::Matrix3(const Vector3& p_euler) {
+
+ set_euler( p_euler );
+
+}
+
+Matrix3::Matrix3(const Quat& p_quat) {
+
+ real_t d = p_quat.length_squared();
+ real_t s = 2.0 / d;
+ real_t xs = p_quat.x * s, ys = p_quat.y * s, zs = p_quat.z * s;
+ real_t wx = p_quat.w * xs, wy = p_quat.w * ys, wz = p_quat.w * zs;
+ real_t xx = p_quat.x * xs, xy = p_quat.x * ys, xz = p_quat.x * zs;
+ real_t yy = p_quat.y * ys, yz = p_quat.y * zs, zz = p_quat.z * zs;
+ set( 1.0 - (yy + zz), xy - wz, xz + wy,
+ xy + wz, 1.0 - (xx + zz), yz - wx,
+ xz - wy, yz + wx, 1.0 - (xx + yy)) ;
+
+}
+
+Matrix3::Matrix3(const Vector3& p_axis, real_t p_phi) {
+
+ Vector3 axis_sq(p_axis.x*p_axis.x,p_axis.y*p_axis.y,p_axis.z*p_axis.z);
+
+ real_t cosine= Math::cos(p_phi);
+ real_t sine= Math::sin(p_phi);
+
+ elements[0][0] = axis_sq.x + cosine * ( 1.0 - axis_sq.x );
+ elements[0][1] = p_axis.x * p_axis.y * ( 1.0 - cosine ) + p_axis.z * sine;
+ elements[0][2] = p_axis.z * p_axis.x * ( 1.0 - cosine ) - p_axis.y * sine;
+
+ elements[1][0] = p_axis.x * p_axis.y * ( 1.0 - cosine ) - p_axis.z * sine;
+ elements[1][1] = axis_sq.y + cosine * ( 1.0 - axis_sq.y );
+ elements[1][2] = p_axis.y * p_axis.z * ( 1.0 - cosine ) + p_axis.x * sine;
+
+ elements[2][0] = p_axis.z * p_axis.x * ( 1.0 - cosine ) + p_axis.y * sine;
+ elements[2][1] = p_axis.y * p_axis.z * ( 1.0 - cosine ) - p_axis.x * sine;
+ elements[2][2] = axis_sq.z + cosine * ( 1.0 - axis_sq.z );
+
+}
+
generated by cgit v1.2.3 (git 2.25.1) at 2025-10-06 02:13:57 +0000