d8223ffa75
That year should bring the long-awaited OpenGL ES 3.0 compatible renderer
with state-of-the-art rendering techniques tuned to work as low as middle
end handheld devices - without compromising with the possibilities given
for higher end desktop games of course. Great times ahead for the Godot
community and the gamers that will play our games!
(cherry picked from commit c7bc44d5ad)
479 lines
13 KiB
C++
479 lines
13 KiB
C++
/*************************************************************************/
|
|
/* matrix3.cpp */
|
|
/*************************************************************************/
|
|
/* This file is part of: */
|
|
/* GODOT ENGINE */
|
|
/* http://www.godotengine.org */
|
|
/*************************************************************************/
|
|
/* Copyright (c) 2007-2017 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 );
|
|
|
|
}
|
|
|