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-rw-r--r--core/math/matrix3.cpp379
1 files changed, 174 insertions, 205 deletions
diff --git a/core/math/matrix3.cpp b/core/math/matrix3.cpp
index 1fabfbbd4c..5f73d91ef3 100644
--- a/core/math/matrix3.cpp
+++ b/core/math/matrix3.cpp
@@ -30,46 +30,44 @@
#include "math_funcs.h"
#include "os/copymem.h"
-#define cofac(row1,col1, row2, col2)\
+#define cofac(row1, col1, row2, col2) \
(elements[row1][col1] * elements[row2][col2] - elements[row1][col2] * elements[row2][col1])
-void Basis::from_z(const Vector3& p_z) {
+void Basis::from_z(const Vector3 &p_z) {
- if (Math::abs(p_z.z) > Math_SQRT12 ) {
+ 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]);
+ 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);
+ 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;
+ elements[2] = p_z;
}
void Basis::invert() {
-
- real_t co[3]={
+ 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;
+ real_t det = elements[0][0] * co[0] +
+ elements[0][1] * co[1] +
+ elements[0][2] * co[2];
- 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 );
+ 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 Basis::orthonormalize() {
@@ -77,20 +75,19 @@ void Basis::orthonormalize() {
// Gram-Schmidt Process
- Vector3 x=get_axis(0);
- Vector3 y=get_axis(1);
- Vector3 z=get_axis(2);
+ Vector3 x = get_axis(0);
+ Vector3 y = get_axis(1);
+ Vector3 z = get_axis(2);
x.normalize();
- y = (y-x*(x.dot(y)));
+ y = (y - x * (x.dot(y)));
y.normalize();
- z = (z-x*(x.dot(z))-y*(y.dot(z)));
+ z = (z - x * (x.dot(z)) - y * (y.dot(z)));
z.normalize();
- set_axis(0,x);
- set_axis(1,y);
- set_axis(2,z);
-
+ set_axis(0, x);
+ set_axis(1, y);
+ set_axis(2, z);
}
Basis Basis::orthonormalized() const {
@@ -102,16 +99,15 @@ Basis Basis::orthonormalized() const {
bool Basis::is_orthogonal() const {
Basis id;
- Basis m = (*this)*transposed();
+ Basis m = (*this) * transposed();
- return isequal_approx(id,m);
+ return isequal_approx(id, m);
}
bool Basis::is_rotation() const {
return Math::isequal_approx(determinant(), 1) && is_orthogonal();
}
-
bool Basis::is_symmetric() const {
if (Math::abs(elements[0][1] - elements[1][0]) > CMP_EPSILON)
@@ -124,21 +120,20 @@ bool Basis::is_symmetric() const {
return true;
}
-
Basis Basis::diagonalize() {
//NOTE: only implemented for symmetric matrices
//with the Jacobi iterative method method
-
+
ERR_FAIL_COND_V(!is_symmetric(), Basis());
const int ite_max = 1024;
- real_t off_matrix_norm_2 = elements[0][1] * elements[0][1] + elements[0][2] * elements[0][2] + elements[1][2] * elements[1][2];
+ real_t off_matrix_norm_2 = elements[0][1] * elements[0][1] + elements[0][2] * elements[0][2] + elements[1][2] * elements[1][2];
int ite = 0;
Basis acc_rot;
- while (off_matrix_norm_2 > CMP_EPSILON2 && ite++ < ite_max ) {
+ while (off_matrix_norm_2 > CMP_EPSILON2 && ite++ < ite_max) {
real_t el01_2 = elements[0][1] * elements[0][1];
real_t el02_2 = elements[0][2] * elements[0][2];
real_t el12_2 = elements[1][2] * elements[1][2];
@@ -151,7 +146,7 @@ Basis Basis::diagonalize() {
} else {
i = 0;
j = 1;
- }
+ }
} else {
if (el12_2 > el02_2) {
i = 1;
@@ -163,17 +158,17 @@ Basis Basis::diagonalize() {
}
// Compute the rotation angle
- real_t angle;
+ real_t angle;
if (Math::abs(elements[j][j] - elements[i][i]) < CMP_EPSILON) {
angle = Math_PI / 4;
} else {
- angle = 0.5 * Math::atan(2 * elements[i][j] / (elements[j][j] - elements[i][i]));
+ angle = 0.5 * Math::atan(2 * elements[i][j] / (elements[j][j] - elements[i][i]));
}
// Compute the rotation matrix
Basis rot;
rot.elements[i][i] = rot.elements[j][j] = Math::cos(angle);
- rot.elements[i][j] = - (rot.elements[j][i] = Math::sin(angle));
+ rot.elements[i][j] = -(rot.elements[j][i] = Math::sin(angle));
// Update the off matrix norm
off_matrix_norm_2 -= elements[i][j] * elements[i][j];
@@ -188,41 +183,41 @@ Basis Basis::diagonalize() {
Basis Basis::inverse() const {
- Basis inv=*this;
+ Basis inv = *this;
inv.invert();
return inv;
}
void Basis::transpose() {
- SWAP(elements[0][1],elements[1][0]);
- SWAP(elements[0][2],elements[2][0]);
- SWAP(elements[1][2],elements[2][1]);
+ SWAP(elements[0][1], elements[1][0]);
+ SWAP(elements[0][2], elements[2][0]);
+ SWAP(elements[1][2], elements[2][1]);
}
Basis Basis::transposed() const {
- Basis tr=*this;
+ Basis tr = *this;
tr.transpose();
return tr;
}
// Multiplies the matrix from left by the scaling matrix: M -> S.M
// See the comment for Basis::rotated for further explanation.
-void Basis::scale(const Vector3& p_scale) {
+void Basis::scale(const Vector3 &p_scale) {
- elements[0][0]*=p_scale.x;
- elements[0][1]*=p_scale.x;
- elements[0][2]*=p_scale.x;
- elements[1][0]*=p_scale.y;
- elements[1][1]*=p_scale.y;
- elements[1][2]*=p_scale.y;
- elements[2][0]*=p_scale.z;
- elements[2][1]*=p_scale.z;
- elements[2][2]*=p_scale.z;
+ elements[0][0] *= p_scale.x;
+ elements[0][1] *= p_scale.x;
+ elements[0][2] *= p_scale.x;
+ elements[1][0] *= p_scale.y;
+ elements[1][1] *= p_scale.y;
+ elements[1][2] *= p_scale.y;
+ elements[2][0] *= p_scale.z;
+ elements[2][1] *= p_scale.z;
+ elements[2][2] *= p_scale.z;
}
-Basis Basis::scaled( const Vector3& p_scale ) const {
+Basis Basis::scaled(const Vector3 &p_scale) const {
Basis m = *this;
m.scale(p_scale);
@@ -236,12 +231,10 @@ Vector3 Basis::get_scale() const {
// (such that it can be represented by a Quat or Euler angles), we absorb the sign flip into the scaling matrix.
// As such, it works in conjuction with get_rotation().
real_t det_sign = determinant() > 0 ? 1 : -1;
- return det_sign*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()
- );
-
+ return det_sign * 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());
}
// Multiplies the matrix from left by the rotation matrix: M -> R.M
@@ -250,19 +243,19 @@ Vector3 Basis::get_scale() const {
// The main use of Basis is as Transform.basis, which is used a the transformation matrix
// of 3D object. Rotate here refers to rotation of the object (which is R * (*this)),
// not the matrix itself (which is R * (*this) * R.transposed()).
-Basis Basis::rotated(const Vector3& p_axis, real_t p_phi) const {
+Basis Basis::rotated(const Vector3 &p_axis, real_t p_phi) const {
return Basis(p_axis, p_phi) * (*this);
}
-void Basis::rotate(const Vector3& p_axis, real_t p_phi) {
+void Basis::rotate(const Vector3 &p_axis, real_t p_phi) {
*this = rotated(p_axis, p_phi);
}
-Basis Basis::rotated(const Vector3& p_euler) const {
+Basis Basis::rotated(const Vector3 &p_euler) const {
return Basis(p_euler) * (*this);
}
-void Basis::rotate(const Vector3& p_euler) {
+void Basis::rotate(const Vector3 &p_euler) {
*this = rotated(p_euler);
}
@@ -274,7 +267,7 @@ Vector3 Basis::get_rotation() const {
real_t det = m.determinant();
if (det < 0) {
// Ensure that the determinant is 1, such that result is a proper rotation matrix which can be represented by Euler angles.
- m.scale(Vector3(-1,-1,-1));
+ m.scale(Vector3(-1, -1, -1));
}
return m.get_euler();
@@ -304,67 +297,64 @@ Vector3 Basis::get_euler() const {
ERR_FAIL_COND_V(is_rotation() == false, euler);
euler.y = Math::asin(elements[0][2]);
- if ( euler.y < Math_PI*0.5) {
- if ( euler.y > -Math_PI*0.5) {
- euler.x = Math::atan2(-elements[1][2],elements[2][2]);
- euler.z = Math::atan2(-elements[0][1],elements[0][0]);
+ if (euler.y < Math_PI * 0.5) {
+ if (euler.y > -Math_PI * 0.5) {
+ euler.x = Math::atan2(-elements[1][2], elements[2][2]);
+ euler.z = Math::atan2(-elements[0][1], elements[0][0]);
} else {
- real_t r = Math::atan2(elements[1][0],elements[1][1]);
+ real_t r = Math::atan2(elements[1][0], elements[1][1]);
euler.z = 0.0;
euler.x = euler.z - r;
-
}
} else {
- real_t r = Math::atan2(elements[0][1],elements[1][1]);
+ real_t r = Math::atan2(elements[0][1], elements[1][1]);
euler.z = 0;
euler.x = r - euler.z;
}
return euler;
-
-
}
// set_euler expects a vector containing the Euler angles in the format
// (c,b,a), where a is the angle of the first rotation, and c is the last.
// The current implementation uses XYZ convention (Z is the first rotation).
-void Basis::set_euler(const Vector3& p_euler) {
+void Basis::set_euler(const Vector3 &p_euler) {
real_t c, s;
c = Math::cos(p_euler.x);
s = Math::sin(p_euler.x);
- Basis xmat(1.0,0.0,0.0,0.0,c,-s,0.0,s,c);
+ Basis 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);
- Basis ymat(c,0.0,s,0.0,1.0,0.0,-s,0.0,c);
+ Basis 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);
- Basis zmat(c,-s,0.0,s,c,0.0,0.0,0.0,1.0);
+ Basis 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);
+ *this = xmat * (ymat * zmat);
}
-bool Basis::isequal_approx(const Basis& a, const Basis& b) const {
+bool Basis::isequal_approx(const Basis &a, const Basis &b) const {
- for (int i=0;i<3;i++) {
- for (int j=0;j<3;j++) {
- if (Math::isequal_approx(a.elements[i][j],b.elements[i][j]) == false)
- return false;
- }
- }
+ for (int i = 0; i < 3; i++) {
+ for (int j = 0; j < 3; j++) {
+ if (Math::isequal_approx(a.elements[i][j], b.elements[i][j]) == false)
+ return false;
+ }
+ }
- return true;
+ return true;
}
-bool Basis::operator==(const Basis& p_matrix) const {
+bool Basis::operator==(const Basis &p_matrix) const {
- for (int i=0;i<3;i++) {
- for (int j=0;j<3;j++) {
+ 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;
}
@@ -373,22 +363,22 @@ bool Basis::operator==(const Basis& p_matrix) const {
return true;
}
-bool Basis::operator!=(const Basis& p_matrix) const {
+bool Basis::operator!=(const Basis &p_matrix) const {
- return (!(*this==p_matrix));
+ return (!(*this == p_matrix));
}
Basis::operator String() const {
String mtx;
- for (int i=0;i<3;i++) {
+ for (int i = 0; i < 3; i++) {
- for (int j=0;j<3;j++) {
+ for (int j = 0; j < 3; j++) {
- if (i!=0 || j!=0)
- mtx+=", ";
+ if (i != 0 || j != 0)
+ mtx += ", ";
- mtx+=rtos( elements[i][j] );
+ mtx += rtos(elements[i][j]);
}
}
@@ -401,21 +391,18 @@ Basis::operator Quat() const {
real_t trace = elements[0][0] + elements[1][1] + elements[2][2];
real_t temp[4];
- if (trace > 0.0)
- {
+ if (trace > 0.0) {
real_t s = Math::sqrt(trace + 1.0);
- temp[3]=(s * 0.5);
+ temp[3] = (s * 0.5);
s = 0.5 / s;
- temp[0]=((elements[2][1] - elements[1][2]) * s);
- temp[1]=((elements[0][2] - elements[2][0]) * s);
- temp[2]=((elements[1][0] - elements[0][1]) * s);
- }
- else
- {
+ temp[0] = ((elements[2][1] - elements[1][2]) * s);
+ temp[1] = ((elements[0][2] - elements[2][0]) * s);
+ temp[2] = ((elements[1][0] - elements[0][1]) * s);
+ } else {
int i = elements[0][0] < elements[1][1] ?
- (elements[1][1] < elements[2][2] ? 2 : 1) :
- (elements[0][0] < elements[2][2] ? 2 : 0);
+ (elements[1][1] < elements[2][2] ? 2 : 1) :
+ (elements[0][0] < elements[2][2] ? 2 : 0);
int j = (i + 1) % 3;
int k = (i + 2) % 3;
@@ -428,11 +415,10 @@ Basis::operator Quat() const {
temp[k] = (elements[k][i] + elements[i][k]) * s;
}
- return Quat(temp[0],temp[1],temp[2],temp[3]);
-
+ return Quat(temp[0], temp[1], temp[2], temp[3]);
}
-static const Basis _ortho_bases[24]={
+static const Basis _ortho_bases[24] = {
Basis(1, 0, 0, 0, 1, 0, 0, 0, 1),
Basis(0, -1, 0, 1, 0, 0, 0, 0, 1),
Basis(-1, 0, 0, 0, -1, 0, 0, 0, 1),
@@ -462,164 +448,147 @@ static const Basis _ortho_bases[24]={
int Basis::get_orthogonal_index() const {
//could be sped up if i come up with a way
- Basis orth=*this;
- for(int i=0;i<3;i++) {
- for(int j=0;j<3;j++) {
+ Basis orth = *this;
+ for (int i = 0; i < 3; i++) {
+ for (int j = 0; j < 3; j++) {
real_t v = orth[i][j];
- if (v>0.5)
- v=1.0;
- else if (v<-0.5)
- v=-1.0;
+ if (v > 0.5)
+ v = 1.0;
+ else if (v < -0.5)
+ v = -1.0;
else
- v=0;
+ v = 0;
- orth[i][j]=v;
+ orth[i][j] = v;
}
}
- for(int i=0;i<24;i++) {
+ for (int i = 0; i < 24; i++) {
- if (_ortho_bases[i]==orth)
+ if (_ortho_bases[i] == orth)
return i;
-
-
}
return 0;
}
-void Basis::set_orthogonal_index(int p_index){
+void Basis::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];
+ ERR_FAIL_INDEX(p_index, 24);
+ *this = _ortho_bases[p_index];
}
-
-void Basis::get_axis_and_angle(Vector3 &r_axis,real_t& r_angle) const {
+void Basis::get_axis_and_angle(Vector3 &r_axis, real_t &r_angle) const {
ERR_FAIL_COND(is_rotation() == false);
+ real_t angle, x, y, z; // variables for result
+ real_t epsilon = 0.01; // margin to allow for rounding errors
+ real_t epsilon2 = 0.1; // margin to distinguish between 0 and 180 degrees
- real_t angle,x,y,z; // variables for result
- real_t epsilon = 0.01; // margin to allow for rounding errors
- real_t 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)) {
+ 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;
+ r_axis = Vector3(0, 1, 0);
+ r_angle = 0;
return;
}
// otherwise this singularity is angle = 180
angle = Math_PI;
- real_t xx = (elements[0][0]+1)/2;
- real_t yy = (elements[1][1]+1)/2;
- real_t zz = (elements[2][2]+1)/2;
- real_t xy = (elements[1][0]+elements[0][1])/4;
- real_t xz = (elements[2][0]+elements[0][2])/4;
- real_t yz = (elements[2][1]+elements[1][2])/4;
+ real_t xx = (elements[0][0] + 1) / 2;
+ real_t yy = (elements[1][1] + 1) / 2;
+ real_t zz = (elements[2][2] + 1) / 2;
+ real_t xy = (elements[1][0] + elements[0][1]) / 4;
+ real_t xz = (elements[2][0] + elements[0][2]) / 4;
+ real_t yz = (elements[2][1] + elements[1][2]) / 4;
if ((xx > yy) && (xx > zz)) { // elements[0][0] is the largest diagonal term
- if (xx< epsilon) {
+ if (xx < epsilon) {
x = 0;
y = 0.7071;
z = 0.7071;
} else {
x = Math::sqrt(xx);
- y = xy/x;
- z = xz/x;
+ y = xy / x;
+ z = xz / x;
}
} else if (yy > zz) { // elements[1][1] is the largest diagonal term
- if (yy< epsilon) {
+ if (yy < epsilon) {
x = 0.7071;
y = 0;
z = 0.7071;
} else {
y = Math::sqrt(yy);
- x = xy/y;
- z = yz/y;
+ x = xy / y;
+ z = yz / y;
}
} else { // elements[2][2] is the largest diagonal term so base result on this
- if (zz< epsilon) {
+ if (zz < epsilon) {
x = 0.7071;
y = 0.7071;
z = 0;
} else {
z = Math::sqrt(zz);
- x = xz/z;
- y = yz/z;
+ x = xz / z;
+ y = yz / z;
}
}
- r_axis=Vector3(x,y,z);
- r_angle=angle;
+ r_axis = Vector3(x, y, z);
+ r_angle = angle;
return;
}
// as we have reached here there are no singularities so we can handle normally
- real_t 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])); // s=|axis||sin(angle)|, used to normalise
+ real_t 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])); // s=|axis||sin(angle)|, used to normalise
- angle = Math::acos(( elements[0][0] + elements[1][1] + elements[2][2] - 1)/2);
+ angle = Math::acos((elements[0][0] + elements[1][1] + elements[2][2] - 1) / 2);
if (angle < 0) s = -s;
- x = (elements[2][1] - elements[1][2])/s;
- y = (elements[0][2] - elements[2][0])/s;
- z = (elements[1][0] - elements[0][1])/s;
+ x = (elements[2][1] - elements[1][2]) / s;
+ y = (elements[0][2] - elements[2][0]) / s;
+ z = (elements[1][0] - elements[0][1]) / s;
- r_axis=Vector3(x,y,z);
- r_angle=angle;
+ r_axis = Vector3(x, y, z);
+ r_angle = angle;
}
-Basis::Basis(const Vector3& p_euler) {
-
- set_euler( p_euler );
+Basis::Basis(const Vector3 &p_euler) {
+ set_euler(p_euler);
}
-Basis::Basis(const Quat& p_quat) {
+Basis::Basis(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)) ;
-
+ 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));
}
-Basis::Basis(const Vector3& p_axis, real_t p_phi) {
+Basis::Basis(const Vector3 &p_axis, real_t p_phi) {
// Rotation matrix from axis and angle, see https://en.wikipedia.org/wiki/Rotation_matrix#Rotation_matrix_from_axis_and_angle
- 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);
+ Vector3 axis_sq(p_axis.x * p_axis.x, p_axis.y * p_axis.y, p_axis.z * p_axis.z);
- 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;
+ real_t cosine = Math::cos(p_phi);
+ real_t sine = Math::sin(p_phi);
- 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[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[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 );
+ 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 2025-02-16 16:20:45 +0000