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-rw-r--r--src/core/Basis.cpp451
1 files changed, 196 insertions, 255 deletions
diff --git a/src/core/Basis.cpp b/src/core/Basis.cpp
index 5919558..73d9cd5 100644
--- a/src/core/Basis.cpp
+++ b/src/core/Basis.cpp
@@ -1,18 +1,16 @@
#include "Basis.hpp"
#include "Defs.hpp"
-#include "Vector3.hpp"
#include "Quat.hpp"
+#include "Vector3.hpp"
#include <algorithm>
namespace godot {
-
-Basis::Basis(const Vector3& row0, const Vector3& row1, const Vector3& row2)
-{
- elements[0]=row0;
- elements[1]=row1;
- elements[2]=row2;
+Basis::Basis(const Vector3 &row0, const Vector3 &row1, const Vector3 &row2) {
+ elements[0] = row0;
+ elements[1] = row1;
+ elements[2] = row2;
}
Basis::Basis(real_t xx, real_t xy, real_t xz, real_t yx, real_t yy, real_t yz, real_t zx, real_t zy, real_t zz) {
@@ -22,58 +20,52 @@ Basis::Basis(real_t xx, real_t xy, real_t xz, real_t yx, real_t yy, real_t yz, r
Basis::Basis() {
- elements[0][0]=1;
- elements[0][1]=0;
- elements[0][2]=0;
- elements[1][0]=0;
- elements[1][1]=1;
- elements[1][2]=0;
- elements[2][0]=0;
- elements[2][1]=0;
- elements[2][2]=1;
+ elements[0][0] = 1;
+ elements[0][1] = 0;
+ elements[0][2] = 0;
+ elements[1][0] = 0;
+ elements[1][1] = 1;
+ elements[1][2] = 0;
+ elements[2][0] = 0;
+ elements[2][1] = 0;
+ elements[2][2] = 1;
}
-
-
-
-
-const Vector3& Basis::operator[](int axis) const {
+const Vector3 &Basis::operator[](int axis) const {
return elements[axis];
}
-Vector3&Basis:: operator[](int axis) {
+Vector3 &Basis::operator[](int axis) {
return elements[axis];
}
-#define cofac(row1,col1, row2, col2)\
-(elements[row1][col1] * elements[row2][col2] - elements[row1][col2] * elements[row2][col1])
+#define cofac(row1, col1, row2, col2) \
+ (elements[row1][col1] * elements[row2][col2] - elements[row1][col2] * elements[row2][col1])
-void Basis::invert()
-{
- real_t co[3]={
+void Basis::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];
+ 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 );
+ 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);
}
#undef cofac
-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 ((::fabs(a.elements[i][j]-b.elements[i][j]) < CMP_EPSILON) == false)
+ for (int i = 0; i < 3; i++) {
+ for (int j = 0; j < 3; j++) {
+ if ((::fabs(a.elements[i][j] - b.elements[i][j]) < CMP_EPSILON) == false)
return false;
}
}
@@ -81,102 +73,89 @@ bool Basis::isequal_approx(const Basis& a, const Basis& b) const {
return true;
}
-
-bool Basis::is_orthogonal() 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 ::fabs(determinant()-1) < CMP_EPSILON && is_orthogonal();
+bool Basis::is_rotation() const {
+ return ::fabs(determinant() - 1) < CMP_EPSILON && is_orthogonal();
}
-void Basis::transpose()
-{
- std::swap(elements[0][1],elements[1][0]);
- std::swap(elements[0][2],elements[2][0]);
- std::swap(elements[1][2],elements[2][1]);
+void Basis::transpose() {
+ std::swap(elements[0][1], elements[1][0]);
+ std::swap(elements[0][2], elements[2][0]);
+ std::swap(elements[1][2], elements[2][1]);
}
-Basis Basis::inverse() const
-{
+Basis Basis::inverse() const {
Basis b = *this;
b.invert();
return b;
}
-Basis Basis::transposed() const
-{
+Basis Basis::transposed() const {
Basis b = *this;
b.transpose();
return b;
}
-real_t Basis::determinant() const
-{
- return elements[0][0]*(elements[1][1]*elements[2][2] - elements[2][1]*elements[1][2]) -
- elements[1][0]*(elements[0][1]*elements[2][2] - elements[2][1]*elements[0][2]) +
- elements[2][0]*(elements[0][1]*elements[1][2] - elements[1][1]*elements[0][2]);
+real_t Basis::determinant() const {
+ return elements[0][0] * (elements[1][1] * elements[2][2] - elements[2][1] * elements[1][2]) -
+ elements[1][0] * (elements[0][1] * elements[2][2] - elements[2][1] * elements[0][2]) +
+ elements[2][0] * (elements[0][1] * elements[1][2] - elements[1][1] * elements[0][2]);
}
Vector3 Basis::get_axis(int p_axis) const {
// get actual basis axis (elements is transposed for performance)
- return Vector3( elements[0][p_axis], elements[1][p_axis], elements[2][p_axis] );
+ return Vector3(elements[0][p_axis], elements[1][p_axis], elements[2][p_axis]);
}
-void Basis::set_axis(int p_axis, const Vector3& p_value) {
+void Basis::set_axis(int p_axis, const Vector3 &p_value) {
// get actual basis axis (elements is transposed for performance)
- elements[0][p_axis]=p_value.x;
- elements[1][p_axis]=p_value.y;
- elements[2][p_axis]=p_value.z;
+ elements[0][p_axis] = p_value.x;
+ elements[1][p_axis] = p_value.y;
+ elements[2][p_axis] = p_value.z;
}
-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_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::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;
+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;
}
-Basis Basis::scaled( const Vector3& p_scale ) const
-{
+Basis Basis::scaled(const Vector3 &p_scale) const {
Basis b = *this;
b.scale(p_scale);
return b;
}
-Vector3 Basis::get_scale() const
-{
+Vector3 Basis::get_scale() const {
// We are assuming M = R.S, and performing a polar decomposition to extract R and S.
// FIXME: We eventually need a proper polar decomposition.
// As a cheap workaround until then, to ensure that R is a proper rotation matrix with determinant +1
// (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());
}
// get_euler_xyz returns a vector containing the Euler angles in the format
@@ -322,23 +301,20 @@ void Basis::set_euler_yxz(const Vector3 &p_euler) {
*this = ymat * xmat * zmat;
}
-
-
// transposed dot products
-real_t Basis::tdotx(const Vector3& v) const {
+real_t Basis::tdotx(const Vector3 &v) const {
return elements[0][0] * v[0] + elements[1][0] * v[1] + elements[2][0] * v[2];
}
-real_t Basis::tdoty(const Vector3& v) const {
+real_t Basis::tdoty(const Vector3 &v) const {
return elements[0][1] * v[0] + elements[1][1] * v[1] + elements[2][1] * v[2];
}
-real_t Basis::tdotz(const Vector3& v) const {
+real_t Basis::tdotz(const Vector3 &v) const {
return elements[0][2] * v[0] + elements[1][2] * v[1] + elements[2][2] * v[2];
}
-bool Basis::operator==(const Basis& p_matrix) const
-{
- for (int i=0;i<3;i++) {
- for (int j=0;j<3;j++) {
+bool Basis::operator==(const Basis &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;
}
@@ -347,69 +323,61 @@ bool Basis::operator==(const Basis& p_matrix) const
return true;
}
-bool Basis::operator!=(const Basis& p_matrix) const
-{
- return (!(*this==p_matrix));
+bool Basis::operator!=(const Basis &p_matrix) const {
+ return (!(*this == p_matrix));
}
-Vector3 Basis::xform(const Vector3& p_vector) const {
+Vector3 Basis::xform(const Vector3 &p_vector) const {
return Vector3(
- elements[0].dot(p_vector),
- elements[1].dot(p_vector),
- elements[2].dot(p_vector)
- );
+ elements[0].dot(p_vector),
+ elements[1].dot(p_vector),
+ elements[2].dot(p_vector));
}
-Vector3 Basis::xform_inv(const Vector3& p_vector) const {
+Vector3 Basis::xform_inv(const Vector3 &p_vector) const {
return Vector3(
- (elements[0][0]*p_vector.x ) + ( elements[1][0]*p_vector.y ) + ( elements[2][0]*p_vector.z ),
- (elements[0][1]*p_vector.x ) + ( elements[1][1]*p_vector.y ) + ( elements[2][1]*p_vector.z ),
- (elements[0][2]*p_vector.x ) + ( elements[1][2]*p_vector.y ) + ( elements[2][2]*p_vector.z )
- );
+ (elements[0][0] * p_vector.x) + (elements[1][0] * p_vector.y) + (elements[2][0] * p_vector.z),
+ (elements[0][1] * p_vector.x) + (elements[1][1] * p_vector.y) + (elements[2][1] * p_vector.z),
+ (elements[0][2] * p_vector.x) + (elements[1][2] * p_vector.y) + (elements[2][2] * p_vector.z));
}
-void Basis::operator*=(const Basis& p_matrix)
-{
+void Basis::operator*=(const Basis &p_matrix) {
set(
- p_matrix.tdotx(elements[0]), p_matrix.tdoty(elements[0]), p_matrix.tdotz(elements[0]),
- p_matrix.tdotx(elements[1]), p_matrix.tdoty(elements[1]), p_matrix.tdotz(elements[1]),
- p_matrix.tdotx(elements[2]), p_matrix.tdoty(elements[2]), p_matrix.tdotz(elements[2]));
-
+ p_matrix.tdotx(elements[0]), p_matrix.tdoty(elements[0]), p_matrix.tdotz(elements[0]),
+ p_matrix.tdotx(elements[1]), p_matrix.tdoty(elements[1]), p_matrix.tdotz(elements[1]),
+ p_matrix.tdotx(elements[2]), p_matrix.tdoty(elements[2]), p_matrix.tdotz(elements[2]));
}
-Basis Basis::operator*(const Basis& p_matrix) const
-{
+Basis Basis::operator*(const Basis &p_matrix) const {
return Basis(
- p_matrix.tdotx(elements[0]), p_matrix.tdoty(elements[0]), p_matrix.tdotz(elements[0]),
- p_matrix.tdotx(elements[1]), p_matrix.tdoty(elements[1]), p_matrix.tdotz(elements[1]),
- p_matrix.tdotx(elements[2]), p_matrix.tdoty(elements[2]), p_matrix.tdotz(elements[2]) );
-
+ p_matrix.tdotx(elements[0]), p_matrix.tdoty(elements[0]), p_matrix.tdotz(elements[0]),
+ p_matrix.tdotx(elements[1]), p_matrix.tdoty(elements[1]), p_matrix.tdotz(elements[1]),
+ p_matrix.tdotx(elements[2]), p_matrix.tdoty(elements[2]), p_matrix.tdotz(elements[2]));
}
-
-void Basis::operator+=(const Basis& p_matrix) {
+void Basis::operator+=(const Basis &p_matrix) {
elements[0] += p_matrix.elements[0];
elements[1] += p_matrix.elements[1];
elements[2] += p_matrix.elements[2];
}
-Basis Basis::operator+(const Basis& p_matrix) const {
+Basis Basis::operator+(const Basis &p_matrix) const {
Basis ret(*this);
ret += p_matrix;
return ret;
}
-void Basis::operator-=(const Basis& p_matrix) {
+void Basis::operator-=(const Basis &p_matrix) {
elements[0] -= p_matrix.elements[0];
elements[1] -= p_matrix.elements[1];
elements[2] -= p_matrix.elements[2];
}
-Basis Basis::operator-(const Basis& p_matrix) const {
+Basis Basis::operator-(const Basis &p_matrix) const {
Basis ret(*this);
ret -= p_matrix;
@@ -418,21 +386,19 @@ Basis Basis::operator-(const Basis& p_matrix) const {
void Basis::operator*=(real_t p_val) {
- elements[0]*=p_val;
- elements[1]*=p_val;
- elements[2]*=p_val;
+ elements[0] *= p_val;
+ elements[1] *= p_val;
+ elements[2] *= p_val;
}
Basis Basis::operator*(real_t p_val) const {
- Basis ret(*this);
- ret *= p_val;
- return ret;
+ Basis ret(*this);
+ ret *= p_val;
+ return ret;
}
-
-Basis::operator String() const
-{
+Basis::operator String() const {
String s;
for (int i = 0; i < 3; i++) {
@@ -449,82 +415,77 @@ Basis::operator String() const
/* create / set */
-
void Basis::set(real_t xx, real_t xy, real_t xz, real_t yx, real_t yy, real_t yz, real_t zx, real_t zy, real_t zz) {
- elements[0][0]=xx;
- elements[0][1]=xy;
- elements[0][2]=xz;
- elements[1][0]=yx;
- elements[1][1]=yy;
- elements[1][2]=yz;
- elements[2][0]=zx;
- elements[2][1]=zy;
- elements[2][2]=zz;
+ elements[0][0] = xx;
+ elements[0][1] = xy;
+ elements[0][2] = xz;
+ elements[1][0] = yx;
+ elements[1][1] = yy;
+ elements[1][2] = yz;
+ elements[2][0] = zx;
+ elements[2][1] = zy;
+ elements[2][2] = zz;
}
Vector3 Basis::get_column(int i) const {
- return Vector3(elements[0][i],elements[1][i],elements[2][i]);
+ return Vector3(elements[0][i], elements[1][i], elements[2][i]);
}
Vector3 Basis::get_row(int i) const {
- return Vector3(elements[i][0],elements[i][1],elements[i][2]);
+ return Vector3(elements[i][0], elements[i][1], elements[i][2]);
}
Vector3 Basis::get_main_diagonal() const {
- return Vector3(elements[0][0],elements[1][1],elements[2][2]);
+ return Vector3(elements[0][0], elements[1][1], elements[2][2]);
}
-void Basis::set_row(int i, const Vector3& p_row) {
- elements[i][0]=p_row.x;
- elements[i][1]=p_row.y;
- elements[i][2]=p_row.z;
+void Basis::set_row(int i, const Vector3 &p_row) {
+ elements[i][0] = p_row.x;
+ elements[i][1] = p_row.y;
+ elements[i][2] = p_row.z;
}
-Basis Basis::transpose_xform(const Basis& m) const
-{
+Basis Basis::transpose_xform(const Basis &m) const {
return Basis(
- elements[0].x * m[0].x + elements[1].x * m[1].x + elements[2].x * m[2].x,
- elements[0].x * m[0].y + elements[1].x * m[1].y + elements[2].x * m[2].y,
- elements[0].x * m[0].z + elements[1].x * m[1].z + elements[2].x * m[2].z,
- elements[0].y * m[0].x + elements[1].y * m[1].x + elements[2].y * m[2].x,
- elements[0].y * m[0].y + elements[1].y * m[1].y + elements[2].y * m[2].y,
- elements[0].y * m[0].z + elements[1].y * m[1].z + elements[2].y * m[2].z,
- elements[0].z * m[0].x + elements[1].z * m[1].x + elements[2].z * m[2].x,
- elements[0].z * m[0].y + elements[1].z * m[1].y + elements[2].z * m[2].y,
- elements[0].z * m[0].z + elements[1].z * m[1].z + elements[2].z * m[2].z);
-}
-
-void Basis::orthonormalize()
-{
+ elements[0].x * m[0].x + elements[1].x * m[1].x + elements[2].x * m[2].x,
+ elements[0].x * m[0].y + elements[1].x * m[1].y + elements[2].x * m[2].y,
+ elements[0].x * m[0].z + elements[1].x * m[1].z + elements[2].x * m[2].z,
+ elements[0].y * m[0].x + elements[1].y * m[1].x + elements[2].y * m[2].x,
+ elements[0].y * m[0].y + elements[1].y * m[1].y + elements[2].y * m[2].y,
+ elements[0].y * m[0].z + elements[1].y * m[1].z + elements[2].y * m[2].z,
+ elements[0].z * m[0].x + elements[1].z * m[1].x + elements[2].z * m[2].x,
+ elements[0].z * m[0].y + elements[1].z * m[1].y + elements[2].z * m[2].y,
+ elements[0].z * m[0].z + elements[1].z * m[1].z + elements[2].z * m[2].z);
+}
+
+void Basis::orthonormalize() {
ERR_FAIL_COND(determinant() == 0);
// 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
-{
+Basis Basis::orthonormalized() const {
Basis b = *this;
b.orthonormalize();
return b;
}
-bool Basis::is_symmetric() const
-{
+bool Basis::is_symmetric() const {
if (::fabs(elements[0][1] - elements[1][0]) > CMP_EPSILON)
return false;
if (::fabs(elements[0][2] - elements[2][0]) > CMP_EPSILON)
@@ -535,8 +496,7 @@ bool Basis::is_symmetric() const
return true;
}
-Basis Basis::diagonalize()
-{
+Basis Basis::diagonalize() {
// I love copy paste
if (!is_symmetric())
@@ -548,7 +508,7 @@ Basis Basis::diagonalize()
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];
@@ -583,7 +543,7 @@ Basis Basis::diagonalize()
// Compute the rotation matrix
Basis rot;
rot.elements[i][i] = rot.elements[j][j] = ::cos(angle);
- rot.elements[i][j] = - (rot.elements[j][i] = ::sin(angle));
+ rot.elements[i][j] = -(rot.elements[j][i] = ::sin(angle));
// Update the off matrix norm
off_matrix_norm_2 -= elements[i][j] * elements[i][j];
@@ -596,8 +556,7 @@ Basis Basis::diagonalize()
return acc_rot;
}
-
-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),
@@ -624,95 +583,84 @@ static const Basis _ortho_bases[24]={
Basis(0, -1, 0, 0, 0, -1, 1, 0, 0)
};
-
-int Basis::get_orthogonal_index() const
-{
+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_COND(p_index >= 24);
- *this=_ortho_bases[p_index];
-
+ *this = _ortho_bases[p_index];
}
+Basis::Basis(const Vector3 &p_euler) {
-
-Basis::Basis(const Vector3& p_euler) {
-
- set_euler( p_euler );
-
+ set_euler(p_euler);
}
-}
+} // namespace godot
#include "Quat.hpp"
namespace godot {
-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= ::cos(p_phi);
- real_t sine= ::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 = ::cos(p_phi);
+ real_t sine = ::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);
}
Basis::operator Quat() const {
@@ -722,21 +670,18 @@ 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 = ::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;
@@ -749,11 +694,7 @@ 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]);
}
-
-
-
-}
+} // namespace godot