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Diffstat (limited to 'include/godot_cpp/core/Basis.cpp')
| -rw-r--r-- | include/godot_cpp/core/Basis.cpp | 664 |
1 files changed, 0 insertions, 664 deletions
diff --git a/include/godot_cpp/core/Basis.cpp b/include/godot_cpp/core/Basis.cpp deleted file mode 100644 index dff6e4f..0000000 --- a/include/godot_cpp/core/Basis.cpp +++ /dev/null @@ -1,664 +0,0 @@ -#include "Basis.hpp" - - -#include "Defs.hpp" - -#include "Vector3.hpp" - -#include "Quat.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(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) { - - set(xx, xy, xz, yx, yy, yz, zx, zy, zz); -} - -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; -} - - - - - -const Vector3& Basis::operator[](int axis) const { - - return elements[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]) - -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]; - - - 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 ); -} -#undef cofac - -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) - return false; - } - } - - return true; -} - - -bool Basis::is_orthogonal() const -{ - Basis id; - Basis m = (*this)*transposed(); - - return isequal_approx(id,m); -} - -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]); -} - -Basis Basis::inverse() const -{ - Basis b = *this; - b.invert(); - return b; -} - -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]); -} - -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] ); -} -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; -} - -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 -{ - 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; -} - -Basis Basis::scaled( const Vector3& p_scale ) const -{ - Basis b = *this; - b.scale(p_scale); - return b; -} - -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() - ); -} - -Vector3 Basis::get_euler() const -{ - // Euler angles in XYZ convention. - // See https://en.wikipedia.org/wiki/Euler_angles#Rotation_matrix - // - // 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 - - Vector3 euler; - - if (is_rotation() == false) - return euler; - - euler.y = ::asin(elements[0][2]); - if ( euler.y < Math_PI*0.5) { - if ( euler.y > -Math_PI*0.5) { - euler.x = ::atan2(-elements[1][2],elements[2][2]); - euler.z = ::atan2(-elements[0][1],elements[0][0]); - - } else { - real_t r = ::atan2(elements[1][0],elements[1][1]); - euler.z = 0.0; - euler.x = euler.z - r; - - } - } else { - real_t r = ::atan2(elements[0][1],elements[1][1]); - euler.z = 0; - euler.x = r - euler.z; - } - - return euler; -} - -void Basis::set_euler(const Vector3& p_euler) -{ - real_t c, s; - - c = ::cos(p_euler.x); - s = ::sin(p_euler.x); - Basis xmat(1.0,0.0,0.0,0.0,c,-s,0.0,s,c); - - c = ::cos(p_euler.y); - s = ::sin(p_euler.y); - Basis ymat(c,0.0,s,0.0,1.0,0.0,-s,0.0,c); - - c = ::cos(p_euler.z); - s = ::sin(p_euler.z); - 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); -} - -// transposed dot products -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 { - return elements[0][1] * v[0] + elements[1][1] * v[1] + elements[2][1] * v[2]; -} -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++) { - if (elements[i][j] != p_matrix.elements[i][j]) - return false; - } - } - - return true; -} - -bool Basis::operator!=(const Basis& p_matrix) const -{ - return (!(*this==p_matrix)); -} - -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) - ); -} - -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 ) - ); -} -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])); - -} - -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]) ); - -} - - -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 ret(*this); - ret += p_matrix; - return ret; -} - -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 ret(*this); - ret -= p_matrix; - return ret; -} - -void Basis::operator*=(real_t 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::operator String() const -{ - String s; - // @Todo - return s; -} - -/* 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; -} -Vector3 Basis::get_column(int i) const { - - 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]); -} -Vector3 Basis::get_main_diagonal() const { - 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; -} - -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() -{ - ERR_FAIL_COND(determinant() != 0); - - // 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); -} - -Basis Basis::orthonormalized() const -{ - Basis b = *this; - b.orthonormalize(); - return b; -} - -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) - return false; - if (::fabs(elements[1][2] - elements[2][1]) > CMP_EPSILON) - return false; - - return true; -} - -Basis Basis::diagonalize() -{ - // I love copy paste - - if (!is_symmetric()) - return 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]; - - int ite = 0; - Basis acc_rot; - 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]; - // Find the pivot element - int i, j; - if (el01_2 > el02_2) { - if (el12_2 > el01_2) { - i = 1; - j = 2; - } else { - i = 0; - j = 1; - } - } else { - if (el12_2 > el02_2) { - i = 1; - j = 2; - } else { - i = 0; - j = 2; - } - } - - // Compute the rotation angle - real_t angle; - if (::fabs(elements[j][j] - elements[i][i]) < CMP_EPSILON) { - angle = Math_PI / 4; - } else { - angle = 0.5 * ::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] = ::cos(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]; - - // Apply the rotation - *this = rot * *this * rot.transposed(); - acc_rot = rot * acc_rot; - } - - return acc_rot; -} - - -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), - Basis(0, 1, 0, -1, 0, 0, 0, 0, 1), - Basis(1, 0, 0, 0, 0, -1, 0, 1, 0), - Basis(0, 0, 1, 1, 0, 0, 0, 1, 0), - Basis(-1, 0, 0, 0, 0, 1, 0, 1, 0), - Basis(0, 0, -1, -1, 0, 0, 0, 1, 0), - 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), - Basis(0, -1, 0, -1, 0, 0, 0, 0, -1), - Basis(1, 0, 0, 0, 0, 1, 0, -1, 0), - Basis(0, 0, -1, 1, 0, 0, 0, -1, 0), - Basis(-1, 0, 0, 0, 0, -1, 0, -1, 0), - Basis(0, 0, 1, -1, 0, 0, 0, -1, 0), - Basis(0, 0, 1, 0, 1, 0, -1, 0, 0), - Basis(0, -1, 0, 0, 0, 1, -1, 0, 0), - Basis(0, 0, -1, 0, -1, 0, -1, 0, 0), - Basis(0, 1, 0, 0, 0, -1, -1, 0, 0), - Basis(0, 0, 1, 0, -1, 0, 1, 0, 0), - Basis(0, 1, 0, 0, 0, 1, 1, 0, 0), - Basis(0, 0, -1, 0, 1, 0, 1, 0, 0), - Basis(0, -1, 0, 0, 0, -1, 1, 0, 0) -}; - - -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++) { - - real_t 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 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]; - -} - - - -Basis::Basis(const Vector3& p_euler) { - - set_euler( p_euler ); - -} - -} - -#include "Quat.hpp" - -namespace godot { - -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)) ; - -} - -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); - - 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 ); - -} - -Basis::operator Quat() const { - ERR_FAIL_COND_V(is_rotation() == false, Quat()); - - real_t trace = elements[0][0] + elements[1][1] + elements[2][2]; - real_t temp[4]; - - if (trace > 0.0) - { - real_t s = ::sqrt(trace + 1.0); - 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 - { - int i = elements[0][0] < elements[1][1] ? - (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; - - real_t s = ::sqrt(elements[i][i] - elements[j][j] - elements[k][k] + 1.0); - temp[i] = s * 0.5; - s = 0.5 / s; - - temp[3] = (elements[k][j] - elements[j][k]) * s; - temp[j] = (elements[j][i] + elements[i][j]) * s; - temp[k] = (elements[k][i] + elements[i][k]) * s; - } - - return Quat(temp[0],temp[1],temp[2],temp[3]); - -} - - - - -} |