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Diffstat (limited to 'include/godot_cpp/core/Basis.cpp')
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1 files changed, 680 insertions, 0 deletions
diff --git a/include/godot_cpp/core/Basis.cpp b/include/godot_cpp/core/Basis.cpp new file mode 100644 index 0000000..06a1937 --- /dev/null +++ b/include/godot_cpp/core/Basis.cpp @@ -0,0 +1,680 @@ +#include "Basis.h" + + +#include "Defs.h" + +#include "Vector3.h" + +#include "Quat.h" + +#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]; + + if ( det != 0 ) { + // WTF + __builtin_trap(); // WTF WTF WTF + + // I shouldn't do this + // @Todo @Fixme @Todo @Todo + } + 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() +{ + if (determinant() != 0) { + // not this crap again + __builtin_trap(); // WTF WTF WTF + // somebody please complain some day + // so I can fix this + + // need propert error reporting here. + } + + // 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 + if (p_index >= 24) { + __builtin_trap(); // kiiiiill me + // I don't want to do shady stuff like that + // @Todo WTF WTF + } + + + *this=_ortho_bases[p_index]; + +} + + + +Basis::Basis(const Vector3& p_euler) { + + set_euler( p_euler ); + +} + +} + +#include "Quat.h" + +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]); + +} + + + + +} |