From 5d543692eb85a3bacf4b1fae59e4ec90d24f67eb Mon Sep 17 00:00:00 2001 From: Karroffel Date: Fri, 3 Mar 2017 03:14:34 +0100 Subject: [PATCH] Added Basis.h and stub Quat.h --- include/godot/core/Basis.h | 644 +++++++++++++++++++++++++++++++++++++ include/godot/core/Quat.h | 171 ++++++++++ 2 files changed, 815 insertions(+) create mode 100644 include/godot/core/Basis.h create mode 100644 include/godot/core/Quat.h diff --git a/include/godot/core/Basis.h b/include/godot/core/Basis.h new file mode 100644 index 00000000..5636dc41 --- /dev/null +++ b/include/godot/core/Basis.h @@ -0,0 +1,644 @@ +#ifndef BASIS_H +#define BASIS_H + +#include "Vector3.h" + +#include + +typedef float real_t; // @Todo move this to a global Godot.h + +#define CMP_EPSILON 0.00001 // @Todo move this somewhere more global +#define CMP_EPSILON2 (CMP_EPSILON*CMP_EPSILON) // @Todo same as above +#define Math_PI 3.14159265358979323846 // I feel like I'm talking to myself + + + +namespace godot { + +class Quat; + +class Basis { +public: + + Vector3 elements[3]; + + Basis(const Quat& p_quat); // euler + Basis(const Vector3& p_euler); // euler + Basis(const Vector3& p_axis, real_t p_phi); + + Basis(const Vector3& row0, const Vector3& row1, const Vector3& row2) + { + elements[0]=row0; + elements[1]=row1; + elements[2]=row2; + } + + 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() { + + 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& operator[](int axis) const { + + return elements[axis]; + } + Vector3& 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 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 + + + void 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 inverse() const + { + Basis b = *this; + b.invert(); + return b; + } + + Basis transposed() const + { + Basis b = *this; + b.transpose(); + return b; + } + + real_t 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 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 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 rotate(const Vector3& p_axis, real_t p_phi) + { + *this = rotated(p_axis, p_phi); + } + + Basis rotated(const Vector3& p_axis, real_t p_phi) const + { + return Basis(p_axis, p_phi) * (*this); + } + + Vector3 get_rotation() const; // need?! + + void 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 scaled( const Vector3& p_scale ) const + { + Basis b = *this; + b.scale(p_scale); + return b; + } + + Vector3 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 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 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 tdotx(const Vector3& v) const { + return elements[0][0] * v[0] + elements[1][0] * v[1] + elements[2][0] * v[2]; + } + real_t tdoty(const Vector3& v) const { + return elements[0][1] * v[0] + elements[1][1] * v[1] + elements[2][1] * v[2]; + } + real_t tdotz(const Vector3& v) const { + return elements[0][2] * v[0] + elements[1][2] * v[1] + elements[2][2] * v[2]; + } + + bool isequal_approx(const Basis& a, const Basis& b) const; // need? + + bool 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 operator!=(const Basis& p_matrix) const + { + return (!(*this==p_matrix)); + } + + Vector3 xform(const Vector3& p_vector) const { + + return Vector3( + elements[0].dot(p_vector), + elements[1].dot(p_vector), + elements[2].dot(p_vector) + ); + } + + Vector3 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 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 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 operator+=(const Basis& p_matrix) { + + elements[0] += p_matrix.elements[0]; + elements[1] += p_matrix.elements[1]; + elements[2] += p_matrix.elements[2]; + } + + Basis operator+(const Basis& p_matrix) const { + + Basis ret(*this); + ret += p_matrix; + return ret; + } + + void operator-=(const Basis& p_matrix) { + + elements[0] -= p_matrix.elements[0]; + elements[1] -= p_matrix.elements[1]; + elements[2] -= p_matrix.elements[2]; + } + + Basis operator-(const Basis& p_matrix) const { + + Basis ret(*this); + ret -= p_matrix; + return ret; + } + + void operator*=(real_t p_val) { + + elements[0]*=p_val; + elements[1]*=p_val; + elements[2]*=p_val; + } + + Basis operator*(real_t p_val) const { + + Basis ret(*this); + ret *= p_val; + return ret; + } + + int get_orthogonal_index() const; // down below + + void set_orthogonal_index(int p_index); // down below + + bool is_orthogonal() const; // need? + bool is_rotation() const; // need? + + operator String() const; + + void get_axis_and_angle(Vector3 &r_axis,real_t& r_angle) const; + + /* create / set */ + + + void 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 get_column(int i) const { + + return Vector3(elements[0][i],elements[1][i],elements[2][i]); + } + + Vector3 get_row(int i) const { + + return Vector3(elements[i][0],elements[i][1],elements[i][2]); + } + Vector3 get_main_diagonal() const { + return Vector3(elements[0][0],elements[1][1],elements[2][2]); + } + + void 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 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 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 orthonormalized() const + { + Basis b = *this; + b.orthonormalize(); + return b; + } + + bool 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 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; + } + + operator Quat() const; + + +}; + +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 ); + +} + + + + +} + +#endif // BASIS_H diff --git a/include/godot/core/Quat.h b/include/godot/core/Quat.h new file mode 100644 index 00000000..ccdeefcf --- /dev/null +++ b/include/godot/core/Quat.h @@ -0,0 +1,171 @@ +#ifndef QUAT_H +#define QUAT_H + +#include + +#include "Vector3.h" + +namespace godot { + +#define CMP_EPSILON 0.00001 + +typedef float real_t; + +class Quat{ +public: + + real_t x,y,z,w; + + real_t length_squared() const; + real_t length() const; + void normalize(); + Quat normalized() const; + Quat inverse() const; + real_t dot(const Quat& q) const; + void set_euler(const Vector3& p_euler); + Vector3 get_euler() const; + Quat slerp(const Quat& q, const real_t& t) const; + Quat slerpni(const Quat& q, const real_t& t) const; + Quat cubic_slerp(const Quat& q, const Quat& prep, const Quat& postq,const real_t& t) const; + + void get_axis_and_angle(Vector3& r_axis, real_t &r_angle) const { + r_angle = 2 * ::acos(w); + r_axis.x = x / ::sqrt(1-w*w); + r_axis.y = y / ::sqrt(1-w*w); + r_axis.z = z / ::sqrt(1-w*w); + } + + void operator*=(const Quat& q); + Quat operator*(const Quat& q) const; + + + + Quat operator*(const Vector3& v) const + { + return Quat( w * v.x + y * v.z - z * v.y, + w * v.y + z * v.x - x * v.z, + w * v.z + x * v.y - y * v.x, + -x * v.x - y * v.y - z * v.z); + } + + Vector3 xform(const Vector3& v) const { + + Quat q = *this * v; + q *= this->inverse(); + return Vector3(q.x,q.y,q.z); + } + + void operator+=(const Quat& q); + void operator-=(const Quat& q); + void operator*=(const real_t& s); + void operator/=(const real_t& s); + Quat operator+(const Quat& q2) const; + Quat operator-(const Quat& q2) const; + Quat operator-() const; + Quat operator*(const real_t& s) const; + Quat operator/(const real_t& s) const; + + + bool operator==(const Quat& p_quat) const; + bool operator!=(const Quat& p_quat) const; + + operator String() const; + + inline void set( real_t p_x, real_t p_y, real_t p_z, real_t p_w) { + x=p_x; y=p_y; z=p_z; w=p_w; + } + inline Quat(real_t p_x, real_t p_y, real_t p_z, real_t p_w) { + x=p_x; y=p_y; z=p_z; w=p_w; + } + Quat(const Vector3& axis, const real_t& angle); + + Quat(const Vector3& v0, const Vector3& v1) // shortest arc + { + Vector3 c = v0.cross(v1); + real_t d = v0.dot(v1); + + if (d < -1.0 + CMP_EPSILON) { + x=0; + y=1; + z=0; + w=0; + } else { + + real_t s = ::sqrt((1.0 + d) * 2.0); + real_t rs = 1.0 / s; + + x=c.x*rs; + y=c.y*rs; + z=c.z*rs; + w=s * 0.5; + } + } + + inline Quat() {x=y=z=0; w=1; } + + +}; + + +real_t Quat::dot(const Quat& q) const { + return x * q.x+y * q.y+z * q.z+w * q.w; +} + +real_t Quat::length_squared() const { + return dot(*this); +} + +void Quat::operator+=(const Quat& q) { + x += q.x; y += q.y; z += q.z; w += q.w; +} + +void Quat::operator-=(const Quat& q) { + x -= q.x; y -= q.y; z -= q.z; w -= q.w; +} + +void Quat::operator*=(const real_t& s) { + x *= s; y *= s; z *= s; w *= s; +} + + +void Quat::operator/=(const real_t& s) { + + *this *= 1.0 / s; +} + +Quat Quat::operator+(const Quat& q2) const { + const Quat& q1 = *this; + return Quat( q1.x+q2.x, q1.y+q2.y, q1.z+q2.z, q1.w+q2.w ); +} + +Quat Quat::operator-(const Quat& q2) const { + const Quat& q1 = *this; + return Quat( q1.x-q2.x, q1.y-q2.y, q1.z-q2.z, q1.w-q2.w); +} + +Quat Quat::operator-() const { + const Quat& q2 = *this; + return Quat( -q2.x, -q2.y, -q2.z, -q2.w); +} + +Quat Quat::operator*(const real_t& s) const { + return Quat(x * s, y * s, z * s, w * s); +} + +Quat Quat::operator/(const real_t& s) const { + return *this * (1.0 / s); +} + + +bool Quat::operator==(const Quat& p_quat) const { + return x==p_quat.x && y==p_quat.y && z==p_quat.z && w==p_quat.w; +} + +bool Quat::operator!=(const Quat& p_quat) const { + return x!=p_quat.x || y!=p_quat.y || z!=p_quat.z || w!=p_quat.w; +} + + +} + +#endif // QUAT_H