#ifndef TRANSFORM_H #define TRANSFORM_H #include "Basis.h" #include "Plane.h" #include "Rect3.h" namespace godot { class Transform { public: Basis basis; Vector3 origin; void invert(); Transform inverse() const; void affine_invert(); Transform affine_inverse() const; Transform rotated(const Vector3& p_axis,real_t p_phi) const; void rotate(const Vector3& p_axis,real_t p_phi); void rotate_basis(const Vector3& p_axis,real_t p_phi); void set_look_at( const Vector3& p_eye, const Vector3& p_target, const Vector3& p_up ); Transform looking_at( const Vector3& p_target, const Vector3& p_up ) const; void scale(const Vector3& p_scale); Transform scaled(const Vector3& p_scale) const; void scale_basis(const Vector3& p_scale); void translate( real_t p_tx, real_t p_ty, real_t p_tz ); void translate( const Vector3& p_translation ); Transform translated( const Vector3& p_translation ) const; const Basis& get_basis() const { return basis; } void set_basis(const Basis& p_basis) { basis=p_basis; } const Vector3& get_origin() const { return origin; } void set_origin(const Vector3& p_origin) { origin=p_origin; } void orthonormalize(); Transform orthonormalized() const; bool operator==(const Transform& p_transform) const; bool operator!=(const Transform& p_transform) const; Vector3 xform(const Vector3& p_vector) const; Vector3 xform_inv(const Vector3& p_vector) const; Plane xform(const Plane& p_plane) const; Plane xform_inv(const Plane& p_plane) const; Rect3 xform(const Rect3& p_aabb) const; Rect3 xform_inv(const Rect3& p_aabb) const; void operator*=(const Transform& p_transform); Transform operator*(const Transform& p_transform) const; Transform interpolate_with(const Transform& p_transform, real_t p_c) const; Transform inverse_xform(const Transform& t) const { Vector3 v = t.origin - origin; return Transform(basis.transpose_xform(t.basis), basis.xform(v)); } 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,real_t tx, real_t ty, real_t tz) { basis.elements[0][0]=xx; basis.elements[0][1]=xy; basis.elements[0][2]=xz; basis.elements[1][0]=yx; basis.elements[1][1]=yy; basis.elements[1][2]=yz; basis.elements[2][0]=zx; basis.elements[2][1]=zy; basis.elements[2][2]=zz; origin.x=tx; origin.y=ty; origin.z=tz; } operator String() const; Transform(const Basis& p_basis, const Vector3& p_origin=Vector3()); Transform() {} }; Vector3 Transform::xform(const Vector3& p_vector) const { return Vector3( basis[0].dot(p_vector)+origin.x, basis[1].dot(p_vector)+origin.y, basis[2].dot(p_vector)+origin.z ); } Vector3 Transform::xform_inv(const Vector3& p_vector) const { Vector3 v = p_vector - origin; return Vector3( (basis.elements[0][0]*v.x ) + ( basis.elements[1][0]*v.y ) + ( basis.elements[2][0]*v.z ), (basis.elements[0][1]*v.x ) + ( basis.elements[1][1]*v.y ) + ( basis.elements[2][1]*v.z ), (basis.elements[0][2]*v.x ) + ( basis.elements[1][2]*v.y ) + ( basis.elements[2][2]*v.z ) ); } Plane Transform::xform(const Plane& p_plane) const { Vector3 point=p_plane.normal*p_plane.d; Vector3 point_dir=point+p_plane.normal; point=xform(point); point_dir=xform(point_dir); Vector3 normal=point_dir-point; normal.normalize(); real_t d=normal.dot(point); return Plane(normal,d); } Plane Transform::xform_inv(const Plane& p_plane) const { Vector3 point=p_plane.normal*p_plane.d; Vector3 point_dir=point+p_plane.normal; xform_inv(point); xform_inv(point_dir); Vector3 normal=point_dir-point; normal.normalize(); real_t d=normal.dot(point); return Plane(normal,d); } Rect3 Transform::xform(const Rect3& p_aabb) const { /* define vertices */ Vector3 x=basis.get_axis(0)*p_aabb.size.x; Vector3 y=basis.get_axis(1)*p_aabb.size.y; Vector3 z=basis.get_axis(2)*p_aabb.size.z; Vector3 pos = xform( p_aabb.pos ); //could be even further optimized Rect3 new_aabb; new_aabb.pos=pos; new_aabb.expand_to( pos+x ); new_aabb.expand_to( pos+y ); new_aabb.expand_to( pos+z ); new_aabb.expand_to( pos+x+y ); new_aabb.expand_to( pos+x+z ); new_aabb.expand_to( pos+y+z ); new_aabb.expand_to( pos+x+y+z ); return new_aabb; } Rect3 Transform::xform_inv(const Rect3& p_aabb) const { /* define vertices */ Vector3 vertices[8]={ Vector3(p_aabb.pos.x+p_aabb.size.x, p_aabb.pos.y+p_aabb.size.y, p_aabb.pos.z+p_aabb.size.z), Vector3(p_aabb.pos.x+p_aabb.size.x, p_aabb.pos.y+p_aabb.size.y, p_aabb.pos.z), Vector3(p_aabb.pos.x+p_aabb.size.x, p_aabb.pos.y, p_aabb.pos.z+p_aabb.size.z), Vector3(p_aabb.pos.x+p_aabb.size.x, p_aabb.pos.y, p_aabb.pos.z), Vector3(p_aabb.pos.x, p_aabb.pos.y+p_aabb.size.y, p_aabb.pos.z+p_aabb.size.z), Vector3(p_aabb.pos.x, p_aabb.pos.y+p_aabb.size.y, p_aabb.pos.z), Vector3(p_aabb.pos.x, p_aabb.pos.y, p_aabb.pos.z+p_aabb.size.z), Vector3(p_aabb.pos.x, p_aabb.pos.y, p_aabb.pos.z) }; Rect3 ret; ret.pos=xform_inv(vertices[0]); for (int i=1;i<8;i++) { ret.expand_to( xform_inv(vertices[i]) ); } return ret; } } namespace godot { void Transform::affine_invert() { basis.invert(); origin = basis.xform(-origin); } Transform Transform::affine_inverse() const { Transform ret=*this; ret.affine_invert(); return ret; } void Transform::invert() { basis.transpose(); origin = basis.xform(-origin); } Transform Transform::inverse() const { // FIXME: this function assumes the basis is a rotation matrix, with no scaling. // Transform::affine_inverse can handle matrices with scaling, so GDScript should eventually use that. Transform ret=*this; ret.invert(); return ret; } void Transform::rotate(const Vector3& p_axis,real_t p_phi) { *this = rotated(p_axis, p_phi); } Transform Transform::rotated(const Vector3& p_axis,real_t p_phi) const{ return Transform(Basis( p_axis, p_phi ), Vector3()) * (*this); } void Transform::rotate_basis(const Vector3& p_axis,real_t p_phi) { basis.rotate(p_axis,p_phi); } Transform Transform::looking_at( const Vector3& p_target, const Vector3& p_up ) const { Transform t = *this; t.set_look_at(origin,p_target,p_up); return t; } void Transform::set_look_at( const Vector3& p_eye, const Vector3& p_target, const Vector3& p_up ) { // Reference: MESA source code Vector3 v_x, v_y, v_z; /* Make rotation matrix */ /* Z vector */ v_z = p_eye - p_target; v_z.normalize(); v_y = p_up; v_x=v_y.cross(v_z); /* Recompute Y = Z cross X */ v_y=v_z.cross(v_x); v_x.normalize(); v_y.normalize(); basis.set_axis(0,v_x); basis.set_axis(1,v_y); basis.set_axis(2,v_z); origin=p_eye; } Transform Transform::interpolate_with(const Transform& p_transform, real_t p_c) const { /* not sure if very "efficient" but good enough? */ Vector3 src_scale = basis.get_scale(); Quat src_rot = basis; Vector3 src_loc = origin; Vector3 dst_scale = p_transform.basis.get_scale(); Quat dst_rot = p_transform.basis; Vector3 dst_loc = p_transform.origin; Transform dst; dst.basis=src_rot.slerp(dst_rot,p_c); dst.basis.scale(src_scale.linear_interpolate(dst_scale,p_c)); dst.origin=src_loc.linear_interpolate(dst_loc,p_c); return dst; } void Transform::scale(const Vector3& p_scale) { basis.scale(p_scale); origin*=p_scale; } Transform Transform::scaled(const Vector3& p_scale) const { Transform t = *this; t.scale(p_scale); return t; } void Transform::scale_basis(const Vector3& p_scale) { basis.scale(p_scale); } void Transform::translate( real_t p_tx, real_t p_ty, real_t p_tz) { translate( Vector3(p_tx,p_ty,p_tz) ); } void Transform::translate( const Vector3& p_translation ) { for( int i = 0; i < 3; i++ ) { origin[i] += basis[i].dot(p_translation); } } Transform Transform::translated( const Vector3& p_translation ) const { Transform t=*this; t.translate(p_translation); return t; } void Transform::orthonormalize() { basis.orthonormalize(); } Transform Transform::orthonormalized() const { Transform _copy = *this; _copy.orthonormalize(); return _copy; } bool Transform::operator==(const Transform& p_transform) const { return (basis==p_transform.basis && origin==p_transform.origin); } bool Transform::operator!=(const Transform& p_transform) const { return (basis!=p_transform.basis || origin!=p_transform.origin); } void Transform::operator*=(const Transform& p_transform) { origin=xform(p_transform.origin); basis*=p_transform.basis; } Transform Transform::operator*(const Transform& p_transform) const { Transform t=*this; t*=p_transform; return t; } Transform::operator String() const { return basis.operator String() + " - " + origin.operator String(); } Transform::Transform(const Basis& p_basis, const Vector3& p_origin) { basis=p_basis; origin=p_origin; } } #endif // TRANSFORM_H