/**************************************************************************/ /* transform_3d.h */ /**************************************************************************/ /* This file is part of: */ /* GODOT ENGINE */ /* https://godotengine.org */ /**************************************************************************/ /* Copyright (c) 2014-present Godot Engine contributors (see AUTHORS.md). */ /* Copyright (c) 2007-2014 Juan Linietsky, Ariel Manzur. */ /* */ /* Permission is hereby granted, free of charge, to any person obtaining */ /* a copy of this software and associated documentation files (the */ /* "Software"), to deal in the Software without restriction, including */ /* without limitation the rights to use, copy, modify, merge, publish, */ /* distribute, sublicense, and/or sell copies of the Software, and to */ /* permit persons to whom the Software is furnished to do so, subject to */ /* the following conditions: */ /* */ /* The above copyright notice and this permission notice shall be */ /* included in all copies or substantial portions of the Software. */ /* */ /* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, */ /* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF */ /* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. */ /* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY */ /* CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, */ /* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE */ /* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. */ /**************************************************************************/ #ifndef TRANSFORM_3D_H #define TRANSFORM_3D_H #include "core/math/aabb.h" #include "core/math/basis.h" #include "core/math/plane.h" #include "core/templates/vector.h" struct _NO_DISCARD_ Transform3D { Basis basis; Vector3 origin; void invert(); Transform3D inverse() const; void affine_invert(); Transform3D affine_inverse() const; Transform3D rotated(const Vector3 &p_axis, real_t p_angle) const; Transform3D rotated_local(const Vector3 &p_axis, real_t p_angle) const; void rotate(const Vector3 &p_axis, real_t p_angle); void rotate_basis(const Vector3 &p_axis, real_t p_angle); void set_look_at(const Vector3 &p_eye, const Vector3 &p_target, const Vector3 &p_up = Vector3(0, 1, 0), bool p_use_model_front = false); Transform3D looking_at(const Vector3 &p_target, const Vector3 &p_up = Vector3(0, 1, 0), bool p_use_model_front = false) const; void scale(const Vector3 &p_scale); Transform3D scaled(const Vector3 &p_scale) const; Transform3D scaled_local(const Vector3 &p_scale) const; void scale_basis(const Vector3 &p_scale); void translate_local(real_t p_tx, real_t p_ty, real_t p_tz); void translate_local(const Vector3 &p_translation); Transform3D translated(const Vector3 &p_translation) const; Transform3D translated_local(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(); Transform3D orthonormalized() const; void orthogonalize(); Transform3D orthogonalized() const; bool is_equal_approx(const Transform3D &p_transform) const; bool is_finite() const; bool operator==(const Transform3D &p_transform) const; bool operator!=(const Transform3D &p_transform) const; _FORCE_INLINE_ Vector3 xform(const Vector3 &p_vector) const; _FORCE_INLINE_ AABB xform(const AABB &p_aabb) const; _FORCE_INLINE_ Vector xform(const Vector &p_array) const; // NOTE: These are UNSAFE with non-uniform scaling, and will produce incorrect results. // They use the transpose. // For safe inverse transforms, xform by the affine_inverse. _FORCE_INLINE_ Vector3 xform_inv(const Vector3 &p_vector) const; _FORCE_INLINE_ AABB xform_inv(const AABB &p_aabb) const; _FORCE_INLINE_ Vector xform_inv(const Vector &p_array) const; // Safe with non-uniform scaling (uses affine_inverse). _FORCE_INLINE_ Plane xform(const Plane &p_plane) const; _FORCE_INLINE_ Plane xform_inv(const Plane &p_plane) const; // These fast versions use precomputed affine inverse, and should be used in bottleneck areas where // multiple planes are to be transformed. _FORCE_INLINE_ Plane xform_fast(const Plane &p_plane, const Basis &p_basis_inverse_transpose) const; static _FORCE_INLINE_ Plane xform_inv_fast(const Plane &p_plane, const Transform3D &p_inverse, const Basis &p_basis_transpose); void operator*=(const Transform3D &p_transform); Transform3D operator*(const Transform3D &p_transform) const; void operator*=(const real_t p_val); Transform3D operator*(const real_t p_val) const; Transform3D interpolate_with(const Transform3D &p_transform, real_t p_c) const; _FORCE_INLINE_ Transform3D inverse_xform(const Transform3D &t) const { Vector3 v = t.origin - origin; return Transform3D(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.set(xx, xy, xz, yx, yy, yz, zx, zy, zz); origin.x = tx; origin.y = ty; origin.z = tz; } operator String() const; Transform3D() {} Transform3D(const Basis &p_basis, const Vector3 &p_origin = Vector3()); Transform3D(const Vector3 &p_x, const Vector3 &p_y, const Vector3 &p_z, const Vector3 &p_origin); Transform3D(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 ox, real_t oy, real_t oz); }; _FORCE_INLINE_ Vector3 Transform3D::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); } _FORCE_INLINE_ Vector3 Transform3D::xform_inv(const Vector3 &p_vector) const { Vector3 v = p_vector - origin; return Vector3( (basis.rows[0][0] * v.x) + (basis.rows[1][0] * v.y) + (basis.rows[2][0] * v.z), (basis.rows[0][1] * v.x) + (basis.rows[1][1] * v.y) + (basis.rows[2][1] * v.z), (basis.rows[0][2] * v.x) + (basis.rows[1][2] * v.y) + (basis.rows[2][2] * v.z)); } // Neither the plane regular xform or xform_inv are particularly efficient, // as they do a basis inverse. For xforming a large number // of planes it is better to pre-calculate the inverse transpose basis once // and reuse it for each plane, by using the 'fast' version of the functions. _FORCE_INLINE_ Plane Transform3D::xform(const Plane &p_plane) const { Basis b = basis.inverse(); b.transpose(); return xform_fast(p_plane, b); } _FORCE_INLINE_ Plane Transform3D::xform_inv(const Plane &p_plane) const { Transform3D inv = affine_inverse(); Basis basis_transpose = basis.transposed(); return xform_inv_fast(p_plane, inv, basis_transpose); } _FORCE_INLINE_ AABB Transform3D::xform(const AABB &p_aabb) const { /* https://dev.theomader.com/transform-bounding-boxes/ */ Vector3 min = p_aabb.position; Vector3 max = p_aabb.position + p_aabb.size; Vector3 tmin, tmax; for (int i = 0; i < 3; i++) { tmin[i] = tmax[i] = origin[i]; for (int j = 0; j < 3; j++) { real_t e = basis[i][j] * min[j]; real_t f = basis[i][j] * max[j]; if (e < f) { tmin[i] += e; tmax[i] += f; } else { tmin[i] += f; tmax[i] += e; } } } AABB r_aabb; r_aabb.position = tmin; r_aabb.size = tmax - tmin; return r_aabb; } _FORCE_INLINE_ AABB Transform3D::xform_inv(const AABB &p_aabb) const { /* define vertices */ Vector3 vertices[8] = { Vector3(p_aabb.position.x + p_aabb.size.x, p_aabb.position.y + p_aabb.size.y, p_aabb.position.z + p_aabb.size.z), Vector3(p_aabb.position.x + p_aabb.size.x, p_aabb.position.y + p_aabb.size.y, p_aabb.position.z), Vector3(p_aabb.position.x + p_aabb.size.x, p_aabb.position.y, p_aabb.position.z + p_aabb.size.z), Vector3(p_aabb.position.x + p_aabb.size.x, p_aabb.position.y, p_aabb.position.z), Vector3(p_aabb.position.x, p_aabb.position.y + p_aabb.size.y, p_aabb.position.z + p_aabb.size.z), Vector3(p_aabb.position.x, p_aabb.position.y + p_aabb.size.y, p_aabb.position.z), Vector3(p_aabb.position.x, p_aabb.position.y, p_aabb.position.z + p_aabb.size.z), Vector3(p_aabb.position.x, p_aabb.position.y, p_aabb.position.z) }; AABB ret; ret.position = xform_inv(vertices[0]); for (int i = 1; i < 8; i++) { ret.expand_to(xform_inv(vertices[i])); } return ret; } Vector Transform3D::xform(const Vector &p_array) const { Vector array; array.resize(p_array.size()); const Vector3 *r = p_array.ptr(); Vector3 *w = array.ptrw(); for (int i = 0; i < p_array.size(); ++i) { w[i] = xform(r[i]); } return array; } Vector Transform3D::xform_inv(const Vector &p_array) const { Vector array; array.resize(p_array.size()); const Vector3 *r = p_array.ptr(); Vector3 *w = array.ptrw(); for (int i = 0; i < p_array.size(); ++i) { w[i] = xform_inv(r[i]); } return array; } _FORCE_INLINE_ Plane Transform3D::xform_fast(const Plane &p_plane, const Basis &p_basis_inverse_transpose) const { // Transform a single point on the plane. Vector3 point = p_plane.normal * p_plane.d; point = xform(point); // Use inverse transpose for correct normals with non-uniform scaling. Vector3 normal = p_basis_inverse_transpose.xform(p_plane.normal); normal.normalize(); real_t d = normal.dot(point); return Plane(normal, d); } _FORCE_INLINE_ Plane Transform3D::xform_inv_fast(const Plane &p_plane, const Transform3D &p_inverse, const Basis &p_basis_transpose) { // Transform a single point on the plane. Vector3 point = p_plane.normal * p_plane.d; point = p_inverse.xform(point); // Note that instead of precalculating the transpose, an alternative // would be to use the transpose for the basis transform. // However that would be less SIMD friendly (requiring a swizzle). // So the cost is one extra precalced value in the calling code. // This is probably worth it, as this could be used in bottleneck areas. And // where it is not a bottleneck, the non-fast method is fine. // Use transpose for correct normals with non-uniform scaling. Vector3 normal = p_basis_transpose.xform(p_plane.normal); normal.normalize(); real_t d = normal.dot(point); return Plane(normal, d); } #endif // TRANSFORM_3D_H