💿🐜 Antkeeper source code
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140 lines
3.3 KiB
140 lines
3.3 KiB
/*
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* Copyright (C) 2023 Christopher J. Howard
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*
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* This file is part of Antkeeper source code.
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*
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* Antkeeper source code is free software: you can redistribute it and/or modify
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* it under the terms of the GNU General Public License as published by
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* the Free Software Foundation, either version 3 of the License, or
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* (at your option) any later version.
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*
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* Antkeeper source code is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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* GNU General Public License for more details.
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*
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* You should have received a copy of the GNU General Public License
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* along with Antkeeper source code. If not, see <http://www.gnu.org/licenses/>.
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*/
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#ifndef ANTKEEPER_MATH_TRANSFORMATION_SE3_HPP
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#define ANTKEEPER_MATH_TRANSFORMATION_SE3_HPP
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#include <engine/math/vector.hpp>
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#include <engine/math/quaternion.hpp>
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namespace math {
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/**
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* SE(3) proper rigid transformation (rototranslation).
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*
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* @tparam T Scalar type.
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*/
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template <class T>
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struct se3
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{
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public:
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/// Scalar type.
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using scalar_type = T;
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/// Vector type.
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using vector_type = vec3<T>;
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/// Quaternion type.
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using quaternion_type = quat<T>;
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/// Transformation matrix type.
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using matrix_type = mat4<T>;
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/// Vector representing the translation component of the transformation.
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vector_type t;
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/// Quaternion representing the rotation component of the transformation.
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quaternion_type r;
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/// Returns the inverse of this transformation.
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[[nodiscard]] constexpr se3 inverse() const noexcept
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{
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return {-t * r, conjugate(r)};
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}
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/// Returns a matrix representation of this transformation.
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/// @{
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[[nodiscard]] constexpr matrix_type matrix() const noexcept
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{
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matrix_type m = mat4<T>(mat3<T>(r));
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m[3].x() = t.x();
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m[3].y() = t.y();
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m[3].z() = t.z();
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return m;
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}
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[[nodiscard]] inline constexpr explicit operator matrix_type() const noexcept
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{
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return matrix();
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}
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/// @}
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/**
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* Transforms a vector by this transformation.
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*
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* @param v Untransformed vector.
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*
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* @return Transformed vector.
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*/
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/// @{
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[[nodiscard]] inline constexpr vector_type transform(const vector_type& v) const noexcept
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{
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return r * v + t;
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}
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[[nodiscard]] inline constexpr vector_type operator*(const vector_type& v) const noexcept
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{
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return transform(v);
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}
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/// @}
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/**
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* Transforms an SE(3) transformation by this transformation.
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*
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* @param xf SE(3) transformation.
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*
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* @return Frame in this se3's space.
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*/
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/// @{
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[[nodiscard]] constexpr se3 transform(const se3& xf) const noexcept
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{
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return {xf.transform(t), normalize(xf.r * r)};
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}
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[[nodiscard]] inline constexpr se3 operator*(const se3& xf) const noexcept
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{
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return transform(xf);
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}
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/// @}
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/*
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* Type-casts the transform scalars using `static_cast`.
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*
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* @tparam U Target scalar type.
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*
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* @return Type-casted transform.
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*/
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template <class U>
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[[nodiscard]] inline constexpr explicit operator se3<U>() const noexcept
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{
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return {vec3<U>(t), quat<U>(r)};
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}
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/// Returns an identity transformation.
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[[nodiscard]] static inline constexpr se3 identity() noexcept
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{
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return {vector_type::zero(), quaternion_type::identity()};
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}
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};
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} // namespace math
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#endif // ANTKEEPER_MATH_TRANSFORMATION_SE3_HPP
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