matrix.hpp

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// Copyright Take Vos 2021-2022.
// Distributed under the Boost Software License, Version 1.0.
// (See accompanying file LICENSE_1_0.txt or copy at https://www.boost.org/LICENSE_1_0.txt)
 
#pragma once
 
#include "vector.hpp"
#include "extent.hpp"
#include "point.hpp"
#include "rectangle.hpp"
#include "quad.hpp"
#include "circle.hpp"
#include "line_segment.hpp"
#include "corner_radii.hpp"
#include "axis_aligned_rectangle.hpp"
#include <array>
 
namespace hi {
inline namespace v1 {
namespace geo {
 
template<int D>
class matrix {
public:
    static_assert(D == 2 || D == 3, "Only 2D or 3D rotation-matrices are supported");
 
    constexpr matrix(matrix const&) noexcept = default;
    constexpr matrix(matrix&&) noexcept = default;
    constexpr matrix& operator=(matrix const&) noexcept = default;
    constexpr matrix& operator=(matrix&&) noexcept = default;
 
    constexpr matrix() noexcept
    {
        hilet a = f32x4::broadcast(1.0f);
        _col0 = a.x000();
        _col1 = a._0y00();
        _col2 = a._00z0();
        _col3 = a._000w();
    };
 
    constexpr matrix(f32x4 col0, f32x4 col1, f32x4 col2, f32x4 col3 = f32x4{0.0f, 0.0f, 0.0f, 1.0f}) noexcept :
        _col0(col0), _col1(col1), _col2(col2), _col3(col3)
    {
    }
 
    constexpr matrix(vector3 col0, vector3 col1, vector3 col2, vector3 col3 = vector3{}) noexcept
        requires(D == 3)
        :
        _col0(static_cast<f32x4>(col0)),
        _col1(static_cast<f32x4>(col1)),
        _col2(static_cast<f32x4>(col2)),
        _col3(static_cast<f32x4>(col3).xyz1())
    {
    }
 
    constexpr matrix(
        float c0r0,
        float c1r0,
        float c2r0,
        float c0r1,
        float c1r1,
        float c2r1,
        float c0r2,
        float c1r2,
        float c2r2) noexcept
        requires(D == 3)
        :
        _col0(c0r0, c0r1, c0r2, 0.0f), _col1(c1r0, c1r1, c1r2, 0.0f), _col2(c2r0, c2r1, c2r2, 0.0f), _col3(0.0f, 0.0f, 0.0f, 1.0f)
    {
    }
 
    constexpr matrix(
        float c0r0,
        float c1r0,
        float c2r0,
        float c3r0,
        float c0r1,
        float c1r1,
        float c2r1,
        float c3r1,
        float c0r2,
        float c1r2,
        float c2r2,
        float c3r2,
        float c0r3,
        float c1r3,
        float c2r3,
        float c3r3) noexcept
        requires(D == 3)
        :
        _col0(c0r0, c0r1, c0r2, c0r3), _col1(c1r0, c1r1, c1r2, c1r3), _col2(c2r0, c2r1, c2r2, c2r3), _col3(c3r0, c3r1, c3r2, c3r3)
    {
    }
 
    template<int E>
        requires(E < D)
    [[nodiscard]] constexpr matrix(matrix<E> const& other) noexcept :
        _col0(get<0>(other)), _col1(get<1>(other)), _col2(get<2>(other)), _col3(get<3>(other))
    {
    }
 
    template<int E>
        requires(E < D)
    constexpr matrix& operator=(matrix<E> const& rhs) noexcept
    {
        _col0 = get<0>(rhs);
        _col1 = get<1>(rhs);
        _col2 = get<2>(rhs);
        _col3 = get<3>(rhs);
        return *this;
    }
 
    [[nodiscard]] constexpr explicit operator std::array<f32x4, 4>() const noexcept
    {
        hi_axiom(holds_invariant());
        return {_col0, _col1, _col2, _col3};
    }
 
    [[nodiscard]] constexpr static matrix
    uniform(aarectangle src_rectangle, aarectangle dst_rectangle, alignment alignment) noexcept;
 
    template<int I>
    [[nodiscard]] friend constexpr f32x4 const& get(matrix const& rhs) noexcept
    {
        if constexpr (I == 0) {
            return rhs._col0;
        } else if constexpr (I == 1) {
            return rhs._col1;
        } else if constexpr (I == 2) {
            return rhs._col2;
        } else if constexpr (I == 3) {
            return rhs._col3;
        } else {
            hi_static_no_default();
        }
    }
 
    template<int I>
    [[nodiscard]] friend constexpr f32x4& get(matrix& rhs) noexcept
    {
        if constexpr (I == 0) {
            return rhs._col0;
        } else if constexpr (I == 1) {
            return rhs._col1;
        } else if constexpr (I == 2) {
            return rhs._col2;
        } else if constexpr (I == 3) {
            return rhs._col3;
        } else {
            hi_static_no_default();
        }
    }
 
    [[nodiscard]] constexpr bool holds_invariant() const noexcept
    {
        return true;
    }
 
    [[nodiscard]] constexpr f32x4 operator*(f32x4 const& rhs) const noexcept
    {
        return {_col0 * rhs.xxxx() + _col1 * rhs.yyyy() + _col2 * rhs.zzzz() + _col3 * rhs.wwww()};
    }
 
    [[nodiscard]] constexpr float operator*(float const& rhs) const noexcept
    {
        // As if _col0 * rhs.xxxx() in operator*(f32x4 rhs)
        auto abs_scale = hypot<D>(_col0 * f32x4::broadcast(rhs));
 
        // We want to keep the sign of the original scaler, even if the matrix has rotation.
        return std::copysign(abs_scale, rhs);
    }
 
    [[nodiscard]] constexpr corner_radii operator*(corner_radii const& rhs) const noexcept
    {
        return {*this * get<0>(rhs), *this * get<1>(rhs), *this * get<2>(rhs), *this * get<3>(rhs)};
    }
 
    template<int E>
    [[nodiscard]] constexpr auto operator*(vector<float, E> const& rhs) const noexcept
    {
        hi_axiom(rhs.holds_invariant());
        return vector<float, std::max(D, E)>{
            _col0 * static_cast<f32x4>(rhs).xxxx() + _col1 * static_cast<f32x4>(rhs).yyyy() +
            _col2 * static_cast<f32x4>(rhs).zzzz()};
    }
 
    template<int E>
    [[nodiscard]] constexpr auto operator*(extent<float, E> const& rhs) const noexcept
    {
        hi_axiom(rhs.holds_invariant());
        return extent<float, std::max(D, E)>{
            _col0 * static_cast<f32x4>(rhs).xxxx() + _col1 * static_cast<f32x4>(rhs).yyyy() +
            _col2 * static_cast<f32x4>(rhs).zzzz()};
    }
 
    template<int E>
    [[nodiscard]] constexpr auto operator*(point<float, E> const& rhs) const noexcept
    {
        hi_axiom(rhs.holds_invariant());
        return point<float, std::max(D, E)>{
            _col0 * static_cast<f32x4>(rhs).xxxx() + _col1 * static_cast<f32x4>(rhs).yyyy() +
            _col2 * static_cast<f32x4>(rhs).zzzz() + _col3 * static_cast<f32x4>(rhs).wwww()};
    }
 
    [[nodiscard]] constexpr rectangle operator*(aarectangle const& rhs) const noexcept
    {
        return *this * rectangle{rhs};
    }
 
    [[nodiscard]] constexpr rectangle operator*(rectangle const& rhs) const noexcept
    {
        return rectangle{*this * rhs.origin, *this * rhs.right, *this * rhs.up};
    }
 
    [[nodiscard]] constexpr quad operator*(quad const& rhs) const noexcept
    {
        return quad{*this * rhs.p0, *this * rhs.p1, *this * rhs.p2, *this * rhs.p3};
    }
 
    [[nodiscard]] constexpr circle operator*(circle const& rhs) const noexcept
    {
        return circle{*this * midpoint(rhs), *this * rhs.radius()};
    }
 
    [[nodiscard]] constexpr line_segment operator*(line_segment const& rhs) const noexcept
    {
        return line_segment{*this * rhs.origin(), *this * rhs.direction()};
    }
 
    [[nodiscard]] constexpr auto operator*(matrix const& rhs) const noexcept
    {
        return matrix{*this * get<0>(rhs), *this * get<1>(rhs), *this * get<2>(rhs), *this * get<3>(rhs)};
    }
 
    [[nodiscard]] friend constexpr matrix transpose(matrix const& rhs) noexcept
    {
        auto tmp = transpose(rhs._col0, rhs._col1, rhs._col2, rhs._col3);
        return {std::get<0>(tmp), std::get<1>(tmp), std::get<2>(tmp), std::get<3>(tmp)};
    }
 
 
    template<char DstX, char DstY, char DstZ, char DstW = 'w'>
    [[nodiscard]] friend constexpr matrix reflect(matrix const& rhs) noexcept
        requires(D == 3)
    {
        return matrix{reflect_column<DstX>(), reflect_column<DstY>(), reflect_column<DstZ>(), reflect_column<DstW>()} * rhs;
    }
 
    template<int E>
    [[nodiscard]] constexpr bool operator==(matrix<E> const& rhs) const noexcept
    {
        return _col0 == rhs._col0 && _col1 == rhs._col1 && _col2 == rhs._col2 && _col3 == rhs._col3;
    }
 
    [[nodiscard]] constexpr matrix operator~() const
    {
        //                   rc
        // var s0 : Number = i00 * i11 -
        //                  i10 * i01;
        // var c0 : Number = i20 * i31 -
        //                  i30 * i21;
        hilet s0c0 = _col0 * _col1.yxwz();
 
        // var s1 : Number = i00 * i12 -
        //                  i10 * i02;
        // var c1 : Number = i20 * i32 -
        //                  i30 * i22;
        hilet s1c1 = _col0 * _col2.yxwz();
        hilet s0c0s1c1 = hsub(s0c0, s1c1);
 
        // var s2 : Number = i00 * i13 -
        //                  i10 * i03;
        // var c2 : Number = i20 * i33 -
        //                  i30 * i23;
        hilet s2c2 = _col0 * _col3.yxwz();
 
        // var s3 : Number = i01 * i12 -
        //                  i11 * i02;
        // var c3 : Number = i21 * i32 -
        //                  i31 * i22;
        hilet s3c3 = _col1 * _col2.yxwz();
        hilet s2c2s3c3 = hsub(s2c2, s3c3);
 
        // var s4 : Number = i01 * i13 -
        //                  i11 * i03;
        // var c4 : Number = i21 * i33 -
        //                  i31 * i23;
        hilet s4c4 = _col1 * _col3.yxwz();
 
        // var s5 : Number = i02 * i13 -
        //                  i12 * i03;
        // var c5 : Number = i22 * i33 -
        //                  i32 * i23;
        hilet s5c5 = _col2 * _col3.yxwz();
        hilet s4c4s5c5 = hsub(s4c4, s5c5);
 
        // det = (s0 * c5 +
        //       -s1 * c4 +
        //        s2 * c3 +
        //        s3 * c2 +
        //       -s4 * c1 +
        //        s5 * c0)
        hilet s0123 = s0c0s1c1.xz00() + s2c2s3c3._00xz();
        hilet s45__ = s4c4s5c5.xz00();
 
        hilet c5432 = s4c4s5c5.wy00() + s2c2s3c3._00wy();
        hilet c10__ = s0c0s1c1.wy00();
 
        hilet det_prod_half0 = neg<0b0010>(s0123 * c5432);
        hilet det_prod_half1 = neg<0b0001>(s45__ * c10__);
 
        hilet det_sum0 = hadd(det_prod_half0, det_prod_half1);
        hilet det_sum1 = hadd(det_sum0, det_sum0);
        hilet det = hadd(det_sum1, det_sum1).xxxx();
 
        if (det.x() == 0.0f) {
            throw std::domain_error("Divide by zero");
        }
 
        hilet invdet = rcp(det);
 
        hilet t = transpose(*this);
 
        //   rc     rc          rc          rc
        // m.i00 := (i11 *  c5 + i12 * -c4 + i13 *  c3) * invdet;
        // m.i10 := (i10 * -c5 + i12 *  c2 + i13 * -c1) * invdet;
        // m.i20 := (i10 *  c4 + i11 * -c2 + i13 *  c0) * invdet;
        // m.i30 := (i10 * -c3 + i11 *  c1 + i12 * -c0) * invdet;
        auto tmp_c5543 = neg<0b1010>(c5432.xxyz());
        auto tmp_c4221 = neg<0b0101>(c5432.yww0() + c10__._000x());
        auto tmp_c3100 = neg<0b1010>(c5432.z000() + c10__._0xyy());
        hilet inv_col0 = ((t._col1.yxxx() * tmp_c5543) + (t._col1.zzyy() * tmp_c4221) + (t._col1.wwwz() * tmp_c3100)) * invdet;
 
        // m.i01 := (i01 * -c5 + i02 *  c4 + i03 * -c3) * invdet;
        // m.i11 := (i00 *  c5 + i02 * -c2 + i03 *  c1) * invdet;
        // m.i21 := (i00 * -c4 + i01 *  c2 + i03 * -c0) * invdet;
        // m.i31 := (i00 *  c3 + i01 * -c1 + i02 *  c0) * invdet;
        tmp_c5543 = -tmp_c5543;
        tmp_c4221 = -tmp_c4221;
        tmp_c3100 = -tmp_c3100;
        hilet inv_col1 = ((t._col0.yxxx() * tmp_c5543) + (t._col0.zzyy() * tmp_c4221) + (t._col0.wwwz() * tmp_c3100)) * invdet;
 
        // m.i02 := (i31 *  s5 + i32 * -s4 + i33 *  s3) * invdet;
        // m.i12 := (i30 * -s5 + i32 *  s2 + i33 * -s1) * invdet;
        // m.i22 := (i30 *  s4 + i31 * -s2 + i33 *  s0) * invdet;
        // m.i32 := (i30 * -s3 + i31 *  s1 + i32 * -s0) * invdet;
        auto tmp_s5543 = neg<0b1010>(s45__.yyx0() + s0123._000w());
        auto tmp_s4221 = neg<0b0101>(s45__.x000() + s0123._0zzy());
        auto tmp_s3100 = neg<0b1010>(s0123.wyxx());
        hilet inv_col2 = ((t._col3.yxxx() * tmp_s5543) + (t._col3.zzyy() * tmp_s4221) + (t._col3.wwwz() * tmp_s3100)) * invdet;
 
        // m.i03 := (i21 * -s5 + i22 *  s4 + i23 * -s3) * invdet;
        // m.i13 := (i20 *  s5 + i22 * -s2 + i23 *  s1) * invdet;
        // m.i23 := (i20 * -s4 + i21 *  s2 + i23 * -s0) * invdet;
        // m.i33 := (i20 *  s3 + i21 * -s1 + i22 *  s0) * invdet;
        tmp_s5543 = -tmp_s5543;
        tmp_s4221 = -tmp_s4221;
        tmp_s3100 = -tmp_s3100;
        hilet inv_col3 = ((t._col2.yxxx() * tmp_s5543) + (t._col2.zzyy() * tmp_s4221) + (t._col2.wwwz() * tmp_s3100)) * invdet;
 
        return {inv_col0, inv_col1, inv_col2, inv_col3};
    }
 
private:
    f32x4 _col0;
    f32x4 _col1;
    f32x4 _col2;
    f32x4 _col3;
 
    template<char Axis>
    [[nodiscard]] static constexpr f32x4 reflect_column() noexcept
    {
        if constexpr (Axis == 'x') {
            return f32x4{1.0f, 0.0f, 0.0f, 0.0f};
        } else if constexpr (Axis == 'X') {
            return f32x4{-1.0f, 0.0f, 0.0f, 0.0f};
        } else if constexpr (Axis == 'y') {
            return f32x4{0.0f, 1.0f, 0.0f, 0.0f};
        } else if constexpr (Axis == 'Y') {
            return f32x4{0.0f, -1.0f, 0.0f, 0.0f};
        } else if constexpr (Axis == 'z') {
            return f32x4{0.0f, 0.0f, 1.0f, 0.0f};
        } else if constexpr (Axis == 'Z') {
            return f32x4{0.0f, 0.0f, -1.0f, 0.0f};
        } else if constexpr (Axis == 'w') {
            return f32x4{0.0f, 0.0f, 0.0f, 1.0f};
        } else if constexpr (Axis == 'W') {
            return f32x4{0.0f, 0.0f, 0.0f, -1.0f};
        } else {
            hi_static_no_default();
        }
    }
};
 
} // namespace geo
 
using matrix2 = geo::matrix<2>;
 
using matrix3 = geo::matrix<3>;
 
}} // namespace hi::inline v1