transform.h

#pragma once
 
/* <editor-fold desc="MIT License">
 
Copyright(c) 2018 Robert Osfield
 
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.
 
</editor-fold> */
 
#include <vsg/maths/common.h>
 
namespace vsg
{
    template<typename T>
    constexpr t_mat4<T> rotate(const t_quat<T>& q)
    {
        T qxx(q.x * q.x);
        T qyy(q.y * q.y);
        T qzz(q.z * q.z);
        T qxy(q.x * q.y);
        T qxz(q.x * q.z);
        T qyz(q.y * q.z);
        T qwx(q.w * q.x);
        T qwy(q.w * q.y);
        T qwz(q.w * q.z);
 
        const T zero(numbers<T>::zero());
        const T one(numbers<T>::one());
        const T two(numbers<T>::two());
 
        return t_mat4<T>(one - two * (qyy + qzz), two * (qxy + qwz), two * (qxz - qwy), zero,
                         two * (qxy - qwz), one - two * (qxx + qzz), two * (qyz + qwx), zero,
                         two * (qxz + qwy), two * (qyz - qwx), one - two * (qxx + qyy), zero,
                         zero, zero, zero, one);
    }

    template<typename T>
    t_mat4<T> rotate(T angle_radians, T x, T y, T z)
    {
        const T zero(numbers<T>::zero());
        const T one(numbers<T>::one());
        const T c = std::cos(angle_radians);
        const T s = std::sin(angle_radians);
        const T one_minus_c = one - c;
        return t_mat4<T>(x * x * one_minus_c + c, y * x * one_minus_c + z * s, x * z * one_minus_c - y * s, zero,
                         x * y * one_minus_c - z * s, y * y * one_minus_c + c, y * z * one_minus_c + x * s, zero,
                         x * z * one_minus_c + y * s, y * z * one_minus_c - x * s, z * z * one_minus_c + c, zero,
                         zero, zero, zero, one);
    }

    template<typename T>
    t_mat4<T> rotate(T angle_radians, const t_vec3<T>& v)
    {
        return rotate(angle_radians, v.value[0], v.value[1], v.value[2]);
    }

    template<typename T>
    constexpr t_mat4<T> translate(T x, T y, T z)
    {
        const T zero(numbers<T>::zero());
        const T one(numbers<T>::one());
        return t_mat4<T>(one, zero, zero, zero,
                         zero, one, zero, zero,
                         zero, zero, one, zero,
                         x, y, z, one);
    }

    template<typename T>
    constexpr t_mat4<T> translate(const t_vec3<T>& v)
    {
        return translate(v.value[0], v.value[1], v.value[2]);
    }

    template<typename T>
    constexpr t_mat4<T> scale(T s)
    {
        const T zero(numbers<T>::zero());
        const T one(numbers<T>::one());
        return t_mat4<T>(s, zero, zero, zero,
                         zero, s, zero, zero,
                         zero, zero, s, zero,
                         zero, zero, zero, one);
    }

    template<typename T>
    constexpr t_mat4<T> scale(T sx, T sy, T sz)
    {
        const T zero(numbers<T>::zero());
        const T one(numbers<T>::one());
        return t_mat4<T>(sx, zero, zero, zero,
                         zero, sy, zero, zero,
                         zero, zero, sz, zero,
                         zero, zero, zero, one);
    }

    template<typename T>
    constexpr t_mat4<T> scale(const t_vec3<T>& v)
    {
        return scale(v.value[0], v.value[1], v.value[2]);
    }

    template<typename T>
    constexpr t_mat3<T> transpose(const t_mat3<T>& m)
    {
        return t_mat3<T>(m[0][0], m[1][0], m[2][0],
                         m[0][1], m[1][1], m[2][1],
                         m[0][2], m[1][2], m[2][2]);
    }

    template<typename T>
    constexpr t_mat4<T> transpose(const t_mat4<T>& m)
    {
        return t_mat4<T>(m[0][0], m[1][0], m[2][0], m[3][0],
                         m[0][1], m[1][1], m[2][1], m[3][1],
                         m[0][2], m[1][2], m[2][2], m[3][2],
                         m[0][3], m[1][3], m[2][3], m[3][3]);
    }

    //.                      https://vincent-p.github.io/posts/vulkan_perspective_matrix/
    template<typename T>
    constexpr t_mat4<T> perspective(T fovy_radians, T aspectRatio, T zNear, T zFar)
    {
        const T zero(numbers<T>::zero());
        const T one(numbers<T>::one());
        T f = static_cast<T>(one / std::tan(fovy_radians * numbers<T>::half()));
        T r = static_cast<T>(one / (zFar - zNear));
        return t_mat4<T>(f / aspectRatio, zero, zero, zero,
                         zero, -f, zero, zero,
                         zero, zero, zNear * r, -one,
                         zero, zero, (zFar * zNear) * r, zero);
    }

    template<typename T>
    constexpr t_mat4<T> perspective(T left, T right, T bottom, T top, T zNear, T zFar)
    {
        const T zero(numbers<T>::zero());
        const T one(numbers<T>::one());
        const T two(numbers<T>::two());
        return t_mat4<T>(two * zNear / (right - left), zero, zero, zero,
                         zero, two * zNear / (bottom - top), zero, zero,
                         (right + left) / (right - left), (bottom + top) / (bottom - top), zNear / (zFar - zNear), -one,
                         zero, zero, zNear * zFar / (zFar - zNear), zero);
    }

    template<typename T>
    constexpr t_mat4<T> orthographic(T left, T right, T bottom, T top, T zNear, T zFar)
    {
        const T zero(numbers<T>::zero());
        const T one(numbers<T>::one());
        const T two(numbers<T>::two());
        return t_mat4<T>(two / (right - left), zero, zero, zero,
                         zero, two / (bottom - top), zero, zero,
                         zero, zero, one / (zFar - zNear), zero,
                         -(right + left) / (right - left), -(bottom + top) / (bottom - top), zFar / (zFar - zNear), one);
    }
 
    template<typename T>
    constexpr t_mat4<T> lookAt(const t_vec3<T>& eye, const t_vec3<T>& center, const t_vec3<T>& up)
    {
        using vec_type = t_vec3<T>;
 
        const T zero(numbers<T>::zero());
        const T one(numbers<T>::one());
 
        vec_type forward = normalize(center - eye);
        vec_type up_normal = normalize(up);
        vec_type side = normalize(cross(forward, up_normal));
        vec_type u = normalize(cross(side, forward));
 
        return t_mat4<T>(side[0], u[0], -forward[0], zero,
                         side[1], u[1], -forward[1], zero,
                         side[2], u[2], -forward[2], zero,
                         zero, zero, zero, one) *
               vsg::translate(-eye.x, -eye.y, -eye.z);
    }
 
    template<typename T>
    constexpr t_mat4<T> computeBillboardMatrix(const t_vec3<T>& centerEye, T autoscaleDistance)
    {
        const T zero(numbers<T>::zero());
        const T one(numbers<T>::one());
 
        auto distance = -centerEye.z;
        auto scale = (distance < autoscaleDistance) ? distance / autoscaleDistance : one;
        t_mat4<T> mS(scale, zero, zero, zero,
                     zero, scale, zero, zero,
                     zero, zero, scale, zero,
                     zero, zero, zero, one);
 
        t_mat4<T> mT(one, zero, zero, zero,
                     zero, one, zero, zero,
                     zero, zero, one, zero,
                     centerEye.x, centerEye.y, centerEye.z, one);
 
        return mT * mS;
    }

    enum class CoordinateConvention
    {
        NO_PREFERENCE,
        X_UP, // x up, y left/west, z out/south
        Y_UP, // x right/east, y up, z out/south
        Z_UP  // x right/east, y forward/north, z up
    };

    extern VSG_DECLSPEC bool transform(CoordinateConvention source, CoordinateConvention destination, dmat4& matrix);

    extern VSG_DECLSPEC mat3 inverse_3x3(const mat4& m);

    extern VSG_DECLSPEC dmat3 inverse_3x3(const dmat4& m);

    extern VSG_DECLSPEC mat4 inverse_4x3(const mat4& m);

    extern VSG_DECLSPEC dmat4 inverse_4x3(const dmat4& m);

    extern VSG_DECLSPEC mat4 inverse_4x4(const mat4& m);

    extern VSG_DECLSPEC dmat4 inverse_4x4(const dmat4& m);

    extern VSG_DECLSPEC mat4 inverse(const mat4& m);

    extern VSG_DECLSPEC dmat4 inverse(const dmat4& m);

    extern VSG_DECLSPEC float determinant(const mat4& m);

    extern VSG_DECLSPEC double determinant(const dmat4& m);

    extern VSG_DECLSPEC bool decompose(const mat4& m, vec3& translation, quat& rotation, vec3& scale);

    extern VSG_DECLSPEC bool decompose(const dmat4& m, dvec3& translation, dquat& rotation, dvec3& scale);

    extern VSG_DECLSPEC bool decompose(const ldmat4& m, ldvec3& translation, ldquat& rotation, ldvec3& scale);

    extern VSG_DECLSPEC sphere computeFrustumBound(const mat4& m);

    extern VSG_DECLSPEC dsphere computeFrustumBound(const dmat4& m);

    struct VSG_DECLSPEC ComputeTransform : public ConstVisitor
    {
        dvec3 origin;
        dmat4 matrix;
 
        void apply(const Transform& transform) override;
        void apply(const MatrixTransform& mt) override;
        void apply(const CoordinateFrame& cf) override;
        void apply(const Camera& camera) override;
    };

    template<typename T>
    dmat4 computeTransform(const T& nodePath)
    {
        return visit<ComputeTransform>(nodePath).matrix;
    }
 
} // namespace vsg