redner/transform.h at master · budmonde/redner · GitHub

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#pragma once

#include "redner.h"
#include "vector.h"
#include "matrix.h"

template <typename T>
DEVICE
inline TMatrix4x4<T> look_at_matrix(const TVector3<T> &pos,
                                    const TVector3<T> &look,
                                    const TVector3<T> &up) {
    auto look_pos = look - pos;
    assert(length_squared(look_pos) > 1e-20f);
    auto d = normalize(look_pos);
    auto cross_d_up = cross(d, normalize(up));
    assert(length_squared(cross_d_up) > 1e-20f);
    auto right = normalize(cross_d_up);
    auto cross_right_d = cross(right, d);
    assert(length_squared(cross_right_d) > 1e-20f);
    auto new_up = normalize(cross_right_d);
    return TMatrix4x4<T>{
        right.x, new_up.x,  d.x, pos.x,
        right.y, new_up.y,  d.y, pos.y,
        right.z, new_up.z,  d.z, pos.z,
           T(0),     T(0), T(0),   T(1)
    };
}

template <typename T>
DEVICE
inline void d_look_at_matrix(const TVector3<T> &pos,
                             const TVector3<T> &look,
                             const TVector3<T> &up,
                             const TMatrix4x4<T> &d_mat,
                             TVector3<T> &d_pos,
                             TVector3<T> &d_look,
                             TVector3<T> &d_up) {
    auto look_pos = look - pos;
    auto d = normalize(look_pos);
    auto normalized_up = normalize(up);
    auto cross_d_up = cross(d, normalized_up);
    auto right = normalize(cross_d_up);
    auto cross_right_d = cross(right, d);
    // auto new_up = normalize(cross_right_d);
    // return TMatrix4x4<T>{
    //     right.x, new_up.x,  d.x, pos.x,
    //     right.y, new_up.y,  d.y, pos.y,
    //     right.z, new_up.z,  d.z, pos.z,
    //        T(0),     T(0), T(0),   T(1)
    // };
    auto d_right =  TVector3<T>{d_mat(0, 0), d_mat(1, 0), d_mat(2, 0)};
    auto d_new_up = TVector3<T>{d_mat(0, 1), d_mat(1, 1), d_mat(2, 1)};
    auto d_d =      TVector3<T>{d_mat(0, 2), d_mat(1, 2), d_mat(2, 2)};
    d_pos +=        TVector3<T>{d_mat(0, 3), d_mat(1, 3), d_mat(2, 3)};
    // auto new_up = normalize(cross_right_d);
    auto d_cross_right_d = d_normalize(cross_right_d, d_new_up);
    // auto cross_right_d = cross(right, d);
    d_cross(right, d, d_cross_right_d, d_right, d_d);
    // auto right = normalize(cross_d_up);
    auto d_cross_d_up = d_normalize(cross_d_up, d_right);
    // auto cross_d_up = cross(d, normalized_up);
    auto d_normalized_up = Vector3{0, 0, 0};
    d_cross(d, normalized_up, d_cross_d_up, d_d, d_normalized_up);
    // auto normalized_up = normalize(up);
    d_up += d_normalize(up, d_normalized_up);
    // auto d = normalize(look_pos);
    auto d_look_pos = d_normalize(look_pos, d_d);
    // auto look_pos = look - pos;
    d_look += d_look_pos;
    d_pos -= d_look_pos;
}

template <typename T>
DEVICE
inline TVector3<T> xfm_point(const TMatrix4x4<T> &xform,
                             const TVector3<T> &pt) {
    auto tpt = TVector4<T>{
        xform(0, 0) * pt[0] + xform(0, 1) * pt[1] + xform(0, 2) * pt[2] + xform(0, 3),
        xform(1, 0) * pt[0] + xform(1, 1) * pt[1] + xform(1, 2) * pt[2] + xform(1, 3),
        xform(2, 0) * pt[0] + xform(2, 1) * pt[1] + xform(2, 2) * pt[2] + xform(2, 3),
        xform(3, 0) * pt[0] + xform(3, 1) * pt[1] + xform(3, 2) * pt[2] + xform(3, 3)};
    auto inv_w = 1.f / tpt[3];
    return TVector3<T>{tpt[0], tpt[1], tpt[2]} * inv_w;
}

template <typename T>
DEVICE
inline auto xfm_vector(const TMatrix4x4<T> &xform,
                       const TVector3<T> &vec) {
    return TVector3<T>{
        xform(0, 0) * vec[0] + xform(0, 1) * vec[1] + xform(0, 2) * vec[2],
        xform(1, 0) * vec[0] + xform(1, 1) * vec[1] + xform(1, 2) * vec[2],
        xform(2, 0) * vec[0] + xform(2, 1) * vec[1] + xform(2, 2) * vec[2]};
}

template <typename T>
DEVICE
inline void d_xfm_point(const TMatrix4x4<T> &xform,
                        const TVector3<T> &pt,
                        const TVector3<T> &d_out,
                        TMatrix4x4<T> &d_xform,
                        TVector3<T> &d_pt) {
    auto tpt = TVector4<T>{
        xform(0, 0) * pt[0] + xform(0, 1) * pt[1] + xform(0, 2) * pt[2] + xform(0, 3),
        xform(1, 0) * pt[0] + xform(1, 1) * pt[1] + xform(1, 2) * pt[2] + xform(1, 3),
        xform(2, 0) * pt[0] + xform(2, 1) * pt[1] + xform(2, 2) * pt[2] + xform(2, 3),
        xform(3, 0) * pt[0] + xform(3, 1) * pt[1] + xform(3, 2) * pt[2] + xform(3, 3)};
    auto inv_w = 1.f / tpt[3];
    // out = TVector3<T>{tpt[0], tpt[1], tpt[2]} * inv_w
    auto d_tpt03 = d_out * inv_w;
    auto d_inv_w = sum(d_out * TVector3<T>{tpt[0], tpt[1], tpt[2]});
    // inv_w = 1.f / tpt[3]
    auto d_tpt3 = -d_inv_w * inv_w * inv_w;
    auto d_tpt = TVector4<T>{d_tpt03[0], d_tpt03[1], d_tpt03[2], d_tpt3};
    // auto tpt = TVector4<T>{
    //     xform(0, 0) * pt[0] + xform(0, 1) * pt[1] + xform(0, 2) * pt[2] + xform(0, 3),
    //     xform(1, 0) * pt[0] + xform(1, 1) * pt[1] + xform(1, 2) * pt[2] + xform(1, 3),
    //     xform(2, 0) * pt[0] + xform(2, 1) * pt[1] + xform(2, 2) * pt[2] + xform(2, 3),
    //     xform(3, 0) * pt[0] + xform(3, 1) * pt[1] + xform(3, 2) * pt[2] + xform(3, 3)};
    d_xform(0, 0) += d_tpt[0] * pt[0];
    d_xform(0, 1) += d_tpt[0] * pt[1];
    d_xform(0, 2) += d_tpt[0] * pt[2];
    d_xform(0, 3) += d_tpt[0];
    d_xform(1, 0) += d_tpt[1] * pt[0];
    d_xform(1, 1) += d_tpt[1] * pt[1];
    d_xform(1, 2) += d_tpt[1] * pt[2];
    d_xform(1, 3) += d_tpt[1];
    d_xform(2, 0) += d_tpt[2] * pt[0];
    d_xform(2, 1) += d_tpt[2] * pt[1];
    d_xform(2, 2) += d_tpt[2] * pt[2];
    d_xform(2, 3) += d_tpt[2];
    d_xform(3, 0) += d_tpt[3] * pt[0];
    d_xform(3, 1) += d_tpt[3] * pt[1];
    d_xform(3, 2) += d_tpt[3] * pt[2];
    d_xform(3, 3) += d_tpt[3];
    d_pt[0] += d_tpt[0] * xform(0, 0) +
               d_tpt[1] * xform(1, 0) +
               d_tpt[2] * xform(2, 0) +
               d_tpt[3] * xform(3, 0);
    d_pt[1] += d_tpt[0] * xform(0, 1) +
               d_tpt[1] * xform(1, 1) +
               d_tpt[2] * xform(2, 1) +
               d_tpt[3] * xform(3, 1);
    d_pt[2] += d_tpt[0] * xform(0, 2) +
               d_tpt[1] * xform(1, 2) +
               d_tpt[2] * xform(2, 2) +
               d_tpt[3] * xform(3, 2);
}

template <typename T>
DEVICE
inline void d_xfm_vector(const TMatrix4x4<T> &xform,
                         const TVector3<T> &vec,
                         const TVector3<T> &d_out,
                         TMatrix4x4<T> &d_xform,
                         TVector3<T> &d_vec) {
    // out =
    // xform(0, 0) * vec[0] + xform(0, 1) * vec[1] + xform(0, 2) * vec[2]
    // xform(1, 0) * vec[0] + xform(1, 1) * vec[1] + xform(1, 2) * vec[2]
    // xform(2, 0) * vec[0] + xform(2, 1) * vec[1] + xform(2, 2) * vec[2]
    d_xform(0, 0) += d_out[0] * vec[0];
    d_xform(0, 1) += d_out[0] * vec[1];
    d_xform(0, 2) += d_out[0] * vec[2];
    d_xform(1, 0) += d_out[1] * vec[0];
    d_xform(1, 1) += d_out[1] * vec[1];
    d_xform(1, 2) += d_out[1] * vec[2];
    d_xform(2, 0) += d_out[2] * vec[0];
    d_xform(2, 1) += d_out[2] * vec[1];
    d_xform(2, 2) += d_out[2] * vec[2];
    d_vec[0] += d_out[0] * xform(0, 0) +
                d_out[1] * xform(1, 0) +
                d_out[2] * xform(2, 0);
    d_vec[1] += d_out[0] * xform(0, 1) +
                d_out[1] * xform(1, 1) +
                d_out[2] * xform(2, 1);
    d_vec[2] += d_out[0] * xform(0, 2) +
                d_out[1] * xform(1, 2) +
                d_out[2] * xform(2, 2);
}