UE4 & OpenGL坐标系

UE4 使用左手系（DX），OpenGL固定管线使用右手系，可以通过可编程的管线在OpenGL渲染管线中使用和UE4一样的左手系。

三维空间的坐标系

• 局部空间(Local Space，或者称为物体空间(Object Space))
• 世界空间(World Space)
• 观察空间(View Space，或者称为视觉空间(Eye Space)) 或是视图坐标系
• 裁剪空间(Clip Space) 或是投影坐标系
• 屏幕空间(Screen Space)

左右手坐标系变换在裁剪空间和观察空间进行。

投影坐标系

正射投影矩阵

正射投影 正射投影

右手系-正射投影矩阵

正射投影矩阵-右手系

  template<typename T>
    GLM_FUNC_QUALIFIER mat<4, 4, T, defaultp> orthoRH_NO(T left, T right, T bottom, T top, T zNear, T zFar)
    {
        mat<4, 4, T, defaultp> Result(1);
        Result[0][0] = static_cast<T>(2) / (right - left);
        Result[1][1] = static_cast<T>(2) / (top - bottom);
        Result[2][2] = - static_cast<T>(2) / (zFar - zNear);
        Result[3][0] = - (right + left) / (right - left);
        Result[3][1] = - (top + bottom) / (top - bottom);
        Result[3][2] = - (zFar + zNear) / (zFar - zNear);
        return Result;
    }

左手系-正射投影矩阵

正射投影矩阵-右手系

template<typename T>
    GLM_FUNC_QUALIFIER mat<4, 4, T, defaultp> orthoLH_ZO(T left, T right, T bottom, T top, T zNear, T zFar)
    {
        mat<4, 4, T, defaultp> Result(1);
        Result[0][0] = static_cast<T>(2) / (right - left);
        Result[1][1] = static_cast<T>(2) / (top - bottom);
        Result[2][2] = static_cast<T>(1) / (zFar - zNear);
        Result[3][0] = - (right + left) / (right - left);
        Result[3][1] = - (top + bottom) / (top - bottom);
        Result[3][2] = - zNear / (zFar - zNear);
        return Result;
    }

透视投影

透视投影
透视投影推导
透视投影推导

右手系-透视投影

右手系透视投影 视角和宽高比
透视投影矩阵-右手系

emplate<typename T>
    GLM_FUNC_QUALIFIER mat<4, 4, T, defaultp> perspectiveRH_NO(T fovy, T aspect, T zNear, T zFar)
    {
        assert(abs(aspect - std::numeric_limits<T>::epsilon()) > static_cast<T>(0));

        T const tanHalfFovy = tan(fovy / static_cast<T>(2));

        mat<4, 4, T, defaultp> Result(static_cast<T>(0));
        Result[0][0] = static_cast<T>(1) / (aspect * tanHalfFovy);
        Result[1][1] = static_cast<T>(1) / (tanHalfFovy);
        Result[2][2] = - (zFar + zNear) / (zFar - zNear);
        Result[2][3] = - static_cast<T>(1);
        Result[3][2] = - (static_cast<T>(2) * zFar * zNear) / (zFar - zNear);
        return Result;
    }

左手系-透视投影

透视投影左手系
透视投影-左手

template<typename T>
    GLM_FUNC_QUALIFIER mat<4, 4, T, defaultp> perspectiveLH_ZO(T fovy, T aspect, T zNear, T zFar)
    {
        assert(abs(aspect - std::numeric_limits<T>::epsilon()) > static_cast<T>(0));

        T const tanHalfFovy = tan(fovy / static_cast<T>(2));

        mat<4, 4, T, defaultp> Result(static_cast<T>(0));
        Result[0][0] = static_cast<T>(1) / (aspect * tanHalfFovy);
        Result[1][1] = static_cast<T>(1) / (tanHalfFovy);
        Result[2][2] = zFar / (zFar - zNear);
        Result[2][3] = static_cast<T>(1);
        Result[3][2] = -(zFar * zNear) / (zFar - zNear);
        return Result;
    }

视图坐标系

视图矩阵的推导

//右手系
template<typename T, qualifier Q>
    GLM_FUNC_QUALIFIER mat<4, 4, T, Q> lookAtRH(vec<3, T, Q> const& eye, vec<3, T, Q> const& center, vec<3, T, Q> const& up)
    {
             //forward:W
        vec<3, T, Q> const f(normalize(center - eye));
              //right:V
        vec<3, T, Q> const s(normalize(cross(f, up)));
              //up:U
        vec<3, T, Q> const u(cross(s, f));

        mat<4, 4, T, Q> Result(1);
        Result[0][0] = s.x;
        Result[1][0] = s.y;
        Result[2][0] = s.z;
        Result[0][1] = u.x;
        Result[1][1] = u.y;
        Result[2][1] = u.z;
        Result[0][2] =-f.x;
        Result[1][2] =-f.y;
        Result[2][2] =-f.z;
        Result[3][0] =-dot(s, eye);
        Result[3][1] =-dot(u, eye);
        Result[3][2] = dot(f, eye);
        return Result;
    }
  //左手系
    template<typename T, qualifier Q>
    GLM_FUNC_QUALIFIER mat<4, 4, T, Q> lookAtLH(vec<3, T, Q> const& eye, vec<3, T, Q> const& center, vec<3, T, Q> const& up)
    {
        vec<3, T, Q> const f(normalize(center - eye));
        vec<3, T, Q> const s(normalize(cross(up, f)));
        vec<3, T, Q> const u(cross(f, s));

        mat<4, 4, T, Q> Result(1);
        Result[0][0] = s.x;
        Result[1][0] = s.y;
        Result[2][0] = s.z;
        Result[0][1] = u.x;
        Result[1][1] = u.y;
        Result[2][1] = u.z;
        Result[0][2] = f.x;
        Result[1][2] = f.y;
        Result[2][2] = f.z;
        Result[3][0] = -dot(s, eye);
        Result[3][1] = -dot(u, eye);
        Result[3][2] = -dot(f, eye);
        return Result;
    }

参考文章

1. 投影矩阵推导过程
2. UE4 & OpenGL坐标系