UE4 & OpenGL坐標系

UE4 使用左手系（DX），OpenGL固定管線使用右手系，可以通過可編程的管線在OpenGL渲染管線中使用和UE4一樣的左手系，即修改觀察矩陣和投影矩陣。WebGL屬于可編程的管線，可以使用左手和右手系。

三維空間的坐標系

• 局部空間(Local Space，或者稱為物體空間(Object Space))
• 世界空間(World Space)
• 觀察空間(View Space，或者稱為視覺空間(Eye Space)) 或是視圖坐標系
• 裁剪空間(Clip Space) 或是投影坐標系
• 歸一化設備坐標系（Normalized device coordinates）
• 屏幕空間(Screen Space)
  

左右手坐標系變換在裁剪空間和觀察空間進行。

GLM

GLM更改默認的慣用手，使用GLM FORCE LEFT handled。若要更改默認的“近剪裁平面”和“遠剪裁平面”定義，請使用GLM FORCE DEPTH ZERO To ONE。

使用D3D坐標系。

#define GLM_FORCE_LEFT_HANDED #define GLM_FORCE_DEPTH_ZERO_TO_ONE

投影坐標系

正射投影矩陣

右手系-正射投影矩陣

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-正射投影矩陣

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;}

透視投影

右手系-透視投影

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-透視投影

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;}

視圖坐標系

//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:Wvec<3, T, Q> const f(normalize(center - eye));//right:Vvec<3, T, Q> const s(normalize(cross(f, up)));//up:Uvec<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;}

參考文章

投影矩陣推導過程

LearnOpenGL

UE4 & OpenGL坐標系

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