/// @ref gtc_matrix_transform /// @file glm/gtc/matrix_transform.inl #include "../geometric.hpp" #include "../trigonometric.hpp" #include "../matrix.hpp" namespace glm { template <typename T, precision P> GLM_FUNC_QUALIFIER tmat4x4<T, P> translate(tmat4x4<T, P> const & m, tvec3<T, P> const & v) { tmat4x4<T, P> Result(m); Result[3] = m[0] * v[0] + m[1] * v[1] + m[2] * v[2] + m[3]; return Result; } template <typename T, precision P> GLM_FUNC_QUALIFIER tmat4x4<T, P> rotate(tmat4x4<T, P> const & m, T angle, tvec3<T, P> const & v) { T const a = angle; T const c = cos(a); T const s = sin(a); tvec3<T, P> axis(normalize(v)); tvec3<T, P> temp((T(1) - c) * axis); tmat4x4<T, P> Rotate(uninitialize); Rotate[0][0] = c + temp[0] * axis[0]; Rotate[0][1] = temp[0] * axis[1] + s * axis[2]; Rotate[0][2] = temp[0] * axis[2] - s * axis[1]; Rotate[1][0] = temp[1] * axis[0] - s * axis[2]; Rotate[1][1] = c + temp[1] * axis[1]; Rotate[1][2] = temp[1] * axis[2] + s * axis[0]; Rotate[2][0] = temp[2] * axis[0] + s * axis[1]; Rotate[2][1] = temp[2] * axis[1] - s * axis[0]; Rotate[2][2] = c + temp[2] * axis[2]; tmat4x4<T, P> Result(uninitialize); Result[0] = m[0] * Rotate[0][0] + m[1] * Rotate[0][1] + m[2] * Rotate[0][2]; Result[1] = m[0] * Rotate[1][0] + m[1] * Rotate[1][1] + m[2] * Rotate[1][2]; Result[2] = m[0] * Rotate[2][0] + m[1] * Rotate[2][1] + m[2] * Rotate[2][2]; Result[3] = m[3]; return Result; } template <typename T, precision P> GLM_FUNC_QUALIFIER tmat4x4<T, P> rotate_slow(tmat4x4<T, P> const & m, T angle, tvec3<T, P> const & v) { T const a = angle; T const c = cos(a); T const s = sin(a); tmat4x4<T, P> Result; tvec3<T, P> axis = normalize(v); Result[0][0] = c + (static_cast<T>(1) - c) * axis.x * axis.x; Result[0][1] = (static_cast<T>(1) - c) * axis.x * axis.y + s * axis.z; Result[0][2] = (static_cast<T>(1) - c) * axis.x * axis.z - s * axis.y; Result[0][3] = static_cast<T>(0); Result[1][0] = (static_cast<T>(1) - c) * axis.y * axis.x - s * axis.z; Result[1][1] = c + (static_cast<T>(1) - c) * axis.y * axis.y; Result[1][2] = (static_cast<T>(1) - c) * axis.y * axis.z + s * axis.x; Result[1][3] = static_cast<T>(0); Result[2][0] = (static_cast<T>(1) - c) * axis.z * axis.x + s * axis.y; Result[2][1] = (static_cast<T>(1) - c) * axis.z * axis.y - s * axis.x; Result[2][2] = c + (static_cast<T>(1) - c) * axis.z * axis.z; Result[2][3] = static_cast<T>(0); Result[3] = tvec4<T, P>(0, 0, 0, 1); return m * Result; } template <typename T, precision P> GLM_FUNC_QUALIFIER tmat4x4<T, P> scale(tmat4x4<T, P> const & m, tvec3<T, P> const & v) { tmat4x4<T, P> Result(uninitialize); Result[0] = m[0] * v[0]; Result[1] = m[1] * v[1]; Result[2] = m[2] * v[2]; Result[3] = m[3]; return Result; } template <typename T, precision P> GLM_FUNC_QUALIFIER tmat4x4<T, P> scale_slow(tmat4x4<T, P> const & m, tvec3<T, P> const & v) { tmat4x4<T, P> Result(T(1)); Result[0][0] = v.x; Result[1][1] = v.y; Result[2][2] = v.z; return m * Result; } template <typename T> GLM_FUNC_QUALIFIER tmat4x4<T, defaultp> ortho ( T left, T right, T bottom, T top, T zNear, T zFar ) { # if GLM_COORDINATE_SYSTEM == GLM_LEFT_HANDED return orthoLH(left, right, bottom, top, zNear, zFar); # else return orthoRH(left, right, bottom, top, zNear, zFar); # endif } template <typename T> GLM_FUNC_QUALIFIER tmat4x4<T, defaultp> orthoLH ( T left, T right, T bottom, T top, T zNear, T zFar ) { tmat4x4<T, defaultp> Result(1); Result[0][0] = static_cast<T>(2) / (right - left); Result[1][1] = static_cast<T>(2) / (top - bottom); Result[3][0] = - (right + left) / (right - left); Result[3][1] = - (top + bottom) / (top - bottom); # if GLM_DEPTH_CLIP_SPACE == GLM_DEPTH_ZERO_TO_ONE Result[2][2] = static_cast<T>(1) / (zFar - zNear); Result[3][2] = - zNear / (zFar - zNear); # else Result[2][2] = static_cast<T>(2) / (zFar - zNear); Result[3][2] = - (zFar + zNear) / (zFar - zNear); # endif return Result; } template <typename T> GLM_FUNC_QUALIFIER tmat4x4<T, defaultp> orthoRH ( T left, T right, T bottom, T top, T zNear, T zFar ) { tmat4x4<T, defaultp> Result(1); Result[0][0] = static_cast<T>(2) / (right - left); Result[1][1] = static_cast<T>(2) / (top - bottom); Result[3][0] = - (right + left) / (right - left); Result[3][1] = - (top + bottom) / (top - bottom); # if GLM_DEPTH_CLIP_SPACE == GLM_DEPTH_ZERO_TO_ONE Result[2][2] = - static_cast<T>(1) / (zFar - zNear); Result[3][2] = - zNear / (zFar - zNear); # else Result[2][2] = - static_cast<T>(2) / (zFar - zNear); Result[3][2] = - (zFar + zNear) / (zFar - zNear); # endif return Result; } template <typename T> GLM_FUNC_QUALIFIER tmat4x4<T, defaultp> ortho ( T left, T right, T bottom, T top ) { tmat4x4<T, defaultp> Result(static_cast<T>(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); Result[3][0] = - (right + left) / (right - left); Result[3][1] = - (top + bottom) / (top - bottom); return Result; } template <typename T> GLM_FUNC_QUALIFIER tmat4x4<T, defaultp> frustum ( T left, T right, T bottom, T top, T nearVal, T farVal ) { # if GLM_COORDINATE_SYSTEM == GLM_LEFT_HANDED return frustumLH(left, right, bottom, top, nearVal, farVal); # else return frustumRH(left, right, bottom, top, nearVal, farVal); # endif } template <typename T> GLM_FUNC_QUALIFIER tmat4x4<T, defaultp> frustumLH ( T left, T right, T bottom, T top, T nearVal, T farVal ) { tmat4x4<T, defaultp> Result(0); Result[0][0] = (static_cast<T>(2) * nearVal) / (right - left); Result[1][1] = (static_cast<T>(2) * nearVal) / (top - bottom); Result[2][0] = (right + left) / (right - left); Result[2][1] = (top + bottom) / (top - bottom); Result[2][3] = static_cast<T>(1); # if GLM_DEPTH_CLIP_SPACE == GLM_DEPTH_ZERO_TO_ONE Result[2][2] = farVal / (farVal - nearVal); Result[3][2] = -(farVal * nearVal) / (farVal - nearVal); # else Result[2][2] = (farVal + nearVal) / (farVal - nearVal); Result[3][2] = - (static_cast<T>(2) * farVal * nearVal) / (farVal - nearVal); # endif return Result; } template <typename T> GLM_FUNC_QUALIFIER tmat4x4<T, defaultp> frustumRH ( T left, T right, T bottom, T top, T nearVal, T farVal ) { tmat4x4<T, defaultp> Result(0); Result[0][0] = (static_cast<T>(2) * nearVal) / (right - left); Result[1][1] = (static_cast<T>(2) * nearVal) / (top - bottom); Result[2][0] = (right + left) / (right - left); Result[2][1] = (top + bottom) / (top - bottom); Result[2][3] = static_cast<T>(-1); # if GLM_DEPTH_CLIP_SPACE == GLM_DEPTH_ZERO_TO_ONE Result[2][2] = farVal / (nearVal - farVal); Result[3][2] = -(farVal * nearVal) / (farVal - nearVal); # else Result[2][2] = - (farVal + nearVal) / (farVal - nearVal); Result[3][2] = - (static_cast<T>(2) * farVal * nearVal) / (farVal - nearVal); # endif return Result; } template <typename T> GLM_FUNC_QUALIFIER tmat4x4<T, defaultp> perspective(T fovy, T aspect, T zNear, T zFar) { # if GLM_COORDINATE_SYSTEM == GLM_LEFT_HANDED return perspectiveLH(fovy, aspect, zNear, zFar); # else return perspectiveRH(fovy, aspect, zNear, zFar); # endif } template <typename T> GLM_FUNC_QUALIFIER tmat4x4<T, defaultp> perspectiveRH(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)); tmat4x4<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][3] = - static_cast<T>(1); # if GLM_DEPTH_CLIP_SPACE == GLM_DEPTH_ZERO_TO_ONE Result[2][2] = zFar / (zNear - zFar); Result[3][2] = -(zFar * zNear) / (zFar - zNear); # else Result[2][2] = - (zFar + zNear) / (zFar - zNear); Result[3][2] = - (static_cast<T>(2) * zFar * zNear) / (zFar - zNear); # endif return Result; } template <typename T> GLM_FUNC_QUALIFIER tmat4x4<T, defaultp> perspectiveLH(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)); tmat4x4<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][3] = static_cast<T>(1); # if GLM_DEPTH_CLIP_SPACE == GLM_DEPTH_ZERO_TO_ONE Result[2][2] = zFar / (zFar - zNear); Result[3][2] = -(zFar * zNear) / (zFar - zNear); # else Result[2][2] = (zFar + zNear) / (zFar - zNear); Result[3][2] = - (static_cast<T>(2) * zFar * zNear) / (zFar - zNear); # endif return Result; } template <typename T> GLM_FUNC_QUALIFIER tmat4x4<T, defaultp> perspectiveFov(T fov, T width, T height, T zNear, T zFar) { # if GLM_COORDINATE_SYSTEM == GLM_LEFT_HANDED return perspectiveFovLH(fov, width, height, zNear, zFar); # else return perspectiveFovRH(fov, width, height, zNear, zFar); # endif } template <typename T> GLM_FUNC_QUALIFIER tmat4x4<T, defaultp> perspectiveFovRH(T fov, T width, T height, T zNear, T zFar) { assert(width > static_cast<T>(0)); assert(height > static_cast<T>(0)); assert(fov > static_cast<T>(0)); T const rad = fov; T const h = glm::cos(static_cast<T>(0.5) * rad) / glm::sin(static_cast<T>(0.5) * rad); T const w = h * height / width; ///todo max(width , Height) / min(width , Height)? tmat4x4<T, defaultp> Result(static_cast<T>(0)); Result[0][0] = w; Result[1][1] = h; Result[2][3] = - static_cast<T>(1); # if GLM_DEPTH_CLIP_SPACE == GLM_DEPTH_ZERO_TO_ONE Result[2][2] = zFar / (zNear - zFar); Result[3][2] = -(zFar * zNear) / (zFar - zNear); # else Result[2][2] = - (zFar + zNear) / (zFar - zNear); Result[3][2] = - (static_cast<T>(2) * zFar * zNear) / (zFar - zNear); # endif return Result; } template <typename T> GLM_FUNC_QUALIFIER tmat4x4<T, defaultp> perspectiveFovLH(T fov, T width, T height, T zNear, T zFar) { assert(width > static_cast<T>(0)); assert(height > static_cast<T>(0)); assert(fov > static_cast<T>(0)); T const rad = fov; T const h = glm::cos(static_cast<T>(0.5) * rad) / glm::sin(static_cast<T>(0.5) * rad); T const w = h * height / width; ///todo max(width , Height) / min(width , Height)? tmat4x4<T, defaultp> Result(static_cast<T>(0)); Result[0][0] = w; Result[1][1] = h; Result[2][3] = static_cast<T>(1); # if GLM_DEPTH_CLIP_SPACE == GLM_DEPTH_ZERO_TO_ONE Result[2][2] = zFar / (zFar - zNear); Result[3][2] = -(zFar * zNear) / (zFar - zNear); # else Result[2][2] = (zFar + zNear) / (zFar - zNear); Result[3][2] = - (static_cast<T>(2) * zFar * zNear) / (zFar - zNear); # endif return Result; } template <typename T> GLM_FUNC_QUALIFIER tmat4x4<T, defaultp> infinitePerspective(T fovy, T aspect, T zNear) { # if GLM_COORDINATE_SYSTEM == GLM_LEFT_HANDED return infinitePerspectiveLH(fovy, aspect, zNear); # else return infinitePerspectiveRH(fovy, aspect, zNear); # endif } template <typename T> GLM_FUNC_QUALIFIER tmat4x4<T, defaultp> infinitePerspectiveRH(T fovy, T aspect, T zNear) { T const range = tan(fovy / static_cast<T>(2)) * zNear; T const left = -range * aspect; T const right = range * aspect; T const bottom = -range; T const top = range; tmat4x4<T, defaultp> Result(static_cast<T>(0)); Result[0][0] = (static_cast<T>(2) * zNear) / (right - left); Result[1][1] = (static_cast<T>(2) * zNear) / (top - bottom); Result[2][2] = - static_cast<T>(1); Result[2][3] = - static_cast<T>(1); Result[3][2] = - static_cast<T>(2) * zNear; return Result; } template <typename T> GLM_FUNC_QUALIFIER tmat4x4<T, defaultp> infinitePerspectiveLH(T fovy, T aspect, T zNear) { T const range = tan(fovy / static_cast<T>(2)) * zNear; T const left = -range * aspect; T const right = range * aspect; T const bottom = -range; T const top = range; tmat4x4<T, defaultp> Result(T(0)); Result[0][0] = (static_cast<T>(2) * zNear) / (right - left); Result[1][1] = (static_cast<T>(2) * zNear) / (top - bottom); Result[2][2] = static_cast<T>(1); Result[2][3] = static_cast<T>(1); Result[3][2] = - static_cast<T>(2) * zNear; return Result; } // Infinite projection matrix: http://www.terathon.com/gdc07_lengyel.pdf template <typename T> GLM_FUNC_QUALIFIER tmat4x4<T, defaultp> tweakedInfinitePerspective(T fovy, T aspect, T zNear, T ep) { T const range = tan(fovy / static_cast<T>(2)) * zNear; T const left = -range * aspect; T const right = range * aspect; T const bottom = -range; T const top = range; tmat4x4<T, defaultp> Result(static_cast<T>(0)); Result[0][0] = (static_cast<T>(2) * zNear) / (right - left); Result[1][1] = (static_cast<T>(2) * zNear) / (top - bottom); Result[2][2] = ep - static_cast<T>(1); Result[2][3] = static_cast<T>(-1); Result[3][2] = (ep - static_cast<T>(2)) * zNear; return Result; } template <typename T> GLM_FUNC_QUALIFIER tmat4x4<T, defaultp> tweakedInfinitePerspective(T fovy, T aspect, T zNear) { return tweakedInfinitePerspective(fovy, aspect, zNear, epsilon<T>()); } template <typename T, typename U, precision P> GLM_FUNC_QUALIFIER tvec3<T, P> project ( tvec3<T, P> const & obj, tmat4x4<T, P> const & model, tmat4x4<T, P> const & proj, tvec4<U, P> const & viewport ) { tvec4<T, P> tmp = tvec4<T, P>(obj, static_cast<T>(1)); tmp = model * tmp; tmp = proj * tmp; tmp /= tmp.w; # if GLM_DEPTH_CLIP_SPACE == GLM_DEPTH_ZERO_TO_ONE tmp.x = tmp.x * static_cast<T>(0.5) + static_cast<T>(0.5); tmp.y = tmp.y * static_cast<T>(0.5) + static_cast<T>(0.5); # else tmp = tmp * static_cast<T>(0.5) + static_cast<T>(0.5); # endif tmp[0] = tmp[0] * T(viewport[2]) + T(viewport[0]); tmp[1] = tmp[1] * T(viewport[3]) + T(viewport[1]); return tvec3<T, P>(tmp); } template <typename T, typename U, precision P> GLM_FUNC_QUALIFIER tvec3<T, P> unProject ( tvec3<T, P> const & win, tmat4x4<T, P> const & model, tmat4x4<T, P> const & proj, tvec4<U, P> const & viewport ) { tmat4x4<T, P> Inverse = inverse(proj * model); tvec4<T, P> tmp = tvec4<T, P>(win, T(1)); tmp.x = (tmp.x - T(viewport[0])) / T(viewport[2]); tmp.y = (tmp.y - T(viewport[1])) / T(viewport[3]); # if GLM_DEPTH_CLIP_SPACE == GLM_DEPTH_ZERO_TO_ONE tmp.x = tmp.x * static_cast<T>(2) - static_cast<T>(1); tmp.y = tmp.y * static_cast<T>(2) - static_cast<T>(1); # else tmp = tmp * static_cast<T>(2) - static_cast<T>(1); # endif tvec4<T, P> obj = Inverse * tmp; obj /= obj.w; return tvec3<T, P>(obj); } template <typename T, precision P, typename U> GLM_FUNC_QUALIFIER tmat4x4<T, P> pickMatrix(tvec2<T, P> const & center, tvec2<T, P> const & delta, tvec4<U, P> const & viewport) { assert(delta.x > static_cast<T>(0) && delta.y > static_cast<T>(0)); tmat4x4<T, P> Result(static_cast<T>(1)); if(!(delta.x > static_cast<T>(0) && delta.y > static_cast<T>(0))) return Result; // Error tvec3<T, P> Temp( (static_cast<T>(viewport[2]) - static_cast<T>(2) * (center.x - static_cast<T>(viewport[0]))) / delta.x, (static_cast<T>(viewport[3]) - static_cast<T>(2) * (center.y - static_cast<T>(viewport[1]))) / delta.y, static_cast<T>(0)); // Translate and scale the picked region to the entire window Result = translate(Result, Temp); return scale(Result, tvec3<T, P>(static_cast<T>(viewport[2]) / delta.x, static_cast<T>(viewport[3]) / delta.y, static_cast<T>(1))); } template <typename T, precision P> GLM_FUNC_QUALIFIER tmat4x4<T, P> lookAt(tvec3<T, P> const & eye, tvec3<T, P> const & center, tvec3<T, P> const & up) { # if GLM_COORDINATE_SYSTEM == GLM_LEFT_HANDED return lookAtLH(eye, center, up); # else return lookAtRH(eye, center, up); # endif } template <typename T, precision P> GLM_FUNC_QUALIFIER tmat4x4<T, P> lookAtRH ( tvec3<T, P> const & eye, tvec3<T, P> const & center, tvec3<T, P> const & up ) { tvec3<T, P> const f(normalize(center - eye)); tvec3<T, P> const s(normalize(cross(f, up))); tvec3<T, P> const u(cross(s, f)); tmat4x4<T, P> 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; } template <typename T, precision P> GLM_FUNC_QUALIFIER tmat4x4<T, P> lookAtLH ( tvec3<T, P> const & eye, tvec3<T, P> const & center, tvec3<T, P> const & up ) { tvec3<T, P> const f(normalize(center - eye)); tvec3<T, P> const s(normalize(cross(up, f))); tvec3<T, P> const u(cross(f, s)); tmat4x4<T, P> 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; } }//namespace glm