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///////////////////////////////////////////////////////////////////////////////////
/// OpenGL Mathematics (glm.g-truc.net)
///
/// Copyright (c) 2005 - 2013 G-Truc Creation (www.g-truc.net)
/// 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.
///
/// @ref gtc_matrix_transform
/// @file glm/gtc/matrix_transform.inl
/// @date 2009-04-29 / 2011-06-15
/// @author Christophe Riccio
///////////////////////////////////////////////////////////////////////////////////
namespace glm
{
template <typename T>
GLM_FUNC_QUALIFIER detail::tmat4x4<T> translate
(
detail::tmat4x4<T> const & m,
detail::tvec3<T> const & v
)
{
detail::tmat4x4<T> Result(m);
Result[3] = m[0] * v[0] + m[1] * v[1] + m[2] * v[2] + m[3];
return Result;
}
template <typename T>
GLM_FUNC_QUALIFIER detail::tmat4x4<T> rotate
(
detail::tmat4x4<T> const & m,
T const & angle,
detail::tvec3<T> const & v
)
{
#ifdef GLM_FORCE_RADIANS
T a = angle;
#else
T a = radians(angle);
#endif
T c = cos(a);
T s = sin(a);
detail::tvec3<T> axis = normalize(v);
detail::tvec3<T> temp = (T(1) - c) * axis;
detail::tmat4x4<T> Rotate(detail::tmat4x4<T>::null);
Rotate[0][0] = c + temp[0] * axis[0];
Rotate[0][1] = 0 + temp[0] * axis[1] + s * axis[2];
Rotate[0][2] = 0 + temp[0] * axis[2] - s * axis[1];
Rotate[1][0] = 0 + temp[1] * axis[0] - s * axis[2];
Rotate[1][1] = c + temp[1] * axis[1];
Rotate[1][2] = 0 + temp[1] * axis[2] + s * axis[0];
Rotate[2][0] = 0 + temp[2] * axis[0] + s * axis[1];
Rotate[2][1] = 0 + temp[2] * axis[1] - s * axis[0];
Rotate[2][2] = c + temp[2] * axis[2];
detail::tmat4x4<T> Result(detail::tmat4x4<T>::null);
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>
GLM_FUNC_QUALIFIER detail::tmat4x4<T> scale
(
detail::tmat4x4<T> const & m,
detail::tvec3<T> const & v
)
{
detail::tmat4x4<T> Result(detail::tmat4x4<T>::null);
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>
GLM_FUNC_QUALIFIER detail::tmat4x4<T> translate_slow
(
detail::tmat4x4<T> const & m,
detail::tvec3<T> const & v
)
{
detail::tmat4x4<T> Result(T(1));
Result[3] = detail::tvec4<T>(v, T(1));
return m * Result;
//detail::tmat4x4<valType> Result(m);
Result[3] = m[0] * v[0] + m[1] * v[1] + m[2] * v[2] + m[3];
//Result[3][0] = m[0][0] * v[0] + m[1][0] * v[1] + m[2][0] * v[2] + m[3][0];
//Result[3][1] = m[0][1] * v[0] + m[1][1] * v[1] + m[2][1] * v[2] + m[3][1];
//Result[3][2] = m[0][2] * v[0] + m[1][2] * v[1] + m[2][2] * v[2] + m[3][2];
//Result[3][3] = m[0][3] * v[0] + m[1][3] * v[1] + m[2][3] * v[2] + m[3][3];
//return Result;
}
template <typename T>
GLM_FUNC_QUALIFIER detail::tmat4x4<T> rotate_slow
(
detail::tmat4x4<T> const & m,
T const & angle,
detail::tvec3<T> const & v
)
{
#ifdef GLM_FORCE_RADIANS
T const a = angle;
#else
T const a = radians(angle);
#endif
T c = cos(a);
T s = sin(a);
detail::tmat4x4<T> Result;
detail::tvec3<T> axis = normalize(v);
Result[0][0] = c + (1 - c) * axis.x * axis.x;
Result[0][1] = (1 - c) * axis.x * axis.y + s * axis.z;
Result[0][2] = (1 - c) * axis.x * axis.z - s * axis.y;
Result[0][3] = 0;
Result[1][0] = (1 - c) * axis.y * axis.x - s * axis.z;
Result[1][1] = c + (1 - c) * axis.y * axis.y;
Result[1][2] = (1 - c) * axis.y * axis.z + s * axis.x;
Result[1][3] = 0;
Result[2][0] = (1 - c) * axis.z * axis.x + s * axis.y;
Result[2][1] = (1 - c) * axis.z * axis.y - s * axis.x;
Result[2][2] = c + (1 - c) * axis.z * axis.z;
Result[2][3] = 0;
Result[3] = detail::tvec4<T>(0, 0, 0, 1);
return m * Result;
}
template <typename T>
GLM_FUNC_QUALIFIER detail::tmat4x4<T> scale_slow
(
detail::tmat4x4<T> const & m,
detail::tvec3<T> const & v
)
{
detail::tmat4x4<T> Result(T(1));
Result[0][0] = v.x;
Result[1][1] = v.y;
Result[2][2] = v.z;
return m * Result;
}
template <typename valType>
GLM_FUNC_QUALIFIER detail::tmat4x4<valType> ortho
(
valType const & left,
valType const & right,
valType const & bottom,
valType const & top,
valType const & zNear,
valType const & zFar
)
{
detail::tmat4x4<valType> Result(1);
Result[0][0] = valType(2) / (right - left);
Result[1][1] = valType(2) / (top - bottom);
Result[2][2] = - valType(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;
}
template <typename valType>
GLM_FUNC_QUALIFIER detail::tmat4x4<valType> ortho(
valType const & left,
valType const & right,
valType const & bottom,
valType const & top)
{
detail::tmat4x4<valType> Result(1);
Result[0][0] = valType(2) / (right - left);
Result[1][1] = valType(2) / (top - bottom);
Result[2][2] = - valType(1);
Result[3][0] = - (right + left) / (right - left);
Result[3][1] = - (top + bottom) / (top - bottom);
return Result;
}
template <typename valType>
GLM_FUNC_QUALIFIER detail::tmat4x4<valType> frustum
(
valType const & left,
valType const & right,
valType const & bottom,
valType const & top,
valType const & nearVal,
valType const & farVal
)
{
detail::tmat4x4<valType> Result(0);
Result[0][0] = (valType(2) * nearVal) / (right - left);
Result[1][1] = (valType(2) * nearVal) / (top - bottom);
Result[2][0] = (right + left) / (right - left);
Result[2][1] = (top + bottom) / (top - bottom);
Result[2][2] = -(farVal + nearVal) / (farVal - nearVal);
Result[2][3] = valType(-1);
Result[3][2] = -(valType(2) * farVal * nearVal) / (farVal - nearVal);
return Result;
}
template <typename valType>
GLM_FUNC_QUALIFIER detail::tmat4x4<valType> perspective
(
valType const & fovy,
valType const & aspect,
valType const & zNear,
valType const & zFar
)
{
assert(aspect != valType(0));
assert(zFar != zNear);
#ifdef GLM_FORCE_RADIANS
valType const rad = fovy;
#else
valType const rad = glm::radians(fovy);
#endif
valType tanHalfFovy = tan(rad / valType(2));
detail::tmat4x4<valType> Result(valType(0));
Result[0][0] = valType(1) / (aspect * tanHalfFovy);
Result[1][1] = valType(1) / (tanHalfFovy);
Result[2][2] = - (zFar + zNear) / (zFar - zNear);
Result[2][3] = - valType(1);
Result[3][2] = - (valType(2) * zFar * zNear) / (zFar - zNear);
return Result;
}
template <typename valType>
GLM_FUNC_QUALIFIER detail::tmat4x4<valType> perspectiveFov
(
valType const & fov,
valType const & width,
valType const & height,
valType const & zNear,
valType const & zFar
)
{
#ifdef GLM_FORCE_RADIANS
valType rad = fov;
#else
valType rad = glm::radians(fov);
#endif
valType h = glm::cos(valType(0.5) * rad) / glm::sin(valType(0.5) * rad);
valType w = h * height / width; ///todo max(width , Height) / min(width , Height)?
detail::tmat4x4<valType> Result(valType(0));
Result[0][0] = w;
Result[1][1] = h;
Result[2][2] = - (zFar + zNear) / (zFar - zNear);
Result[2][3] = - valType(1);
Result[3][2] = - (valType(2) * zFar * zNear) / (zFar - zNear);
return Result;
}
template <typename T>
GLM_FUNC_QUALIFIER detail::tmat4x4<T> infinitePerspective
(
T fovy,
T aspect,
T zNear
)
{
#ifdef GLM_FORCE_RADIANS
T const range = tan(fovy / T(2)) * zNear;
#else
T const range = tan(radians(fovy / T(2))) * zNear;
#endif
T left = -range * aspect;
T right = range * aspect;
T bottom = -range;
T top = range;
detail::tmat4x4<T> Result(T(0));
Result[0][0] = (T(2) * zNear) / (right - left);
Result[1][1] = (T(2) * zNear) / (top - bottom);
Result[2][2] = - T(1);
Result[2][3] = - T(1);
Result[3][2] = - T(2) * zNear;
return Result;
}
template <typename T>
GLM_FUNC_QUALIFIER detail::tmat4x4<T> tweakedInfinitePerspective
(
T fovy,
T aspect,
T zNear
)
{
#ifdef GLM_FORCE_RADIANS
T range = tan(fovy / T(2)) * zNear;
#else
T range = tan(radians(fovy / T(2))) * zNear;
#endif
T left = -range * aspect;
T right = range * aspect;
T bottom = -range;
T top = range;
detail::tmat4x4<T> Result(T(0));
Result[0][0] = (T(2) * zNear) / (right - left);
Result[1][1] = (T(2) * zNear) / (top - bottom);
Result[2][2] = T(0.0001) - T(1);
Result[2][3] = T(-1);
Result[3][2] = - (T(0.0001) - T(2)) * zNear;
return Result;
}
template <typename T, typename U>
GLM_FUNC_QUALIFIER detail::tvec3<T> project
(
detail::tvec3<T> const & obj,
detail::tmat4x4<T> const & model,
detail::tmat4x4<T> const & proj,
detail::tvec4<U> const & viewport
)
{
detail::tvec4<T> tmp = detail::tvec4<T>(obj, T(1));
tmp = model * tmp;
tmp = proj * tmp;
tmp /= tmp.w;
tmp = tmp * T(0.5) + T(0.5);
tmp[0] = tmp[0] * T(viewport[2]) + T(viewport[0]);
tmp[1] = tmp[1] * T(viewport[3]) + T(viewport[1]);
return detail::tvec3<T>(tmp);
}
template <typename T, typename U>
GLM_FUNC_QUALIFIER detail::tvec3<T> unProject
(
detail::tvec3<T> const & win,
detail::tmat4x4<T> const & model,
detail::tmat4x4<T> const & proj,
detail::tvec4<U> const & viewport
)
{
detail::tmat4x4<T> inverse = glm::inverse(proj * model);
detail::tvec4<T> tmp = detail::tvec4<T>(win, T(1));
tmp.x = (tmp.x - T(viewport[0])) / T(viewport[2]);
tmp.y = (tmp.y - T(viewport[1])) / T(viewport[3]);
tmp = tmp * T(2) - T(1);
detail::tvec4<T> obj = inverse * tmp;
obj /= obj.w;
return detail::tvec3<T>(obj);
}
template <typename T, typename U>
detail::tmat4x4<T> pickMatrix
(
detail::tvec2<T> const & center,
detail::tvec2<T> const & delta,
detail::tvec4<U> const & viewport
)
{
assert(delta.x > T(0) && delta.y > T(0));
detail::tmat4x4<T> Result(1.0f);
if(!(delta.x > T(0) && delta.y > T(0)))
return Result; // Error
detail::tvec3<T> Temp(
(T(viewport[2]) - T(2) * (center.x - T(viewport[0]))) / delta.x,
(T(viewport[3]) - T(2) * (center.y - T(viewport[1]))) / delta.y,
T(0));
// Translate and scale the picked region to the entire window
Result = translate(Result, Temp);
return scale(Result, detail::tvec3<T>(T(viewport[2]) / delta.x, T(viewport[3]) / delta.y, T(1)));
}
template <typename T>
GLM_FUNC_QUALIFIER detail::tmat4x4<T> lookAt
(
detail::tvec3<T> const & eye,
detail::tvec3<T> const & center,
detail::tvec3<T> const & up
)
{
detail::tvec3<T> f = normalize(center - eye);
detail::tvec3<T> u = normalize(up);
detail::tvec3<T> s = normalize(cross(f, u));
u = cross(s, f);
detail::tmat4x4<T> 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
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