539 lines
14 KiB
Plaintext
539 lines
14 KiB
Plaintext
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///////////////////////////////////////////////////////////////////////////////////
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/// OpenGL Mathematics (glm.g-truc.net)
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///
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/// Copyright (c) 2005 - 2015 G-Truc Creation (www.g-truc.net)
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/// Permission is hereby granted, free of charge, to any person obtaining a copy
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/// of this software and associated documentation files (the "Software"), to deal
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/// in the Software without restriction, including without limitation the rights
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/// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
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/// copies of the Software, and to permit persons to whom the Software is
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/// furnished to do so, subject to the following conditions:
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///
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/// The above copyright notice and this permission notice shall be included in
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/// all copies or substantial portions of the Software.
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///
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/// Restrictions:
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/// By making use of the Software for military purposes, you choose to make
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/// a Bunny unhappy.
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///
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/// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
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/// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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/// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
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/// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
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/// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
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/// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
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/// THE SOFTWARE.
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///
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/// @ref gtc_matrix_transform
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/// @file glm/gtc/matrix_transform.inl
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/// @date 2009-04-29 / 2011-06-15
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/// @author Christophe Riccio
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///////////////////////////////////////////////////////////////////////////////////
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#include "../geometric.hpp"
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#include "../trigonometric.hpp"
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#include "../matrix.hpp"
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namespace glm
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{
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template <typename T, precision P>
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GLM_FUNC_QUALIFIER tmat4x4<T, P> translate
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(
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tmat4x4<T, P> const & m,
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tvec3<T, P> const & v
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)
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{
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tmat4x4<T, P> Result(m);
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Result[3] = m[0] * v[0] + m[1] * v[1] + m[2] * v[2] + m[3];
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return Result;
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}
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template <typename T, precision P>
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GLM_FUNC_QUALIFIER tmat4x4<T, P> rotate
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(
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tmat4x4<T, P> const & m,
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T angle,
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tvec3<T, P> const & v
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)
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{
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T const a = angle;
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T const c = cos(a);
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T const s = sin(a);
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tvec3<T, P> axis(normalize(v));
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tvec3<T, P> temp((T(1) - c) * axis);
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tmat4x4<T, P> Rotate(uninitialize);
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Rotate[0][0] = c + temp[0] * axis[0];
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Rotate[0][1] = 0 + temp[0] * axis[1] + s * axis[2];
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Rotate[0][2] = 0 + temp[0] * axis[2] - s * axis[1];
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Rotate[1][0] = 0 + temp[1] * axis[0] - s * axis[2];
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Rotate[1][1] = c + temp[1] * axis[1];
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Rotate[1][2] = 0 + temp[1] * axis[2] + s * axis[0];
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Rotate[2][0] = 0 + temp[2] * axis[0] + s * axis[1];
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Rotate[2][1] = 0 + temp[2] * axis[1] - s * axis[0];
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Rotate[2][2] = c + temp[2] * axis[2];
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tmat4x4<T, P> Result(uninitialize);
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Result[0] = m[0] * Rotate[0][0] + m[1] * Rotate[0][1] + m[2] * Rotate[0][2];
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Result[1] = m[0] * Rotate[1][0] + m[1] * Rotate[1][1] + m[2] * Rotate[1][2];
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Result[2] = m[0] * Rotate[2][0] + m[1] * Rotate[2][1] + m[2] * Rotate[2][2];
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Result[3] = m[3];
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return Result;
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}
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template <typename T, precision P>
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GLM_FUNC_QUALIFIER tmat4x4<T, P> rotate_slow
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(
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tmat4x4<T, P> const & m,
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T angle,
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tvec3<T, P> const & v
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)
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{
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T const a = angle;
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T const c = cos(a);
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T const s = sin(a);
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tmat4x4<T, P> Result;
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tvec3<T, P> axis = normalize(v);
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Result[0][0] = c + (1 - c) * axis.x * axis.x;
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Result[0][1] = (1 - c) * axis.x * axis.y + s * axis.z;
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Result[0][2] = (1 - c) * axis.x * axis.z - s * axis.y;
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Result[0][3] = 0;
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Result[1][0] = (1 - c) * axis.y * axis.x - s * axis.z;
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Result[1][1] = c + (1 - c) * axis.y * axis.y;
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Result[1][2] = (1 - c) * axis.y * axis.z + s * axis.x;
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Result[1][3] = 0;
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Result[2][0] = (1 - c) * axis.z * axis.x + s * axis.y;
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Result[2][1] = (1 - c) * axis.z * axis.y - s * axis.x;
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Result[2][2] = c + (1 - c) * axis.z * axis.z;
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Result[2][3] = 0;
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Result[3] = tvec4<T, P>(0, 0, 0, 1);
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return m * Result;
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}
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template <typename T, precision P>
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GLM_FUNC_QUALIFIER tmat4x4<T, P> scale
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(
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tmat4x4<T, P> const & m,
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tvec3<T, P> const & v
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)
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{
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tmat4x4<T, P> Result(uninitialize);
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Result[0] = m[0] * v[0];
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Result[1] = m[1] * v[1];
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Result[2] = m[2] * v[2];
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Result[3] = m[3];
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return Result;
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}
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template <typename T, precision P>
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GLM_FUNC_QUALIFIER tmat4x4<T, P> scale_slow
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(
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tmat4x4<T, P> const & m,
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tvec3<T, P> const & v
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)
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{
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tmat4x4<T, P> Result(T(1));
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Result[0][0] = v.x;
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Result[1][1] = v.y;
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Result[2][2] = v.z;
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return m * Result;
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}
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template <typename T>
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GLM_FUNC_QUALIFIER tmat4x4<T, defaultp> ortho
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(
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T left,
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T right,
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T bottom,
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T top,
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T zNear,
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T zFar
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)
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{
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tmat4x4<T, defaultp> Result(1);
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Result[0][0] = static_cast<T>(2) / (right - left);
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Result[1][1] = static_cast<T>(2) / (top - bottom);
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Result[2][2] = - static_cast<T>(2) / (zFar - zNear);
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Result[3][0] = - (right + left) / (right - left);
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Result[3][1] = - (top + bottom) / (top - bottom);
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Result[3][2] = - (zFar + zNear) / (zFar - zNear);
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return Result;
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}
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template <typename T>
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GLM_FUNC_QUALIFIER tmat4x4<T, defaultp> ortho
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(
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T left,
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T right,
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T bottom,
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T top
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)
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{
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tmat4x4<T, defaultp> Result(1);
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Result[0][0] = static_cast<T>(2) / (right - left);
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Result[1][1] = static_cast<T>(2) / (top - bottom);
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Result[2][2] = - static_cast<T>(1);
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Result[3][0] = - (right + left) / (right - left);
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Result[3][1] = - (top + bottom) / (top - bottom);
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return Result;
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}
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template <typename T>
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GLM_FUNC_QUALIFIER tmat4x4<T, defaultp> frustum
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(
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T left,
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T right,
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T bottom,
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T top,
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T nearVal,
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T farVal
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)
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{
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tmat4x4<T, defaultp> Result(0);
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Result[0][0] = (static_cast<T>(2) * nearVal) / (right - left);
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Result[1][1] = (static_cast<T>(2) * nearVal) / (top - bottom);
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Result[2][0] = (right + left) / (right - left);
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Result[2][1] = (top + bottom) / (top - bottom);
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Result[2][2] = -(farVal + nearVal) / (farVal - nearVal);
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Result[2][3] = static_cast<T>(-1);
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Result[3][2] = -(static_cast<T>(2) * farVal * nearVal) / (farVal - nearVal);
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return Result;
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}
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template <typename T>
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GLM_FUNC_QUALIFIER tmat4x4<T, defaultp> perspective
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(
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T fovy,
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T aspect,
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T zNear,
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T zFar
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)
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{
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#ifdef GLM_LEFT_HANDED
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return perspectiveLH(fovy, aspect, zNear, zFar);
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#else
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return perspectiveRH(fovy, aspect, zNear, zFar);
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#endif
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}
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template <typename T>
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GLM_FUNC_QUALIFIER tmat4x4<T, defaultp> perspectiveRH
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(
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T fovy,
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T aspect,
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T zNear,
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T zFar
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)
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{
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assert(abs(aspect - std::numeric_limits<T>::epsilon()) > static_cast<T>(0));
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T const tanHalfFovy = tan(fovy / static_cast<T>(2));
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tmat4x4<T, defaultp> Result(static_cast<T>(0));
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Result[0][0] = static_cast<T>(1) / (aspect * tanHalfFovy);
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Result[1][1] = static_cast<T>(1) / (tanHalfFovy);
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Result[2][2] = - (zFar + zNear) / (zFar - zNear);
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Result[2][3] = - static_cast<T>(1);
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Result[3][2] = - (static_cast<T>(2) * zFar * zNear) / (zFar - zNear);
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return Result;
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}
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template <typename T>
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GLM_FUNC_QUALIFIER tmat4x4<T, defaultp> perspectiveLH
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(
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T fovy,
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T aspect,
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T zNear,
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T zFar
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)
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{
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assert(abs(aspect - std::numeric_limits<T>::epsilon()) > static_cast<T>(0));
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T const tanHalfFovy = tan(fovy / static_cast<T>(2));
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tmat4x4<T, defaultp> Result(static_cast<T>(0));
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Result[0][0] = static_cast<T>(1) / (aspect * tanHalfFovy);
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Result[1][1] = static_cast<T>(1) / (tanHalfFovy);
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Result[2][2] = (zFar + zNear) / (zFar - zNear);
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Result[2][3] = static_cast<T>(1);
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Result[3][2] = -(static_cast<T>(2) * zFar * zNear) / (zFar - zNear);
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return Result;
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}
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template <typename T>
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GLM_FUNC_QUALIFIER tmat4x4<T, defaultp> perspectiveFov
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(
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T fov,
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T width,
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T height,
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T zNear,
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T zFar
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)
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{
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#ifdef GLM_LEFT_HANDED
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return perspectiveFovLH(fov, width, height, zNear, zFar);
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#else
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return perspectiveFovRH(fov, width, height, zNear, zFar);
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#endif
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}
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template <typename T>
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GLM_FUNC_QUALIFIER tmat4x4<T, defaultp> perspectiveFovRH
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(
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T fov,
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T width,
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T height,
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T zNear,
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T zFar
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)
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{
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assert(width > static_cast<T>(0));
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assert(height > static_cast<T>(0));
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assert(fov > static_cast<T>(0));
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T const rad = fov;
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T const h = glm::cos(static_cast<T>(0.5) * rad) / glm::sin(static_cast<T>(0.5) * rad);
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T const w = h * height / width; ///todo max(width , Height) / min(width , Height)?
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tmat4x4<T, defaultp> Result(static_cast<T>(0));
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Result[0][0] = w;
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Result[1][1] = h;
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Result[2][2] = - (zFar + zNear) / (zFar - zNear);
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Result[2][3] = - static_cast<T>(1);
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Result[3][2] = - (static_cast<T>(2) * zFar * zNear) / (zFar - zNear);
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return Result;
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}
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template <typename T>
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GLM_FUNC_QUALIFIER tmat4x4<T, defaultp> perspectiveFovLH
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(
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T fov,
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T width,
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T height,
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T zNear,
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T zFar
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)
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{
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assert(width > static_cast<T>(0));
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assert(height > static_cast<T>(0));
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assert(fov > static_cast<T>(0));
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T const rad = fov;
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T const h = glm::cos(static_cast<T>(0.5) * rad) / glm::sin(static_cast<T>(0.5) * rad);
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T const w = h * height / width; ///todo max(width , Height) / min(width , Height)?
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tmat4x4<T, defaultp> Result(static_cast<T>(0));
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Result[0][0] = w;
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Result[1][1] = h;
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Result[2][2] = (zFar + zNear) / (zFar - zNear);
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Result[2][3] = static_cast<T>(1);
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Result[3][2] = - (static_cast<T>(2) * zFar * zNear) / (zFar - zNear);
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return Result;
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}
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template <typename T>
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GLM_FUNC_QUALIFIER tmat4x4<T, defaultp> infinitePerspective
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(
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T fovy,
|
||
|
|
T aspect,
|
||
|
|
T zNear
|
||
|
|
)
|
||
|
|
{
|
||
|
|
T const range = tan(fovy / 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] = (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;
|
||
|
|
}
|
||
|
|
|
||
|
|
// 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 / 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] = 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, 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 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]);
|
||
|
|
tmp = tmp * T(2) - T(1);
|
||
|
|
|
||
|
|
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 > T(0) && delta.y > T(0));
|
||
|
|
tmat4x4<T, P> Result(1.0f);
|
||
|
|
|
||
|
|
if(!(delta.x > T(0) && delta.y > T(0)))
|
||
|
|
return Result; // Error
|
||
|
|
|
||
|
|
tvec3<T, P> 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, tvec3<T, P>(T(viewport[2]) / delta.x, T(viewport[3]) / delta.y, 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
|
||
|
|
)
|
||
|
|
{
|
||
|
|
#ifdef 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
|