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284 lines
7.5 KiB
C++
284 lines
7.5 KiB
C++
///////////////////////////////////////////////////////////////////////////////////
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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 gtx_quaternion
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/// @file glm/gtx/quaternion.inl
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/// @date 2005-12-21 / 2011-06-07
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/// @author Christophe Riccio
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///////////////////////////////////////////////////////////////////////////////////
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#include <limits>
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#include "../gtc/constants.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 tvec3<T, P> cross
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(
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tvec3<T, P> const & v,
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tquat<T, P> const & q
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)
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{
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return inverse(q) * v;
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}
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template <typename T, precision P>
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GLM_FUNC_QUALIFIER tvec3<T, P> cross
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(
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tquat<T, P> const & q,
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tvec3<T, P> const & v
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)
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{
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return q * v;
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}
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template <typename T, precision P>
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GLM_FUNC_QUALIFIER tquat<T, P> squad
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(
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tquat<T, P> const & q1,
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tquat<T, P> const & q2,
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tquat<T, P> const & s1,
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tquat<T, P> const & s2,
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T const & h)
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{
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return mix(mix(q1, q2, h), mix(s1, s2, h), static_cast<T>(2) * (static_cast<T>(1) - h) * h);
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}
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template <typename T, precision P>
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GLM_FUNC_QUALIFIER tquat<T, P> intermediate
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(
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tquat<T, P> const & prev,
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tquat<T, P> const & curr,
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tquat<T, P> const & next
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)
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{
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tquat<T, P> invQuat = inverse(curr);
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return exp((log(next + invQuat) + log(prev + invQuat)) / static_cast<T>(-4)) * curr;
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}
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template <typename T, precision P>
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GLM_FUNC_QUALIFIER tquat<T, P> exp
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(
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tquat<T, P> const & q
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)
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{
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tvec3<T, P> u(q.x, q.y, q.z);
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T Angle = glm::length(u);
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if (Angle < epsilon<T>())
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return tquat<T, P>();
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tvec3<T, P> v(u / Angle);
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return tquat<T, P>(cos(Angle), sin(Angle) * v);
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}
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template <typename T, precision P>
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GLM_FUNC_QUALIFIER tquat<T, P> log
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(
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tquat<T, P> const & q
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)
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{
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tvec3<T, P> u(q.x, q.y, q.z);
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T Vec3Len = length(u);
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if (Vec3Len < epsilon<T>())
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{
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if(q.w > static_cast<T>(0))
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return tquat<T, P>(log(q.w), static_cast<T>(0), static_cast<T>(0), static_cast<T>(0));
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else if(q.w < static_cast<T>(0))
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return tquat<T, P>(log(-q.w), pi<T>(), static_cast<T>(0), static_cast<T>(0));
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else
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return tquat<T, P>(std::numeric_limits<T>::infinity(), std::numeric_limits<T>::infinity(), std::numeric_limits<T>::infinity(), std::numeric_limits<T>::infinity());
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}
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else
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{
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T QuatLen = sqrt(Vec3Len * Vec3Len + q.w * q.w);
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T t = atan(Vec3Len, T(q.w)) / Vec3Len;
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return tquat<T, P>(log(QuatLen), t * q.x, t * q.y, t * q.z);
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}
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}
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template <typename T, precision P>
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GLM_FUNC_QUALIFIER tquat<T, P> pow(tquat<T, P> const & x, T const & y)
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{
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//Raising to the power of 0 should yield 1
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//Needed to prevent a division by 0 error later on
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if(y > -epsilon<T>() && y < epsilon<T>())
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return tquat<T, P>(1,0,0,0);
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//To deal with non-unit quaternions
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T magnitude = sqrt(x.x * x.x + x.y * x.y + x.z * x.z + x.w *x.w);
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//Equivalent to raising a real number to a power
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//Needed to prevent a division by 0 error later on
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if(abs(x.w / magnitude) > static_cast<T>(1) - epsilon<T>() && abs(x.w / magnitude) < static_cast<T>(1) + epsilon<T>())
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return tquat<T, P>(pow(x.w, y),0,0,0);
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T Angle = acos(x.w / magnitude);
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T NewAngle = Angle * y;
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T Div = sin(NewAngle) / sin(Angle);
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T Mag = pow(magnitude, y-1);
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return tquat<T, P>(cos(NewAngle) * magnitude * Mag, x.x * Div * Mag, x.y * Div * Mag, x.z * Div * Mag);
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}
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template <typename T, precision P>
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GLM_FUNC_QUALIFIER tvec3<T, P> rotate
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(
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tquat<T, P> const & q,
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tvec3<T, P> const & v
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)
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{
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return q * v;
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}
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template <typename T, precision P>
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GLM_FUNC_QUALIFIER tvec4<T, P> rotate
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(
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tquat<T, P> const & q,
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tvec4<T, P> const & v
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)
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{
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return q * v;
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}
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template <typename T, precision P>
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GLM_FUNC_QUALIFIER T extractRealComponent
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(
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tquat<T, P> const & q
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)
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{
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T w = static_cast<T>(1) - q.x * q.x - q.y * q.y - q.z * q.z;
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if(w < T(0))
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return T(0);
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else
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return -sqrt(w);
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}
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template <typename T, precision P>
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GLM_FUNC_QUALIFIER T length2
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(
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tquat<T, P> const & q
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)
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{
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return q.x * q.x + q.y * q.y + q.z * q.z + q.w * q.w;
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}
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template <typename T, precision P>
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GLM_FUNC_QUALIFIER tquat<T, P> shortMix
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(
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tquat<T, P> const & x,
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tquat<T, P> const & y,
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T const & a
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)
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{
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if(a <= static_cast<T>(0)) return x;
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if(a >= static_cast<T>(1)) return y;
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T fCos = dot(x, y);
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tquat<T, P> y2(y); //BUG!!! tquat<T> y2;
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if(fCos < static_cast<T>(0))
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{
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y2 = -y;
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fCos = -fCos;
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}
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//if(fCos > 1.0f) // problem
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T k0, k1;
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if(fCos > (static_cast<T>(1) - epsilon<T>()))
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{
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k0 = static_cast<T>(1) - a;
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k1 = static_cast<T>(0) + a; //BUG!!! 1.0f + a;
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}
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else
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{
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T fSin = sqrt(T(1) - fCos * fCos);
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T fAngle = atan(fSin, fCos);
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T fOneOverSin = static_cast<T>(1) / fSin;
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k0 = sin((static_cast<T>(1) - a) * fAngle) * fOneOverSin;
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k1 = sin((static_cast<T>(0) + a) * fAngle) * fOneOverSin;
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}
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return tquat<T, P>(
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k0 * x.w + k1 * y2.w,
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k0 * x.x + k1 * y2.x,
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k0 * x.y + k1 * y2.y,
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k0 * x.z + k1 * y2.z);
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}
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template <typename T, precision P>
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GLM_FUNC_QUALIFIER tquat<T, P> fastMix
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(
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tquat<T, P> const & x,
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tquat<T, P> const & y,
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T const & a
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)
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{
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return glm::normalize(x * (static_cast<T>(1) - a) + (y * a));
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}
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template <typename T, precision P>
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GLM_FUNC_QUALIFIER tquat<T, P> rotation
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(
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tvec3<T, P> const & orig,
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tvec3<T, P> const & dest
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)
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{
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T cosTheta = dot(orig, dest);
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tvec3<T, P> rotationAxis;
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if(cosTheta >= static_cast<T>(1) - epsilon<T>())
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return quat();
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if(cosTheta < static_cast<T>(-1) + epsilon<T>())
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{
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// special case when vectors in opposite directions :
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// there is no "ideal" rotation axis
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// So guess one; any will do as long as it's perpendicular to start
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// This implementation favors a rotation around the Up axis (Y),
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// since it's often what you want to do.
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rotationAxis = cross(tvec3<T, P>(0, 0, 1), orig);
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if(length2(rotationAxis) < epsilon<T>()) // bad luck, they were parallel, try again!
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rotationAxis = cross(tvec3<T, P>(1, 0, 0), orig);
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rotationAxis = normalize(rotationAxis);
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return angleAxis(pi<T>(), rotationAxis);
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}
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// Implementation from Stan Melax's Game Programming Gems 1 article
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rotationAxis = cross(orig, dest);
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T s = sqrt((T(1) + cosTheta) * static_cast<T>(2));
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T invs = static_cast<T>(1) / s;
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return tquat<T, P>(
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s * static_cast<T>(0.5f),
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rotationAxis.x * invs,
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rotationAxis.y * invs,
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rotationAxis.z * invs);
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}
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}//namespace glm
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