108 lines
3.0 KiB
C++
108 lines
3.0 KiB
C++
namespace glm
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{
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template<typename T, qualifier Q>
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GLM_FUNC_QUALIFIER qua<T, Q> mix(qua<T, Q> const& x, qua<T, Q> const& y, T a)
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{
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GLM_STATIC_ASSERT(std::numeric_limits<T>::is_iec559, "'mix' only accept floating-point inputs");
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T const cosTheta = dot(x, y);
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// Perform a linear interpolation when cosTheta is close to 1 to avoid side effect of sin(angle) becoming a zero denominator
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if(cosTheta > static_cast<T>(1) - epsilon<T>())
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{
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// Linear interpolation
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return qua<T, Q>(
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mix(x.w, y.w, a),
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mix(x.x, y.x, a),
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mix(x.y, y.y, a),
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mix(x.z, y.z, a));
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}
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else
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{
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// Essential Mathematics, page 467
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T angle = acos(cosTheta);
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return (sin((static_cast<T>(1) - a) * angle) * x + sin(a * angle) * y) / sin(angle);
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}
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}
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template<typename T, qualifier Q>
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GLM_FUNC_QUALIFIER qua<T, Q> lerp(qua<T, Q> const& x, qua<T, Q> const& y, T a)
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{
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GLM_STATIC_ASSERT(std::numeric_limits<T>::is_iec559, "'lerp' only accept floating-point inputs");
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// Lerp is only defined in [0, 1]
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assert(a >= static_cast<T>(0));
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assert(a <= static_cast<T>(1));
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return x * (static_cast<T>(1) - a) + (y * a);
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}
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template<typename T, qualifier Q>
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GLM_FUNC_QUALIFIER qua<T, Q> slerp(qua<T, Q> const& x, qua<T, Q> const& y, T a)
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{
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GLM_STATIC_ASSERT(std::numeric_limits<T>::is_iec559, "'slerp' only accept floating-point inputs");
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qua<T, Q> z = y;
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T cosTheta = dot(x, y);
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// If cosTheta < 0, the interpolation will take the long way around the sphere.
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// To fix this, one quat must be negated.
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if(cosTheta < static_cast<T>(0))
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{
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z = -y;
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cosTheta = -cosTheta;
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}
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// Perform a linear interpolation when cosTheta is close to 1 to avoid side effect of sin(angle) becoming a zero denominator
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if(cosTheta > static_cast<T>(1) - epsilon<T>())
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{
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// Linear interpolation
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return qua<T, Q>(
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mix(x.w, z.w, a),
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mix(x.x, z.x, a),
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mix(x.y, z.y, a),
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mix(x.z, z.z, a));
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}
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else
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{
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// Essential Mathematics, page 467
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T angle = acos(cosTheta);
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return (sin((static_cast<T>(1) - a) * angle) * x + sin(a * angle) * z) / sin(angle);
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}
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}
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template<typename T, qualifier Q>
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GLM_FUNC_QUALIFIER qua<T, Q> conjugate(qua<T, Q> const& q)
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{
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return qua<T, Q>(q.w, -q.x, -q.y, -q.z);
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}
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template<typename T, qualifier Q>
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GLM_FUNC_QUALIFIER qua<T, Q> inverse(qua<T, Q> const& q)
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{
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return conjugate(q) / dot(q, q);
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}
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template<typename T, qualifier Q>
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GLM_FUNC_QUALIFIER vec<4, bool, Q> isnan(qua<T, Q> const& q)
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{
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GLM_STATIC_ASSERT(std::numeric_limits<T>::is_iec559, "'isnan' only accept floating-point inputs");
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return vec<4, bool, Q>(isnan(q.x), isnan(q.y), isnan(q.z), isnan(q.w));
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}
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template<typename T, qualifier Q>
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GLM_FUNC_QUALIFIER vec<4, bool, Q> isinf(qua<T, Q> const& q)
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{
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GLM_STATIC_ASSERT(std::numeric_limits<T>::is_iec559, "'isinf' only accept floating-point inputs");
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return vec<4, bool, Q>(isinf(q.x), isinf(q.y), isinf(q.z), isinf(q.w));
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}
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}//namespace glm
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#if GLM_CONFIG_SIMD == GLM_ENABLE
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# include "quaternion_common_simd.inl"
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#endif
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