| 1 | namespace glm |
| 2 | { |
| 3 | template<typename T, qualifier Q> |
| 4 | GLM_FUNC_QUALIFIER qua<T, Q> mix(qua<T, Q> const& x, qua<T, Q> const& y, T a) |
| 5 | { |
| 6 | GLM_STATIC_ASSERT(std::numeric_limits<T>::is_iec559, "'mix' only accept floating-point inputs"); |
| 7 | |
| 8 | T const cosTheta = dot(x, y); |
| 9 | |
| 10 | // Perform a linear interpolation when cosTheta is close to 1 to avoid side effect of sin(angle) becoming a zero denominator |
| 11 | if(cosTheta > static_cast<T>(1) - epsilon<T>()) |
| 12 | { |
| 13 | // Linear interpolation |
| 14 | return qua<T, Q>( |
| 15 | mix(x.w, y.w, a), |
| 16 | mix(x.x, y.x, a), |
| 17 | mix(x.y, y.y, a), |
| 18 | mix(x.z, y.z, a)); |
| 19 | } |
| 20 | else |
| 21 | { |
| 22 | // Essential Mathematics, page 467 |
| 23 | T angle = acos(cosTheta); |
| 24 | return (sin((static_cast<T>(1) - a) * angle) * x + sin(a * angle) * y) / sin(angle); |
| 25 | } |
| 26 | } |
| 27 | |
| 28 | template<typename T, qualifier Q> |
| 29 | GLM_FUNC_QUALIFIER qua<T, Q> lerp(qua<T, Q> const& x, qua<T, Q> const& y, T a) |
| 30 | { |
| 31 | GLM_STATIC_ASSERT(std::numeric_limits<T>::is_iec559, "'lerp' only accept floating-point inputs"); |
| 32 | |
| 33 | // Lerp is only defined in [0, 1] |
| 34 | assert(a >= static_cast<T>(0)); |
| 35 | assert(a <= static_cast<T>(1)); |
| 36 | |
| 37 | return x * (static_cast<T>(1) - a) + (y * a); |
| 38 | } |
| 39 | |
| 40 | template<typename T, qualifier Q> |
| 41 | GLM_FUNC_QUALIFIER qua<T, Q> slerp(qua<T, Q> const& x, qua<T, Q> const& y, T a) |
| 42 | { |
| 43 | GLM_STATIC_ASSERT(std::numeric_limits<T>::is_iec559, "'slerp' only accept floating-point inputs"); |
| 44 | |
| 45 | qua<T, Q> z = y; |
| 46 | |
| 47 | T cosTheta = dot(x, y); |
| 48 | |
| 49 | // If cosTheta < 0, the interpolation will take the long way around the sphere. |
| 50 | // To fix this, one quat must be negated. |
| 51 | if(cosTheta < static_cast<T>(0)) |
| 52 | { |
| 53 | z = -y; |
| 54 | cosTheta = -cosTheta; |
| 55 | } |
| 56 | |
| 57 | // Perform a linear interpolation when cosTheta is close to 1 to avoid side effect of sin(angle) becoming a zero denominator |
| 58 | if(cosTheta > static_cast<T>(1) - epsilon<T>()) |
| 59 | { |
| 60 | // Linear interpolation |
| 61 | return qua<T, Q>( |
| 62 | mix(x.w, z.w, a), |
| 63 | mix(x.x, z.x, a), |
| 64 | mix(x.y, z.y, a), |
| 65 | mix(x.z, z.z, a)); |
| 66 | } |
| 67 | else |
| 68 | { |
| 69 | // Essential Mathematics, page 467 |
| 70 | T angle = acos(cosTheta); |
| 71 | return (sin((static_cast<T>(1) - a) * angle) * x + sin(a * angle) * z) / sin(angle); |
| 72 | } |
| 73 | } |
| 74 | |
| 75 | template<typename T, qualifier Q> |
| 76 | GLM_FUNC_QUALIFIER qua<T, Q> conjugate(qua<T, Q> const& q) |
| 77 | { |
| 78 | return qua<T, Q>(q.w, -q.x, -q.y, -q.z); |
| 79 | } |
| 80 | |
| 81 | template<typename T, qualifier Q> |
| 82 | GLM_FUNC_QUALIFIER qua<T, Q> inverse(qua<T, Q> const& q) |
| 83 | { |
| 84 | return conjugate(q) / dot(q, q); |
| 85 | } |
| 86 | |
| 87 | template<typename T, qualifier Q> |
| 88 | GLM_FUNC_QUALIFIER vec<4, bool, Q> isnan(qua<T, Q> const& q) |
| 89 | { |
| 90 | GLM_STATIC_ASSERT(std::numeric_limits<T>::is_iec559, "'isnan' only accept floating-point inputs"); |
| 91 | |
| 92 | return vec<4, bool, Q>(isnan(q.x), isnan(q.y), isnan(q.z), isnan(q.w)); |
| 93 | } |
| 94 | |
| 95 | template<typename T, qualifier Q> |
| 96 | GLM_FUNC_QUALIFIER vec<4, bool, Q> isinf(qua<T, Q> const& q) |
| 97 | { |
| 98 | GLM_STATIC_ASSERT(std::numeric_limits<T>::is_iec559, "'isinf' only accept floating-point inputs"); |
| 99 | |
| 100 | return vec<4, bool, Q>(isinf(q.x), isinf(q.y), isinf(q.z), isinf(q.w)); |
| 101 | } |
| 102 | }//namespace glm |
| 103 | |
| 104 | #if GLM_CONFIG_SIMD == GLM_ENABLE |
| 105 | # include "quaternion_common_simd.inl" |
| 106 | #endif |
| 107 | |