/// @ref gtx_easing #include <cmath> namespace glm{ template <typename genType> GLM_FUNC_QUALIFIER genType linearInterpolation(genType const& a) { // Only defined in [0, 1] assert(a >= zero<genType>()); assert(a <= one<genType>()); return a; } template <typename genType> GLM_FUNC_QUALIFIER genType quadraticEaseIn(genType const& a) { // Only defined in [0, 1] assert(a >= zero<genType>()); assert(a <= one<genType>()); return a * a; } template <typename genType> GLM_FUNC_QUALIFIER genType quadraticEaseOut(genType const& a) { // Only defined in [0, 1] assert(a >= zero<genType>()); assert(a <= one<genType>()); return -(a * (a - static_cast<genType>(2))); } template <typename genType> GLM_FUNC_QUALIFIER genType quadraticEaseInOut(genType const& a) { // Only defined in [0, 1] assert(a >= zero<genType>()); assert(a <= one<genType>()); if(a < static_cast<genType>(0.5)) { return static_cast<genType>(2) * a * a; } else { return (-static_cast<genType>(2) * a * a) + (4 * a) - one<genType>(); } } template <typename genType> GLM_FUNC_QUALIFIER genType cubicEaseIn(genType const& a) { // Only defined in [0, 1] assert(a >= zero<genType>()); assert(a <= one<genType>()); return a * a * a; } template <typename genType> GLM_FUNC_QUALIFIER genType cubicEaseOut(genType const& a) { // Only defined in [0, 1] assert(a >= zero<genType>()); assert(a <= one<genType>()); genType const f = a - one<genType>(); return f * f * f + one<genType>(); } template <typename genType> GLM_FUNC_QUALIFIER genType cubicEaseInOut(genType const& a) { // Only defined in [0, 1] assert(a >= zero<genType>()); assert(a <= one<genType>()); if (a < static_cast<genType>(0.5)) { return static_cast<genType>(4) * a * a * a; } else { genType const f = ((static_cast<genType>(2) * a) - static_cast<genType>(2)); return static_cast<genType>(0.5) * f * f * f + one<genType>(); } } template <typename genType> GLM_FUNC_QUALIFIER genType quarticEaseIn(genType const& a) { // Only defined in [0, 1] assert(a >= zero<genType>()); assert(a <= one<genType>()); return a * a * a * a; } template <typename genType> GLM_FUNC_QUALIFIER genType quarticEaseOut(genType const& a) { // Only defined in [0, 1] assert(a >= zero<genType>()); assert(a <= one<genType>()); genType const f = (a - one<genType>()); return f * f * f * (one<genType>() - a) + one<genType>(); } template <typename genType> GLM_FUNC_QUALIFIER genType quarticEaseInOut(genType const& a) { // Only defined in [0, 1] assert(a >= zero<genType>()); assert(a <= one<genType>()); if(a < static_cast<genType>(0.5)) { return static_cast<genType>(8) * a * a * a * a; } else { genType const f = (a - one<genType>()); return -static_cast<genType>(8) * f * f * f * f + one<genType>(); } } template <typename genType> GLM_FUNC_QUALIFIER genType quinticEaseIn(genType const& a) { // Only defined in [0, 1] assert(a >= zero<genType>()); assert(a <= one<genType>()); return a * a * a * a * a; } template <typename genType> GLM_FUNC_QUALIFIER genType quinticEaseOut(genType const& a) { // Only defined in [0, 1] assert(a >= zero<genType>()); assert(a <= one<genType>()); genType const f = (a - one<genType>()); return f * f * f * f * f + one<genType>(); } template <typename genType> GLM_FUNC_QUALIFIER genType quinticEaseInOut(genType const& a) { // Only defined in [0, 1] assert(a >= zero<genType>()); assert(a <= one<genType>()); if(a < static_cast<genType>(0.5)) { return static_cast<genType>(16) * a * a * a * a * a; } else { genType const f = ((static_cast<genType>(2) * a) - static_cast<genType>(2)); return static_cast<genType>(0.5) * f * f * f * f * f + one<genType>(); } } template <typename genType> GLM_FUNC_QUALIFIER genType sineEaseIn(genType const& a) { // Only defined in [0, 1] assert(a >= zero<genType>()); assert(a <= one<genType>()); return sin((a - one<genType>()) * half_pi<genType>()) + one<genType>(); } template <typename genType> GLM_FUNC_QUALIFIER genType sineEaseOut(genType const& a) { // Only defined in [0, 1] assert(a >= zero<genType>()); assert(a <= one<genType>()); return sin(a * half_pi<genType>()); } template <typename genType> GLM_FUNC_QUALIFIER genType sineEaseInOut(genType const& a) { // Only defined in [0, 1] assert(a >= zero<genType>()); assert(a <= one<genType>()); return static_cast<genType>(0.5) * (one<genType>() - cos(a * pi<genType>())); } template <typename genType> GLM_FUNC_QUALIFIER genType circularEaseIn(genType const& a) { // Only defined in [0, 1] assert(a >= zero<genType>()); assert(a <= one<genType>()); return one<genType>() - sqrt(one<genType>() - (a * a)); } template <typename genType> GLM_FUNC_QUALIFIER genType circularEaseOut(genType const& a) { // Only defined in [0, 1] assert(a >= zero<genType>()); assert(a <= one<genType>()); return sqrt((static_cast<genType>(2) - a) * a); } template <typename genType> GLM_FUNC_QUALIFIER genType circularEaseInOut(genType const& a) { // Only defined in [0, 1] assert(a >= zero<genType>()); assert(a <= one<genType>()); if(a < static_cast<genType>(0.5)) { return static_cast<genType>(0.5) * (one<genType>() - std::sqrt(one<genType>() - static_cast<genType>(4) * (a * a))); } else { return static_cast<genType>(0.5) * (std::sqrt(-((static_cast<genType>(2) * a) - static_cast<genType>(3)) * ((static_cast<genType>(2) * a) - one<genType>())) + one<genType>()); } } template <typename genType> GLM_FUNC_QUALIFIER genType exponentialEaseIn(genType const& a) { // Only defined in [0, 1] assert(a >= zero<genType>()); assert(a <= one<genType>()); if(a <= zero<genType>()) return a; else { genType const Complementary = a - one<genType>(); genType const Two = static_cast<genType>(2); return glm::pow(Two, Complementary * static_cast<genType>(10)); } } template <typename genType> GLM_FUNC_QUALIFIER genType exponentialEaseOut(genType const& a) { // Only defined in [0, 1] assert(a >= zero<genType>()); assert(a <= one<genType>()); if(a >= one<genType>()) return a; else { return one<genType>() - glm::pow(static_cast<genType>(2), -static_cast<genType>(10) * a); } } template <typename genType> GLM_FUNC_QUALIFIER genType exponentialEaseInOut(genType const& a) { // Only defined in [0, 1] assert(a >= zero<genType>()); assert(a <= one<genType>()); if(a < static_cast<genType>(0.5)) return static_cast<genType>(0.5) * glm::pow(static_cast<genType>(2), (static_cast<genType>(20) * a) - static_cast<genType>(10)); else return -static_cast<genType>(0.5) * glm::pow(static_cast<genType>(2), (-static_cast<genType>(20) * a) + static_cast<genType>(10)) + one<genType>(); } template <typename genType> GLM_FUNC_QUALIFIER genType elasticEaseIn(genType const& a) { // Only defined in [0, 1] assert(a >= zero<genType>()); assert(a <= one<genType>()); return std::sin(static_cast<genType>(13) * half_pi<genType>() * a) * glm::pow(static_cast<genType>(2), static_cast<genType>(10) * (a - one<genType>())); } template <typename genType> GLM_FUNC_QUALIFIER genType elasticEaseOut(genType const& a) { // Only defined in [0, 1] assert(a >= zero<genType>()); assert(a <= one<genType>()); return std::sin(-static_cast<genType>(13) * half_pi<genType>() * (a + one<genType>())) * glm::pow(static_cast<genType>(2), -static_cast<genType>(10) * a) + one<genType>(); } template <typename genType> GLM_FUNC_QUALIFIER genType elasticEaseInOut(genType const& a) { // Only defined in [0, 1] assert(a >= zero<genType>()); assert(a <= one<genType>()); if(a < static_cast<genType>(0.5)) return static_cast<genType>(0.5) * std::sin(static_cast<genType>(13) * half_pi<genType>() * (static_cast<genType>(2) * a)) * glm::pow(static_cast<genType>(2), static_cast<genType>(10) * ((static_cast<genType>(2) * a) - one<genType>())); else return static_cast<genType>(0.5) * (std::sin(-static_cast<genType>(13) * half_pi<genType>() * ((static_cast<genType>(2) * a - one<genType>()) + one<genType>())) * glm::pow(static_cast<genType>(2), -static_cast<genType>(10) * (static_cast<genType>(2) * a - one<genType>())) + static_cast<genType>(2)); } template <typename genType> GLM_FUNC_QUALIFIER genType backEaseIn(genType const& a, genType const& o) { // Only defined in [0, 1] assert(a >= zero<genType>()); assert(a <= one<genType>()); genType z = ((o + one<genType>()) * a) - o; return (a * a * z); } template <typename genType> GLM_FUNC_QUALIFIER genType backEaseOut(genType const& a, genType const& o) { // Only defined in [0, 1] assert(a >= zero<genType>()); assert(a <= one<genType>()); genType n = a - one<genType>(); genType z = ((o + one<genType>()) * n) + o; return (n * n * z) + one<genType>(); } template <typename genType> GLM_FUNC_QUALIFIER genType backEaseInOut(genType const& a, genType const& o) { // Only defined in [0, 1] assert(a >= zero<genType>()); assert(a <= one<genType>()); genType s = o * static_cast<genType>(1.525); genType x = static_cast<genType>(0.5); genType n = a / static_cast<genType>(0.5); if (n < static_cast<genType>(1)) { genType z = ((s + static_cast<genType>(1)) * n) - s; genType m = n * n * z; return x * m; } else { n -= static_cast<genType>(2); genType z = ((s + static_cast<genType>(1)) * n) + s; genType m = (n*n*z) + static_cast<genType>(2); return x * m; } } template <typename genType> GLM_FUNC_QUALIFIER genType backEaseIn(genType const& a) { return backEaseIn(a, static_cast<genType>(1.70158)); } template <typename genType> GLM_FUNC_QUALIFIER genType backEaseOut(genType const& a) { return backEaseOut(a, static_cast<genType>(1.70158)); } template <typename genType> GLM_FUNC_QUALIFIER genType backEaseInOut(genType const& a) { return backEaseInOut(a, static_cast<genType>(1.70158)); } template <typename genType> GLM_FUNC_QUALIFIER genType bounceEaseOut(genType const& a) { // Only defined in [0, 1] assert(a >= zero<genType>()); assert(a <= one<genType>()); if(a < static_cast<genType>(4.0 / 11.0)) { return (static_cast<genType>(121) * a * a) / static_cast<genType>(16); } else if(a < static_cast<genType>(8.0 / 11.0)) { return (static_cast<genType>(363.0 / 40.0) * a * a) - (static_cast<genType>(99.0 / 10.0) * a) + static_cast<genType>(17.0 / 5.0); } else if(a < static_cast<genType>(9.0 / 10.0)) { return (static_cast<genType>(4356.0 / 361.0) * a * a) - (static_cast<genType>(35442.0 / 1805.0) * a) + static_cast<genType>(16061.0 / 1805.0); } else { return (static_cast<genType>(54.0 / 5.0) * a * a) - (static_cast<genType>(513.0 / 25.0) * a) + static_cast<genType>(268.0 / 25.0); } } template <typename genType> GLM_FUNC_QUALIFIER genType bounceEaseIn(genType const& a) { // Only defined in [0, 1] assert(a >= zero<genType>()); assert(a <= one<genType>()); return one<genType>() - bounceEaseOut(one<genType>() - a); } template <typename genType> GLM_FUNC_QUALIFIER genType bounceEaseInOut(genType const& a) { // Only defined in [0, 1] assert(a >= zero<genType>()); assert(a <= one<genType>()); if(a < static_cast<genType>(0.5)) { return static_cast<genType>(0.5) * (one<genType>() - bounceEaseOut(a * static_cast<genType>(2))); } else { return static_cast<genType>(0.5) * bounceEaseOut(a * static_cast<genType>(2) - one<genType>()) + static_cast<genType>(0.5); } } }//namespace glm