437 lines
12 KiB
Plaintext
437 lines
12 KiB
Plaintext
|
/// @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
|