In the mathematical field of numerical analysis, interpolation is a method of constructing new data points within the range of a discrete set of known data points....
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A game engine is a system designed for the creation and development of video games. There are many game engines that are designed to work on video game consoles and personal computers...
In mathematical analysis, a differentiability class is a classification of functions according to the properties of their derivatives. Higher order differentiability classes correspond to the existence of more derivatives. Functions that have derivatives of all orders are called smooth.Most of...
between two input values based on a third one that should be between the first two. The returned value is clamped between 0 and 1.
The slope (i.e. derivative) of the smoothstep function starts at 0 and ends at 0. This makes it easy to create a sequence of transitions using smoothstep to interpolate each segment rather than using a more sophisticated or expensive interpolation technique.
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In numerical analysis, Hermite interpolation, named after Charles Hermite, is a method of interpolating data points as a polynomial function. The generated Hermite polynomial is closely related to the Newton polynomial, in that both are derived from the calculation of divided differences.Unlike...
after doing a clamp:
An example implementation provided by AMD follows.
float smoothstep(float edge0, float edge1, float x)
{
// Scale, bias and saturate x to 0..1 range
x = saturate((x - edge0)/(edge1 - edge0));
// Evaluate polynomial
return x*x*(3 - 2*x);
}
Ken Perlin is a professor in the Department of Computer Science at New York University, founding director of the Media Research Lab at NYU, and the Director of the Games for Learning Institute. His research interests include graphics, animation, multimedia, and science education...
suggests an improved version of the smoothstep function which has zero 1st and 2nd order derivatives at t=0 and t=1:
Reference implementation:
float smootherstep(float edge0, float edge1, float x)
{
// Scale, and clamp x to 0..1 range
x = clamp((x - edge0)/(edge1 - edge0), 0, 1);
// Evaluate polynomial
return x*x*x*(x*(x*6 - 15) + 10);
}
