Cubic/Curve Smooth Interpolation in C#
bicubic, c#, linear-interpolation, math
Solution
What you want is a Cubic Hermite Spline:
where p0 is the start point, p1 is the end point, m0 is the start tangent, and m1 is the end tangent
Problem
Below is a cubic interpolation function: ``` public float Smooth(float start, float end, float amount) { // Clamp to 0-1; amount = (amount > 1f) ? 1f : amount; amount = (amount < 0f) ? 0f : amount; // Cubicly adjust the amount value. amount = (amount * amount) * (3f - (2f * amount)); return (start + ((end - start) * amount)); } ``` This function will cubically interpolate between the start and end value given an amount between 0.0f - 1.0f. If you were to plot this curve, you'd end up with something like this: Expired Imageshack image removed The cubic function here is: ``` amount = (amount * amount) * (3f - (2f * amount)); ``` How do I adjust this to produce two produce tangents in and out? To produce curves like this: (Linear start to cubic end) Expired Imageshack image removed As one function and like this as another: (Cubic start to linear end) Expired Imageshack image removed Anyone got any ideas? Thanks in advance.