I looked through the internet, and in terms of Bicubic Interpolation, I can't find a simple equation for it. Wikipedia's page on the subject wasn't very helpful, so is there any easy method to learning how Bicubic Interpolation works and how to implement it? I'm using it to generate Perlin Noise, but using bilinear interpolation is way to choppy for my needs (I already tried it).
If anyone can point me in the right direction by either a good website or just an answer, I would greatly appreciate it. (I'm using C# by the way)
Answer
Using this (Thanks to Ahmet Kakıcı who found this), I figured out how to add Bicubic Interpolation. For those also looking for the answer, here is what I used:
private float CubicPolate( float v0, float v1, float v2, float v3, float fracy ) {
float A = (v3-v2)-(v0-v1);
float B = (v0-v1)-A;
float C = v2-v0;
float D = v1;
return A*Mathf.Pow(fracy,3)+B*Mathf.Pow(fracy,2)+C*fracy+D;
}
In order to get 2D Interpolation, I first got the x, then interpolated the y. Eg.
float x1 = CubicPolate( ndata[0,0], ndata[1,0], ndata[2,0], ndata[3,0], fracx );
float x2 = CubicPolate( ndata[0,1], ndata[1,1], ndata[2,1], ndata[3,1], fracx );
float x3 = CubicPolate( ndata[0,2], ndata[1,2], ndata[2,2], ndata[3,2], fracx );
float x4 = CubicPolate( ndata[0,3], ndata[1,3], ndata[2,3], ndata[3,3], fracx );
float y1 = CubicPolate( x1, x2, x3, x4, fracy );
Where ndata is defined as:
float[,] ndata = new float[4,4];
for( int X = 0; X < 4; X++ )
for( int Y = 0; Y < 4; Y++ )
//Smoothing done by averaging the general area around the coords.
ndata[X,Y] = SmoothedNoise( intx+(X-1), inty+(Y-1) );
(intx and inty are the floored values of the requested coordinates. fracx and fracy are the fractional parts of the inputted coordinates, to be x-intx, and y-inty, respectively)