/* This error function was taken from http://www.volume-gfx.com/
* However, it has a major flaw when points sampled have a very similar value
* The only way to fix it is to sample from more points, have a maximum container size, or sample random points
* This can still lead to the error falsely being calculated as negligible though for certain functions, such as noise functions
* The only way (to my knowledge) is to sample points on a uniform grid as the original DMC paper suggests
* It can be done efficiently though, like sampling the corners and mid points initially, then the in-between points, etc
* And breaking early if the error exceeds the threshold
*/
public float GetError(float threshold)
{
float error = 0;
float[] values = new float[4];
Vector2[] positions = new Vector2[5];
Vector2[] middle_positions =
{
new Vector2(0.5f, 0.0f),
new Vector2(0.0f, 0.5f),
new Vector2(0.5f, 0.5f),
new Vector2(1.0f, 0.5f),
new Vector2(0.5f, 1.0f)
};
for (int i = 0; i < 5; i++)
{
positions[i] = position + size * middle_positions[i];
if (i < 4)
{
values[i] = Sampler.Sample(position + size * new Vector2(i / 2, i % 2));
}
}
for (int i = 0; i < 5; i++)
{
float center_value = Sampler.Sample(positions[i]);
Vector2 gradient = Sampler.GetGradient(positions[i]);
float interpolated = Interpolate(values[0], values[1], values[2], values[3], middle_positions[i]);
float mag = Math.Max(1.0f, gradient.Length());
error += Math.Abs(center_value - interpolated) / mag;
if (error >= threshold)
{
break;
}
}
return(error);
}