/// <summary>
/// Ridged multi-fractal
/// </summary>
/// <param name="x">Initial x coordinate</param>
/// <param name="y">Initial y coordinate</param>
/// <param name="freq">Frequency</param>
/// <param name="numOctaves">Number of octaves</param>
/// <param name="persistence">Persistence</param>
/// <param name="basis">Basis function. Generates values between 0 and 1</param>
/// <returns>Returns the generated fractal value between 0 and 1</returns>
public static float RidgedFractal( float x, float y, float freq, int numOctaves, float persistence, Basis2dFunction basis )
{
float offset = 1.0f;
float signal = Math.Abs( basis( x, y ) );
signal = offset - signal; // invert and translate (note that "offset" should be ~= 1.0)
signal *= signal; // square the signal, to increase "sharpness" of ridges
float result = signal;
float gain = 1.8f;
float exp = 1;
float max = 1;
for ( int octave = 1; octave < numOctaves; ++octave )
{
x *= freq;
y *= freq;
float weight = Utils.Clamp( signal * gain, 0, 1 );
signal = offset - Math.Abs( basis( x, y ) );
signal *= signal;
signal *= weight;
max += 1.0f / exp;
result += signal / exp;
exp *= freq;
}
return ( result / max );
}
/// <summary>
/// Simple fractal
/// </summary>
/// <param name="x">Initial x coordinate</param>
/// <param name="y">Initial y coordinate</param>
/// <param name="freq">Frequency</param>
/// <param name="numOctaves">Number of octaves</param>
/// <param name="persistence">Persistence</param>
/// <param name="basis">Basis function. Generates values between 0 and 1</param>
/// <returns>Returns the generated fractal value between 0 and 1</returns>
public static float SimpleFractal( float x, float y, float freq, int numOctaves, float persistence, Basis2dFunction basis )
{
float amp = 1;
float total = 0;
float max = 0;
for ( int octave = 0; octave < numOctaves; ++octave )
{
total += basis( x, y ) * amp;
max += amp;
amp *= persistence;
x *= freq;
y *= freq;
}
return ( total + max ) / ( max * 2 );
}
/// <summary>
/// Tiles a 2d function
/// </summary>
private float Tiled2dFunction( float x, float y, Basis2dFunction basis )
{
x = Utils.Wrap( x, m_StartX, m_StartX + m_Width );
y = Utils.Wrap( y, m_StartY, m_StartY + m_Height );
float wrapX = x - m_Width;
float wrapY = y - m_Height;
float fX = x - m_StartX;
float fY = y - m_StartY;
float invX = m_Width - fX;
float invY = m_Height - fY;
float v0 = basis( x, y ) * invX * invY;
float v1 = basis( wrapX, y ) * fX * invY;
float v2 = basis( wrapX, wrapY ) * fX * fY;
float v3 = basis( x, wrapY ) * invX * fY;
return ( v0 + v1 + v2 + v3 ) * m_InvWH;
}