/// <summary>
/// Gets the Debauchies scaling function
/// </summary>
/// <param name="x">Array of x-coordinates to map to scaling function</param>
/// <param name="levels">Levels of approximatation</param>
/// <returns>The scaling function at successive levels of approximation</returns>
public IEnumerable <Vector2[]> GetScalingFunction(int levels, WaveletKind wavelet)
{
if (levels < 0)
{
throw new ArgumentOutOfRangeException($"{nameof(GetScalingFunction)} parameter {nameof(levels)} ({levels}) must be 0 or larger");
}
var coefficients = WaveletCoefficients.GetScalingCoefficients(wavelet).ToArray();
var previous = WaveletCoefficients.GetInitialScalingValues(wavelet).ToArray().Select((x, index) => new Vector2(index, x)).ToArray();
float maxRange = coefficients.Length - 1f;
var current = previous;
yield return(previous);
for (int level = 1; level <= levels; level++)
{
current = GetScalingLevel(level, previous, coefficients);
yield return(current);
previous = current;
}
Vector2[] GetScalingLevel(int level, Vector2[] previous, float[] scalingCoefs)
{
var scaling = new Vector2[PointsAtLevel(scalingCoefs.Length, level)];
float maxRange = scalingCoefs.Length - 1f;
float distancePerIndex = maxRange / (scaling.Length - 1);
for (int n = 0; n < scaling.Length; n += 2)
{
scaling[n] = previous[n / 2];
}
for (int n = 1; n < scaling.Length; n += 2)
{
float sum = 0;
float r = n / (float)(1 << level);
for (int k = 0; k < scalingCoefs.Length; k++)
{
float rPrevious = 2 * r - k;
int rIndex = (int)MathF.Round(rPrevious / distancePerIndex);
if (rPrevious >= 0 && rPrevious <= maxRange)
{
sum += scalingCoefs[k] * scaling[rIndex].Y;
}
}
scaling[n] = new Vector2(r, sum);
}
return(scaling);
}
}
/// <summary>
/// Gets the Debauchies scaling function
/// </summary>
/// <param name="levels">Levels of approximatation</param>
/// <param name="waveletKind">Wavelet kind to calculate</param>
/// <returns>The wavelet function at the specified level of approximation</returns>
public Vector2[] GetWaveletFunction(int levels, WaveletKind waveletKind)
{
if (levels < 0)
{
throw new ArgumentOutOfRangeException($"{nameof(GetScalingFunction)} parameter {nameof(levels)} ({levels}) must be 0 or larger");
}
var scaling = GetScalingFunction(levels, waveletKind).Last().ToArray();
var coefficients = WaveletCoefficients.GetWaveletCoefficients(waveletKind).ToArray();
return(GetWaveletLevel(scaling, coefficients));
Vector2[] GetWaveletLevel(Vector2[] scaling, float[] waveletCoefs)
{
var wavelet = new Vector2[scaling.Length];
float maxRange = waveletCoefs.Length - 1f;
float distancePerPoint = maxRange / (wavelet.Length - 1);
for (int n = 0; n < wavelet.Length; n++)
{
float sum = 0;
float r = n * distancePerPoint;
for (int k = 0; k < waveletCoefs.Length; k++)
{
float rPrevious = 2 * r - k;
int rIndex = (int)MathF.Round(rPrevious / distancePerPoint);
if (rPrevious >= 0 && rPrevious <= maxRange)
{
sum += waveletCoefs[k] * scaling[rIndex].Y;
}
}
wavelet[n] = new Vector2(r, sum);
}
return(wavelet);
}
}
public int GetMaxRange(WaveletKind waveletKind) => WaveletCoefficients.GetScalingCoefficients(waveletKind).Length - 1;