/// <summary>
/// Performs the Extended Wilkinson algorithm which returns an optimal labeling for numeric numbers based on the given settings
/// </summary>
/// <param name="availableSpace">States how much space in world units there is available for the axis</param>
/// <param name="horizontalAxis">If set to true, the axis is orientated horizontally</param>
/// <param name="targetDensity">Specifies how many labels should be placed per world unit</param>
/// <param name="dataMin">The minimum of the data range</param>
/// <param name="dataMax">The maximum of the dtaa range</param>
/// <param name="axisMin">Gives the chosen minimum of the axis labeling</param>
/// <param name="axisMax">Gives the chosen maximum of the axis labeling</param>
/// <returns>An axis configuration which includes styling and the chosen labels</returns>
public static IDisplayAxis PerformExtendedWilkinson(IAxis axis, float availableSpace, float targetDensity, out float axisMin, out float axisMax)
{
float bestScore = -2;
axisMin = axis.NumericDataMin;
axisMax = axis.NumericDataMax;
if (axisMin == axisMax)
{
Debug.LogError("Cannot work on same min and max data");
return(null);
}
IDisplayAxis bestOption = null;
for (int j = 1; j < int.MaxValue; j++) // there are break statements which terminate this loop
{
foreach (float q in Q) // (j,q): determines step size
{
float sm = SimplicityMax(q, j);
if (Vector4.Dot(new Vector4(sm, 1, 1, 1), weights) < bestScore)
{
// finish the search
j = int.MaxValue - 1;
break;
}
for (int k = 2; k < int.MaxValue; k++) // try different numbers of labels
{
float dm = DensityMax(k / availableSpace, targetDensity);
if (Vector4.Dot(new Vector4(sm, 1, dm, 1), weights) < bestScore)
{
break;
}
float delta = (axis.NumericDataMax - axis.NumericDataMin) / (k + 1) / (j * q);
for (int z = Mathf.CeilToInt(Mathf.Log10(delta)); z < int.MaxValue; z++) // power of 10 multiplier for the step size
{
float lStep = q * j * Mathf.Pow(10, z);
float cm = CoverageMax(axis.NumericDataMin, axis.NumericDataMax, lStep * (k - 1));
if (Vector4.Dot(new Vector4(sm, cm, dm, 1), weights) < bestScore)
{
break;
}
for (float start = Mathf.Floor(axis.NumericDataMax / lStep) - (k - 1); start <= Mathf.Ceil(axis.NumericDataMin / lStep); start += 1f / j) // possible start labels
{
float lmin = start * lStep;
float lmax = lmin + (k - 1) * lStep;
float s = Simplicity(q, j, lmin, lmax, lStep);
float d = Density(k / availableSpace, targetDensity);
float c = Coverage(axis.NumericDataMin, axis.NumericDataMax, lmin, lmax);
if (Vector4.Dot(new Vector4(s, c, d, 1), weights) < bestScore)
{
continue;
}
List <float> stepSequence = Enumerable.Range(0, k).Select(x => lmin + x * lStep).ToList();
//List<string> labels = stepSequence.Select(value => value.ToString("0.##")).ToList();
// optimize legibility
List <IDisplayAxis> possibilities = axis.GeneratePossibleConfigurations(minTextSize, maxTextSize, stepSequence);
float legibility;
IDisplayAxis localBest = DisplayAxis.FindBestLegibility(possibilities, out legibility, minTextSize, targetTextSize, 0.02f, availableSpace);
float score = Vector4.Dot(new Vector4(s, c, d, legibility), weights);
if (score > bestScore)
{
bestOption = localBest;
bestScore = score;
axisMax = lmax;
axisMin = lmin;
}
}
}
}
}
}
return(bestOption);
}