/// <summary>
/// Create a new collection of key points with cumulative values.
/// </summary>
/// <param name = "typeProvider">
/// The provider which gives information about the type, required to do interpolation between the key points.
/// </param>
public CumulativeKeyPointCollection(AbstractTypeInterpolationProvider <TValue, TMath> typeProvider)
: base(typeProvider)
{
_zero = CastOperator <double, TMath> .Cast(0);
_minusOne = CastOperator <double, TMath> .Cast(-1);
}
/// <summary>
/// Retrieve values for all dimensions for all 4 control points.
/// </summary>
/// <returns>
/// A 2 dimensional array with all the dimension values for all 4 control points.
/// The first dimension of the array indicates the control point, the second the dimension.
/// </returns>
double[][] RetrieveValues(int smallerIndex, int biggerIndex, AbstractTypeInterpolationProvider <TValue, TMath> typeProvider)
{
// Retrieve required values.
TValue p0 = KeyPoints[smallerIndex != 0 ? smallerIndex - 1 : smallerIndex];
TValue p1 = KeyPoints[smallerIndex];
TValue p2 = KeyPoints[biggerIndex];
TValue p3 = KeyPoints[biggerIndex != KeyPoints.Count - 1 ? biggerIndex + 1 : biggerIndex];
// Retrieve required dimension values.
double[] p0Values = typeProvider.GetDimensionValues(p0).Cast <double>().ToArray();
double[] p1Values = typeProvider.GetDimensionValues(p1).Cast <double>().ToArray();
double[] p2Values = typeProvider.GetDimensionValues(p2).Cast <double>().ToArray();
double[] p3Values = typeProvider.GetDimensionValues(p3).Cast <double>().ToArray();
return(new[] { p0Values, p1Values, p2Values, p3Values });
}
protected override TValue TangentAt(int smallerIndex, int biggerIndex, TMath position, double percentage)
{
AbstractTypeInterpolationProvider <TValue, TMath> typeProvider = KeyPoints.TypeProvider;
// Retrieve values for all dimensions for all 4 control points.
double[][] values = RetrieveValues(smallerIndex, biggerIndex, typeProvider);
// Set up hermite base function derivatives.
double t = percentage;
double t2 = Math.Pow(t, 2);
double baseFunction00 = (6 * t2) - (6 * t);
double baseFunction10 = (3 * t2) - (4 * t) + 1;
double baseFunction01 = (6 * t) - (6 * t2);
double baseFunction11 = (3 * t2) - (2 * t);
// Get tangent by calculating derivative.
double tension = 1 - Tension;
TMath[] tangent = new TMath[typeProvider.AmountOfDimensions];
for (int i = 0; i < typeProvider.AmountOfDimensions; ++i)
{
// Original: (((2*t^3)-(3*t^2)+1)*b) + (((-2*t^3)+(3*t^2))*c) + ((t^3-(2*t^2)+t)*(n*(c-a))) + ((t^3-t^2)*(n*(d-b)))
// First derivative: ((3*d+3*c-3*b-3*a)*n-6*c+6*b)*t^2 + ((-2*d-4*c+2*b+4*a)*n+6*c-6*b)*t + (c-a)*n
// Calculate tangents.
double tangentSmaller = tension * (values[2][i] - values[0][i]);
double tangentBigger = tension * (values[3][i] - values[1][i]);
// Multiply derived hermite base functions with the points (and tangents) and sum up.
double result =
(baseFunction00 * values[1][i])
+ (baseFunction01 * values[2][i])
+ (baseFunction10 * tangentSmaller)
+ (baseFunction11 * tangentBigger);
// Sum up all functions.
tangent[i] = CastOperator <double, TMath> .Cast(result);
}
return(typeProvider.CreateInstance(position, tangent));
}
protected override TValue Interpolate(int smallerIndex, int biggerIndex, TMath position, double percentage)
{
AbstractTypeInterpolationProvider <TValue, TMath> typeProvider = KeyPoints.TypeProvider;
// Retrieve required values.
TValue smaller = KeyPoints[smallerIndex];
TValue bigger = KeyPoints[biggerIndex];
// Retrieve required dimension values.
TMath[] smallerValues = typeProvider.GetDimensionValues(smaller);
TMath[] biggerValues = typeProvider.GetDimensionValues(bigger);
// Linear interpolation.
TMath[] interpolated = new TMath[typeProvider.AmountOfDimensions];
for (int i = 0; i < typeProvider.AmountOfDimensions; ++i)
{
var valueRange = new Interval <TMath>(smallerValues[i], biggerValues[i]);
interpolated[i] = valueRange.GetValueAt(percentage);
}
return(typeProvider.CreateInstance(position, interpolated));
}
protected override TValue Interpolate(int smallerIndex, int biggerIndex, TMath position, double percentage)
{
AbstractTypeInterpolationProvider <TValue, TMath> typeProvider = KeyPoints.TypeProvider;
// Retrieve values for all dimensions for all 4 control points.
double[][] values = RetrieveValues(smallerIndex, biggerIndex, typeProvider);
// Set up hermite base functions.
double t = percentage;
double t2 = Math.Pow(t, 2);
double t3 = Math.Pow(t, 3);
double baseFunction00 = (2 * t3) - (3 * t2) + 1;
double baseFunction10 = t3 - (2 * t2) + t;
double baseFunction01 = (-2 * t3) + (3 * t2);
double baseFunction11 = t3 - t2;
// Interpolate.
double tension = 1 - Tension;
TMath[] interpolated = new TMath[typeProvider.AmountOfDimensions];
for (int i = 0; i < typeProvider.AmountOfDimensions; ++i)
{
// Calculate tangents.
double tangentSmaller = tension * (values[2][i] - values[0][i]);
double tangentBigger = tension * (values[3][i] - values[1][i]);
// Multiply hermite base functions with the points (and tangents) and sum up.
double result =
(baseFunction00 * values[1][i])
+ (baseFunction01 * values[2][i])
+ (baseFunction10 * tangentSmaller)
+ (baseFunction11 * tangentBigger);
// Sum up all functions.
interpolated[i] = CastOperator <double, TMath> .Cast(result);
}
return(typeProvider.CreateInstance(position, interpolated));
}
/// <summary>
/// Create a new interpolation provider which can interpolate over AbsoluteKeyPoints.
/// </summary>
public AbsoluteKeyPointInterpolationProvider(AbstractTypeInterpolationProvider <TValue, TMath> keyPointInterpolationProvider)
: base(keyPointInterpolationProvider.AmountOfDimensions)
{
_keyPointInterpolationProvider = keyPointInterpolationProvider;
}
/// <summary>
/// Create a new collection of key points.
/// </summary>
/// <param name = "typeProvider">
/// The provider which gives information about the type, required to do interpolation between the key points.
/// </param>
protected AbstractKeyPointCollection(AbstractTypeInterpolationProvider <TValue, TMath> typeProvider)
{
TypeProvider = typeProvider;
}
/// <summary>
/// Create a new collection of key points with absolute values.
/// </summary>
/// <param name = "typeProvider">
/// The provider which gives information about the type, required to do interpolation between the key points.
/// </param>
/// <param name = "referenceKeyPoint">
/// A key point which is used to measure the distance to all other added key points.
/// Don't adjust this key point after adding it.
/// </param>
public AbsoluteKeyPointCollection(AbstractTypeInterpolationProvider <TValue, TMath> typeProvider, TValue referenceKeyPoint)
: base(typeProvider)
{
_referenceKeyPoint = referenceKeyPoint;
}