public override Vector2F GetTangent(float parameter)
{
int numberOfKeys = Count;
if (numberOfKeys == 0)
{
return(new Vector2F());
}
CurveKey2F firstKey = Items[0];
CurveKey2F lastKey = Items[numberOfKeys - 1];
float curveStart = firstKey.Parameter;
float curveEnd = lastKey.Parameter;
if (PreLoop == CurveLoopType.Constant && parameter < curveStart ||
PostLoop == CurveLoopType.Constant && parameter > curveEnd)
{
return(Vector2F.UnitX);
}
// Correct parameter.
float loopedParameter = LoopParameter(parameter);
ICurve <float, float> xSpline, ySpline;
// Note: Tangents from splines are relative to the spline parameter range [0,1]. We have
// to divide by the spline length measured in the curve parameter unit.
// Handle CurveLoopType.Linear:
// If parameter is outside: Use spline tangent. Exceptions are Bézier and Hermite
// were the exact tangent is given in the outer keys.
if (loopedParameter < curveStart)
{
Debug.Assert(PreLoop == CurveLoopType.Linear);
Vector2F tangent;
switch (firstKey.Interpolation)
{
case SplineInterpolation.Bezier:
tangent = (firstKey.Point - firstKey.TangentIn) * 3;
break;
case SplineInterpolation.Hermite:
tangent = firstKey.TangentIn;
break;
case SplineInterpolation.StepLeft:
case SplineInterpolation.StepCentered:
case SplineInterpolation.StepRight:
tangent = Vector2F.UnitX;
break;
default:
if (numberOfKeys > 1)
{
GetSplines(0, out xSpline, out ySpline);
tangent = new Vector2F(xSpline.GetTangent(0), ySpline.GetTangent(0));
((IRecyclable)xSpline).Recycle();
((IRecyclable)ySpline).Recycle();
}
else
{
tangent = Vector2F.UnitX;
}
break;
}
float splineLength = (numberOfKeys > 1) ? Items[1].Parameter - curveStart : 0;
return((splineLength > 0) ? tangent / splineLength : tangent);
}
else if (loopedParameter > curveEnd)
{
Debug.Assert(PostLoop == CurveLoopType.Linear);
Vector2F tangent;
switch (lastKey.Interpolation)
{
case SplineInterpolation.Bezier:
tangent = (lastKey.TangentOut - lastKey.Point) * 3;
break;
case SplineInterpolation.Hermite:
tangent = lastKey.TangentOut;
break;
case SplineInterpolation.StepLeft:
case SplineInterpolation.StepCentered:
case SplineInterpolation.StepRight:
tangent = Vector2F.UnitX;
break;
default:
if (numberOfKeys > 1)
{
GetSplines(numberOfKeys - 2, out xSpline, out ySpline);
tangent = new Vector2F(xSpline.GetTangent(1), ySpline.GetTangent(1));
((IRecyclable)xSpline).Recycle();
((IRecyclable)ySpline).Recycle();
}
else
{
tangent = Vector2F.UnitX;
}
break;
}
float splineLength = (numberOfKeys > 1) ? curveEnd - Items[numberOfKeys - 2].Parameter : 0;
return((splineLength > 0) ? tangent / splineLength : tangent);
}
else
{
if (numberOfKeys == 1)
{
// Degenerate curves with 1 key.
// Note: The following tangents are not scaled because we do not have enough information.
if (PostLoop == CurveLoopType.Linear)
{
// Pick outgoing tangent.
CurveKey2F p = firstKey;
if (p.Interpolation == SplineInterpolation.Bezier)
{
return((p.TangentOut - p.Point) * 3);
}
if (p.Interpolation == SplineInterpolation.Hermite)
{
return(p.TangentOut);
}
}
else if (PreLoop == CurveLoopType.Linear)
{
// Pick incoming tangent.
CurveKey2F p = firstKey;
if (p.Interpolation == SplineInterpolation.Bezier)
{
return((p.Point - p.TangentIn) * 3);
}
if (p.Interpolation == SplineInterpolation.Hermite)
{
return(p.TangentIn);
}
}
return(Vector2F.UnitX);
}
int index = GetKeyIndex(loopedParameter);
if (index == numberOfKeys - 1)
{
index--; // For the last key we take the previous spline.
}
Debug.Assert(0 <= index && index < numberOfKeys - 1);
CurveKey2F p2 = Items[index];
CurveKey2F p3 = Items[index + 1];
// Special case: Step interpolation.
if (p2.Interpolation == SplineInterpolation.StepLeft ||
p2.Interpolation == SplineInterpolation.StepCentered ||
p2.Interpolation == SplineInterpolation.StepRight)
{
return(Vector2F.UnitX);
}
float splineStart = p2.Parameter;
float splineEnd = p3.Parameter;
float splineLength = splineEnd - splineStart;
// Get splines for this segment.
GetSplines(index, out xSpline, out ySpline);
// Find correct parameter.
float relativeParameter = 0;
if (!Numeric.IsZero(splineLength))
{
if (Items[index].Interpolation == SplineInterpolation.Bezier ||
Items[index].Interpolation == SplineInterpolation.BSpline ||
Items[index].Interpolation == SplineInterpolation.CatmullRom ||
Items[index].Interpolation == SplineInterpolation.Hermite)
{
// x spline is not linearly proportional. Need root finding.
relativeParameter = CurveHelper.GetParameter(xSpline, loopedParameter, 20);
if (Numeric.IsNaN(relativeParameter) && Items[index].Interpolation == SplineInterpolation.BSpline)
{
// Search neighbor splines. BSpline do not normally go exactly from p2 to p3.
// Try left neighbor spline first.
if (index - 1 >= 0 && Items[index - 1].Interpolation == SplineInterpolation.BSpline)
{
((IRecyclable)xSpline).Recycle();
((IRecyclable)ySpline).Recycle();
GetSplines(index - 1, out xSpline, out ySpline);
relativeParameter = CurveHelper.GetParameter(xSpline, loopedParameter, 20);
}
// If we didn't get a solution search the right neighbor.
if (Numeric.IsNaN(relativeParameter) && index + 1 < numberOfKeys - 1 &&
Items[index + 1].Interpolation == SplineInterpolation.BSpline)
{
((IRecyclable)xSpline).Recycle();
((IRecyclable)ySpline).Recycle();
GetSplines(index + 1, out xSpline, out ySpline);
relativeParameter = CurveHelper.GetParameter(xSpline, loopedParameter, 20);
}
}
Debug.Assert(
Items[index].Interpolation == SplineInterpolation.BSpline
|| // BSplines do sometimes not include the boundary points, but for the rest we expect a solution.
Numeric.AreEqual(
xSpline.GetPoint(relativeParameter),
loopedParameter,
Math.Max(Math.Abs(splineLength) * Numeric.EpsilonF * 10, Numeric.EpsilonF)));
}
else
{
relativeParameter = (loopedParameter - splineStart) / splineLength;
}
}
float tangentX = xSpline.GetTangent(relativeParameter);
float tangentY = ySpline.GetTangent(relativeParameter);
if (IsInMirroredOscillation(parameter))
{
tangentY = -tangentY; // Mirrored direction.
}
((IRecyclable)xSpline).Recycle();
((IRecyclable)ySpline).Recycle();
return(new Vector2F(tangentX, tangentY) / splineLength);
}
}
public override Vector2F GetPoint(float parameter)
{
int numberOfKeys = Count;
if (numberOfKeys == 0)
{
return(new Vector2F(float.NaN, float.NaN));
}
float interpolatedX = parameter; // The x result must be equal to the parameter.
CurveKey2F firstKey = Items[0];
CurveKey2F lastKey = Items[numberOfKeys - 1];
float curveStart = firstKey.Parameter;
float curveEnd = lastKey.Parameter;
// Correct parameter.
float loopedParameter = LoopParameter(parameter);
ICurve <float, float> xSpline, ySpline;
#region ----- Handle Linear Pre- and PostLoops -----
// If parameter is outside: Use spline tangent. Exceptions are Bézier and Hermite
// were the exact tangent is given in the outer keys.
if (loopedParameter < curveStart)
{
Debug.Assert(PreLoop == CurveLoopType.Linear);
// Get tangent.
Vector2F tangent;
switch (firstKey.Interpolation)
{
case SplineInterpolation.Bezier:
tangent = (firstKey.Point - firstKey.TangentIn) * 3;
break;
case SplineInterpolation.Hermite:
tangent = firstKey.TangentIn;
break;
default:
{
if (numberOfKeys == 1)
{
return(new Vector2F(parameter, firstKey.Point.Y));
}
GetSplines(0, out xSpline, out ySpline);
tangent = new Vector2F(xSpline.GetTangent(0), ySpline.GetTangent(0));
((IRecyclable)xSpline).Recycle();
((IRecyclable)ySpline).Recycle();
break;
}
}
float k = 0;
if (Numeric.IsZero(tangent.X) == false)
{
k = tangent.Y / tangent.X;
}
return(new Vector2F(interpolatedX, firstKey.Point.Y + k * (loopedParameter - curveStart)));
}
else if (loopedParameter > curveEnd)
{
Debug.Assert(PostLoop == CurveLoopType.Linear);
// Get tangent.
Vector2F tangent;
switch (lastKey.Interpolation)
{
case SplineInterpolation.Bezier:
tangent = (lastKey.TangentOut - lastKey.Point) * 3;
break;
case SplineInterpolation.Hermite:
tangent = lastKey.TangentOut;
break;
default:
{
if (numberOfKeys == 1)
{
return(new Vector2F(parameter, firstKey.Point.Y));
}
GetSplines(numberOfKeys - 2, out xSpline, out ySpline);
tangent = new Vector2F(xSpline.GetTangent(1), ySpline.GetTangent(1));
((IRecyclable)xSpline).Recycle();
((IRecyclable)ySpline).Recycle();
break;
}
}
float k = 0;
if (Numeric.IsZero(tangent.X) == false)
{
k = tangent.Y / tangent.X;
}
return(new Vector2F(interpolatedX, lastKey.Point.Y + k * (loopedParameter - curveEnd)));
}
#endregion
// Special case: Only 1 point.
if (numberOfKeys == 1)
{
return(new Vector2F(parameter, firstKey.Point.Y));
}
float cycleOffset = GetCycleOffset(parameter);
// Special case: Parameter = parameter of last key.
if (loopedParameter == lastKey.Parameter &&
Items[numberOfKeys - 2].Interpolation != SplineInterpolation.BSpline) // BSplines need special handling because they do not go through key points.
{
return(new Vector2F(parameter, lastKey.Point.Y + cycleOffset));
}
// Get near keys.
int index = GetKeyIndex(loopedParameter);
// If the looped parameter == parameter of last key, we want to use the previous key.
if (index == numberOfKeys - 1)
{
index--;
}
Debug.Assert(0 <= index && index < numberOfKeys - 1);
CurveKey2F p2 = Items[index];
CurveKey2F p3 = Items[index + 1];
float splineStart = p2.Parameter;
float splineEnd = p3.Parameter;
float splineLength = (splineEnd - splineStart);
// Get splines for this segment.
GetSplines(index, out xSpline, out ySpline);
// Find correct parameter.
float relativeParameter = 0;
if (!Numeric.IsZero(splineLength))
{
if (Items[index].Interpolation == SplineInterpolation.Bezier ||
Items[index].Interpolation == SplineInterpolation.BSpline ||
Items[index].Interpolation == SplineInterpolation.CatmullRom ||
Items[index].Interpolation == SplineInterpolation.Hermite)
{
// x spline is not linearly proportional. Need root finding.
relativeParameter = CurveHelper.GetParameter(xSpline, loopedParameter, 20);
if (Numeric.IsNaN(relativeParameter) && Items[index].Interpolation == SplineInterpolation.BSpline)
{
// Search neighbor splines. BSpline do not normally go exactly from p2 to p3.
// Try left neighbor spline first.
if (index - 1 >= 0 && Items[index - 1].Interpolation == SplineInterpolation.BSpline)
{
((IRecyclable)xSpline).Recycle();
((IRecyclable)ySpline).Recycle();
GetSplines(index - 1, out xSpline, out ySpline);
relativeParameter = CurveHelper.GetParameter(xSpline, loopedParameter, 20);
}
// If we didn't get a solution search the right neighbor.
if (Numeric.IsNaN(relativeParameter) &&
index + 1 < numberOfKeys - 1 &&
Items[index + 1].Interpolation == SplineInterpolation.BSpline)
{
((IRecyclable)xSpline).Recycle();
((IRecyclable)ySpline).Recycle();
GetSplines(index + 1, out xSpline, out ySpline);
relativeParameter = CurveHelper.GetParameter(xSpline, loopedParameter, 20);
}
}
Debug.Assert(
Items[index].Interpolation == SplineInterpolation.BSpline || // BSplines do sometimes not include the boundary points, but for the rest we expect a solution.
Numeric.AreEqual(xSpline.GetPoint(relativeParameter), loopedParameter, Math.Max(Math.Abs(splineLength) * Numeric.EpsilonF * 10, Numeric.EpsilonF)));
}
else
{
relativeParameter = (loopedParameter - splineStart) / splineLength;
}
}
// Find y value for parameter.
float interpolatedY = ySpline.GetPoint(relativeParameter);
((IRecyclable)xSpline).Recycle();
((IRecyclable)ySpline).Recycle();
return(new Vector2F(interpolatedX, interpolatedY + cycleOffset));
}
/// <summary>
/// Gets the curve parameter for the given curve length (for length-parameterized splines).
/// </summary>
/// <param name="length">The length.</param>
/// <param name="maxNumberOfIterations">
/// The maximum number of iterations which are taken to compute the length.
/// </param>
/// <param name="tolerance">
/// The tolerance value. This method will return an approximation of the precise parameter. The
/// absolute error will be less than this tolerance.
/// </param>
/// <returns>The parameter at which the curve has the given length.</returns>
/// <exception cref="ArgumentOutOfRangeException">
/// <paramref name="tolerance"/> is negative or 0.
/// </exception>
/// <remarks>
/// <para>
/// This method assumes that the spline is length-parameterized; This means: The parameter of a
/// key is equal to the length of the spline at this key. If this is not the case,
/// <see cref="ParameterizeByLength"/> can be called to correct the key parameters
/// automatically.
/// </para>
/// <para>
/// Normally, the spline curve parameter is not linearly proportional to the length. Therefore,
/// if the point at a given curve length is required, this method can be used to compute the
/// curve parameter which will return the point for the given distance. The result of this
/// method can be used in <see cref="GetPoint"/>.
/// </para>
/// <para>
/// This method uses an iterative algorithm. The iterations end when the
/// <paramref name="maxNumberOfIterations"/> were performed, or when the
/// <paramref name="tolerance"/> criterion is met - whichever comes first.
/// </para>
/// </remarks>
public float GetParameterFromLength(float length, int maxNumberOfIterations, float tolerance)
{
if (tolerance <= 0)
{
throw new ArgumentOutOfRangeException("tolerance", "The tolerance must be greater than zero.");
}
int numberOfKeys = Count;
if (numberOfKeys == 0)
{
return(float.NaN);
}
// Handle CurveLoopType.Linear:
float curveStart = Items[0].Parameter;
float curveEnd = Items[numberOfKeys - 1].Parameter;
float curveLength = curveEnd - curveStart;
if (length < curveStart && PreLoop == CurveLoopType.Linear)
{
var tangent = GetTangent(curveStart);
return(curveStart - (curveStart - length) / tangent.Length);
}
if (length > curveEnd && PostLoop == CurveLoopType.Linear)
{
var tangent = GetTangent(curveEnd);
return(curveEnd + (length - curveEnd) / tangent.Length);
}
if (Numeric.IsZero(curveLength))
{
return(curveStart);
}
// Correct parameter.
float loopedLength = LoopParameter(length);
// Find key index for the parameter.
int index = GetKeyIndex(loopedLength);
if (index == numberOfKeys - 1)
{
index--; // For the last key we take the previous spline.
}
// Get spline.
var spline = GetSpline(index);
// Get relative length on the segment from length on whole curve.
float splineStart = Items[index].Parameter;
float splineEnd = Items[index + 1].Parameter;
float splineLength = (splineEnd - splineStart);
loopedLength = loopedLength - splineStart;
Debug.Assert(0 <= loopedLength && loopedLength <= splineLength);
float result = CurveHelper.GetParameter(spline, loopedLength, splineLength, maxNumberOfIterations, tolerance);
float localParameter = Items[index].Parameter + result * splineLength;
((IRecyclable)spline).Recycle();
spline = null;
// Handle looping: We return a parameter that is outside if the original length parameter is outside.
// Otherwise the returned parameter would correspond to the correct parameter on the path, but
// the total distance from the first key would wrong because some "loops" are missing.
if (length < curveStart && PreLoop != CurveLoopType.Constant)
{
int numberOfPeriods = (int)((length - curveEnd) / curveLength);
if (PreLoop == CurveLoopType.Oscillate && numberOfPeriods % 2 == -1)
{
return(curveStart + curveStart - localParameter + curveLength * (numberOfPeriods + 1)); // odd = mirrored
}
else
{
return(localParameter + numberOfPeriods * curveLength);
}
}
else if (length > curveEnd && PostLoop != CurveLoopType.Constant)
{
int numberOfPeriods = (int)((length - curveStart) / curveLength);
if (PostLoop == CurveLoopType.Oscillate && numberOfPeriods % 2 == 1)
{
return(curveEnd + curveEnd - localParameter + curveLength * (numberOfPeriods - 1)); // odd = mirrored
}
else
{
return(localParameter + numberOfPeriods * curveLength);
}
}
else
{
return(localParameter);
}
}