public CubicSplineInterpolationCurve(ICurveParam curveParam)
{
if (canDrawCurve(curveParam))
{
canDraw = true;
this.curveParam = (CubicSplineInterpolationCurveParam)curveParam;
}
}
protected PiecewiseIntervalPolynomialCurveElement GenerateCurve(CubicSplineInterpolationCurveParam curveParam)
{
double[,] coefficientsArray = new double[curveParam.Count, curveParam.Count];
double[,] constantArray = new double[curveParam.Count, 1];
double uVal, dVal, val1, val2;
for (int i = 1; i < curveParam.Count - 1; i++)
{
uVal = (curveParam[i].X.AccurateValue - curveParam[i - 1].X.AccurateValue) / (curveParam[i + 1].X.AccurateValue - curveParam[i - 1].X.AccurateValue);
dVal = 6 / (curveParam[i + 1].X.AccurateValue - curveParam[i - 1].X.AccurateValue) * (
(curveParam[i + 1].Y.AccurateValue - curveParam[i].Y.AccurateValue) / (curveParam[i + 1].X.AccurateValue - curveParam[i].X.AccurateValue) -
(curveParam[i].Y.AccurateValue - curveParam[i - 1].Y.AccurateValue) / (curveParam[i].X.AccurateValue - curveParam[i - 1].X.AccurateValue)
);
coefficientsArray[i, i - 1] = uVal;
coefficientsArray[i, i] = 2;
coefficientsArray[i, i + 1] = 1 - uVal;
constantArray[i, 0] = dVal;
}
switch (curveParam.BorderConditionType)
{
case CSIBorderConditionType.First_Order_Derivative:
val1 = 6 / (curveParam[2].X.AccurateValue - curveParam[1].X.AccurateValue) * (
(curveParam[1].Y.AccurateValue - curveParam[0].Y.AccurateValue) / (curveParam[1].X.AccurateValue - curveParam[0].X.AccurateValue) -
curveParam.LeftBorderValue.AccurateValue
);
val2 = 6 / (curveParam[curveParam.Count - 1].X.AccurateValue - curveParam[curveParam.Count - 2].X.AccurateValue) * (
curveParam.RightBorderValue.AccurateValue -
(curveParam[curveParam.Count - 1].Y.AccurateValue - curveParam[curveParam.Count - 2].Y.AccurateValue) / (curveParam[curveParam.Count - 1].X.AccurateValue - curveParam[curveParam.Count - 2].X.AccurateValue)
);
coefficientsArray[0, 0] = 2;
coefficientsArray[0, 1] = 1;
coefficientsArray[curveParam.Count - 1, curveParam.Count - 2] = 1;
coefficientsArray[curveParam.Count - 1, curveParam.Count - 1] = 2;
constantArray[0, 0] = val1;
constantArray[curveParam.Count - 1, 0] = val2;
break;
case CSIBorderConditionType.Second_Order_Derivative:
coefficientsArray[0, 0] = 1;
coefficientsArray[curveParam.Count - 1, curveParam.Count - 1] = 1;
constantArray[0, 0] = curveParam.LeftBorderValue.AccurateValue;
constantArray[curveParam.Count - 1, 0] = curveParam.RightBorderValue.AccurateValue;
break;
case CSIBorderConditionType.Cyclicity:
val1 = curveParam[1].X.AccurateValue - curveParam[0].X.AccurateValue;
coefficientsArray[0, 0] = val1;
coefficientsArray[0, 1] = 2 * val1;
val1 = curveParam[curveParam.Count - 1].X.AccurateValue - curveParam[curveParam.Count - 2].X.AccurateValue;
coefficientsArray[0, curveParam.Count - 2] = val1;
coefficientsArray[0, curveParam.Count - 1] = 2 * val1;
coefficientsArray[curveParam.Count - 1, 0] = 1;
coefficientsArray[curveParam.Count - 1, curveParam.Count - 1] = -1;
val2 = 6 * (
(curveParam[1].Y.AccurateValue - curveParam[0].Y.AccurateValue) / (curveParam[1].X.AccurateValue - curveParam[0].X.AccurateValue) -
(curveParam[curveParam.Count - 1].Y.AccurateValue - curveParam[curveParam.Count - 2].Y.AccurateValue) / (curveParam[curveParam.Count - 1].X.AccurateValue - curveParam[curveParam.Count - 2].X.AccurateValue)
);
constantArray[0, 0] = val2;
break;
}
LinearEquationSet equations = new LinearEquationSet(new Matrix(coefficientsArray), new Matrix(constantArray));
Matrix result = equations.AnswerMatrix;
List<NormalIntervalPolynomialCurveElement> curves = new List<NormalIntervalPolynomialCurveElement>();
List<DoubleExtension> cutPoints = new List<DoubleExtension>();
cutPoints.Add(curveParam[0].X);
for (int i = 1; i < curveParam.Count; i++)
{
curves.Add(new NormalIntervalPolynomialCurveElement(result[i - 1, 0], result[i, 0], curveParam[i - 1], curveParam[i]));
cutPoints.Add(curveParam[i].X);
}
return new PiecewiseIntervalPolynomialCurveElement(curves, cutPoints);
}
public CubicSplineInterpolationInterpolatedData(CubicSplineInterpolationCurveParam curveParam)
{
this.curveParam = curveParam;
this.curve = GenerateCurve(curveParam);
}
public void DrawCSICurve(string curveName, int borderConditionType, string leftVal, string rightVal)
{
BaseDataPointList pointList = this.basePoints;
double left = 0, right = 0;
if (borderConditionType < 3)
{
if (!Double.TryParse(leftVal, out left) || !Double.TryParse(rightVal, out right))
{
throw new ArgumentException("The left or right border can't be recognized.");
}
}
CubicSplineInterpolationCurveParam curveParam = new CubicSplineInterpolationCurveParam(pointList.SortedPointList, (CSIBorderConditionType)borderConditionType, new DoubleExtension(left), new DoubleExtension(right));
CubicSplineInterpolationCurve curve = new CubicSplineInterpolationCurve(curveParam);
DrawLines(curveName, curve.sampleCurvePoints());
}
/// <summary>
///
/// </summary>
/// <param name="points">型值点</param>
/// <param name="curveType">边界条件类型</param>
/// <param name="val1"></param>
/// <param name="val2"></param>
/// <param name="val3"></param>
/// <param name="val4"></param>
public ParametricCubicSplineInterpolationCurveParam(List<DataPoint> points, PCSIBorderConditionType curveType, DoubleExtension val1, DoubleExtension val2, DoubleExtension val3, DoubleExtension val4)
{
DoubleExtension subValLeftX = DoubleExtension.ZERO, subValRightX = DoubleExtension.ZERO, subValLeftY = DoubleExtension.ZERO, subValRightY = DoubleExtension.ZERO;
CSIBorderConditionType subType = CSIBorderConditionType.First_Order_Derivative;
List<DataPoint> xPointList = new List<DataPoint>();
List<DataPoint> yPointList = new List<DataPoint>();
if (points.Count < 2)
throw new ArgumentException("At least two points are needed for PCSI Curve drawing.");
pointList = new NormalCurvePointList(points);
xPointList.Add(new DataPoint(DoubleExtension.ZERO, points[0].X));
yPointList.Add(new DataPoint(DoubleExtension.ZERO, points[0].Y));
DoubleExtension accumulatedChordLength = DoubleExtension.ZERO;
List<DoubleExtension> cutPoints = new List<DoubleExtension>();
cutPoints.Add(accumulatedChordLength);
for (int i = 1; i < points.Count; i++)
{
accumulatedChordLength += DataPoint.CalculateDistance(points[i - 1], points[i]);
cutPoints.Add(accumulatedChordLength);
xPointList.Add(new DataPoint(accumulatedChordLength, points[i].X));
yPointList.Add(new DataPoint(accumulatedChordLength, points[i].Y));
}
this.interval = new PiecewiseDataInterval(cutPoints);
switch (curveType)
{
case PCSIBorderConditionType.First_Order_Derivative:
subType = CSIBorderConditionType.First_Order_Derivative;
DoubleExtension arcLeft1 = new DoubleExtension(Math.Atan(val1.AccurateValue));
DoubleExtension arcRight1 = new DoubleExtension(Math.Atan(val2.AccurateValue));
subValLeftX = new DoubleExtension(Math.Cos(arcLeft1.AccurateValue));
subValLeftY = new DoubleExtension(Math.Sin(arcLeft1.AccurateValue));
subValRightX = new DoubleExtension(Math.Cos(arcRight1.AccurateValue));
subValRightY = new DoubleExtension(Math.Sin(arcRight1.AccurateValue));
//DataVector referenceArcLeft1 = new DataVector(points[0], points[1]);
//DataVector referenceArcRight1 = new DataVector(points[points.Count - 2], points[points.Count - 1]);
//bool flagLeft = referenceArcLeft.GetTheFlagForCloserArc(arcLeft);
//bool flagRight = referenceArcRight.GetTheFlagForCloserArc(arcRight);
//if (flagLeft)
//{
// subValLeftX = new DoubleExtension(Math.Cos(arcLeft.AccurateValue));
// subValLeftY = new DoubleExtension(Math.Sin(arcLeft.AccurateValue));
//}
//else
//{
// subValLeftX = new DoubleExtension(0 - Math.Cos(arcLeft.AccurateValue));;
// subValLeftY = new DoubleExtension(0 - Math.Sin(arcLeft.AccurateValue));
//}
//if (flagRight)
//{
// subValRightX = new DoubleExtension(Math.Cos(arcRight.AccurateValue));
// subValRightY = new DoubleExtension(Math.Sin(arcRight.AccurateValue));
//}
//else
//{
// subValRightX = new DoubleExtension(Math.Cos(0 - arcRight.AccurateValue));
// subValRightY = new DoubleExtension(Math.Sin(0 - arcRight.AccurateValue));
//}
break;
case PCSIBorderConditionType.Zero_Curvature:
subType = CSIBorderConditionType.Second_Order_Derivative;
break;
case PCSIBorderConditionType.Centre_of_Curvature:
if (val1 == points[0].X && val3 == points[0].Y)
{
throw new ArgumentException("The center of the left border's curvature is the same as the left border point.");
}
if (val2 == points[points.Count - 1].X && val4 == points[points.Count - 1].Y)
{
throw new ArgumentException("The center of the right border's curvature is the same as the right border point.");
}
//
// Second_Order_Derivative
//
//subType = CSIBorderConditionType.Second_Order_Derivative;
//DoubleExtension denominator1 = new DoubleExtension(Math.Pow(val1.AccurateValue - points[0].X.AccurateValue, 2) + Math.Pow(val3.AccurateValue - points[0].Y.AccurateValue, 2));
//DoubleExtension denominator2 = new DoubleExtension(Math.Pow(val2.AccurateValue - points[points.Count - 1].X.AccurateValue, 2) + Math.Pow(val4.AccurateValue - points[points.Count - 1].Y.AccurateValue, 2));
//subValLeftX = (val1 - points[0].X) / denominator1;
//subValLeftY = (val3 - points[0].Y) / denominator1;
//subValRightX = (val2 - points[points.Count - 1].X) / denominator2;
//subValRightY = (val4 - points[points.Count - 1].Y) / denominator2;
//
// First_Order_Derivative
//
subType = CSIBorderConditionType.First_Order_Derivative;
DoubleExtension arcLeft2 = new DoubleExtension(Math.Atan2(val3.AccurateValue - points[0].Y.AccurateValue, val1.AccurateValue - points[0].X.AccurateValue) + Math.PI / 2.0);
DoubleExtension arcRight2 = new DoubleExtension(Math.Atan2(val4.AccurateValue - points[points.Count - 1].Y.AccurateValue, val2.AccurateValue - points[points.Count - 1].X.AccurateValue) + Math.PI / 2.0);
subValLeftX = new DoubleExtension(Math.Cos(arcLeft2.AccurateValue));
subValLeftY = new DoubleExtension(Math.Sin(arcLeft2.AccurateValue));
subValRightX = new DoubleExtension(Math.Cos(arcRight2.AccurateValue));
subValRightY = new DoubleExtension(Math.Sin(arcRight2.AccurateValue));
break;
}
xList = new CubicSplineInterpolationCurveParam(xPointList, subType, subValLeftX, subValRightX);
yList = new CubicSplineInterpolationCurveParam(yPointList, subType, subValLeftY, subValRightY);
}