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);
}
private NormalIntervalPolynomialCurveElement GenerateCurve(PolynomialCurveParam curveParam)
{
Debug.Assert(curveParam.PolynomialCurveType == PolynomialCurveType.Lagrange, @"This interpolated method """"GenerateCurve"""" only supports Lagarange Polynomial Curve.");
double[,] coefficientsArray = new double[count, count];
double[,] constantArray = new double[count, 1];
double coef, x;
for (int i = 0; i < count; i++)
{
constantArray[i, 0] = curveParam[i].Y.AccurateValue;
coef = 1;
x = curveParam[i].X.AccurateValue;
for (int j = 0; j < count; j++)
{
coefficientsArray[i, j] = coef;
coef *= x;
}
}
LinearEquationSet equations = new LinearEquationSet(new Matrix(coefficientsArray), new Matrix(constantArray));
Matrix result = equations.AnswerMatrix;
List<DoubleExtension> coefs = new List<DoubleExtension>();
for (int i = 0; i < count; i++)
{
coefs.Add(new DoubleExtension(result[i, 0]));
}
return new NormalIntervalPolynomialCurveElement(coefs, count, new DataInterval(curveParam.PointList.LeftBorderPoint.X, curveParam.PointList.RightBorderPoint.X));
//OrderedCurvePointList pointList = param.PointList;
//List<NormalIntervalPolynomialCurveElement> polynomialCurve = new List<NormalIntervalPolynomialCurveElement>();
//List<DoubleExtension> coefficients = null;
//List<DoubleExtension> cutPoints = new List<DoubleExtension>();
//cutPoints.Add(pointList[0].X);
//for (int i = 2; i < pointList.Count; i = i + 2)
//{
// coefficients = MathExtension.CalculateQuadraticPolynomialCoefficients(pointList[i - 2], pointList[i - 1], pointList[i]);
// polynomialCurve.Add(new NormalIntervalPolynomialCurveElement(coefficients, 3, pointList[i - 2].X, pointList[i].X));
// cutPoints.Add(pointList[i].X);
//}
//return new PiecewiseIntervalPolynomialCurveElement(polynomialCurve, cutPoints);
}