/// <summary>
/// 要求的：N+1 = curveParam.PointList.Count;
/// 要求的： k = curveParam.Degree;
/// k = i
/// i = j
/// t - t[j] t[i + j + 1] - t
/// N[i, j](t) = ----------------- * N[i - 1, j](t) + ------------------------- * N[i - 1, j + 1](t)
/// t[i + j] - t[j] t[i + j + 1] - t[j + 1]
/// numerator11 * t + numerator10 numerator21 * t + numerator20
/// = ------------------------------- * N[i - 1, j](t) + ------------------------------- * N[i - 1, j + 1](t)
/// denominator10 denominator20
/// numerator11 = 1
/// numerator10 = -t[j]
/// numerator21 = -1
/// numerator20 = t[i + j + 1]
/// denominator10 = t[i + j] - t[j]
/// denominator20 = t[i + j + 1] - t[j + 1]
/// </summary>
/// <param name="curveParam"></param>
/// <returns></returns>
protected virtual void calculateBasisFunction(ICurveParam curveParam)
{
if (curveParam.getCurveType() == InterpolationCurveType.bsCurve)
{
BSplineCurveParam param = (BSplineCurveParam)curveParam;
Dynamic2DArray<PiecewiseIntervalPolynomialCurveElement> basisFunctions = new Dynamic2DArray<PiecewiseIntervalPolynomialCurveElement>();
int total = param.Degree + param.PointList.Count;
DoubleExtension denominator10, denominator20, numerator11, numerator10, numerator21, numerator20;
PiecewiseIntervalPolynomialCurveElement curve1, curve2;
numerator11 = new DoubleExtension(1);
numerator21 = new DoubleExtension(-1);
for (int i = 0; i < total; i++)
{
basisFunctions.SetArrayElement(0, i, new PiecewiseIntervalPolynomialCurveElement(i, param.Interval));
}
for (int i = 1; i <= param.Degree; i++)
{
for (int j = 0; j < total - i; j++)
{
denominator10 = param.Interval.CutPoints[i + j] - param.Interval.CutPoints[j];
denominator20 = param.Interval.CutPoints[i + j + 1] - param.Interval.CutPoints[j + 1];
numerator10 = 0 - param.Interval.CutPoints[j];
numerator20 = param.Interval.CutPoints[i + j + 1];
curve1 = basisFunctions.GetArrayElement(i - 1, j).DivideByNumber(denominator10).MultiplyByLinear(numerator11, numerator10);
curve2 = basisFunctions.GetArrayElement(i - 1, j + 1).DivideByNumber(denominator20).MultiplyByLinear(numerator21, numerator20);
basisFunctions.SetArrayElement(i, j, curve1 + curve2);
}
}
this.basisFunctions = basisFunctions[param.Degree];
}
else
{
throw new UnmatchedCurveParamTypeException(InterpolationCurveType.bsCurve, curveParam.getCurveType());
}
}
public BezierCurve(ICurveParam curveParam)
{
if (canDrawCurve(curveParam))
{
canDraw = true;
this.curveParam = (BezierCurveParam)curveParam;
}
}
public CubicSplineInterpolationCurve(ICurveParam curveParam)
{
if (canDrawCurve(curveParam))
{
canDraw = true;
this.curveParam = (CubicSplineInterpolationCurveParam)curveParam;
}
}
public PolynomialCurve(ICurveParam curveParam)
{
if (canDrawCurve(curveParam))
{
canDraw = true;
this.curveParam = (PolynomialCurveParam)curveParam;
}
}
public NurbsCurve(ICurveParam curveParam)
{
if (canDrawCurve(curveParam))
{
canDraw = true;
this.curveParam = (NurbsCurveParam)curveParam;
}
}
public BSplineCurve(ICurveParam curveParam)
{
if (canDrawCurve(curveParam))
{
canDraw = true;
this.curveParam = (BSplineCurveParam)curveParam;
}
}
protected virtual void InitialCurve(ICurveParam curveParam)
{
if (curveParam.getCurveType() == InterpolationCurveType.bsCurve)
{
BSplineCurveParam param = (BSplineCurveParam)curveParam;
this.curve = new BSplineParametricCurveElement(param);
}
else
{
throw new UnmatchedCurveParamTypeException(InterpolationCurveType.bsCurve, curveParam.getCurveType());
}
}
protected override void InitialCurve(ICurveParam curveParam)
{
if (curveParam.getCurveType() == InterpolationCurveType.nurbsCurve)
{
NurbsCurveParam param = (NurbsCurveParam)curveParam;
this.curve = new NurbsParametricCurveElement(param);
}
else
{
throw new UnmatchedCurveParamTypeException(InterpolationCurveType.nurbsCurve, curveParam.getCurveType());
}
}
private bool canDrawCurve(ICurveParam curveParam)
{
if (curveParam.getCurveType() == InterpolationCurveType.bezierCurve)
{
BezierCurveParam param = (BezierCurveParam)curveParam;
if (param.Count < 2)
throw new InvalidBasePointsException(InterpolationCurveType.bezierCurve, "At least two points are needed to draw Bezier Curve");
}
else
{
throw new UnmatchedCurveParamTypeException(InterpolationCurveType.bezierCurve, curveParam.getCurveType());
}
return true;
}
private bool canDrawCurve(ICurveParam curveParam)
{
if (curveParam.getCurveType() == InterpolationCurveType.csiCurve)
{
CubicSplineInterpolationCurveParam param = (CubicSplineInterpolationCurveParam)curveParam;
if (param.Count < 2)
throw new InvalidBasePointsException(InterpolationCurveType.csiCurve, "At least two points are needed to draw Cubic Spline Interpolation Curve");
if (!param.PointList.NoDuplicatedX())
throw new InvalidBasePointsException(InterpolationCurveType.csiCurve, "At least two points given have the same X value.");
}
else
{
throw new UnmatchedCurveParamTypeException(InterpolationCurveType.csiCurve, curveParam.getCurveType());
}
return true;
}
private bool canDrawCurve(ICurveParam curveParam)
{
if (curveParam.getCurveType() == InterpolationCurveType.nurbsCurve)
{
NurbsCurveParam param = (NurbsCurveParam)curveParam;
if (param.Count <= param.Degree)
throw new InvalidBasePointsException(InterpolationCurveType.nurbsCurve, (param.Degree - param.Count + 1).ToString() + " more data points are needed to draw NURBS Curve");
if (param.Interval.CutPoints[param.Degree] == param.Interval.CutPoints[param.PointList.Count])
throw new InvalidBasePointsException(InterpolationCurveType.bsCurve, "The degree is too high or the base points are insufficient or too many duplicated nodes are specified.");
}
else
{
throw new UnmatchedCurveParamTypeException(InterpolationCurveType.nurbsCurve, curveParam.getCurveType());
}
return true;
}