protected override void calculateBasisFunction(ICurveParam curveParam)
{
if (curveParam.getCurveType() == InterpolationCurveType.nurbsCurve)
{
NurbsCurveParam param = (NurbsCurveParam)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.nurbsCurve, curveParam.getCurveType());
}
}
public void GraphPane_AxisChangeEvent(GraphPane pane)
{
if (sameStepForXY)
{
double realHeight = (zedGraphControl.GraphPane.YAxis.Scale.Max - zedGraphControl.GraphPane.YAxis.Scale.Min) * heightMultiplier;
double realWidth = zedGraphControl.GraphPane.XAxis.Scale.Max - zedGraphControl.GraphPane.XAxis.Scale.Min;
DoubleExtension multiplier, smallVal, bigVal;
if (realHeight > realWidth)
{
multiplier = new DoubleExtension(realHeight / realWidth);
MathExtension.MiddleBasedResize(new DoubleExtension(zedGraphControl.GraphPane.XAxis.Scale.Min), new DoubleExtension(zedGraphControl.GraphPane.XAxis.Scale.Max), multiplier, out smallVal, out bigVal);
zedGraphControl.GraphPane.XAxis.Scale.Min = smallVal.AccurateValue;
zedGraphControl.GraphPane.XAxis.Scale.Max = bigVal.AccurateValue;
zedGraphControl.GraphPane.XAxis.Scale.MajorStep = MathExtension.DynamicRound((bigVal.AccurateValue - smallVal.AccurateValue) / 6);
zedGraphControl.GraphPane.XAxis.Scale.MinorStep = MathExtension.DynamicRound((bigVal.AccurateValue - smallVal.AccurateValue) / 6) / 4;
}
else
{
multiplier = new DoubleExtension(realWidth / realHeight);
MathExtension.MiddleBasedResize(new DoubleExtension(zedGraphControl.GraphPane.YAxis.Scale.Min), new DoubleExtension(zedGraphControl.GraphPane.YAxis.Scale.Max), multiplier, out smallVal, out bigVal);
zedGraphControl.GraphPane.YAxis.Scale.Min = smallVal.AccurateValue;
zedGraphControl.GraphPane.YAxis.Scale.Max = bigVal.AccurateValue;
zedGraphControl.GraphPane.YAxis.Scale.MajorStep = MathExtension.DynamicRound((bigVal.AccurateValue - smallVal.AccurateValue) / 6);
zedGraphControl.GraphPane.YAxis.Scale.MinorStep = MathExtension.DynamicRound((bigVal.AccurateValue - smallVal.AccurateValue) / 6) / 4;
}
}
}
public CubicSplineInterpolationCurveParam(List<DataPoint> points, CSIBorderConditionType curveType, DoubleExtension val1, DoubleExtension val2)
{
pointList = new OrderedCurvePointList(points);
csiConditionType = curveType;
leftVal = val1;
rightVal = val2;
interval = new PiecewiseDataInterval(pointList);
}
public DataVector(DoubleExtension val1, DoubleExtension val2)
{
xDiff = val1;
yDiff = val2;
if (xDiff != 0 || yDiff != 0)
{
isZero = false;
}
}
public DataVector(DataPoint pt1, DataPoint pt2)
{
xDiff = pt2.X - pt1.X;
yDiff = pt2.Y - pt1.Y;
if (xDiff != 0 || yDiff != 0)
{
isZero = false;
}
}
public NormalIntervalPolynomialCurveElement(DoubleExtension val, DataInterval interval)
{
this.degree = 1;
this.coefficients = new List<DoubleExtension>();
this.coefficients.Add(val);
this.interval = interval;
if (val.EqualsToZero)
this.equalsToZero = true;
}
public override DoubleExtension calculate(DoubleExtension doubleExtension)
{
if (!interval.IsBetweenBordersCloseInterval(doubleExtension))
throw new ArgumentOutOfRangeException("doubleExtension", "The value given is out of borders of intervals. Value: " + doubleExtension.ApproximateString + ", Range: [" + interval.LeftBorder.ApproximateString + ", " + interval.RightBorder.ApproximateString + "].");
double result = 0;
double poweredX = 1;
for (int i = 0; i < degree; i++)
{
result += poweredX * fullCoefficents.GetArrayElement(i, 0).AccurateValue;
poweredX *= doubleExtension.AccurateValue - list[i].X.AccurateValue;
}
return new DoubleExtension(result);
}
public override DoubleExtension calculate(DoubleExtension doubleExtension)
{
int i = interval.IndexOfInterval(doubleExtension);
if (i > -1)
{
Debug.Assert(interval[i].IsBetweenBordersCloseInterval(doubleExtension), "Can't find proper interval for given value.");
return polynomialCurves[i].calculate(doubleExtension);
}
else
{
throw new ArgumentOutOfRangeException("doubleExtension", "This parameter is out of range.");
}
}
public override DataPoint calculatePoint(DoubleExtension doubleExtension)
{
Debug.Assert(doubleExtension <= interval.RightBorder && doubleExtension >= interval.LeftBorder, "The parameter is out of range for BezierCurve.");
double xVal = 0;
double yVal = 0;
double basisFunction = 1;
for (int i = 0; i < pointList.Count; i++)
{
basisFunction = calculateBasisFunction(doubleExtension, pointList.Count - 1, i).AccurateValue;
xVal += basisFunction * pointList[i].X.AccurateValue;
yVal += basisFunction * pointList[i].Y.AccurateValue;
}
return new DataPoint(xVal, yVal);
}
public override DataPoint calculatePoint(DoubleExtension doubleExtension)
{
Debug.Assert(interval.IsBetweenBordersCloseInterval(doubleExtension), "Invalid argument for NurbsParametricCurveElement.calculatePoint()");
DoubleExtension xVal = new DoubleExtension(0);
DoubleExtension yVal = new DoubleExtension(0);
DoubleExtension basisFunction;
DoubleExtension denominator = new DoubleExtension(0);
for (int i = 0; i < pointList.Count; i++)
{
basisFunction = basisFunctions[i].calculate(doubleExtension) * weights[i];
xVal += basisFunction * pointList[i].X;
yVal += basisFunction * pointList[i].Y;
denominator += basisFunction.AccurateValue;
}
return new DataPoint(xVal / denominator, yVal / denominator);
}
public DataVector(DoubleExtension arc, bool positive)
{
if (arc == Math.PI / 2.0)
{
xDiff = DoubleExtension.ZERO;
yDiff = DoubleExtension.POSITIVE_ONE;
}
else if (arc == Math.PI / (-2.0))
{
xDiff = DoubleExtension.ZERO;
yDiff = DoubleExtension.NEGATIVE_ONE;
}
else if (positive)
{
xDiff = DoubleExtension.POSITIVE_ONE;
yDiff = new DoubleExtension(Math.Tan(arc.AccurateValue));
}
else
{
xDiff = DoubleExtension.NEGATIVE_ONE;
yDiff = new DoubleExtension(0 - Math.Tan(arc.AccurateValue));
}
isZero = false;
}
public NormalIntervalPolynomialCurveElement DivideByNumber(DoubleExtension val)
{
if (EqualsToZero)
{
return new NormalIntervalPolynomialCurveElement(new DoubleExtension(0), Interval);
}
if (val.EqualsToZero)
{
throw new DivideByZeroException("The polynomial coefficients are divided by 0.");
}
List<DoubleExtension> newCoefficients = new List<DoubleExtension>();
for (int i = 0; i < coefficients.Count; i++)
{
newCoefficients.Add(coefficients[i] / val);
}
return new NormalIntervalPolynomialCurveElement(newCoefficients, newCoefficients.Count, Interval);
}
/// <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);
}
public PiecewiseIntervalPolynomialCurveElement DivideByNumber(DoubleExtension val)
{
List<NormalIntervalPolynomialCurveElement> curve = new List<NormalIntervalPolynomialCurveElement>();
NormalIntervalPolynomialCurveElement item = null;
for (int i = 0; i < Curves.Count; i++)
{
item = Curves[i].DivideByNumber(val);
curve.Add(item);
}
return new PiecewiseIntervalPolynomialCurveElement(curve, Interval);
}
public override DataPoint calculatePoint(DoubleExtension doubleExtension)
{
Debug.Assert(doubleExtension <= interval.RightBorder && doubleExtension >= interval.LeftBorder, "The parameter is out of range for ParametricCubicSplineInterpolationCurve.");
return new DataPoint(xCurve.calculate(doubleExtension), yCurve.calculate(doubleExtension));
}
private DoubleExtension calculateBasisFunction(DoubleExtension doubleExtension, int big, int small)
{
Debug.Assert(doubleExtension <= interval.RightBorder && doubleExtension >= interval.LeftBorder && big >= small, "Invalid argument for BezierCurve.calculateOne()");
return new DoubleExtension(combination[small] * Math.Pow(doubleExtension.AccurateValue, small) * Math.Pow(1 - doubleExtension.AccurateValue, big - small));
}
public abstract DoubleExtension calculate(DoubleExtension doubleExtension);
public static void MiddleBasedResize(DoubleExtension input1, DoubleExtension input2, DoubleExtension multiplier, out DoubleExtension output1, out DoubleExtension output2)
{
DoubleExtension middle = (input1 + input2) / 2;
output1 = middle + (input1 - middle) * multiplier;
output2 = middle + (input2 - middle) * multiplier;
}
public abstract DataPoint calculatePoint(DoubleExtension doubleExtension);
public int IndexOf(DoubleExtension item)
{
return sortedPointList.IndexOfKey(item);
}
public NormalIntervalPolynomialCurveElement(List<DoubleExtension> coefficients, int degree, DoubleExtension borderVal1, DoubleExtension borderVal2)
: this(coefficients, degree, new DataInterval(borderVal1, borderVal2))
{
}
public static NormalIntervalPolynomialCurveElement operator -(NormalIntervalPolynomialCurveElement c1, NormalIntervalPolynomialCurveElement c2)
{
if (c2.equalsToZero) return c1;
int degree = Math.Max(c1.Degree, c2.Degree);
int i = 0;
DoubleExtension val1, val2;
List<DoubleExtension> coefficients = new List<DoubleExtension>();
while (i++ < degree)
{
if (i < c1.Degree)
{
val1 = c1.coefficients[i];
}
else
{
val1 = new DoubleExtension(0);
}
if (i < c2.Degree)
{
val2 = c2.coefficients[i];
}
else
{
val2 = new DoubleExtension(0);
}
coefficients.Add(val1 - val2);
}
return new NormalIntervalPolynomialCurveElement(coefficients, degree, DataInterval.Intersection(c1.Interval, c2.Interval));
}
public override DoubleExtension calculate(DoubleExtension doubleExtension)
{
if (!interval.IsBetweenBordersCloseInterval(doubleExtension))
throw new ArgumentOutOfRangeException("doubleExtension", "The value given is out of borders of intervals. Value: " + doubleExtension.ApproximateString + ", Range: [" + interval.LeftBorder.ApproximateString + ", " + interval.RightBorder.ApproximateString + "].");
DoubleExtension result = new DoubleExtension(0);
DoubleExtension poweredX = new DoubleExtension(1);
for (int i = 0; i < degree; i++)
{
result += poweredX * coefficients[i];
poweredX *= doubleExtension.AccurateValue;
}
return result;
}
public PiecewiseIntervalPolynomialCurveElement MultiplyByLinear(DoubleExtension val1, DoubleExtension val0)
{
List<NormalIntervalPolynomialCurveElement> curve = new List<NormalIntervalPolynomialCurveElement>();
NormalIntervalPolynomialCurveElement item = null;
for (int i = 0; i < Curves.Count; i++)
{
item = Curves[i].MultiplyByLinear(val1, val0);
curve.Add(item);
}
return new PiecewiseIntervalPolynomialCurveElement(curve, Interval);
}
public NormalIntervalPolynomialCurveElement MultiplyByLinear(DoubleExtension val1, DoubleExtension val0)
{
if (EqualsToZero)
{
return new NormalIntervalPolynomialCurveElement(new DoubleExtension(0), Interval);
}
List<DoubleExtension> newCoefficients = new List<DoubleExtension>();
for (int i = 0; i < degree; i++)
{
newCoefficients.Add(coefficients[i] * val0);
}
if (!(coefficients[degree - 1] * val1).EqualsToZero)
{
newCoefficients.Add(coefficients[degree - 1] * val1);
}
if (degree > 1)
{
for (int i = 1; i < degree; i++)
{
newCoefficients[i] += coefficients[i - 1] * val1;
}
}
return new NormalIntervalPolynomialCurveElement(newCoefficients, newCoefficients.Count, Interval);
}
