.NET 模拟&编辑平滑曲线 - ToB企服应用市场:ToB评测及商务社交产业平台

1 var geometryTest = new StreamGeometry();
2 using(var ctx = geometryTest.Open())
3 {
4 ctx.BeginFigure(_points[0], true, false);
5 if(keyPoints.Count % 2 == 0)
6 {
7 //绘制二阶贝塞尔函数，需要保证为偶数点
8 ctx.PolyQuadraticBezierTo(keyPoints, true, true);
9 }
10 else
11 {
12 //绘制二阶贝塞尔函数，需要保证为偶数点
13 keyPoints.Insert(0, keyPoints[0]);
14 ctx.PolyQuadraticBezierTo(keyPoints, true, true);
15 }
16 }

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1 public abstract void PolyQuadraticBezierTo(
2 IList<Point> points,
3 bool isStroked,
4 bool isSmoothJoin);
5
6 public abstract void PolyBezierTo(IList<Point> points, bool isStroked, bool isSmoothJoin);

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1 private const double Tolerance = 0.5;
2
3 /// <summary>
4 /// 获取拟合后的点集
5 /// </summary>
6 /// <param name="points"></param>
7 /// <returns></returns>
8 public static List<Point> GetFittingLinePoints(List<Point> points)
9 {
10 var orderedPoints = (from pt in points orderby pt.X select pt).ToList();
11 var secondDerivatives = SecondDerivativeHelper.GetSecondDerivatives(orderedPoints);
12 List<Point> polyLinePoints = PointFakeApproximationHelper.GetSplinePolyLineApproximation(orderedPoints, secondDerivatives, Tolerance);
13 return polyLinePoints;
14 }

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1 /// <summary>
2 /// 用折线逼近三次多项式并给出公差。
3 /// </summary>
4 /// <param name="leftPoint">三次多项式左点</param>
5 /// <param name="rightPoint">三次多项式右点</param>
6 /// <param name="secondDerivativeLeft">左点三次多项式二阶导数.</param>
7 /// <param name="secondDerivativeRight">右端三次多项式二阶导数.</param>
8 /// <param name="tolerance">公差，即样条到近似折线的最大距离。</param>
9 /// <returns>在给定公差的情况下逼近三次多项式的多边形点的列表。</returns>
10 private static Collection<Point> GetApproximation(Point leftPoint, Point rightPoint, double secondDerivativeLeft, double secondDerivativeRight, double tolerance)
11 {
12 // 左右俩点的X、Y轴值
13 double leftPointX = leftPoint.X, rightPointX = rightPoint.X;
14 double leftPointY = leftPoint.Y, rightPointY = rightPoint.Y;
15 // 次区间多项式系数
16 double a = (secondDerivativeRight - secondDerivativeLeft) / (6 * (rightPointX - leftPointX));
17 double b = (secondDerivativeLeft - 6 * a * leftPointX) / 2;
18 double c = (rightPointY - rightPointX * rightPointX * (a * rightPointX + b) - leftPointY + leftPointX * leftPointX * (a * leftPointX + b)) / (rightPointX - leftPointX);
19 double d = leftPointY - leftPointX * (leftPointX * (a * leftPointX + b) + c);
20
21 //如果a的值为0，则给a赋值double类型的最小正数
22 if(a == 0)
23 a = double.Epsilon;
24
25 //通过多项式与拆线的逼近，获取多边形点的列表
26 Collection<Point> points = CubicPolynomialPolylineApproximation.Approximate(new Polynomial(new double[] { d, c, b, a }), leftPointX, rightPointX, tolerance);
27 return points;
28 }

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