C#的绘图函数中有一个绘制样条曲线的函数DrawCurve，当只传入Pen和Point数组时，采用的是基数样条曲线绘制。如果只是绘制样条曲线，那这个函数已经满足了。但是项目中要求不但要绘制曲线，还要将曲线以方格的形式模拟来实现。为此，就必须知道样条曲线是如何绘制的，才有办法知道都有哪些点，然后再用格子来模拟。
起初，使用了很粗暴的方法，即使用DrawCurve在内存中绘制到Image中，然后从Image中取出黑白点，然后形成黑白点的矩阵，进而利用这些矩阵点对应到像素点来绘制方格。做了简单的实现，但效果不理想。原因有几个。
1.不断使用内存绘制到Image中需要消耗大量的内存。
2.利用像素点来采集矩阵的点时，难以确定一个采集的范围。
3.至少需要对像素进行X和Y的双重循环遍历才能达成，这样时间复杂度会随着X、Y的增加而不断加大。
后面找到了一份模拟实现，经过改造，初步达成了目的。来看看模拟实现的和DrawCurve的拟合效果图，见下图。
注：图中黑色部分使用DrawCurve来绘制，黑色线中间的白色部分采用的是模拟绘制。从测试的结果来看，符合程度比较理想。下面是实现的代码。
using System;using System.Collections.Generic;using System.Drawing;using System.Linq;using System.Text;namespace SplineTest{/// <summary>/// 样条曲线。每根样条曲线包含4个控制点/// </summary>public class Spline{/// <summary>/// 样点数。在点Pk和Pk+1之间，将会生成若干个样点。所以"u"将会从0.00F增长到0.05F./// </summary>private static readonly int _samplePointCount = 20;/// <summary>/// 在基数算法中的t/// </summary>private static readonly float _tension = 0.0F;#region 属性private PointF _startControlPoint;/// <summary>/// "Pk-1"点(起始控制点)/// </summary>public PointF StartControlPoint{get{return this._startControlPoint;}set{this._startControlPoint = value;}}private PointF _startPoint;/// <summary>/// "Pk"点(起始点)/// </summary>public PointF StartPoint{get{return this._startPoint;}set{this._startPoint = value;}}private PointF _endPoint;/// <summary>/// "Pk+1"点(结束点)/// </summary>public PointF EndPoint{get{return this._endPoint;}set{this._endPoint = value;}}private PointF _endControlPoint;/// <summary>/// "Pk+2"点(结束控制点)/// </summary>public PointF EndControlPoint{get{return this._endControlPoint;}set{this._endControlPoint = value;}}private PointF[] _ctrlPoints;/// <summary>/// 曲线点(控制点及模拟的样点)/// </summary>public PointF[] CtrlPoints{get{return this._ctrlPoints;}}private bool _isFirst = false;/// <summary>/// 标识当前样条曲线是否是第一条，如果是m_startControlPoint 和 m_startPoint将会相同。/// 因为在Pk和Pk+1之间需要4个点来决定样条曲线，所以我们需要在Pk-1点前手动添加一个点。/// 这样我们才能在Pk-1和Pk+1之间绘制样条曲线。/// 同样的，，最后一根样条曲线的Pk+2点会与它的"Pk+1"点相同，/// 这样我们才能在Pk+1和Pk+2之间绘制样条曲线。/// </summary>public bool IsFirst{get{return this._isFirst;}set{this._isFirst = value;}}#endregionpublic Spline(){_startControlPoint = new PointF();_startPoint = new PointF();_endPoint = new PointF();_endControlPoint = new PointF();_ctrlPoints = new PointF[_samplePointCount + 1];for (int i = 0; i < _ctrlPoints.Length; i++){_ctrlPoints[i] = new PointF();}}/// <summary>///添加关节。将新控制点添加到控制点列表中，并更新前面的样条曲线。/// </summary>/// <param name="prevSpline">前一根样条曲线</param>/// <param name="currentPoint">当前点</param>public void AddJoint(Spline prevSpline, PointF currentPoint){//前一根样条曲线(prevSpline)为null，说明控制点列表中只有一个点，所以4个控制点样同。//当第2个及之后的控制点添加到控制点列表中时，那第1根样条曲线的Pk+1和Pk+2点需要更新if (null == prevSpline){this._startControlPoint = currentPoint;this._startPoint = currentPoint;this._endPoint = currentPoint;this._endControlPoint = currentPoint;this._isFirst = true;}else//前一根样条曲线不为null，所以更新前一根样条曲线的控制点列表，同时更新当前样条曲线的控制点列表。{//前一根样条曲线是第1根样条曲线，更新它的Pk+1和Pk+2点if (true == prevSpline._isFirst){this._startControlPoint = prevSpline.StartControlPoint;this._startPoint = prevSpline.StartPoint;this._endPoint = currentPoint;this._endControlPoint = currentPoint;GenerateSamplePoint();return;}else///前一根样条曲线不是第1根样条曲线，仅更新它的Pk+2点{prevSpline.EndControlPoint = currentPoint;prevSpline.GenerateSamplePoint();//模拟当前样条曲线的样点this._startControlPoint = prevSpline._startPoint;this._startPoint = prevSpline._endPoint;this._endPoint = currentPoint;this._endControlPoint = currentPoint;GenerateSamplePoint();}}}/// <summary>/// 使用基数算法生成样点/// </summary>public void GenerateSamplePoint(){PointF startControlPoint = this.StartControlPoint;PointF startPoint = this.StartPoint;PointF endPoint = this.EndPoint;PointF endControlPoint = this.EndControlPoint;float step = 1.0F / (float)_samplePointCount;float uValue = 0.00F;for (int i = 0; i < _samplePointCount; i++){PointF pointNew = GenerateSimulatePoint(uValue, startControlPoint, startPoint, endPoint, endControlPoint);this.CtrlPoints[i] = pointNew;uValue += step;}this.CtrlPoints[_ctrlPoints.Length – 1] = endPoint;}/// <summary>/// 绘制样条曲线/// </summary>/// <param name="g"></param>public void Draw(Graphics g, Pen pen){for (int i = 0; i < _ctrlPoints.Length – 1; i++){PointF lastPoint = _ctrlPoints[i];PointF nextPoint = _ctrlPoints[i + 1];g.DrawLine(pen, lastPoint, nextPoint);}}#region GenerateSimulatePoint/// <summary>/// 生成曲线模拟点，该点在startPoint和endPoint之间/// </summary>/// <param name="u">介于0和1之间的变量</param>/// <param name="startControlPoint">起始点startPoint之前的控制点, 协助确定曲线的外观</param>/// <param name="startPoint">目标曲线的起始点startPoint,当u=0时，返回结果为起始点startPoint</param>/// <param name="endPoint">目标曲线的结束点endPoint, 当u=1时,返回结果为结束点endPoint</param>/// <param name="endControlPoint">在起结点startPoint之后的控制点, 协助确定曲线的外观</param>/// <returns>返回介于startPoint和endPoint的点</returns>private PointF GenerateSimulatePoint(float u,PointF startControlPoint,PointF startPoint,PointF endPoint,PointF endControlPoint){float s = (1 – _tension) / 2;PointF resultPoint = new PointF();resultPoint.X = CalculateAxisCoordinate(startControlPoint.X, startPoint.X, endPoint.X, endControlPoint.X, s, u);resultPoint.Y = CalculateAxisCoordinate(startControlPoint.Y, startPoint.Y, endPoint.Y, endControlPoint.Y, s, u);return resultPoint;}/// <summary>/// 计算轴坐标/// </summary>/// <param name="a"></param>/// <param name="b"></param>/// <param name="c"></param>/// <param name="d"></param>/// <param name="s"></param>/// <param name="u"></param>/// <returns></returns>private float CalculateAxisCoordinate(float a, float b, float c, float d, float s, float u){float result = 0.0F;result = a * (2 * s * u * u – s * u * u * u – s * u)+ b * ((2 – s) * u * u * u + (s – 3) * u * u + 1)+ c * ((s – 2) * u * u * u + (3 – 2 * s) * u * u + s * u)+ d * (s * u * u * u – s * u * u);return result;}#endregion/// <summary>/// 获取样条曲线上的点/// </summary>/// <param name="g"></param>/// <param name="pen"></param>/// <param name="points"></param>public static List<PointF> FetchPoints(PointF[] points){if (points == null || points.Length <= 0){return null;}List<Spline> _splines = new List<Spline>();Spline splineNew = null;Spline lastNew = null;foreach (PointF nowPoint in points){if (null == _splines || 0 == _splines.Count){splineNew = new Spline();splineNew.AddJoint(null, nowPoint);_splines.Add(splineNew);}else{splineNew = new Spline();lastNew = _splines[_splines.Count – 1] as Spline;splineNew.AddJoint(lastNew, nowPoint);_splines.Add(splineNew);};}List<PointF> _points = new List<PointF>();foreach (Spline spline in _splines){if (spline.IsFirst){continue;}foreach (PointF point in spline.CtrlPoints){if (_points.Contains(point)){continue;}_points.Add(point);}}return _points;}}/// <summary>/// Graphics扩展/// </summary>public static class GraphicsExtension{/// <summary>/// 绘制样条曲线/// </summary>/// <param name="g"></param>/// <param name="pen"></param>/// <param name="points"></param>public static void DrawSpline(this Graphics g, Pen pen, PointF[] points){if (g == null){return;}if (pen == null){return;}if (points == null || points.Length <= 0){return;}List<Spline> _splines = new List<Spline>();Spline splineNew = null;Spline lastNew = null;foreach (PointF nowPoint in points){if (null == _splines || 0 == _splines.Count){splineNew = new Spline();splineNew.AddJoint(null, nowPoint);_splines.Add(splineNew);}else{splineNew = new Spline();lastNew = _splines[_splines.Count – 1];splineNew.AddJoint(lastNew, nowPoint);_splines.Add(splineNew);}}Spline spline = null;for (int i = 0; i < _splines.Count; i++){spline = _splines[i];if (spline.IsFirst){continue;}spline.Draw(g, pen);}}}}注:
1.Spline部分最核心的算法是CalculateAxisCoordinate，网上有很多类似的实现，但都不理想，这个是比较理想的一个。
2.为了便于在Graphics中直接调用，这里对Graphics增加了一个扩展方法DrawSpline，这样就可以像调用DrawCurve一样调用，即g.DrawSpline(pen,points).
3.在绘制出样条曲线后，还需要能得到其所模拟的点，于是在Spline中增加了一个FetchPoints的方法。
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一遍一遍的……你突然明白自己还活着，
