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

{

///

/// 样条曲线。每根样条曲线包含4个控制点

///

public class Spline

{

///

/// 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.

///

private static readonly int _samplePointCount = 20;

///

/// 在基数算法中的t

///

private static readonly float _tension = 0.0F;

#region 属性

private PointF _startControlPoint;

///

/// "Pk-1"点(起始控制点)

///

public PointF StartControlPoint

{

get

{

return this._startControlPoint;

}

set

{

this._startControlPoint = value;

}

}

private PointF _startPoint;

///

/// "Pk"点(起始点)

///

public PointF StartPoint

{

get

{

return this._startPoint;

}

set

{

this._startPoint = value;

}

}

private PointF _endPoint;

///

/// "Pk+1"点(结束点)

///

public PointF EndPoint

{

get

{

return this._endPoint;

}

set

{

this._endPoint = value;

}

}

private PointF _endControlPoint;

///

/// "Pk+2"点(结束控制点)

///

public PointF EndControlPoint

{

get

{

return this._endControlPoint;

}

set

{

this._endControlPoint = value;

}

}

private PointF[] _ctrlPoints;

///

/// 曲线点(控制点及模拟的样点)

///

public PointF[] CtrlPoints

{

get

{

return this._ctrlPoints;

}

}

private bool _isFirst = false;

///

/// 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。

///

public bool IsFirst

{

get

{

return this._isFirst;

}

set

{

this._isFirst = value;

}

}

#endregion

public 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();

}

}

///

///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。

///

/// 前一根样条曲线

/// 当前点

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();

}

}

}

///

/// 使用基数算法生成样点

///

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;

}

///

/// 绘制样条曲线

///

///

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

///

/// 生成曲线模拟点，该点在startPoint和endPoint之间

///

/// 介于0和1之间的变量

/// 起始点startPoint之前的控制点, 协助确定曲线的外观

/// 目标曲线的起始点startPoint,当u=0时，返回结果为起始点startPoint

/// 目标曲线的结束点endPoint, 当u=1时,返回结果为结束点endPoint

/// 在起结点startPoint之后的控制点, 协助确定曲线的外观

/// 返回介于startPoint和endPoint的点

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;

}

///

/// 计算轴坐标

///

///

///

///

///

///

///

///

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

///

/// 获取样条曲线上的点

///

///

///

///

public static List FetchPoints(PointF[] points)

{

if (points == null || points.Length <= 0)

{

return null;

}

List _splines = new List();

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 _points = new List();

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;

}

}

///

/// Graphics扩展

///

public static class GraphicsExtension

{

///

/// 绘制样条曲线

///

///

///

///

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 _splines = new List();

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。

转载请注明出处http://blog.csdn.net/xxdddail/article/details/47662983。