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; } } #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(); } } /// <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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