中点法转化三次Bezier为二次Bezier,从C#到Flash

以前做一个项目，需要在Swf运行时绘制指定字体的汉字，而汉字字体文件太大，嵌入字体到Swf的做法并不理想，所以要寻找一条“捷径”来实现。

熟悉Flash的朋友都知道，在Flash中，曲线是用二次Bezier拟合的，而TureType字体是用三次Bezier描述的,所以需要实现三次Bezier到二次Bezier的拟合，又因为汉字图形的特殊性，必须实现高度近似的拟合，说白了，就是把拟合的图形叠放到原来的图形上，看看是不是很重合，呵呵~~

 

示意图：

 

 

 

 

C#实现：

 

/// <summary> /// 中点法转化三次Bezier为二次Bezier /// </summary> /// <param name="points">三次Bezier的四个点</param> /// <returns>二次Bezier</returns> private CurvePath[] caclCurvePoints(PointF[] points) { PointF p1 = points[0]; PointF c1 = points[1]; PointF c2 = points[2]; PointF p2 = points[3]; PointF anchor1, anchor2, anchor3, anchor4, anchor5; PointF control1, control2, control3, control4; anchor1 = p1; anchor5 = p2; PointF m1 = GetMidPoint(p1, c1); PointF m2 = GetMidPoint(c1, c2); PointF m3 = GetMidPoint(c2, p2); PointF m4 = GetMidPoint(m1, m2); PointF m5 = GetMidPoint(m2, m3); anchor3 = GetMidPoint(m4, m5); PointF m6 = GetMidPoint(p1, m1); PointF m7 = GetMidPoint(p2, m3); PointF m8 = GetMidPoint(m4, anchor3); PointF m9 = GetMidPoint(anchor3, m5); control1 = GetMidPoint(m6, m1); control2 = GetMidPoint(m4, m8); control3 = GetMidPoint(m9, m5); control4 = GetMidPoint(m3, m7); anchor2 = GetMidPoint(control1, control2); anchor4 = GetMidPoint(control3, control4); CurvePath[] paths=new CurvePath[4]; paths[0] = new CurvePath(control1, anchor2); paths[1] = new CurvePath(control2, anchor3); paths[2] = new CurvePath(control3, anchor4); paths[3] = new CurvePath(control4, anchor5); return paths; } private PointF GetMidPoint(PointF p1, PointF p2) { PointF midPoint = new PointF(0, 0); if (p1.X == p2.X) { midPoint.X = p1.X; } if (p1.X < p2.X) { midPoint.X = p1.X + (p2.X - p1.X) / 2; } if (p1.X > p2.X) { midPoint.X = p2.X + (p1.X - p2.X) / 2; } if (p1.Y == p2.Y) { midPoint.Y = p1.Y; } if (p1.Y < p2.Y) { midPoint.Y = p1.Y + (p2.Y - p1.Y) / 2; } if (p1.Y > p2.Y) { midPoint.Y = p2.Y + (p1.Y - p2.Y) / 2; } return midPoint; }

 

 

附：CurvePath类代码：

public class CurvePath { protected CurvePath() { } public CurvePath(PointF controlPoint,PointF endPoint) { this.type = PathType.Curve; this.pointNum = 0x2; this.points = new PointF[2] { controlPoint, endPoint }; } private PathType type; private byte pointNum; private PointF[] points; public PathType Type { get { return this.type; } } public byte PointNum { get { return this.pointNum; } } public int BytesLength { get { return 2+2*8; } } public System.Drawing.PointF[] Points { get { return this.points; } } public byte[] GetData { get { byte[] bytes = new byte[18]; bytes[0] = (byte)this.type; bytes[1] = this.pointNum; byte[] x1Bytes = BitConverter.GetBytes(this.points[0].X); x1Bytes.CopyTo(bytes, 2); byte[] y1Bytes = BitConverter.GetBytes(this.points[0].Y); x1Bytes.CopyTo(bytes, 6); byte[] x2Bytes = BitConverter.GetBytes(this.points[1].X); x2Bytes.CopyTo(bytes, 10); byte[] y2Bytes = BitConverter.GetBytes(this.points[1].Y); x2Bytes.CopyTo(bytes, 14); return bytes; } } }

 

最终生成的曲线路径数据，就可以发送到Swf中，绘制出来。

 

有关字体轮廓(Cubic Bezier)请参考.NET的System.Drawing.Drawing2D内容。