namespace IStation.Curve
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{
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/// <summary>
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/// 贝塞尔线
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/// </summary>
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public class BezierCurveHelper
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{
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/// <summary>
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/// 获取开放的贝塞尔曲线列表
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/// </summary>
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public static List<Bezier3> CreateOpenCurves(List<CurvePoint> points)
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{
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//http://wenku.baidu.com/link?url=9TGvGfedfkbskSWwfeO_iJJHvIzL0E_mE3wwVlWs1kEvvT9dHDQFdArhcdh8yuCK3pUbw2soJKs5qiQKlzhA885Tgtbu-Cdr1T37ANki_mS
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if (points == null || points.Count() < 4)
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return default;
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int iPointCout = points.Count();
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double a = 0.25;
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double b = 0.25;
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List<Bezier3> controlPoint = new List<Bezier3>();
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//生成4控制点，产生贝塞尔曲线
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for (int i = 0; i < iPointCout - 1; i++)
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{
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Bezier3 bezier = new Bezier3();
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bezier.Point0 = points[i];
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if (i == 0)
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{
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double x1 = points[i].X + a * (points[i + 1].X - points[i].X);
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double y1 = points[i].Y + a * (points[i + 1].Y - points[i].Y);
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bezier.Point1 = new CurvePoint(x1, y1);
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}
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else
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{
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double x1 = points[i].X + a * (points[i + 1].X - points[i - 1].X);
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double y1 = points[i].Y + a * (points[i + 1].Y - points[i - 1].Y);
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bezier.Point1 = new CurvePoint(x1, y1);
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}
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if (i == iPointCout - 2)
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{
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double x2 = points[i + 1].X - b * (points[i + 1].X - points[i].X);
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double y2 = points[i + 1].Y - b * (points[i + 1].Y - points[i].Y);
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bezier.Point2 = new CurvePoint(x2, y2);
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}
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else
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{
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double x2 = points[i + 1].X - b * (points[i + 2].X - points[i].X);
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double y2 = points[i + 1].Y - b * (points[i + 2].Y - points[i].Y);
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bezier.Point2 = new CurvePoint(x2, y2);
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}
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bezier.Point3 = points[i + 1];
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controlPoint.Add(bezier);
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}
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return controlPoint;
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}
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/// <summary>
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/// 获取封闭的贝塞尔曲线列表
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/// </summary>
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public static List<Bezier3> CreateCloseCurves(List<CurvePoint> points)
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{
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//http://blog.csdn.net/microchenhong/article/details/6316332
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int originCount = points.Count();
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//控制点收缩系数 ，经调试0.6较好
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float scale = 0.6f;
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var midpoints = new List<CurvePoint>();
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//生成中点
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for (int i = 0; i < originCount; i++)
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{
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int nexti = (i + 1) % originCount;
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double x = (points[i].X + points[nexti].X) / 2.0;
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double y = (points[i].Y + points[nexti].Y) / 2.0;
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midpoints.Add(new CurvePoint(x, y));
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}
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//平移中点
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var extrapoints = new List<CurvePoint>();//[2 * originCount];
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for (int i = 0; i < originCount * 2; i++)
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{
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extrapoints.Add(new CurvePoint(0, 0));
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}
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for (int i = 0; i < originCount; i++)
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{
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int nexti = (i + 1) % originCount;
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int backi = (i + originCount - 1) % originCount;
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var midinmid = new CurvePoint();
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midinmid.X = (midpoints[i].X + midpoints[backi].X) / 2.0;
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midinmid.Y = (midpoints[i].Y + midpoints[backi].Y) / 2.0;
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double offsetx = points[i].X - midinmid.X;
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double offsety = points[i].Y - midinmid.Y;
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int extraindex = 2 * i;
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extrapoints[extraindex].X = midpoints[backi].X + offsetx;
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extrapoints[extraindex].Y = midpoints[backi].Y + offsety;
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//朝 originPoint[i]方向收缩
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double addx = (extrapoints[extraindex].X - points[i].X) * scale;
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double addy = (extrapoints[extraindex].Y - points[i].Y) * scale;
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extrapoints[extraindex].X = points[i].X + addx;
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extrapoints[extraindex].Y = points[i].Y + addy;
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int extranexti = (extraindex + 1) % (2 * originCount);
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extrapoints[extranexti].X = midpoints[i].X + offsetx;
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extrapoints[extranexti].Y = midpoints[i].Y + offsety;
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//朝 originPoint[i]方向收缩
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addx = (extrapoints[extranexti].X - points[i].X) * scale;
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addy = (extrapoints[extranexti].Y - points[i].Y) * scale;
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extrapoints[extranexti].X = points[i].X + addx;
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extrapoints[extranexti].Y = points[i].Y + addy;
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}
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List<Bezier3> controlPoint = new List<Bezier3>();
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//生成4控制点，产生贝塞尔曲线
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for (int i = 0; i < originCount - 1; i++)
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{
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Bezier3 bezier = new Bezier3();
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bezier.Point0 = points[i];
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int extraindex = 2 * i;
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bezier.Point1 = extrapoints[extraindex + 1];
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int extranexti = (extraindex + 2) % (2 * originCount);
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bezier.Point2 = extrapoints[extranexti];
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int nexti = (i + 1) % originCount;
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bezier.Point3 = points[nexti];
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controlPoint.Add(bezier);
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}
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return controlPoint;
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}
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/// <summary>
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/// 通过 X 获取交点
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/// </summary>
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public static List<CurvePoint> GetSectPointsByX(List<Bezier3> allBeziers, double x)
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{
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if (allBeziers == null || allBeziers.Count() < 1)
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return null;
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var points_sect_list = new List<CurvePoint>();
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foreach (var bezeir in allBeziers)
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{
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//贝塞尔曲线与性能曲线有交点
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if ((x <= bezeir.Point0.X && x >= bezeir.Point3.X) || (x >= bezeir.Point0.X && x <= bezeir.Point3.X))
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{
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#region 贝塞尔曲线集合循环
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//第一次循环
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for (int i = 0; i < 10; i++)
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{
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var start0_uu = i * 0.1;
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var end0_uu = start0_uu + 0.1;
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var start0_p_x = bezeir.GetX(start0_uu);
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//var start0_p_y = bezeir.GetY(start0_uu);
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var end0_p_x = bezeir.GetX(end0_uu);
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//var end0_p_y = bezeir.GetY(end0_uu);
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if ((x <= start0_p_x && x >= end0_p_x) || (x >= start0_p_x && x <= end0_p_x))
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{
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//第二次循环
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for (int j = 0; j < 10; j++)
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{
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var start1_uu = start0_uu + j * 0.01;
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var end1_uu = start1_uu + 0.01;
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var start1_p_x = bezeir.GetX(start1_uu);
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//var start1_p_y = bezeir.GetY(start1_uu);
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var end1_p_x = bezeir.GetX(end1_uu);
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//var end1_p_y = bezeir.GetY(end1_uu);
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if ((x <= start1_p_x && x >= end1_p_x) || (x >= start1_p_x && x <= end1_p_x))
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{
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//第三次循环
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for (int k = 0; k < 10; k++)
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{
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var start2_uu = start1_uu + k * 0.001;
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var end2_uu = start2_uu + 0.001;
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var start2_p_x = bezeir.GetX(start2_uu);
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//var start2_p_y = bezeir.GetY(start2_uu);
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var end2_p_x = bezeir.GetX(end2_uu);
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//var end2_p_y = bezeir.GetY(end2_uu);
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if ((x <= start2_p_x && x >= end2_p_x) || (x >= start2_p_x && x <= end2_p_x))
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{
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var set_x = bezeir.GetX((start2_uu + end2_uu) / 2);
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var set_y = bezeir.GetY((start2_uu + end2_uu) / 2);
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var set_pt = new CurvePoint(set_x, set_y);
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points_sect_list.Add(set_pt);
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break;
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}
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}
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break;
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}
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}
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break;
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}
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}
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#endregion
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}
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}
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return points_sect_list;
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}
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/// <summary>
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/// 通过 Y 获取交点
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/// </summary>
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public static List<CurvePoint> GetSectPointsByY(List<Bezier3> allBeziers, double y)
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{
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if (allBeziers == null || allBeziers.Count() == 0)
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return null;
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var points_sect_list = new List<CurvePoint>();
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foreach (var bezeir in allBeziers)
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{
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//贝塞尔曲线与性能曲线有交点
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if ((y <= bezeir.Point0.Y && y >= bezeir.Point3.X) || (y >= bezeir.Point0.Y && y <= bezeir.Point3.Y))
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{
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#region 贝塞尔曲线集合循环
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//第一次循环
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for (int i = 0; i < 10; i++)
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{
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var start0_uu = i * 0.1;
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var end0_uu = start0_uu + 0.1;
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//var start0_p_x = bezeir.GetX(start0_uu);
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var start0_p_y = bezeir.GetY(start0_uu);
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//var end0_p_x = bezeir.GetX(end0_uu);
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var end0_p_y = bezeir.GetY(end0_uu);
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if ((y <= start0_p_y && y >= end0_p_y) || (y >= start0_p_y && y <= end0_p_y))
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{
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//第二次循环
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for (int j = 0; j < 10; j++)
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{
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var start1_uu = start0_uu + j * 0.01;
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var end1_uu = start1_uu + 0.01;
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// var start1_p_x = bezeir.GetX(start1_uu);
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var start1_p_y = bezeir.GetY(start1_uu);
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// var end1_p_x = bezeir.GetX(end1_uu);
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var end1_p_y = bezeir.GetY(end1_uu);
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if ((y <= start1_p_y && y >= end1_p_y) || (y >= start1_p_y && y <= end1_p_y))
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{
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//第三次循环
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for (int k = 0; k < 10; k++)
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{
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var start2_uu = start1_uu + k * 0.001;
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var end2_uu = start2_uu + 0.001;
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//var start2_p_x = bezeir.GetX(start2_uu);
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var start2_p_y = bezeir.GetY(start2_uu);
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// var end2_p_x = bezeir.GetX(end2_uu);
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var end2_p_y = bezeir.GetY(end2_uu);
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if ((y <= start2_p_y && y >= end2_p_y) || (y >= start2_p_y && y <= end2_p_y))
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{
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var set_x = bezeir.GetX((start2_uu + end2_uu) / 2);
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var set_y = bezeir.GetY((start2_uu + end2_uu) / 2);
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var set_pt = new CurvePoint(set_x, set_y);
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points_sect_list.Add(set_pt);
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break;
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}
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}
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break;
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}
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}
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break;
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}
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}
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#endregion
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}
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}
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return points_sect_list;
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}
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/// <summary>
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/// 通过 曲线表达式 获取交点
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/// </summary>
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public static List<CurvePoint> GetCrossPoints(List<Bezier3> allBeziers, CurveExpress curve)
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{
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if (allBeziers == null || allBeziers.Count() == 0)
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return null;
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var points_sect_list = new List<CurvePoint>();
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foreach (var bezeir in allBeziers)
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{
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var pt = bezeir.GetCrossPoint(curve);
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if (pt != null)
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points_sect_list.Add(pt);
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}
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return points_sect_list;
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}
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/// <summary>
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/// 通过 曲线表达式 获取交点
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/// </summary>
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public static List<CurvePoint> GetCrossPoints(List<CurvePoint> originPoint, CurveExpress curve)
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{
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if (originPoint == null)
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return null;
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if (originPoint.Count() <= 2)
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return null;
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if (originPoint.Count() == 3)
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{
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var b2 = new Bezier2(originPoint);
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var pt = b2.GetCrossPoint(curve);
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if (pt == null)
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return null;
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return new List<CurvePoint>() { pt };
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}
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var allBeziers = CreateOpenCurves(originPoint);
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var points_sect_list = new List<CurvePoint>();
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foreach (var bezeir in allBeziers)
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{
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var pt = bezeir.GetCrossPoint(curve);
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if (pt != null)
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points_sect_list.Add(pt);
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}
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return points_sect_list;
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}
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/// <summary>
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/// 获取距离
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/// </summary>
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public static double Distance(List<CurvePoint> curvePoints, CurvePoint point)
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{
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if (curvePoints == null || curvePoints.Count() == 0)
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return 0;
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if (curvePoints.Count() == 1)
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{
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var point1 = curvePoints.First();
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return Math.Sqrt((point1.X - point.X) * (point1.X - point.X) + (point1.Y - point.Y) * (point1.Y - point.Y));
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}
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if (curvePoints.Count() == 2)
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{
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var point1 = curvePoints.First();
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var point2 = curvePoints.Last();
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return CurveLineHelper.Distance(point1, point2, point);
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}
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if (curvePoints.Count() == 3)
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{
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var b2 = new Bezier2(curvePoints);
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return b2.Distance(point);
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}
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var allBeziers = CreateOpenCurves(curvePoints);
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double min_dis = double.MaxValue;
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foreach (var bezeir in allBeziers)
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{
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var dis = bezeir.Distance(point);
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min_dis = Math.Min(min_dis, dis);
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}
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return min_dis;
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}
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/// <summary>
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/// 获取距离(把曲线压缩到100*100的盒子里面 Boundary 求距离)
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/// </summary>
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public static double Distance(CurveBoundary boundary, List<CurvePoint> curve_real, CurvePoint point_real)
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{
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if (curve_real == null || curve_real.Count() == 0)
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return 0;
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if (boundary == null)
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return Distance(curve_real, point_real);
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double ratio_x = 0;
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if (boundary.MaxX == boundary.MinX)
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{
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ratio_x = 100 / (boundary.MaxX);
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}
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else
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{
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ratio_x = 100 / (boundary.MaxX - boundary.MinX);
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}
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double ratio_y = 0;
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if (boundary.MaxY == boundary.MinY)
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{
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ratio_y = 100 / (boundary.MaxY);
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}
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else
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{
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ratio_y = 100 / (boundary.MaxY - boundary.MinY);
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}
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var point_chart = new CurvePoint() { X = (point_real.X - boundary.MinX) * ratio_x, Y = (point_real.Y - boundary.MinY) * ratio_y };
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var curvePoints = new List<CurvePoint>();
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foreach (var pt in curve_real)
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{
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var point1 = new CurvePoint() { X = (pt.X - boundary.MinX) * ratio_x, Y = (pt.Y - boundary.MinY) * ratio_y };
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curvePoints.Add(point1);
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}
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if (curvePoints.Count() == 1)
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{
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var point1 = curvePoints.First();
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return Math.Sqrt((point1.X - point_chart.X) * (point1.X - point_chart.X) + (point1.Y - point_chart.Y) * (point1.Y - point_chart.Y));
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}
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if (curvePoints.Count() == 2)
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{
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var point1 = curvePoints.First();
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var point2 = curvePoints.Last();
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return CurveLineHelper.Distance(point1, point2, point_chart);
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}
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if (curvePoints.Count() == 3)
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{
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var b2 = new Bezier2(curvePoints);
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return b2.Distance(point_chart);
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}
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var allBeziers = CreateOpenCurves(curvePoints);
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double min_dis = double.MaxValue;
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foreach (var bezeir in allBeziers)
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{
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var dis = bezeir.Distance(point_chart);
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min_dis = Math.Min(min_dis, dis);
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}
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return min_dis;
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}
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/// <summary>
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/// 变成直线端
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/// </summary>
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/// <param name="allBeziers">贝塞尔曲线</param>
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/// <param name="pointNumber">贝赛尔曲线中间插入的点数量</param>
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/// <returns></returns>
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public static List<CurvePoint> GetApexPoints(List<Bezier3> allBeziers, int pointNumber)
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{
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var points_sect_list = new List<CurvePoint>();
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foreach (var bezeir in allBeziers)
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{
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for (int i = 0; i <= pointNumber; i++)
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{
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var uu = i * 1.0 / pointNumber;
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var p_x = bezeir.GetX(uu);
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var p_y = bezeir.GetY(uu);
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points_sect_list.Add(new CurvePoint(p_x, p_y));
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}
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}
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return points_sect_list;
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}
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/// <summary>
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/// 变成直线端(只针对开口的曲线)
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/// </summary>
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/// <param name="originPoint">贝塞尔曲线</param>
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/// <param name="pointNumber">贝赛尔曲线中间插入的点数量</param>
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/// <returns></returns>
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public static List<CurvePoint> GetApexPoints(List<CurvePoint> originPoint, int pointNumber)
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{
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if (originPoint == null)
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return null;
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if (originPoint.Count() <= 2)
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return null;
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if (originPoint.Count() == 3)
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{
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var b2 = new Bezier2(originPoint);
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return b2.GetApexPoints(pointNumber);
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}
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var allBeziers = CreateOpenCurves(originPoint);
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var points_sect_list = new List<CurvePoint>();
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foreach (var bezeir in allBeziers)
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{
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for (int i = 0; i <= pointNumber; i++)
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{
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var uu = i * 1.0 / pointNumber;
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var p_x = bezeir.GetX(uu);
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var p_y = bezeir.GetY(uu);
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points_sect_list.Add(new CurvePoint(p_x, p_y));
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}
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}
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return points_sect_list;
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}
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//三次贝塞尔曲线
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private double bezier3funcX(double uu, List<CurvePoint> controlP)
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{
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double part0 = controlP[0].X * uu * uu * uu;
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double part1 = 3 * controlP[1].X * uu * uu * (1 - uu);
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double part2 = 3 * controlP[2].X * uu * (1 - uu) * (1 - uu);
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double part3 = controlP[3].X * (1 - uu) * (1 - uu) * (1 - uu);
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return part0 + part1 + part2 + part3;
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}
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private double bezier3funcY(double uu, List<CurvePoint> controlP)
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{
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double part0 = controlP[0].Y * uu * uu * uu;
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double part1 = 3 * controlP[1].Y * uu * uu * (1 - uu);
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double part2 = 3 * controlP[2].Y * uu * (1 - uu) * (1 - uu);
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double part3 = controlP[3].Y * (1 - uu) * (1 - uu) * (1 - uu);
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return part0 + part1 + part2 + part3;
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}
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}
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}
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