namespace IStation.Curve
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{
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/// <summary>
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/// 贝塞尔曲线类(三次)
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/// </summary>
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public class Bezier3
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{
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/// <summary>
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///
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/// </summary>
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public Bezier3() { }
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/// <summary>
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///
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/// </summary>
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public Bezier3(List<CurvePoint> points)
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{
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if (points == null || points.Count < 4)
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{
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throw new Exception("参数错误，无法解出三次贝塞尔曲线！");
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}
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this.Point0 = points[0];
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this.Point1 = points[1];
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this.Point2 = points[2];
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this.Point3 = points[3];
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}
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/// <summary>
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/// 开始点
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/// </summary>
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public CurvePoint Point0 { get; set; }
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/// <summary>
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/// 开始点的控制点
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/// </summary>
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public CurvePoint Point1 { get; set; }
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/// <summary>
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/// 结束点的控制点
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/// </summary>
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public CurvePoint Point2 { get; set; }
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/// <summary>
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/// 结束点
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/// </summary>
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public CurvePoint Point3 { get; set; }
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/// <summary>
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/// 获取 X 用于插值
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/// </summary>
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public double GetX(double uu)
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{
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double u0 = Point3.X * uu * uu * uu;
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double u1 = 3 * Point2.X * uu * uu * (1 - uu);
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double u2 = 3 * Point1.X * uu * (1 - uu) * (1 - uu);
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double u3 = Point0.X * (1 - uu) * (1 - uu) * (1 - uu);
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return u0 + u1 + u2 + u3;
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}
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/// <summary>
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/// 获取 Y 用于插值
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/// </summary>
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public double GetY(double uu)
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{
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double u0 = Point3.Y * uu * uu * uu;
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double u1 = 3 * Point2.Y * uu * uu * (1 - uu);
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double u2 = 3 * Point1.Y * uu * (1 - uu) * (1 - uu);
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double u3 = Point0.Y * (1 - uu) * (1 - uu) * (1 - uu);
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return u0 + u1 + u2 + u3;
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}
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/// <summary>
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/// 距离最近的点
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/// </summary>
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public CurvePoint GetClosePoint(CurvePoint ref_pt)
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{
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double boundary_min_x = Math.Min(Point0.X, Point3.X);
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double boundary_max_x = Math.Max(Point0.X, Point3.X);
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double boundary_min_y = Math.Min(Point0.Y, Point3.Y);
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double boundary_max_y = Math.Max(Point0.Y, Point3.Y);
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//由于流量扬程数量差别特别大, 所以假设他们在一个100*100的方格内,求距离
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double ratio_x = 0;
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if (boundary_max_x == boundary_min_x)
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{
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ratio_x = 100 / (boundary_max_x);
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}
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else
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{
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ratio_x = 100 / (boundary_max_x - boundary_min_x);
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}
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double ratio_y = 0;
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if (boundary_max_y == boundary_min_y)
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{
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ratio_y = 100 / (boundary_max_y);
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}
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else
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{
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ratio_y = 100 / (boundary_max_y - boundary_min_y);
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}
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double chart_ref_x = (ref_pt.X - boundary_min_x) * ratio_x;
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double chart_ref_y = (ref_pt.Y - boundary_min_y) * ratio_y;
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CurvePoint sect = null;
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double min_dist = double.MaxValue;
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for (double uu = 0; uu <= 1; uu = uu + 0.01)
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{
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double chart_x = (GetX(uu) - boundary_min_x) * ratio_x - chart_ref_x;
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double chart_y = (GetY(uu) - boundary_min_y) * ratio_y - chart_ref_y;
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double distance = chart_x * chart_x + chart_y * chart_y;
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if (distance < min_dist)
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{
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min_dist = distance;
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sect = new CurvePoint(GetX(uu), GetY(uu));
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}
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}
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return sect;
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}
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/// <summary>
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/// 求与曲线的交点 (可能有多个,但只取第一个点)
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/// </summary>
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public CurvePoint GetCrossPoint(CurveExpress curve)
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{
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if (curve == null)
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return null;
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//第一次迭代
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var index1 = GetCrossPointIndex_不迭代(curve, 0.2, 0, 5);
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if (index1 < 0)
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return null;
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//第二次迭代
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var index2 = GetCrossPointIndex_不迭代(curve, 0.02, 0.2 * index1, 10);
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if (index2 < 0)
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return null;
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double uu = 0.2 * index1 + 0.02 * index2;
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double x_bers = GetX(uu);
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double y_bers = FitHelper.GetFitPointY(curve, x_bers);
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return new CurvePoint(x_bers, y_bers);
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}
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//计算在第几个点相交(可能有多个,但只取第一个点):思路, 不断逼近,一个正数一个负数就表示有交点
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private int GetCrossPointIndex_不迭代(CurveExpress curve, double space, double start, int number)
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{
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double last_dis_y = 0;
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for (int i = 0; i <= number; i++)
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{
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double uu1 = start + space * i;
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double x_bers = GetX(uu1);
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double y_bers = GetY(uu1);
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double y_curve = FitHelper.GetFitPointY(curve, x_bers);
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double current_dis_y = y_bers - y_curve;
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if (uu1 == 0)
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{
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last_dis_y = current_dis_y;
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continue;
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}
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if ((current_dis_y > 0 && last_dis_y < 0) || (current_dis_y < 0 && last_dis_y > 0))
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{
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return i - 1;
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}
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last_dis_y = current_dis_y;
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}
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return -1;
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}
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/// <summary>
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/// 变成一条一条直线段
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/// </summary>
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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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public List<CurvePoint> GetApexPoints(int pointNumber)
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{
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var points_sect_list = new List<CurvePoint>();
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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 = this.GetX(uu);
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var p_y = this.GetY(uu);
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points_sect_list.Add(new CurvePoint(p_x, p_y));
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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 double Distance(CurvePoint point)
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{
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var point1 = GetClosePoint(point);
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return point.Distance(point1);
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}
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/// <summary>
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/// 通过 Y 判断是否在其中
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/// </summary>
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public bool IsInnerByY(double y)
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{
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if (y >= this.Point0.Y && y <= this.Point3.Y)
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return true;
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if (y >= this.Point3.Y && y <= this.Point0.Y)
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return true;
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return false;
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}
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}
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}
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