點到折線最短距離所在點 距離  折線起點 的累積距離

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using ESRI.ArcGIS.Geometry;
using RGeos.Geometry

namespace RGeos.Geometry
{
    public class CulmulateDistance
    {
        /// <summary>
        /// 點到折線最短距離處距離折線起點的累積距離
        /// </summary>
        /// <param name="P">任意一點</param>
        /// <param name="polyline">折線</param>
        /// <returns></returns>
        public static double CulmulateDist_Point_to_Polyline(IPoint P, IPolyline polyline)
        {
            ISegmentCollection segs = polyline as ISegmentCollection;
            double min = double.MaxValue;
            int segIndex = -1;//最短距離所在檔的索引
            for (int i = 0; i < segs.SegmentCount; i++)
            {
                //點到每條線段的最短距離
                double dis = Dist_Point_to_Segment(P, segs.get_Segment(i));
                if (dis < min)
                {
                    min = dis;
                    segIndex = i;//取出最小的一個
                }
            }
            double culmulateDis = 0;
            for (int i = 0; i < segs.SegmentCount; i++)
            {
                if (segIndex != i)
                {
                    culmulateDis += segs.get_Segment(i).Length;
                }
                else
                {
                    ISegment current = segs.get_Segment(i);
                    Vector3d v = new Vector3d();
                    v.X = current.ToPoint.X - current.FromPoint.X;
                    v.Y = current.ToPoint.Y - current.FromPoint.Y;

                    Vector3d w = new Vector3d();
                    w.X = P.X - current.FromPoint.X;
                    w.Y = P.Y - current.FromPoint.Y;

                    double c1 = dot(w, v);//投影長度
                    if (c1 <= 0)//這種情況最短距離在該線段的起點處
                    {
                        break;
                    }
                    double c2 = dot(v, v);
                    if (c2 <= c1)//這種情況最短距離在該線段的終點處                      
                    {
                        culmulateDis += Math.Sqrt(c2);
                        break;
                    }

                    double b = c1 / c2;
                    culmulateDis += Math.Sqrt(c1);
                    IPoint Pb = new PointClass();
                    Pb.X = current.FromPoint.X + b * v.X;
                    Pb.Y = current.FromPoint.Y + b * v.Y;
                    break;
                }
            }
            return culmulateDis;
        }

        public static IPoint GetCentrePoint(IPolygon polygon)
        {
            IArea pArea = polygon as IArea;
            IPoint pt = new PointClass();
            pt.X = pArea.Centroid.X;
            pt.Y = pArea.Centroid.Y;
            return pt;
        }

        public static double Dist_Point_to_Segment(IPoint P, ISegment S)
        {
            Vector3d v = new Vector3d();
            v.X = S.ToPoint.X - S.FromPoint.X;
            v.Y = S.ToPoint.Y - S.FromPoint.Y;

            Vector3d w = new Vector3d();
            w.X = P.X - S.FromPoint.X;
            w.Y = P.Y - S.FromPoint.Y;

            double c1 = dot(w, v);
            if (c1 <= 0)
                return d(P, S.FromPoint);

            double c2 = dot(v, v);
            if (c2 <= c1)
                return d(P, S.ToPoint);

            double b = c1 / c2;
            IPoint Pb = new PointClass();
            Pb.X = S.FromPoint.X + b * v.X;
            Pb.Y = S.FromPoint.Y + b * v.Y;
            return d(P, Pb);
        }
        /// <summary>
        /// 向量的模
        /// </summary>
        /// <param name="v"></param>
        /// <returns></returns>
        public static double norm(Vector3d v)
        {
            return Math.Sqrt(dot2(v, v));  // norm = length of vector
        }
        /// <summary>
        /// 2D數量積，點乘
        /// </summary>
        /// <param name="u"></param>
        /// <param name="v"></param>
        /// <returns></returns>
        public static double dot2(Vector3d u, Vector3d v)
        {
            return ((u).X * (v).X + (u).Y * (v).Y);
        }
        public static double dot(Vector3d u, Vector3d v)
        {
            return ((u).X * (v).X + (u).Y * (v).Y + (u).Z * (v).Z);
        }

        public static double d(IPoint P, IPoint P1)
        {
            return Math.Sqrt((P1.X - P.X) * (P1.X - P.X) + (P1.Y - P.Y) * (P1.Y - P.Y));
        }

        /// <param name="x">增量X</param>
        /// <param name="y">增量Y</param>
        /// <returns>象限角</returns>
        public static double GetQuadrantAngle(double x, double y)
        {
            double theta = Math.Atan(y / x);
            if (x > 0 && y == 0) return 0;
            if (x == 0 && y > 0) return Math.PI / 2;
            if (x < 0 && y == 0) return Math.PI;
            if (x == 0 && y < 0) return 3 * Math.PI / 2;

            if (x > 0 && y > 0) return theta;
            if (x > 0 && y < 0) return Math.PI * 2 + theta;
            if (x < 0 && y > 0) return theta + Math.PI;
            if (x < 0 && y < 0) return theta + Math.PI;
            return theta;
        }
    }
}