A*寻路算法

作者：追风剑情发布于：2016-8-13 11:36 分类：Algorithms

一、定义地图文件格式

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;

namespace MapEditor.Map
{
    /// <summary>
    /// 地图文件
    /// </summary>
    public class MapFile
    {
        public MapHeader header = new MapHeader();
        public Grid[] grids;
    }

    /// <summary>
    /// 地图文件头信息
    /// </summary>
    public class MapHeader
    {
        public int version = 1;
        public int type = 1;
        public string name = "未命名";
        public int width = 1080;
        public int height = 960;
        public int tileWidth = 64;
        public int tileHeight = 32;
        //2.5D行数和列数
        public int rows = 10;
        public int cols = 10;
        //2D行数和列数
        public int rows2d = 10;
        public int cols2d = 10;
        public string background = "";
    }

    /// <summary>
    /// 网格
    /// </summary>
    public class Grid
    {
        //网格索引
        public int index = 0;
        //网格像素坐标
        public int px = 0;
        public int py = 0;
        //网格坐标
        public int gx = 0;
        public int gy = 0;
        //权值
        public int weight = 0;
        //贴图名称
        public string tile = "";

        #region 以下字段用于A*寻路
        //上一个节点索引
        public int prev = 0;
        //起点到当前点的移动代价值
        public int g = 0;
        //当前点到终点的移动代价值
        public int h = 0;
        //起点到终点的移动代价值
        public int f = 0;
        #endregion
    }
}

二、写个像素坐标与2.5D网格坐标相互转换的工具类

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Drawing;

namespace MapEditor.Map
{
    /// <summary>
    /// 2.5D地图坐标转换工具类
    /// </summary>
    public class CoordinateUtil
    {
        /// <summary>
        /// 像素坐标转网格坐标
        /// </summary>
        /// <param name="tileWidth">网格宽度</param>
        /// <param name="tileHeight">网格高度</param>
        /// <param name="px">像素x坐标</param>
        /// <param name="py">像素y坐标</param>
        /// <returns></returns>
        public static Point GetCellPoint(int tileWidth, int tileHeight, int px, int py)
		{
			int xtile = 0;	//网格的x坐标
			int ytile = 0;	//网格的y坐标
	
	        int cx, cy, rx, ry;
	        cx = (int)(px / tileWidth) * tileWidth + tileWidth/2;	//计算出当前X所在的以tileWidth为宽的矩形的中心的X坐标
	        cy = (int)(py / tileHeight) * tileHeight + tileHeight/2;//计算出当前Y所在的以tileHeight为高的矩形的中心的Y坐标
	
	        rx = (px - cx) * tileHeight/2;
	        ry = (py - cy) * tileWidth/2;
	
	        if (Math.Abs(rx)+Math.Abs(ry) <= tileWidth * tileHeight/4)//<=上三角面积
	        {
				xtile = (int)(px / tileWidth);
				ytile = (int)(py / tileHeight) * 2;
	        }
	        else
	        {//偶行
				px = px - tileWidth/2;
				xtile = (int)(px / tileWidth) + 1;
				
				py = py - tileHeight/2;
				ytile = (int)(py / tileHeight) * 2 + 1;
			}

			return new Point(xtile - (ytile&1), ytile);
		}

        /// <summary>
        /// 网格坐标转像素坐标
        /// </summary>
        /// <param name="tileWidth">网格宽度</param>
        /// <param name="tileHeight">网格高度</param>
        /// <param name="tx">网格x坐标</param>
        /// <param name="ty">网格y坐标</param>
        /// <returns></returns>
        public static Point GetPixelPoint(int tileWidth, int tileHeight, int tx, int ty)
		{
			//偶数行tile中心
			int tileCenter = (tx * tileWidth) + tileWidth/2;
			// x象素  如果为奇数行加半个宽
			int xPixel = tileCenter + (ty&1) * tileWidth/2;
			// y象素
			int yPixel = (ty + 1) * tileHeight/2;
			
			return new Point(xPixel, yPixel);
		}

        /// <summary>
        /// 根据网格索引取得网格坐标
        /// </summary>
        /// <param name="gindex">网格索引</param>
        /// <param name="cols">网格列数</param>
        /// <param name="rows">网格行数</param>
		public static Point GetICellPoint( int gindex, int cols )
		{
			int xtile = gindex % cols;
			int ytile = gindex / cols;
			
			return new Point(xtile, ytile);
		}
		
		/// <summary>
		/// 根据网格索引取得象素坐标
		/// </summary>
		/// <param name="gindex">网格索引</param>
        /// <param name="cols">网格列数</param>
        /// <param name="rows">网格行数</param>
        /// <param name="tileWidth">网格宽度</param>
        /// <param name="tileHeight">网格高度</param>
		/// <returns></returns>
		public static Point GetIPixelPoint( int gindex, int cols, int rows, int tileWidth, int tileHeight )
		{
			Point cellPoint = GetICellPoint(gindex, cols);
			Point pixelPoint = GetPixelPoint(tileWidth, tileHeight, cellPoint.X, cellPoint.Y);
			
			return pixelPoint;
		}
		
		/// <summary>
        /// 根据网格坐标取得网格索引
		/// </summary>
		/// <param name="gx">网格x坐标</param>
		/// <param name="gy">网格y坐标</param>
		/// <param name="cols">网格列数</param>
		/// <returns></returns>
		public static int GetCellIndex( int gx, int gy, int cols )
		{
			int gindex = gy * cols + gx;
			
			return gindex;
		}

        /// <summary>
        /// 根据像素坐标取得网格索引
        /// </summary>
        public static int GetIndexPixel(int px, int py, int tileWidth, int tileHeight, int cols)
        {
            Point gp = GetCellPoint(tileWidth, tileHeight, px, py);
            int index = GetCellIndex(gp.X, gp.Y, cols);
            return index;
        }
    }
}

三、A*算法实现

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Drawing;

namespace MapEditor.Map
{
    /// <summary>
    /// A*寻路
    /// </summary>
    public class AStar
    {
        //最大搜索步数
        public static int MAX_FIND_STEP = 5000;
        //开启列表
        HeapSort openList = new HeapSort();
        //关闭列表
        Dictionary<int, bool> closeList = new Dictionary<int, bool>();

        public List<Grid> Find(MapFile map, Grid start, Grid end)
        {
            Console.WriteLine("target index="+end.index);

            if (start.index == end.index)
            {
                start.prev = -1;
                return BackTrack(map, start);
            }

            List<Grid> path = null;
            int step = 0;

            openList.Clear();
            closeList.Clear();
            
            start.prev = -1;
            start.g = 0;
            Grid curGrid = start;
            openList.Push(curGrid);

            while (curGrid != null)
            {
                //(1)从开启列表中取出f值最小的节点
                curGrid = openList.Shift();
                Console.WriteLine("Shift index={0}, f={1}", curGrid.index, curGrid.f);
                //(2)当前节点的周围节点加入到开启列表
                Grid target = PushAroundOpenList(map, curGrid, end);
                if (null != target) {//是否搜索到目标格
                    path = BackTrack(map, target);
                    break;
                }
                //(3)当前节点加入到关闭列表
                if (!closeList.ContainsKey(curGrid.index))
                    closeList.Add(curGrid.index, true);

                step++;
                if (step > MAX_FIND_STEP)
                {
                    Console.WriteLine("停止搜索，超过最大搜索步数 MAX_FIND_STEP=" + MAX_FIND_STEP);
                    break;
                }
            }

            return path;
        }

        //把周围的网格加入开启列表
        Grid PushAroundOpenList(MapFile map, Grid cur, Grid end)
        {
            //计算出周围8向网格的索引号
            int cols = map.header.cols;
            int rows = map.header.rows;
            int maxIndex = cols * rows - 1;//地图网格最大索引号

            int index_u = cur.index - cols*2;//上
            int index_d = cur.index + cols*2;//下
            int index_l = cur.index - 1;//左
            int index_r = cur.index + 1;//右
            int index_lu=0, index_ld=0, index_ru=0, index_rd=0;
            if ((cur.gy & 1) > 0)//奇行
            {
                index_lu = cur.index - cols;//左上
                index_ld = cur.index + cols;//左下
                index_ru = cur.index - cols + 1;//右上
                index_rd = cur.index + cols + 1;//右下
            }
            else
            {
                index_lu = cur.index - cols - 1;//左上
                index_ld = cur.index + cols - 1;//左下
                index_ru = cur.index - cols;//右上
                index_rd = cur.index + cols;//右下
            }

            //判断周围节点中是否包含终点
            int[] around = new int[8] { index_u, index_d, index_l, index_r, index_lu, index_ld, index_ru, index_rd };
            for (int i = 0; i < around.Length; i++)
            {
                if (around[i] == end.index)
                {
                    end.prev = cur.index;
                    return end;
                }
            }

            //周围网格加入开启列表
            if (!closeList.ContainsKey(index_u) && index_u >= 0 && map.grids[index_u].weight == 0)
                CheckInOpenList(cur, map.grids[index_u], end);
            if (!closeList.ContainsKey(index_d) && index_d <= maxIndex && map.grids[index_d].weight == 0)
                CheckInOpenList(cur, map.grids[index_d], end);
            if (!closeList.ContainsKey(index_l) && index_l >= 0 && map.grids[index_l].weight == 0)
                CheckInOpenList(cur, map.grids[index_l], end);
            if (!closeList.ContainsKey(index_r) && index_r <= maxIndex && map.grids[index_r].weight == 0)
                CheckInOpenList(cur, map.grids[index_r], end);

            if (!closeList.ContainsKey(index_lu) && index_lu >= 0 && map.grids[index_lu].weight == 0)
                CheckInOpenList(cur, map.grids[index_lu], end);
            if (!closeList.ContainsKey(index_ld) && index_ld >= 0 && index_ld <= maxIndex && map.grids[index_ld].weight == 0)
                CheckInOpenList(cur, map.grids[index_ld], end);
            if (!closeList.ContainsKey(index_ru) && index_ru >= 0 && map.grids[index_ru].weight == 0)
                CheckInOpenList(cur, map.grids[index_ru], end);
            if (!closeList.ContainsKey(index_rd) && index_rd >= 0 && index_rd <= maxIndex && map.grids[index_rd].weight == 0)
                CheckInOpenList(cur, map.grids[index_rd], end);

            return null;
        }

        void CheckInOpenList(Grid cur, Grid ag, Grid end, int g=1)
        {
            if (openList.Contains(ag.index))
            {
                if (cur.g + g < ag.g)
                {
                    ag.g = cur.g + g;
                    ag.prev = cur.index;
                }
            }
            else
            {
                ag.prev = cur.index;
                ag.g = cur.g + g;
                ag.h = ChebyshevDistance(ag.px, ag.py, end.px, end.py);
                ag.f = ag.g + ag.h;
                openList.Push(ag);
            }
        }

        //路径回溯
        List<Grid> BackTrack(MapFile map, Grid end)
        {
            List<Grid> list = new List<Grid>();
            Grid cur = end;
            while(cur.prev != -1){
                Console.Write("{0}(px:{1},py:{2})->", cur.index, cur.px, cur.py);
                list.Add(cur);
                cur = map.grids[cur.prev];
            }
            list.Add(cur);

            if (list.Count > 2)
                SmoothPath(map, list);

            return list;
        }

        #region 距离评估函数
        //曼哈顿距离
        int ManhattanDistance(int x1, int y1, int x2, int y2)
        {
            return Math.Abs(x2 - x1) + Math.Abs(y2 - y1);
        }

        //欧氏几何平面距离(欧几里得距离)
        int EuclideanDistance(int x1, int y1, int x2, int y2)
        {
            return (int)Math.Sqrt((x2-x1)*(x2-x1)+(y2-y1)*(y2-y1));
        }

        int EuclideanSquareDistance(int x1, int y1, int x2, int y2)
        {
            return (x2 - x1) * (x2 - x1) + (y2 - y1) * (y2 - y1);
        }

        //切比雪夫距离
        int ChebyshevDistance(int x1, int y1, int x2, int y2)
        {
            return Math.Max(Math.Abs(x2-x1), Math.Abs(y2-y1));
        }
        #endregion

        #region 路径平滑处理
        void SmoothPath(MapFile map, List<Grid> path)
        {
            RemoveStraightLine(map, path);
            RemoveTurn(map, path);
        }

        //移除同线的节点
        void RemoveStraightLine(MapFile map, List<Grid> path)
        {
            int i = 0;
            int count;
            while (i < (count= path.Count) - 2)
            {
                for (int j = i + 1, k = i + 2; k < count; j++, k++)
                {
                    if (path[j].px - path[j - 1].px != path[k].px - path[j].px ||
                        path[j].py - path[j - 1].py != path[k].py - path[j].py)
                    {
                        int n = j - i - 1;
                        if(n > 0)
                            path.RemoveRange(i + 1, n);
                        break;
                    }
                }
                i++;
            }
        }

        //移除多余拐点
        void RemoveTurn(MapFile map, List<Grid> path)
        {
            int i = 0;
            int j = path.Count - 1;
            while (j > i + 1)
            {
                for (; j > 0; j--)
                {
                    if(j <= i + 1)
                        break;

                    if (VisualDetection(map, path[i], path[j]))
                    {
                        int n = j - i - 1;//j - (i + 1);
                        for (int k = 0; k < n; k++)
                            Console.WriteLine("移除拐点 {0}", path[i+1+k].index);
                        path.RemoveRange(i + 1, n);
                        break;
                    }
                }

                i++;
                j = path.Count - 1;
            }
        }

        //可视探测
        bool VisualDetection(MapFile map, Grid g1, Grid g2)
        {
            int d = map.header.tileHeight / 2;//探测距离增量
            int dline = (int)CalLineDistance(g1.px, g1.py, g2.px, g2.py);
            int dtimes = dline / d;//两拐点间探测次数
            int deltaX = (g2.px - g1.px) / dtimes;
            int deltaY = (g2.py - g1.py) / dtimes;
            int dx = g1.px, dy = g1.py;//当前探测点坐标

            Console.WriteLine("开始探测: ");
            while (dtimes > 0)
            {
                dx += deltaX;
                dy += deltaY;
                int index = CoordinateUtil.GetIndexPixel(dx, dy, map.header.tileWidth, map.header.tileHeight, map.header.cols);
                Grid g = map.grids[index];
                Console.Write(index + "->");
                if (g.weight > 0)
                    return false;
                dtimes--;
            }
            return true;
        }

        //计算两点间距离
        double CalLineDistance(int x1, int y1, int x2, int y2)
        {
            return Math.Sqrt((x2 - x1) * (x2 - x1) + (y2 - y1) * (y2 - y1));
        }
        #endregion
    }

    /// <summary>
    /// 二叉堆
    /// </summary>
    class HeapSort
    {
        List<Grid> R;
        //声明个字典用来快速检查元素是否已在开启列表中。
        Dictionary<int, bool> openList = new Dictionary<int, bool>();

        public HeapSort()
        {
            R = new List<Grid>();
            //堆排序不会用到0号元素，这里设个占位符。
            R.Add(null);
        }

        public void Clear()
        {
            openList.Clear();
            R.Clear();
            R.Add(null);
        }

        public bool Contains(int index)
        {
            return openList.ContainsKey(index);
        }

        //筛选方法
        private void SiftLess(List<Grid> R, int low, int high)
        {
            int i = low, j = 2 * i;
            Grid tmp = R[i];
            while (j <= high)
            {
                if (j < high && R[j].f > R[j + 1].f)
                {
                    j++;
                }
                if (tmp.f > R[j].f)
                {
                    R[i] = R[j];
                    i = j;
                    j = 2 * i;
                }
                else
                {
                    break;
                }
            }
            R[i] = tmp;
        }

        //添加元素
        public void Push(Grid value)
        {
            if (openList.ContainsKey(value.index))
                return;

            openList.Add(value.index, true);
            R.Add(value);
            int high = R.Count - 1;
            int i = high / 2;//最后一个元素的父节点索引
            int j = high;//最后一个元素索引
            Grid tmp;

            while (i >= 1)
            {
                if (R[i].f > R[j].f)
                {
                    tmp = R[i];
                    R[i] = R[j];
                    R[j] = tmp;
                    j = i;
                    i /= 2;
                }
                else
                {
                    break;
                }
            }
            Console.WriteLine("Push[1]="+R[1].f);
        }

        //移除根元素
        public Grid Shift()
        {
            int high = R.Count - 1;

            if (high < 1)
                return null;

            Grid r1;
            if (high <= 1)
            {
                r1 = R[1];
                R.RemoveAt(1);
                openList.Remove(r1.index);
                return r1;
            }

            r1 = R[1];
            R[1] = R[high];
            openList.Remove(r1.index);
            R.RemoveAt(high);
            SiftLess(R, 1, high - 1);

            return r1;
        }
    }
}

运行测试