用 Levy 飞行查找英国的巨石阵 

被称作 Levy 飞行用于最优化搜索，用其查找英国的巨石阵.

获取英国的多边形和巨石阵的坐标.

In[1]:=

X polygon = Entity["AdministrativeDivision", {"England", "UnitedKingdom"}][ EntityProperty["AdministrativeDivision", "Polygon"]]; stonehenge = Entity["Building", "Stonehenge"][ EntityProperty["Building", "Position"]];

假设可以从2公里的距离看见巨石阵，定义测试是否可以从给定位置看见巨石阵的谓词.

In[2]:=

X stonehengeVisibleQ[start_, {dist_, dir_}] := With[{m = Floor[dist/1000]}, Min[(GeoDistance[GeoPosition[#1], stonehenge] &) /@ GeoDestination[start, GeoDisplacement[{(Range[0, m] dist)/m, dir}]][[1]]] < Quantity[2, "Kilometers"]]

从大本钟开始，执行 Levy 行走直到巨石阵进入视野.

In[3]:=

X searchpath = {Entity["Building", "ClockTower"][ EntityProperty["Building", "Position"]]}; mr = DiscretizeGraphics[Polygon[Reverse /@ polygon[[1, 1, -1]]]]; While[ {d, \[Alpha]} = { 1000 RandomVariate[StableDistribution[1, 1, 1, 10, 2]], RandomReal[{0, 360}]}; gd = GeoDestination[Last[searchpath], GeoDisplacement[{d, \[Alpha]}]]; If[sd = SignedRegionDistance[mr, Reverse[First[ gd = GeoDestination[Last[searchpath], GeoDisplacement[{d, \[Alpha]}]] ]]] < 0, ! stonehengeVisibleQ[Last[searchpath], {d, \[Alpha]}], True], If[sd, AppendTo[searchpath, gd]]]

显示搜索路径.

In[4]:=

X GeoGraphics[{GeoStyling["StreetMap"], polygon , PointSize[Medium], RGBColor[1, 0, 0], Point[stonehenge], RGBColor[ 0.5, 0, 0.5], Thickness[Small], GeoPath[searchpath]}]

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