摘要：
如何求三角形的内心坐标来自：https://zhidao.baidu.com/question/158982463.html如何找到三角形的内部坐标来自：https://zhidao.baidu.com/question/158982463.html三角形的边长是a，b，c，顶点是a（x1，y1）b（x2，y2）c（x3，y3），并且给出了三角形的中心是角平分线的交点，并且到三条边的距离相等的证明。设：在三角形ABC中，三个顶点的坐标为：A（x1，y1），B（x2，y2），C（x3，y3）BC=A，CA=B，AB=C三角形的中心是M（X，Y），则有aMA+
三角形边长为a,b,c,顶点为A(x1,y1)B(x2,y2)C(x3,y3),并给出证明
内心是角平分线的交点，到三边距离相等.
设:在三角形ABC中,三顶点的坐标为：A(x1,y1),B(x2,y2),C(x3,y3) BC=a,CA=b,AB=c
内心为M （X，Y）则有aMA+bMB+cMC=0（三个向量）
MA=（X1-X，Y1-Y）
MB=(X2-X,Y2-Y)
MC=(X3-X,Y3-Y)
则：a(X1-X)+b(X2-X)+c(X3-X)=0，a(Y1-Y)+b(Y2-Y)+c(Y3-Y)=0
∴X=（aX1+bX2+cX3)/(a+b+c)，Y=（aY1+bY2+cY3)/(a+b+c)
∴M（（aX1+bX2+cX3)/(a+b+c)，（aY1+bY2+cY3)/(a+b+c)），真的很麻烦，有具体数的话，你可以求两条角分线，再求交点
三角形内切圆半径公式：r=2S/(a+b+c）
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import arcpy def FieldExists(TableName,FieldName): desc = arcpy.Describe(TableName) FieldName=FieldName.upper() for field in desc.fields: if field.Name.upper() ==FieldName: return True break return False #获得点的距离 def pointDistance(pt1,pt2): return math.sqrt((pt1.X-pt2.X)*(pt1.X-pt2.X)+(pt1.Y-pt2.Y)*(pt1.Y-pt2.Y)) #获得所有的点 def getallpoint(geo): parray = arcpy.Array() for part in geo: # Print the part number # print("Part {}:".format(partnum)) # Step through each vertex in the feature for pnt in part: if pnt == None: # If pnt is None, this represents an interior ring print("Interior Ring:") #n = n + 1 else: parray.add(pnt) return parray infc = arcpy.GetParameterAsText(0) outfc = arcpy.GetParameterAsText(1) arcpy.AddMessage("输入："+infc) arcpy.AddMessage("输出："+outfc) FieldName="X" if not FieldExists(infc,FieldName): arcpy.AddMessage("添加字段：" + FieldName) arcpy.management.AddField(infc,FieldName , "DOUBLE") FieldName="Y" if not FieldExists(infc,FieldName): arcpy.AddMessage("添加字段：" + FieldName) arcpy.management.AddField(infc,FieldName , "DOUBLE") FieldName="R" if not FieldExists(infc,FieldName): arcpy.AddMessage("添加字段："+FieldName) arcpy.management.AddField(infc,FieldName , "DOUBLE") with arcpy.da.UpdateCursor(infc, ["OID@", "SHAPE@","X","Y","R","SHAPE@AREA"]) as cursor: for row in cursor: parray=getallpoint(row[1]) pnum=len(parray) if pnum>4: arcpy.AddMessage("节点大于4"+str(pnum)+",FID="+str(row[0])) continue pt1=parray[0] pt2=parray[1] pt3=parray[2] x1=pt1.X y1=pt1.Y x2=pt2.X y2=pt2.Y x3=pt3.X y3=pt3.Y a=pointDistance(pt2,pt3) b=pointDistance(pt1,pt3) c=pointDistance(pt1,pt2) x=(a*x1+b*x2+c*x3)/(a+b+c) y=(a*y1+b*y2+c*y3)/(a+b+c) s=row[5] #(x1*(y2-y3)+x2*(y3-y1)+x3*(y1-y2))/2.0 r=2.0*s/(a+b+c) row[2]=x row[3] =y row[4] =r cursor.updateRow(row) out_layer="outyl" sr = arcpy.Describe(infc).spatialReference arcpy.MakeXYEventLayer_management(infc, "x", "y", out_layer, spatial_reference=sr) arcpy.Buffer_analysis(out_layer, outfc, buffer_distance_or_field="R")