三角剖分算法和Alpha shapes 算法求解

有没有擅长这两个算法的，针对轨迹点求面积，轨迹点大概如图，求出面积并进行优化

img


#-*- coding:utf-8 -*-
import tkinter
from tkinter import filedialog
import csv
#根据两点坐标计算距离
def caldis(x1,y1,x2,y2):
    return ((x1-x2)**2+(y1-y2)**2)**0.5
#输入三角形三个顶点，计算外接圆圆心及半径
def calcenter(x1,y1,x2,y2,x3,y3):
    y1=-y1  #计算公式是根据平面直角坐标推算的，原点在左下角，但是计算机屏幕坐标原点在右上角，所以计算式y坐标取负
    y2=-y2
    y3=-y3
    if (y1 != y3 and y1 != y2 and y2 != y3): #判断是否有y坐标相等，即三角形某边斜率为0的情况，避免出现坟分母为0的错误
        if(((x3-x1)/(y3-y1))-((x2-x1)/(y2-y1)))==0:
            x2=x2+1
        x=(((y1+y3)/2)+((x1+x3)/2)*((x3-x1)/(y3-y1))-((y1+y2)/2)-((x1+x2)/2)*((x2-x1)/(y2-y1)))/(((x3-x1)/(y3-y1))-((x2-x1)/(y2-y1)))
        y=-((x3-x1)/(y3-y1))*x+((y1+y3)/2)+(((x1+x3)/2)*((x3-x1)/(y3-y1)))
        return (x, -y, caldis(x, y, x1, y1))
    elif (y1 == y3 and y1 != y2 and y2 != y3):#若存在斜率为0的边则计算可简化
        x=(x1+x3)/2
        y=-((x2-x1)/(y2-y1))*x+((y1+y2)/2)+((x2-x1)/(y2-y1))*((x1+x2)/2)
        return (x, -y, caldis(x, y, x1, y1)) #返回值为元组（圆心横坐标x，圆心纵坐标y，外接圆半径r），计算出来的y值要返回屏幕坐标所以再次取负
    elif (y1 != y3 and y1 == y2 and y2 != y3):
        x = (x1 + x2) / 2
        y = -((x3 - x1) / (y3 - y1)) * x + ((y1 + y3) / 2) + ((x3 - x1) / (y3 - y1)) * ((x1 + x3) / 2)
        return (x, -y, caldis(x, y, x1, y1))
    elif (y1 != y3 and y1 != y2 and y2 == y3):
        x = (x3 + x2) / 2
        y = -((x3 - x1) / (y3 - y1)) * x + ((y1 + y3) / 2) + ((x3 - x1) / (y3 - y1)) * ((x1 + x3) / 2)
        return (x, -y, caldis(x, y, x1, y1))
    else:
        return None
class getTIN: #定义窗口及操作类
    def __init__(self):
        self.path=str() #坐标文件路径
        self.pointlist=[] #存放所有点坐标的列表
        self.linelist=[] #存放线的列表，每条线用两个点号表示连线
        self.tk=tkinter.Tk() #定义主窗口
        self.tk.title('MyTIN')
        self.tk.geometry('1200x720')
        self.shengzhang=tkinter.Button(self.tk,text='生长算法',width=15,command=self.drawTIN_shengzhang)
        self.shengzhang.place(x=1050,y=100)  #定义按钮，关联到生长算法计算TIN的的函数
        self.readin=tkinter.Button(self.tk,text='读入坐标文件',width=15,command=self.getfile)
        self.readin.place(x=1050,y=50)
        self.can=tkinter.Canvas(self.tk,width=950,height=620,bg='white')
        self.can.place(x=50,y=50)
        self.tk.mainloop()
    def getfile(self):  #选择坐标文件（*.csv），从文件中读入坐标存入pointlist列表并在绘图区展示出来
        self.path=filedialog.askopenfilename()
        f=open(self.path,'r')
        fd=csv.reader(f)
        self.pointlist=list(fd)
        for i in range(0,len(self.pointlist)):
            self.can.create_oval(int(self.pointlist[i][0])-2,int(self.pointlist[i][1])-2,int(self.pointlist[i][0])+2,int(self.pointlist[i][1])+2,fill='black')
            self.can.create_text(int(self.pointlist[i][0])+7,int(self.pointlist[i][1])-7,text=str(i))
    def drawTIN_shengzhang(self):
        j = 1
        k = 0
        mindis = ((int(self.pointlist[0][0]) - int(self.pointlist[1][0])) ** 2 + (int(self.pointlist[0][1]) - int(self.pointlist[1][1])) ** 2) ** 0.5
        x = len(self.pointlist)
        for i in range(1, x):
            dis = ((int(self.pointlist[0][0]) - int(self.pointlist[i][0])) ** 2 + (int(self.pointlist[0][1]) - int(self.pointlist[i][1])) ** 2) ** 0.5
            if dis < mindis:
                mindis = dis
                j = i
        self.linelist.append((k,j)) #首先计算出距起始点（点号为0）距离最短的点，以这两点的连线作为基线开始生长
        self.shengzhangjixian(k,j)
    def drawTIN(self): #根据线文件在绘图区绘制出TIN
        for i in self.linelist:
            self.can.create_line(self.pointlist[i[0]][0], self.pointlist[i[0]][1], self.pointlist[i[1]][0], self.pointlist[i[1]][1])
    def shengzhangjixian(self,i,j): #根据某一基线开始生长的函数
        x = len(self.pointlist)
        for k in range(0,x): #遍历没一个点，判断是否与基线构成D三角形
            n = 0 #n用于统计外接圆内的点数
            if ((k,i) not in self.linelist) and ((i,k) not in self.linelist) and ((j,k) not in self.linelist) and ((k,j) not in self.linelist):
                for y in range(0,x): #遍历每一个点，判断
                    if y==i or y==j or y==k:
                        continue
                    if(calcenter(int(self.pointlist[i][0]),int(self.pointlist[i][1]),int(self.pointlist[j][0]),int(self.pointlist[j][1]),int(self.pointlist[k][0]),int(self.pointlist[k][1]))==None):
                        continue
                    else:
                        xyr=calcenter(int(self.pointlist[i][0]),int(self.pointlist[i][1]),int(self.pointlist[j][0]),int(self.pointlist[j][1]),int(self.pointlist[k][0]),int(self.pointlist[k][1]))
                    if caldis(xyr[0],xyr[1],int(self.pointlist[y][0]),int(self.pointlist[y][1])) < xyr[2]: #判断点是否在外接圆内
                        n=n+1
                    else:
                        continue
            else:continue
            if n == 0: #判断是否为D三角形
                self.linelist.append((k,i)) #将新生成的边的端点号加入线列表
                self.drawTIN() #调用绘制函数绘制TIN
                self.shengzhangjixian(k,i) #以生成的新边作为基线，迭代计算
                self.linelist.append((k,j))
                self.drawTIN()
                self.shengzhangjixian(k,j)
            else:continue
if __name__ == '__main__':
    MyTIN=getTIN()

三角剖分算法

img