Convex Package-graham Scanning method

Rt,graham scanning method to find convex hull is divided into 3 steps:

1. Find the smallest point in Y

2. With the smallest point o of Y as the origin, all remaining points are relative to the angle of O and are ordered from small to large at the polar angle.

3. For the sorted point set, with the stack, complete the Graham scan.

convexhull.py

#coding =utf-8import mathimport numpyimport Pylab as pl# draw original Def drawgraph (x, y): Pl.title ("The Convex Hull") Pl.xlabel ("x axis") Pl.ylabel ("Y axis") pl.plot (x, y, ' ro ') #画凸包def drawch (x, y): #pl. Plot (x,y1,label= ' DP ', linewidth=4,color= ' Red ') Pl.plot (x,y,color= ' Blue ', linewidth=2) Pl.plot (x[-1],y[-1],x[0],y[0]) lastx=[x[-1],x[0]] Lasty=[y[-1],y[0 ]] Pl.plot (lastx,lasty,color= ' Blue ', linewidth=2) #存点的矩阵, one point per line, column 0->x coordinates, column 1->y coordinates, column 2-> represents the Polar def matrix (rows, cols): cols=3 mat = [[0 for Col. Range (cols)] for row in range (rows)] return mat# return cross product def Crossmut (STACK,P3): P2=stack[-1] p1=stack[-2] vx,vy= (p2[0]-p1[0],p2[1]-p1[1]) wx,wy= (p3[0]-p1[0],p3[1]-p1[1]) retur N (vx*wy-vy*wx) #Graham扫描法O (NLOGN), Mat is a polar-sorted point set def grahamscan (MAT): #print Mat Points=len (MAT) #点数 "" "For K I N Range (points): print mat[k][0],mat[k][1],mat[k][2] "" "Stack=[" Stack.append ((mat[0][0],mat[0][1))) #pus H P0 Stack.append (mat[1][0],mAT[1][1])) #push P1 stack.append ((mat[2][0],mat[2][1)) #push P2 for I in Range (3,points): #print stack P3= (Mat[i][0],mat[i][1]) while Crossmut (STACK,P3) <0:stack.pop () stack.append (p3) return stack #ma Inmax_num = #最大点数x =100*numpy.random.random (max_num) #[0,100) y=100*numpy.random.random (max_num) drawGraph (x, Y) mat = Matrix (max_num,3) #最多能存50个点minn = 300for i in range (max_num): #存点集 mat[i][0],mat[i][1]=x[i],y[i] If y[i]<min N: # (x[tmp],y[tmp])-->y axis Minimum coordinate minn=y[i] tmp = ID = {} #利用字典的排序for i in range (max_num): #计算极角 if (ma T[I][0],MAT[I][1]) = = (X[tmp],y[tmp]): Mat[i][2]=0 else:mat[i][2]=math.atan2 ((Mat[i][1]-y[tmp]), (Mat[i][0]-x[tmp]) ) d[(mat[i][0],mat[i][1])]=mat[i][2]lst=sorted (D.items (), Key=lambda e:e[1]) #按极角由小到大排序for i in Range (max_num): #装排序后 Matrix ((x, y), eth0) =lst[i] Mat[i][0],mat[i][1],mat[i][2]=x,y,eth0stack=grahamscan (MAT) x,y=[],[]for Z in Stack:x.app End (Z[0]) y.append (z[1]) drawch (x, y) pl. Show () 

Ps:graham's complexity is O (NLOGN)

To find the furthest point of the plane can be converted to the first convex hull + rotation jam (it can be proved that the most distant point on the plane must be on the convex package.) ）

Convex Package-graham Scanning method