Simple Random Polygon Cutting Scheme

In the procedural processing, I hope to generate random polygons for a certain area, and then cut them into sub-polygons.
After various attempts, I found a simple solution through python, turtle, and pyclipper.

random polygon

Using python to directly generate random polygons, the algorithm principle: randomly split 360 degrees into various angles, and then connect them through random radii

def get_random_poly(num_vertices, bounds):
    radii=[]
    for i in range(num_vertices):
        radii.append(random.uniform(0.5,1.0))
    min_weight=1.0
    max_weight=10.0
    total_weight=0.0
    angle_weights=[]
    for i in range(num_vertices):
        angle_weights.append(random.uniform(min_weight,max_weight))
        total_weight+=angle_weights[-1]
    angles=[]
    for angle_weight in angle_weights:
        angles.append(angle_weight*2*math.pi/total_weight)
    rx=(bounds[1][0]-bounds[0][0])/2
    ry=(bounds[1][1]-bounds[0][1])/2
    cx=bounds[0][0]+rx
    cy=bounds[0][1]+ry
    points=[]
    theta=0.0
    for i in range(num_vertices):
        points.append((
            cx+rx*radii[i]*math.cos(theta),
            cy+ry*radii[i]*math.sin(theta)))
        theta+=angles[i]
    return points

generate rectangles for splitting polygons

Generated by center point and normal vector

def get_perpendicular_rect(c,pn,hl,hw):
    p0=(c[0]+pn[1]*hl,c[1]-pn[0]*hl)
    p1=(c[0]-pn[1]*hl,c[1]+pn[0]*hl)
    rect=[]
    rect.append((p0[0]+pn[0]*hw,p0[1]+pn[1]*hw))
    rect.append((p0[0]-pn[0]*hw,p0[1]-pn[1]*hw))
    rect.append((p1[0]-pn[0]*hw,p1[1]-pn[1]*hw))
    rect.append((p1[0]+pn[0]*hw,p1[1]+pn[1]*hw))
    return rect

split polygon

The pyclipper library is used to split any polygon. The algorithm prototype is Vatti clipping.
Here, the sub-polygon is divided recursively until the area is smaller than the specified value.

import turtle
import random
import math
import pyclipper
...
# 计算多边形中心点
def get_poly_center(poly):
    c=[0,0]
    for p in poly:
        c[0]+=p[0]
        c[1]+=p[1]
    c[0]/=len(poly)
    c[1]/=len(poly)
    return c
    
# 计算两点距离的sqrt
def get_distsq(p0,p1):
    d=(p1[0]-p0[0],p1[1]-p0[1])
    return d[0]*d[0]+d[1]*d[1]
    
# 获取多边形中最远的点
def get_furthest_point(poly):
    c=get_poly_center(poly)
    f=poly[0]
    sq=get_distsq(c,f)
    for i in range(1,len(poly)):
        sq2=get_distsq(c,poly[i])
        if sq2>sq:
            sq=sq2
            f=poly[i]
    return c,f

# 计算多边形面积，正负可用来判定多边形矢量方向
def get_poly_area(poly):
    area=0
    v0=poly[0]
    v1=poly[1]
    for i in range(2,len(poly)):
        v2=poly[i]
        area+=(v1[0]-v0[0])*(v2[1]-v0[1])-(v1[1]-v0[1])*(v2[0]-v0[0])
        v1=v2
    return area*0.5

# 递归分割多边形，maxarea为最小不可分割面积
def clip_poly(poly,hl,hw,maxarea):
    ret=[]
    c,f=get_furthest_point(poly)
    d=[f[0]-c[0],f[1]-c[1]]
    l=math.sqrt(d[0]*d[0]+d[1]*d[1])
    d[0]/=l
    d[1]/=l
    pc=pyclipper.Pyclipper()
    pc.AddPath(poly,pyclipper.PT_SUBJECT,True)
    pc.AddPath(get_perpendicular_rect(c,d,hl,hw),pyclipper.PT_CLIP,True)
    for r in pc.Execute(pyclipper.CT_DIFFERENCE,pyclipper.PFT_EVENODD,pyclipper.PFT_EVENODD):
        area=get_poly_area(r)
        if area>=0:
            r.reverse()
        if math.fabs(area)<=maxarea:
            ret.append(r)
        else:
            reg=clip_poly(r,hl,hw,maxarea)
            for r2 in reg:
                ret.append(r2)
    return ret

Display the cutting effect through the turtle tool

It should be noted here that the center point of the turtle coordinates is located in the center of the canvas, the x-axis is positively facing the right, and the y-axis is positively facing upwards

...
# 利用鼠标点击事件可多次查看分割效果
def onmouseclick(x,y):
    radius=100
    poly=get_random_poly(10, ((x-radius,y-radius),(x+radius,y+radius)))
    reg=clip_poly(poly,900,3,300)
    for poly in reg:
        poly.append(poly[0])
        for p in poly:
            turtle.goto(p)
            turtle.down()
        turtle.up()

# python主程序入口
if __name__=='__main__':
    ts=turtle.getscreen()
    ts.onclick(onmouseclick)
    turtle.up()
    # 设置随机种子用以固定每次生成的结果
    random.seed(3)
    onmouseclick(0,0)
    turtle.done()

final effect

reference

https://blog.csdn.net/bby1987/article/details/108858785
https://blog.csdn.net/qq_25737169/article/details/113843872
https://blog.csdn.net/ithiker/article/details/127712621