彭罗斯瓷砖的python实现

由于做图形学学python，openmesh库的一些实现形式，了解到彭罗斯瓷砖这个很秀的东西（彭罗斯瓷砖科普），我就试试用下面这个风筝和飞镖的模型写代码生成一个。

肯定是先明白他的连接方式，我研究了一下他有这样的几个特性：
1.飞镖和风筝都有四条边
2.每条边都会连接另一条等长的边
3.根据那个蓝色圆圈和红色圆圈要连接上我发现有以下几种连接方式：

然后看着就如果知道各个点的坐标，根据每一条边来不断随机扩展就可以了，但是这可能会出现形状重合的冲突，这我还没想明白怎么弄，但我决定先编程看看生成以下扩展。

观察一下就可以看出来这个风筝可以看做是由两个等腰三角形拼接的，所以各个角度各个坐标都可以很轻松的算出来。我们把最上面的点看做是第一个点，逆时针转一次是234点，可以得到这个坐标：

a = (5**0.5+1)/2   #黄金分割1.6
beta = np.arccos( (5**0.5+1)    /   (2*5**0.5 + 6))  #风筝测角
alpha = np.pi*2-4*beta   #风筝顶角
# 初始化一个风筝-----------------------------------
x1 = 0
y1 = a*np.cos(beta)
x2 = -a*np.sin(beta)
y2 = 0
x3 = 0
y3 = y1-(1+a)
x4 = a*np.sin(beta)
y4 = 0

其他的风筝和飞镖也用这种顺序标定点的序号，边的话就1、2两点间是第一条边以此类推。我先决定把这个风筝先生成出来，这就很简单了：

xlist = [x1,x2,x3,x4,x1]
ylist = [y1,y2,y3,y4,y1]
plt.plot(xlist,ylist)mesh = om.TriMesh()
vhandle = []
vhandle.append(mesh.add_vertex(np.array([x1,  y1, 0])))
vhandle.append(mesh.add_vertex(np.array([x2,  y2, 0])))
vhandle.append(mesh.add_vertex(np.array([x3,  y3, 0])))
vhandle.append(mesh.add_vertex(np.array([x4,  y4, 0])))
face_vhandles = []
face_vhandles.append(vhandle[0])
face_vhandles.append(vhandle[1])
face_vhandles.append(vhandle[2])
face_vhandles.append(vhandle[3])
mesh.add_face(face_vhandles)plt.show()
om.write_mesh("./penrose.obj", mesh)

用plot和mesh两种办法展示是因为反正是一个二维平面，而且mesh生成的表面是光滑的没有间隙没有边框的图形，看不出来是怎么拼接的，所以plot用来观察是很方便的，但是最终目的是生成mesh，所以mesh也得生成着走一步调一步免得出bug。
生成了一个就要考虑怎么去无限生成更多的。我的思路是一条边一条边的扩展，也就是用一个递归来实现。
先得到这个图形的四条边的坐标，存入变量edgex和edgey，然后还要有一个数组isextend存储这四条边是否被扩展了，因为已经扩展的就不需要再被扩展了，而且刚扩展出来的四边形也只有新生成的几条边需要去继续扩展，这条母边不需要扩展。

edgex = []#用来存点的x坐标
edgey = []#用来存点的x坐标
isextend = []#存是否扩展了
edgex.append([x1,x2,x3,x4])
edgey.append([y1,y2,y3,y4])
isextend.append([0,0,0,0])
digui(edgex[-1],edgey[-1],isextend[-1],1,0)

digui这个函数中前三个变量就是刚才说的，还引入了两个参数，倒数第二个的作用是控制我们的递归递归多少次，最后一个的作用是传入我正在进行扩展的这个图形是风筝0还是飞镖1,。
我用风筝来先进行扩展第一条边扩展一个风筝来讲解我的递归思路：
先上代码：

def digui(x,y,isextendnow,mynum,thistype):n = 3  #用来控制迭代几次if thistype == 0 : #如果是风筝要扩展for i in range(len(isextendnow)):  #查看每一条边if isextendnow[i] == 0 :       #如果这个边没被扩展需要被扩展if i == 0:                 #第一条#扩展个风筝x1 = x[0]y1 = y[0]x2= (x[1]-x[0])*np.cos(2*beta) + (y[1]-y[0])*np.sin(2*beta)+x[0]y2 = (y[1]-y[0])*np.cos(2*beta) - (x[1]-x[0])*np.sin(2*beta)+y[0]x3= (x[2]-x[0])*np.cos(2*beta) + (y[2]-y[0])*np.sin(2*beta)+x[0]y3 = (y[2]-y[0])*np.cos(2*beta) - (x[2]-x[0])*np.sin(2*beta)+y[0]x4 = x[1]y4 = y[1]#扩展个标枪#x1 = x[1]#y1 = y[1]#x2= x[0]#y2 = y[0]#x3 = (x[2]-x[1])*np.cos(np.pi) + (y[2]-y[1])*np.sin(np.pi)+x[1]#x3 = (a+1-2*a*np.cos(beta))*x3/(a+1) + 2*a*np.cos(beta)*x[1]/(a+1)#y3 = (y[2]-y[1])*np.cos(np.pi) - (x[2]-x[1])*np.sin(np.pi)+y[1]#y3 = (a+1-2*a*np.cos(beta))*y3/(a+1) + 2*a*np.cos(beta)*y[1]/(a+1)#x4= (x[0]-x[1])*np.cos(2*beta) + (y[0]-y[1])*np.sin(2*beta)+x[1]#y4 = (y[0]-y[1])*np.cos(2*beta) - (x[0]-x[1])*np.sin(2*beta)+y[1]xlist = [x1,x2,x3,x4,x1]ylist = [y1,y2,y3,y4,y1]plt.plot(xlist,ylist)           #绘制vhandle = []vhandle.append(mesh.add_vertex(np.array([x1,  y1, 0])))vhandle.append(mesh.add_vertex(np.array([x2,  y2, 0])))vhandle.append(mesh.add_vertex(np.array([x3,  y3, 0])))vhandle.append(mesh.add_vertex(np.array([x4,  y4, 0])))face_vhandles = []face_vhandles.append(vhandle[0])face_vhandles.append(vhandle[1])face_vhandles.append(vhandle[2])face_vhandles.append(vhandle[3])mesh.add_face(face_vhandles)isextendnow[0] = 1  #这个边扩展完了edgex.append([x1,x2,x3,x4])edgey.append([y1,y2,y3,y4])# isextend.append([0,0,0,1])isextend.append([1,0,0,0]) #飞镖if mynum < n :       #控制次数递归digui(edgex[-1],edgey[-1],isextend[-1],mynum+1,1)#回去递归

对这个边的扩展主要是找到这样扩展的风筝的四个坐标在哪里，并且画出来存进edgex，edgey，还要更新当前isextend和刚扩展出来的isextend的值，进行下一次递归。
所以这一步的主要就是寻找扩展出来的风筝的四个坐标在哪里，我的思路主要是用齐次坐标进行旋转后得到。因为我看到，无论是哪种连接方式，新图形的四条边都可以由原图形的四条边旋转、伸缩后得到，而且角度和伸缩比例是我们已知的，就拿风筝在第二条边扩展飞镖来看：

飞镖4点可以由风筝点2绕风筝点1旋转得到，飞镖1点可以由风筝点2绕风筝点1旋转伸缩得到，且飞镖2、3点都是风筝原2、1点，这样就可以得到新的四个坐标。
用这样的办法可以得到图形扩展新图形后的坐标，用递归可以一直重复下去。但是什么时候生成什么样的图形？怎样造成图形间不冲突不重叠，因为平铺的要求就是无缝隙、不重叠，这个似乎可以通过添加一些规则来实现，但是这规则又不少，感觉是个力气活。
到目前为止的源码：

import numpy as np
import openmesh as om
import matplotlib.pyplot as plt
kite = 0
javelin = 1  #C语言遗留宏定义习惯
a = (5**0.5+1)/2   #黄金分割1.6
beta = np.arccos( (5**0.5+1)    /   (2*5**0.5 + 6))  #风筝测角
alpha = np.pi*2-4*beta   #风筝顶角def digui(x,y,isextendnow,mynum,thistype):n = 3  #用来控制迭代几次if thistype == 0 : #如果是风筝要扩展for i in range(len(isextendnow)):  #查看每一条边if isextendnow[i] == 0 :       #如果这个边没被扩展需要被扩展if i == 0:                 #第一条#扩展个风筝x1 = x[0]y1 = y[0]x2= (x[1]-x[0])*np.cos(2*beta) + (y[1]-y[0])*np.sin(2*beta)+x[0]y2 = (y[1]-y[0])*np.cos(2*beta) - (x[1]-x[0])*np.sin(2*beta)+y[0]x3= (x[2]-x[0])*np.cos(2*beta) + (y[2]-y[0])*np.sin(2*beta)+x[0]y3 = (y[2]-y[0])*np.cos(2*beta) - (x[2]-x[0])*np.sin(2*beta)+y[0]x4 = x[1]y4 = y[1]#扩展个标枪x1 = x[1]y1 = y[1]x2= x[0]y2 = y[0]x3 = (x[2]-x[1])*np.cos(np.pi) + (y[2]-y[1])*np.sin(np.pi)+x[1]x3 = (a+1-2*a*np.cos(beta))*x3/(a+1) + 2*a*np.cos(beta)*x[1]/(a+1)y3 = (y[2]-y[1])*np.cos(np.pi) - (x[2]-x[1])*np.sin(np.pi)+y[1]y3 = (a+1-2*a*np.cos(beta))*y3/(a+1) + 2*a*np.cos(beta)*y[1]/(a+1)x4= (x[0]-x[1])*np.cos(2*beta) + (y[0]-y[1])*np.sin(2*beta)+x[1]y4 = (y[0]-y[1])*np.cos(2*beta) - (x[0]-x[1])*np.sin(2*beta)+y[1]xlist = [x1,x2,x3,x4,x1]ylist = [y1,y2,y3,y4,y1]plt.plot(xlist,ylist)           #绘制vhandle = []vhandle.append(mesh.add_vertex(np.array([x1,  y1, 0])))vhandle.append(mesh.add_vertex(np.array([x2,  y2, 0])))vhandle.append(mesh.add_vertex(np.array([x3,  y3, 0])))vhandle.append(mesh.add_vertex(np.array([x4,  y4, 0])))face_vhandles = []face_vhandles.append(vhandle[0])face_vhandles.append(vhandle[1])face_vhandles.append(vhandle[2])face_vhandles.append(vhandle[3])mesh.add_face(face_vhandles)isextendnow[0] = 1  #这个边扩展完了edgex.append([x1,x2,x3,x4])edgey.append([y1,y2,y3,y4])# isextend.append([0,0,0,1])isextend.append([1,0,0,0]) #飞镖if mynum < n :       #控制次数递归digui(edgex[-1],edgey[-1],isextend[-1],mynum+1,1)#回去递归if i == 1:                  #如果是第二条x1 = (x[0]-x[2])*np.cos(-alpha) + (y[0]-y[2])*np.sin(-alpha)+x[2]y1 = (y[0]-y[2])*np.cos(-alpha) - (x[0]-x[2])*np.sin(-alpha)+y[2]x2= (x[1]-x[2])*np.cos(-alpha) + (y[1]-y[2])*np.sin(-alpha)+x[2]y2 = (y[1]-y[2])*np.cos(-alpha) - (x[1]-x[2])*np.sin(-alpha)+y[2]x3 = x[2]y3 = y[2]x4 = x[1]y4 = y[1]#加个标枪# x1 = (x[2]-x[1])*np.cos(alpha/2) + (y[2]-y[1])*np.sin(alpha/2)+x[1]# x1 = (a+1-2*a*np.cos(beta))*x1/(a+1)+2*a*np.cos(beta)*x[1]/(a+1)# y1 = (y[2]-y[1])*np.cos(alpha/2) - (x[2]-x[1])*np.sin(alpha/2)+y[1]# y1 = (a+1-2*a*np.cos(beta))*y1/(a+1)+2*a*np.cos(beta)*y[1]/(a+1)# x2= x[2]# y2 = y[2]# x3 = x[1]# y3 = y[1]# x4= (x[2]-x[1])*np.cos(alpha) + (y[2]-y[1])*np.sin(alpha)+x[1]# y4 = (y[2]-y[1])*np.cos(alpha) - (x[2]-x[1])*np.sin(alpha)+y[1]xlist = [x1,x2,x3,x4,x1]ylist = [y1,y2,y3,y4,y1]plt.plot(xlist,ylist)vhandle = []vhandle.append(mesh.add_vertex(np.array([x1,  y1, 0])))vhandle.append(mesh.add_vertex(np.array([x2,  y2, 0])))vhandle.append(mesh.add_vertex(np.array([x3,  y3, 0])))vhandle.append(mesh.add_vertex(np.array([x4,  y4, 0])))face_vhandles = []face_vhandles.append(vhandle[0])face_vhandles.append(vhandle[1])face_vhandles.append(vhandle[2])face_vhandles.append(vhandle[3])mesh.add_face(face_vhandles)isextendnow[1] = 1  #这个边扩展完了edgex.append([x1,x2,x3,x4])edgey.append([y1,y2,y3,y4])isextend.append([0,0,1,0])if mynum < n :digui(edgex[-1],edgey[-1],isextend[-1],mynum+1,0)#回去递归if i == 2:                  #如果是第三条#加个风筝x1 = (x[0]-x[2])*np.cos(alpha) + (y[0]-y[2])*np.sin(alpha)+x[2]y1 = (y[0]-y[2])*np.cos(alpha) - (x[0]-x[2])*np.sin(alpha)+y[2]x2 = x[3]y2 = y[3]x3 = x[2]y3 = y[2]x4= (x[3]-x[2])*np.cos(alpha) + (y[3]-y[2])*np.sin(alpha)+x[2]y4 = (y[3]-y[2])*np.cos(alpha) - (x[3]-x[2])*np.sin(alpha)+y[2]#加个标枪# x1 = (x[2]-x[3])*np.cos(-alpha/2) + (y[2]-y[3])*np.sin(-alpha/2)+x[3]# x1 = (a+1-2*a*np.cos(beta))*x1/(a+1)+2*a*np.cos(beta)*x[3]/(a+1)# y1 = (y[2]-y[3])*np.cos(-alpha/2) - (x[2]-x[3])*np.sin(-alpha/2)+y[3]# y1 = (a+1-2*a*np.cos(beta))*y1/(a+1)+2*a*np.cos(beta)*y[3]/(a+1)# x2= (x[2]-x[3])*np.cos(-alpha) + (y[2]-y[3])*np.sin(-alpha)+x[3]# y2 = (y[2]-y[3])*np.cos(-alpha) - (x[2]-x[3])*np.sin(-alpha)+y[3]# x3 = x[3]# y3 = y[3]# x4= x[2]# y4 = y[2]xlist = [x1,x2,x3,x4,x1]ylist = [y1,y2,y3,y4,y1]plt.plot(xlist,ylist)vhandle = []vhandle.append(mesh.add_vertex(np.array([x1,  y1, 0])))vhandle.append(mesh.add_vertex(np.array([x2,  y2, 0])))vhandle.append(mesh.add_vertex(np.array([x3,  y3, 0])))vhandle.append(mesh.add_vertex(np.array([x4,  y4, 0])))face_vhandles = []face_vhandles.append(vhandle[0])face_vhandles.append(vhandle[1])face_vhandles.append(vhandle[2])face_vhandles.append(vhandle[3])mesh.add_face(face_vhandles)isextendnow[2] = 1  #这个边扩展完了edgex.append([x1,x2,x3,x4])edgey.append([y1,y2,y3,y4])isextend.append([0,1,0,0])if mynum < n :digui(edgex[-1],edgey[-1],isextend[-1],mynum+1,0)#回去递归if i == 3:      x1 = x[0]y1 = y[0]x2 = x[3]y2 = y[3]x3= (x[2]-x[0])*np.cos(-2*beta) + (y[2]-y[0])*np.sin(-2*beta)+x[0]y3 = (y[2]-y[0])*np.cos(-2*beta) - (x[2]-x[0])*np.sin(-2*beta)+y[0]x4= (x[3]-x[0])*np.cos(-2*beta) + (y[3]-y[0])*np.sin(-2*beta)+x[0]y4 = (y[3]-y[0])*np.cos(-2*beta) - (x[3]-x[0])*np.sin(-2*beta)+y[0]#加个标枪x1 = x[3]y1 = y[3]x2= (x[0]-x[3])*np.cos(-2*beta) + (y[0]-y[3])*np.sin(-2*beta)+x[3]y2 = (y[0]-y[3])*np.cos(-2*beta) - (x[0]-x[3])*np.sin(-2*beta)+y[3]x3 = (x[2]-x[3])*np.cos(np.pi) + (y[2]-y[3])*np.sin(np.pi)+x[3]x3 = (a+1-2*a*np.cos(beta))*x3/(a+1) + 2*a*np.cos(beta)*x[3]/(a+1)y3 = (y[2]-y[3])*np.cos(np.pi) - (x[2]-x[3])*np.sin(np.pi)+y[3]y3 = (a+1-2*a*np.cos(beta))*y3/(a+1) + 2*a*np.cos(beta)*y[3]/(a+1)x4= x[0]y4 = y[0]xlist = [x1,x2,x3,x4,x1]ylist = [y1,y2,y3,y4,y1]plt.plot(xlist,ylist)vhandle = []vhandle.append(mesh.add_vertex(np.array([x1,  y1, 0])))vhandle.append(mesh.add_vertex(np.array([x2,  y2, 0])))vhandle.append(mesh.add_vertex(np.array([x3,  y3, 0])))vhandle.append(mesh.add_vertex(np.array([x4,  y4, 0])))face_vhandles = []face_vhandles.append(vhandle[0])face_vhandles.append(vhandle[1])face_vhandles.append(vhandle[2])face_vhandles.append(vhandle[3])mesh.add_face(face_vhandles)isextendnow[0] = 1  #这个边扩展完了edgex.append([x1,x2,x3,x4])edgey.append([y1,y2,y3,y4])# isextend.append([1,0,0,0])isextend.append([0,0,0,1]) #飞镖if mynum < n :digui(edgex[-1],edgey[-1],isextend[-1],mynum+1,1)#回去递归    #-------------------------------------------------如果传进来的是飞镖-------------------------------------------------if thistype == 1:for i in range(len(isextendnow)):  #查看每一条边if isextendnow[i] == 0 :       #如果这个边没被扩展if i == 0:                 #如果是第一条#加个风筝x1 = x[0]y1 = y[0]x2= (x[1]-x[0])*np.cos(2*beta) + (y[1]-y[0])*np.sin(2*beta)+x[0]y2 = (y[1]-y[0])*np.cos(2*beta) - (x[1]-x[0])*np.sin(2*beta)+y[0]x3= (x[2]-x[0])*np.cos(2*beta) + (y[2]-y[0])*np.sin(2*beta)+x[0]y3 = (y[2]-y[0])*np.cos(2*beta) - (x[2]-x[0])*np.sin(2*beta)+y[0]x4 = x[1]y4 = y[1]#加个标枪x1 = x[1]y1 = y[1]x2= x[0]y2 = y[0]x3 = (x[2]-x[1])*np.cos(np.pi) + (y[2]-y[1])*np.sin(np.pi)+x[1]x3 = (a+1-2*a*np.cos(beta))*x3/(a+1) + 2*a*np.cos(beta)*x[1]/(a+1)y3 = (y[2]-y[1])*np.cos(np.pi) - (x[2]-x[1])*np.sin(np.pi)+y[1]y3 = (a+1-2*a*np.cos(beta))*y3/(a+1) + 2*a*np.cos(beta)*y[1]/(a+1)x4= (x[0]-x[1])*np.cos(2*beta) + (y[0]-y[1])*np.sin(2*beta)+x[1]y4 = (y[0]-y[1])*np.cos(2*beta) - (x[0]-x[1])*np.sin(2*beta)+y[1]# xlist = [x1,x2,x3,x4,x1]# ylist = [y1,y2,y3,y4,y1]# plt.plot(xlist,ylist)vhandle = []vhandle.append(mesh.add_vertex(np.array([x1,  y1, 0])))vhandle.append(mesh.add_vertex(np.array([x2,  y2, 0])))vhandle.append(mesh.add_vertex(np.array([x3,  y3, 0])))vhandle.append(mesh.add_vertex(np.array([x4,  y4, 0])))face_vhandles = []face_vhandles.append(vhandle[0])face_vhandles.append(vhandle[1])face_vhandles.append(vhandle[2])face_vhandles.append(vhandle[3])mesh.add_face(face_vhandles)isextendnow[0] = 1  #这个边扩展完了edgex.append([x1,x2,x3,x4])edgey.append([y1,y2,y3,y4])isextend.append([0,0,0,1])# if mynum < n :# digui(edgex[-1],edgey[-1],isextend[-1],mynum+1,1)#回去递归if i == 1:                  #如果是第二条x1 = (x[2]-x[1])*np.cos(alpha/2) + (y[2]-y[1])*np.sin(alpha/2)+x[1]y1 = (y[2]-y[1])*np.cos(alpha/2) - (x[2]-x[1])*np.sin(alpha/2)+y[1]x2 = x[2]y2 = y[2]x3 = x[1]y3 = y[1]x4 = (x[2]-x[1])*np.cos(alpha) + (y[2]-y[1])*np.sin(alpha)+x[1]y4 = (y[2]-y[1])*np.cos(alpha) - (x[2]-x[1])*np.sin(alpha)+y[1]#加个标枪# x1 = (x[2]-x[1])*np.cos(alpha/2) + (y[2]-y[1])*np.sin(alpha/2)+x[1]# x1 = (a+1-2*a*np.cos(beta))*x1/(a+1)+2*a*np.cos(beta)*x[1]/(a+1)# y1 = (y[2]-y[1])*np.cos(alpha/2) - (x[2]-x[1])*np.sin(alpha/2)+y[1]# y1 = (a+1-2*a*np.cos(beta))*y1/(a+1)+2*a*np.cos(beta)*y[1]/(a+1)# x2= x[2]# y2 = y[2]# x3 = x[1]# y3 = y[1]# x4= (x[2]-x[1])*np.cos(alpha) + (y[2]-y[1])*np.sin(alpha)+x[1]# y4 = (y[2]-y[1])*np.cos(alpha) - (x[2]-x[1])*np.sin(alpha)+y[1]xlist = [x1,x2,x3,x4,x1]ylist = [y1,y2,y3,y4,y1]plt.plot(xlist,ylist)vhandle = []vhandle.append(mesh.add_vertex(np.array([x1,  y1, 0])))vhandle.append(mesh.add_vertex(np.array([x2,  y2, 0])))vhandle.append(mesh.add_vertex(np.array([x3,  y3, 0])))vhandle.append(mesh.add_vertex(np.array([x4,  y4, 0])))face_vhandles = []face_vhandles.append(vhandle[0])face_vhandles.append(vhandle[1])face_vhandles.append(vhandle[2])face_vhandles.append(vhandle[3])mesh.add_face(face_vhandles)isextendnow[1] = 1  #这个边扩展完了edgex.append([x1,x2,x3,x4])edgey.append([y1,y2,y3,y4])isextend.append([0,1,0,0])if mynum < n :digui(edgex[-1],edgey[-1],isextend[-1],mynum+1,0)#回去递归if i == 2:                  #如果是第三条#加个风筝x1 = (x[0]-x[2])*np.cos(alpha) + (y[0]-y[2])*np.sin(alpha)+x[2]y1 = (y[0]-y[2])*np.cos(alpha) - (x[0]-x[2])*np.sin(alpha)+y[2]x2 = x[3]y2 = y[3]x3 = x[2]y3 = y[2]x4= (x[3]-x[2])*np.cos(alpha) + (y[3]-y[2])*np.sin(alpha)+x[2]y4 = (y[3]-y[2])*np.cos(alpha) - (x[3]-x[2])*np.sin(alpha)+y[2]#加个标枪x1 = (x[2]-x[3])*np.cos(-alpha/2) + (y[2]-y[3])*np.sin(-alpha/2)+x[3]x1 = (a+1-2*a*np.cos(beta))*x1/(a+1)+2*a*np.cos(beta)*x[3]/(a+1)y1 = (y[2]-y[3])*np.cos(-alpha/2) - (x[2]-x[3])*np.sin(-alpha/2)+y[3]y1 = (a+1-2*a*np.cos(beta))*y1/(a+1)+2*a*np.cos(beta)*y[3]/(a+1)x2= (x[2]-x[3])*np.cos(-alpha) + (y[2]-y[3])*np.sin(-alpha)+x[3]y2 = (y[2]-y[3])*np.cos(-alpha) - (x[2]-x[3])*np.sin(-alpha)+y[3]x3 = x[3]y3 = y[3]x4= x[2]y4 = y[2]# xlist = [x1,x2,x3,x4,x1]# ylist = [y1,y2,y3,y4,y1]# plt.plot(xlist,ylist)vhandle = []vhandle.append(mesh.add_vertex(np.array([x1,  y1, 0])))vhandle.append(mesh.add_vertex(np.array([x2,  y2, 0])))vhandle.append(mesh.add_vertex(np.array([x3,  y3, 0])))vhandle.append(mesh.add_vertex(np.array([x4,  y4, 0])))face_vhandles = []face_vhandles.append(vhandle[0])face_vhandles.append(vhandle[1])face_vhandles.append(vhandle[2])face_vhandles.append(vhandle[3])mesh.add_face(face_vhandles)isextendnow[2] = 1  #这个边扩展完了edgex.append([x1,x2,x3,x4])edgey.append([y1,y2,y3,y4])isextend.append([0,1,0,0])# if mynum < n :# digui(edgex[-1],edgey[-1],isextend[-1],mynum+1,1)#回去递归if i == 3:      x1 = x[0]y1 = y[0]x2 = x[3]y2 = y[3]x3= (x[2]-x[0])*np.cos(-2*beta) + (y[2]-y[0])*np.sin(-2*beta)+x[0]y3 = (y[2]-y[0])*np.cos(-2*beta) - (x[2]-x[0])*np.sin(-2*beta)+y[0]x4= (x[3]-x[0])*np.cos(-2*beta) + (y[3]-y[0])*np.sin(-2*beta)+x[0]y4 = (y[3]-y[0])*np.cos(-2*beta) - (x[3]-x[0])*np.sin(-2*beta)+y[0]#加个标枪x1 = x[3]y1 = y[3]x2= (x[0]-x[3])*np.cos(-2*beta) + (y[0]-y[3])*np.sin(-2*beta)+x[3]y2 = (y[0]-y[3])*np.cos(-2*beta) - (x[0]-x[3])*np.sin(-2*beta)+y[3]x3 = (x[2]-x[3])*np.cos(np.pi) + (y[2]-y[3])*np.sin(np.pi)+x[3]x3 = (a+1-2*a*np.cos(beta))*x3/(a+1) + 2*a*np.cos(beta)*x[3]/(a+1)y3 = (y[2]-y[3])*np.cos(np.pi) - (x[2]-x[3])*np.sin(np.pi)+y[3]y3 = (a+1-2*a*np.cos(beta))*y3/(a+1) + 2*a*np.cos(beta)*y[3]/(a+1)x4= x[0]y4 = y[0]# xlist = [x1,x2,x3,x4,x1]# ylist = [y1,y2,y3,y4,y1]# plt.plot(xlist,ylist)vhandle = []vhandle.append(mesh.add_vertex(np.array([x1,  y1, 0])))vhandle.append(mesh.add_vertex(np.array([x2,  y2, 0])))vhandle.append(mesh.add_vertex(np.array([x3,  y3, 0])))vhandle.append(mesh.add_vertex(np.array([x4,  y4, 0])))face_vhandles = []face_vhandles.append(vhandle[0])face_vhandles.append(vhandle[1])face_vhandles.append(vhandle[2])face_vhandles.append(vhandle[3])mesh.add_face(face_vhandles)isextendnow[0] = 1  #这个边扩展完了edgex.append([x1,x2,x3,x4])edgey.append([y1,y2,y3,y4])isextend.append([0,0,0,1])# if mynum < n :# digui(edgex[-1],edgey[-1],isextend[-1],mynum+1,1)#回去递归    # 初始化一个风筝-----------------------------------------------------------------
x1 = 0
y1 = a*np.cos(beta)
x2 = -a*np.sin(beta)
y2 = 0
x3 = 0
y3 = y1-(1+a)
x4 = a*np.sin(beta)
y4 = 0xlist = [x1,x2,x3,x4,x1]
ylist = [y1,y2,y3,y4,y1]
plt.plot(xlist,ylist)mesh = om.TriMesh()vhandle = []
vhandle.append(mesh.add_vertex(np.array([x1,  y1, 0])))
vhandle.append(mesh.add_vertex(np.array([x2,  y2, 0])))
vhandle.append(mesh.add_vertex(np.array([x3,  y3, 0])))
vhandle.append(mesh.add_vertex(np.array([x4,  y4, 0])))face_vhandles = []face_vhandles.append(vhandle[0])
face_vhandles.append(vhandle[1])
face_vhandles.append(vhandle[2])
face_vhandles.append(vhandle[3])mesh.add_face(face_vhandles)
#------------------------------------------------------------------------
edgex = []#用来存点的x坐标
edgey = []#用来存点的x坐标
isextend = []#存是否扩展了
edgex.append([x1,x2,x3,x4])
edgey.append([y1,y2,y3,y4])
isextend.append([0,0,0,0])
digui(edgex[-1],edgey[-1],isextend[-1],1,0)
print(isextend)
plt.show()
om.write_mesh("./penrose.obj", mesh)

现在的生成效果：

显然这冲突是一个蛮需要解决的问题。在目前图形下，下一条边要扩展的是风筝还是飞镖？这虽然是随机的，但是有很多情况是不能实现的，比如我剩了一个飞镖的窟窿你要填一个风筝进去，这显然不可嫩。也就是说这应该是由条件限制的，但这个条件有没有一种简洁的表达形式我再思考一下。

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彭罗斯瓷砖的python实现

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