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Andrej
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#!/usr/bin/python3
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import numpy as np
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from scipy.spatial import Delaunay
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import matplotlib.pyplot as plt
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import shapely.geometry as geo
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#import sys
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#np.set_printoptions(threshold=sys.maxsize)
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def get_mesh(fd,fh,h0,bbox,pfix):
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'''
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A simple mesh generator based on:
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Persson, G. Strang, A Simple Mesh Generator in MATLAB.
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SIAM Review, Volume 46 (2), pp. 329-345, June 2004
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'''
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geps = 0.001*h0
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ttol = 0.1
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Fscale = 1.2
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deltat = 0.2
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deps = np.sqrt(np.finfo(float).eps)*h0
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dptol = 0.001
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maxIter = 500
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X, Y = np.meshgrid(np.arange(bbox[0,0],bbox[1,0]+h0,h0),\
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np.arange(bbox[0,1],bbox[1,1]+h0*0.5*np.sqrt(3),h0*0.5*np.sqrt(3)))
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X[1:-1:2,:] += (0.5*h0)
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p = np.column_stack((X.flatten('F'),Y.flatten('F')))
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p = p[np.nonzero(np.apply_along_axis(fd,1,p) < geps)].squeeze()
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r0 = 1/np.apply_along_axis(fh,1,p)**2
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R0 = np.max(r0)
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p = p[np.random.rand(p.shape[0]) < r0/R0]
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if len(pfix):
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p = np.vstack((pfix, p))
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N = p.shape[0]
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pold = np.Inf
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counter = 0
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while True:
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if np.max(np.sqrt(np.sum((p-pold)**2,1))/h0) > ttol:
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pold = np.copy(p)
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T = Delaunay(p)
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tri = T.simplices
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pmid = (p[tri[:,0],:]+p[tri[:,1],:]+p[tri[:,2],:])/3
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inner = np.apply_along_axis(fd,1,pmid) < -geps
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tri = tri[inner,:]
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bars = np.vstack((tri[:,[0,1]],tri[:,[1,2]],tri[:,[0,2]]))
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bars.sort(1)
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bars = remove_duplicate_row(bars)
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bvec = p[bars[:,0],:] - p[bars[:,1],:]
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L = np.sqrt(np.sum(bvec**2,1))
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hbars = np.apply_along_axis(fh, 1,(p[bars[:,0],:]+p[bars[:,1],:])/2)
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L0 = hbars*Fscale*np.sqrt(np.sum(L**2)/np.sum(hbars**2))
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F = [np.max(L0 - [L], 0)]
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Fvec = (F/L).T * bvec
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#sparse and back to full does not work the same in python as in matlab
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#forced to do the loop, figure out better way
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row = bars[:,[0,0,1,1]].flatten('F')
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column = (np.ones(np.shape(F),dtype=np.int32).T @ [[0,1,0,1]]).flatten('F')
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Ffrac = np.hstack((Fvec,-Fvec)).flatten('F')
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Ftot = np.zeros([N,2])
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for i in range(len(row)):
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Ftot[row[i],column[i]] += Ffrac[i]
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if len(pfix):
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Ftot[0:pfix.shape[0]-1,:] = 0
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p += (deltat*Ftot)
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#bring back to boundary
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d = np.apply_along_axis(fd,1,p)
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ix = d>0 #index of points outside boundary
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dx = np.column_stack((p[ix,0]+deps, p[ix,1]))
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dy = np.column_stack((p[ix,0], p[ix,1]+deps))
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gradx = (np.apply_along_axis(fd,1,dx)-d[ix])/deps
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grady = (np.apply_along_axis(fd,1,dy)-d[ix])/deps
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p[ix,:] -= np.column_stack((d[ix]*gradx,d[ix]*grady))
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#print(np.max(np.sqrt(np.sum(deltat*Ftot[d<-geps,:]**2,1))/h0))
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counter += 1
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#print(counter)
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if Ftot[d<-geps,:].size == 0 or counter > maxIter:
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print(counter)
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return p, tri
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if np.max(np.sqrt(np.sum(deltat*Ftot[d<-geps,:]**2,1))/h0) < dptol:
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print(counter)
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return p, tri
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def remove_duplicate_row(M):
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#remove dupplicate rows of the array
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A = np.ascontiguousarray(M).view(np.dtype((np.void,M.dtype.itemsize*M.shape[1])))
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_, idx = np.unique(A, return_index=True)
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return M[idx]
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def print_mesh(p, tri, title='', output=''):
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plt.figure()
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plt.triplot(p[:,0], p[:,1], tri, color='black')
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plt.axis('equal')
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plt.axis(False)
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if title:
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plt.title(title)
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if output:
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plt.savefig(output)
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plt.close()
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return
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plt.show()
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return
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def ddiff(d1, d2):
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return max(d1, -d2)
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def dunion(d1, d2):
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return min(d1, d2)
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def dintersect(d1, d2):
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return max(d1, d2)
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def dcircle(p, xc, yc, r):
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return np.sqrt((p[0]-xc)**2+(p[1]-yc)**2)-r
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def drectangle(p, x1, x2, y1, y2):
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return -min(min(min(-y1+p[1],y2-p[1]),-x1+p[0]), x2-p[0])
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def protate(p, phi):
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A = np.array([[np.cos(phi),-np.sin(phi)],[np.sin(phi),np.cos(phi)]])
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return (A@p.T).T
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def _dpoly(p, poly, ring):
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ds = ring.distance(p)
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inside = ring.contains(p) or poly.contains(p)
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return (-1)**inside*ds
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def dpoly(p, poly):
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return _dpoly(geo.asPoint(p), geo.asPolygon(poly),geo.asLinearRing(poly))
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if __name__ == "__main__":
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#print("test 1")
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#fd = lambda x: ddiff(dcircle(x, 0, 0, 1), dcircle(x, 0.5, -0.2, 0.2))
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#fh = lambda x: 0.8
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#bbox = np.array([[-1, -1],[1, 1]])
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#p, tri = get_mesh(fd, fh, 0.1, bbox, [])
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#print_mesh(p, tri)
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print("test 2")
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import time
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poly = np.array([[0,0],[0,1],[1,1],[1,2],[2,2],[2,1],[3,1],[3,0]])
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polyG = geo.asPolygon(poly)
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ringG = geo.asLinearRing(poly)
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fd = lambda x: dpoly(x,poly)
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fh = lambda x: 0.15-0.22*fd(x)
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bbox = np.array([[0,0],[3,3]])
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t = time.time()
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p, tri = get_mesh(fd, fh, 0.1, bbox, poly)
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elap = time.time()-t
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print("prvi = {}s".format(elap))
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fd = lambda x: _dpoly(geo.asPoint(x), polyG, ringG)
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fh = lambda x: 0.15-0.22*fd(x)
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t = time.time()
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p, tri = get_mesh(fd, fh, 0.1, bbox, poly)
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elap = time.time()-t
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print("drugi = {}s".format(elap))
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print_mesh(p, tri)
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#print("test 3")
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#fd = lambda x: drectangle(protate(x,np.pi/4),0,1,0,1)
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#bbox = np.array([[-2,-2],[2,2]])
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#p, tri = get_mesh(fd, fh, 0.08, bbox, [])
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#print_mesh(p, tri)
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