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ChebyshevObject2D.py
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ChebyshevObject2D.py
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from ChebyshevObject import *
class ChebyshevObject2D(ChebyshevObject):
def __init__(self, sites, oriFun=None, aniFun=None, extent=1, withMP=True, tag=''):
super().__init__(sites, oriFun, aniFun, extent, withMP, tag, 2)
def logMeta(self):
self.log.logThis('#/Cell', ['Min', 'Max', 'Med'], ','.join(['% 4s'] * 3))
numNeighbors = list(map(len, self.cellAdjacency))
numParts = list(map(len, self.cellVertexSets))
numVerts = list(map(len, map(np.concatenate, self.cellVertexSets)))
for nVals, tag in zip([numNeighbors, numParts, numVerts], ['Adj.', 'Parts', 'Verts']):
self.log.logThis(tag, [min(nVals), max(nVals), np.median(nVals)], ','.join(['% 4d'] * 3))
def getSitesSectorGeometry(self, sIdx, di, sJdx, dj):
return [self.cellSectors[sIdx][di].vertices, self.cellSectors[sJdx][dj].vertices]
def processDissolvedSectors(self, dData):
self.cellVertexSets, self.cellPlaneKeys = list(zip(*dData))
def plot(self, withSites=True, withCentroids=True, withAdjacency=True, withBBs=True, fileName=''):
if not mplFound:
warnings.warn('matplotlib missing.')
return
fig = plt.figure('Voronoi Plot')
ax = fig.add_axes([0, 0, 1, 1])
legendElements = []
for sIdx in self.sIdxs:
for cellVerts in self.cellVertexSets[sIdx]:
ax.fill(cellVerts[:, 0], cellVerts[:, 1], color=self.colors[sIdx] / 255)
if withAdjacency:
adjacencyPlot = ax.plot(self.sites[self.cellAdjacencyEdges, 0].T, self.sites[self.cellAdjacencyEdges, 1].T, color='white', linewidth=1, label='Adjacency')
legendElements.append(adjacencyPlot[0])
if withSites:
dirVecs = np.tile([edgeNormals[:4]], [self.numSites, 1, 1]) * self.lambdas.reshape(-1, 4, 1)
oriPts = self.sites.reshape(-1, 1, 2) + innerNxM(dirVecs, self.Ms) * self.cellScale / 5
sitesPlot = ax.plot(np.vstack(oriPts[:, [[0, 2], [1, 3]], 0]).T, np.vstack(oriPts[:, [[0, 2], [1, 3]], 1]).T, color='black')
legendElements.append(ax.scatter([], [], marker='+', color='black', label='Sites'))
if withCentroids:
centroidsPlot = ax.scatter(self.cellCentroids[:, 0], self.cellCentroids[:, 1], color='yellow', s=15, label='$L_2$ Centroids')
legendElements.append(centroidsPlot)
if withBBs:
bbCentersPlot = ax.scatter(self.cellBBcenters[:, 0], self.cellBBcenters[:, 1], color='green', s=15, label='$L_\infty$ BB Centers')
legendElements.append(bbCentersPlot)
for sIdx in self.sIdxs:
ax.plot(self.cellBBs[sIdx][[0, 1, 2, 3, 0], 0], self.cellBBs[sIdx][[0, 1, 2, 3, 0], 1], color=self.colors[sIdx] / 255, linewidth=1)
ax.set_aspect('equal', 'box')
fig.legend(handles=legendElements, facecolor='gray')
plt.axis(False)
if fileName:
plt.savefig(resDir + fileName)
plt.show()
def exportToObj(self, fileName='', withSites=True, withCentroids=True, withAdjacency=True, withBBs=True, numIter=None):
llPrefix = '' if numIter is None else 'lr%04d_'%numIter
fileName = fileName if fileName else self.tag + '.obj'
numVerts = 0
verts = []
cells = []
for sIdx in self.sIdxs:
for cellVerts in self.cellVertexSets[sIdx]:
cells.append(np.arange(len(cellVerts)) + numVerts)
verts.append(cellVerts)
numVerts += len(cellVerts)
vertices = [padHor(np.vstack(verts))]
faces = [cells]
edges = [[]]
tags = [llPrefix + 'cells']
if withSites:
vertices.append(padHor(self.sites))
faces.append([])
edges.append([])
tags.append(llPrefix + 'sites')
if withCentroids:
vertices.append(padHor(self.cellCentroids))
faces.append([])
edges.append([])
tags.append(llPrefix + 'centroids')
if withAdjacency:
vertices.append(padHor(self.sites))
faces.append([])
edges.append(self.cellAdjacencyEdges)
tags.append(llPrefix + 'adjacency')
if withBBs:
bbVerts = []
bbEdges = []
for sIdx in self.sIdxs:
bbVerts.append(np.vstack([self.cellBBs[sIdx], self.cellBBcenters[sIdx]]))
bbEdges.append(np.int32([[0, 1], [1, 2], [2, 3], [3, 0]]) + sIdx * 5)
vertices.append(padHor(np.vstack(bbVerts)))
faces.append([])
edges.append(np.vstack(bbEdges))
tags.append(llPrefix + 'BBs')
writeObjFile(resDir + llPrefix + fileName, vertices, faces, edges, subTags=tags)
def exportToSvg(self, fileName='infinityVoronoi.svg', size=512, withSites=True):
theDom = minidom.parseString('<svg xmlns=\"http://www.w3.org/2000/svg\" height=\"%d\" width=\"%d\"></svg>'%(size, size))
for sIdx in self.sIdxs:
g = theDom.createElement('g')
g.setAttribute('style', 'fill:%s;'%rgb2hex(self.colors[sIdx]))
theDom.childNodes[0].appendChild(g)
for cellVerts in self.cellVertexSets[sIdx]:
p = theDom.createElement('path')
verts = (cellVerts * [1, -1] + 1) / 2 * size
p.setAttribute('d', 'M' + (('L%.6f %.6f ' * len(verts))%tuple(verts.ravel()))[1:] + 'Z')
g.appendChild(p)
if withSites:
g = theDom.createElement('g')
g.setAttribute('style', 'stroke:#000;stroke-width:2px;stroke-linecap:round;')
theDom.childNodes[0].appendChild(g)
for sIdx in self.sIdxs:
aniVecs = edgeNormals[:4] * self.lambdas[sIdx].reshape(-1, 1)
aniOriVecs = self.sites[sIdx] + np.dot(aniVecs, self.Ms[sIdx].T) * self.cellScale / 5
aniOriPts = (aniOriVecs * [1, -1] + 1) / 2 * size
p = theDom.createElement('path')
p.setAttribute('d', 'M%.6f %.6f L%.6f %.6f'%(aniOriPts[0, 0], aniOriPts[0, 1], aniOriPts[2, 0], aniOriPts[2, 1]))
g.appendChild(p)
p = theDom.createElement('path')
p.setAttribute('d', 'M%.6f %.6f L%.6f %.6f'%(aniOriPts[1, 0], aniOriPts[1, 1], aniOriPts[3, 0], aniOriPts[3, 1]))
g.appendChild(p)
fh = open(resDir + fileName, 'w')
fh.write(theDom.toprettyxml())
fh.close()
if __name__ == '__main__':
n = 10
e = 1.0
sites = generateJitteredGridPoints(n, 2, e)
def oriFun(xys):
xs,ys = xys.T
uvs = (xys + [0.5,0]) / np.sqrt((xs + 0.5)**2 + ys**2).reshape(-1,1)**3 + (xys - [0.5,0]) / np.sqrt((xs - 0.5)**2 + ys**2).reshape(-1,1)**3
a = np.arctan2(uvs[:,0], uvs[:,1])
m = np.abs(xs) < 0.5
a[m] = np.cos(xs[m] * np.pi) * -np.sign(ys[m]) * np.sign(xs[m])
return np.pi - a
def aniFun(xys):
xs,ys = xys.T
s = np.min(np.abs(ys + [[0.5], [-0.5]] * np.sin(xs*np.pi)), axis=0)
s[xs>0.5] = np.abs(0.5 - norm([0.5,0] - xys[xs>0.5]))
s[xs<-0.5] = np.abs(0.5 - norm([-0.5,0] - xys[xs<-0.5]))
return np.tile([2-s, np.ones(len(xys))], [2,1]).T
cObj = ChebyshevObject2D(sites, oriFun, aniFun, e, withMP=True)
if IN_IDLE:
# compute the diagram once and plot it
cObj.computeDiagram()
cObj.plot()
else:
# run the relaxation (156 iterations) and save the demo image as SVG
cObj.lloydRelax(0.001)
cObj.exportToSvg()