def findWeightedCentroids(seeds, stepsize, sigma, heighpar, bnd, X, Y, plot):
aimax = 30
ai = aimax
stepsize = 10
decFactor = 0.5
print("Start finding weighted centroids")
stdevs = [maxsize]
sumdists = [maxsize]
centroids = seeds
minseeds = seeds
while True:
seeds = allMoveSafeTowards(seeds, centroids, stepsize, bnd)
cells = voronoi(seeds, bnd)
areas = poly_areas(cells)
stdev = np.round(np.std(areas), 4)
heights = gauss_heights(areas, heighpar)
phi = init_phi(X, Y, seeds, heights, sigma)
centroids = wCentroids(cells, phi, X, Y)
sumdist = sumDist(seeds, centroids)
# plot the result
if (plot):
plot_voronoi(cells, seeds, centroids, X, Y, phi)
if sumdist >= min(sumdists):
ai -= 1
else:
ai = aimax
minseeds = seeds
if ai == 0:
seeds = minseeds
centroids = minseeds
stdevs.append(min(stdevs))
sumdists.append(min(sumdists))
stepsize = decFactor * stepsize
ai = aimax
continue
if np.array_equal(np.round(seeds, 2), np.round(centroids, 2)):
break
stdevs.append(stdev)
sumdists.append(sumdist)
return stdevs[1:]
def eaStepsizeControl(seeds, sigma, heighpar, bnd, X, Y, plot):
aimax = 10
ai = aimax
stepsize = 10
decFactor = 0.5
minStepsize = 0.5
print("Start equalizing areas with stepsize control")
stdevs = [maxsize]
centroids = seeds
minseeds = seeds
while True:
if stepsize < minStepsize:
break
seeds = allMoveSafeTowards(seeds, centroids, stepsize, bnd)
cells = voronoi(seeds, bnd)
areas = poly_areas(cells)
stdev = np.round(np.std(areas), 4)
heights = gauss_heights(areas, heighpar)
phi = init_phi(X, Y, seeds, heights, sigma)
centroids = wCentroids(cells, phi, X, Y)
# plot the result
if (plot):
plot_voronoi(cells, seeds, centroids, X, Y, phi)
if stdev >= min(stdevs):
ai -= 1
else:
ai = aimax
minseeds = seeds
if ai == 0:
seeds = minseeds
centroids = minseeds
stdevs.append(min(stdevs))
stepsize = decFactor * stepsize
ai = aimax
continue
stdevs.append(stdev)
return stdevs[1:]
def lloyd(seeds,stepsize, bnd, X, Y, plot):
print("Start Lloyd algorithm")
stdevs = [maxsize]
centroids = seeds
while True:
seeds = allMoveSafeTowards(seeds, centroids, stepsize, bnd)
cells = voronoi(seeds,bnd)
areas = poly_areas(cells)
centroids = uCentroids(cells)
# plot the result
if(plot):
plot_voronoi(cells, seeds, centroids, X, Y, phi)
stdev = np.round(np.std(areas),4)
if np.array_equal(np.round(seeds,3),np.round(centroids,3)):
break
if len(stdevs) > 6 and len(set(stdevs[-6:])) < 3:
break
stdevs.append(stdev)
return stdevs[1:]
X, Y = np.meshgrid(x_range, y_range)
# -----------------------------------------------------------------------------------
# Algorithm
# -----------------------------------------------------------------------------------
stdevs = []
stdevs.append(maxsize)
centroids = seeds
# Moves seeds towards the weighted centroids until the voronoi tesselation yields
# a higher standard deviation of the areas
while True:
# iteration
seeds = allMoveSafeTowards(seeds, centroids, stepsize, bnd)
cells = voronoi(seeds, bnd)
areas = poly_areas(cells)
heights = gauss_heights(areas, heighPar)
phi = init_phi(X, Y, seeds, heights, sigma)
centroids = wCentroids(cells, phi, X, Y)
# plot the result
# plot_voronoi(cells, seeds,centroids, X, Y, phi)
stdev = np.round(np.std(areas), 4)
print(stdev)
if stdev >= stdevs[-1]:
break
stdevs.append(stdev)