def getWKSColors(context, mesh, K=3, WKS_E=6, WKS_CURRENT_E=0, wks_variance=0.0):
K = min(len(mesh.data.vertices)-1, K);
k_exists, cache_k = getMatrixCache(context, mesh, 'WKS_k');
WKS_L_Exists, WKS_L = getMatrixCache(context, mesh, 'WKS_L');
WKS_VORONOI_Exists, WKS_VORONOI = getMatrixCache(context, mesh, 'WKS_VORONOI');
WKS_EVA_Exists, WKS_EVA = getMatrixCache(context, mesh, 'WKS_eva');
WKS_EVE_Exists, WKS_EVE = getMatrixCache(context, mesh, 'WKS_eve');
wks_e_exists, cache_wks_e = getMatrixCache(context, mesh, 'WKS_E');
wks_matrix_exists, WKS_MATRIX = getMatrixCache(context, mesh, 'WKS_MATRIX');
wks_relative_sigma_exists, WKS_RELATIVE_SIGMA = getMatrixCache(context, mesh, 'WKS_RELATIVE_SIGMA');
if(not k_exists):
setMatrixCache(context, mesh, 'WKS_k', K);
if(not WKS_L_Exists):
WKS_L = getWKSLaplacianMatrixCotangent(context, mesh);
print('GETTING WKS LAPLACIANS :');
setMatrixCache(context, mesh, 'WKS_L', WKS_L);
if(not WKS_VORONOI_Exists):
print('GETTING WKS VORONOI :');
WKS_VORONOI, __ = getMeshVoronoiAreas(context, mesh);
setMatrixCache(context, mesh, 'WKS_VORONOI', WKS_VORONOI);
if(cache_k != K or not WKS_EVA_Exists or not WKS_EVE_Exists):
print('GETTING WKS EIGENS : ', '%s = %s'%(cache_k, K), WKS_EVA_Exists, WKS_EVE_Exists);
WKS_EVA, WKS_EVE = getWKSEigens(mesh, WKS_L, WKS_VORONOI, K);
setMatrixCache(context, mesh, 'WKS_k', K);
setMatrixCache(context, mesh, 'WKS_eva', WKS_EVA);
setMatrixCache(context, mesh, 'WKS_eve', WKS_EVE);
if(cache_wks_e != WKS_E or not wks_e_exists or not wks_matrix_exists or wks_variance != WKS_RELATIVE_SIGMA):
if(wks_variance > 0.0):
WKS_MATRIX = get_wks(WKS_EVA, WKS_EVE, num_steps=WKS_E, relative_sigma=wks_variance);
else:
WKS_MATRIX = get_wks(WKS_EVA, WKS_EVE, num_steps=WKS_E);
setMatrixCache(context, mesh, 'WKS_E', WKS_E);
setMatrixCache(context, mesh, 'WKS_MATRIX', WKS_MATRIX);
setMatrixCache(context, mesh, 'WKS_RELATIVE_SIGMA', wks_variance);
print('GETTING WKS COLORS VALUES');
# wks_matrix = getWKS(mesh, WKS_EVA, WKS_EVE, WKS_E, wks_variance );
# wks_sum = np.sum(wks_matrix, 1);
# wks = wks_sum/np.max(wks_sum);
wks = WKS_MATRIX[:,min(int(WKS_E-1), WKS_CURRENT_E)];
print('FINISHED AND RETURNING THE COMPUTED WKS VALUES :');
return wks, K;
def getHKSColors(context, mesh, K=5, HKS_T=20.0, HKS_CURRENT_T = 20):
K = min(len(mesh.data.vertices)-1, K);
k_exists, cache_k = getMatrixCache(context, mesh, 'WKS_k');
WKS_L_Exists, WKS_L = getMatrixCache(context, mesh, 'WKS_L');
WKS_VORONOI_Exists, WKS_VORONOI = getMatrixCache(context, mesh, 'WKS_VORONOI');
WKS_EVA_Exists, WKS_EVA = getMatrixCache(context, mesh, 'WKS_eva');
WKS_EVE_Exists, WKS_EVE = getMatrixCache(context, mesh, 'WKS_eve');
hks_t_exists, cache_hks_t = getMatrixCache(context, mesh, 'HKS_T');
hks_matrix_exists, HKS_MATRIX = getMatrixCache(context, mesh, 'HKS_MATRIX');
if(not k_exists):
setMatrixCache(context, mesh, 'WKS_k', K);
if(not WKS_L_Exists):
print('GETTING HKS LAPLACIANS :');
# HKS_L = getLaplacianMatrixCotangent(context, mesh, []);
WKS_L = getWKSLaplacianMatrixCotangent(context, mesh);
setMatrixCache(context, mesh, 'WKS_L', WKS_L);
if(not WKS_VORONOI_Exists):
print('GETTING WKS VORONOI :');
WKS_VORONOI, __ = getMeshVoronoiAreas(context, mesh);
setMatrixCache(context, mesh, 'WKS_VORONOI', WKS_VORONOI);
if(cache_k != K or not WKS_EVA_Exists or not WKS_EVE_Exists):
print('GETTING HKS EIGENS : ', '%s = %s'%(cache_k, K), WKS_EVA_Exists, WKS_EVE_Exists);
# HKS_EVA, HKS_EVE = getHKSEigens(mesh, HKS_L, K);
WKS_EVA, WKS_EVE = getWKSEigens(mesh, WKS_L, WKS_VORONOI, K);
setMatrixCache(context, mesh, 'WKS_k', K);
setMatrixCache(context, mesh, 'WKS_eva', WKS_EVA);
setMatrixCache(context, mesh, 'WKS_eve', WKS_EVE);
if(cache_hks_t != HKS_T or not hks_t_exists or not hks_matrix_exists):
HKS_MATRIX = get_hks(WKS_EVA, WKS_EVE, WKS_VORONOI, num_times=HKS_T);
setMatrixCache(context, mesh, 'HKS_T', HKS_T);
setMatrixCache(context, mesh, 'HKS_MATRIX', HKS_MATRIX);
print('GETTING HKS COLOR VALUES');
heat = HKS_MATRIX[:,min(int(HKS_T-1), HKS_CURRENT_T)];
print('FINISHED AND RETURNING THE COMPUTED HKS VALUES :');
return heat, K;
def getGISIFColors(context,
mesh,
K=20,
threshold_ratio=0.1,
show_group_index=0,
linear_gisif_iterations=0):
K = min(len(mesh.data.vertices) - 1, K)
k_exists, cache_k = getMatrixCache(context, mesh, 'WKS_k')
WKS_L_Exists, WKS_L = getMatrixCache(context, mesh, 'WKS_L')
WKS_VORONOI_Exists, WKS_VORONOI = getMatrixCache(context, mesh,
'WKS_VORONOI')
WKS_EVA_Exists, WKS_EVA = getMatrixCache(context, mesh, 'WKS_eva')
WKS_EVE_Exists, WKS_EVE = getMatrixCache(context, mesh, 'WKS_eve')
GISIF_THRESHOLD_Exists, GISIF_Threshold = getMatrixCache(
context, mesh, 'GISIF_Threshold')
GISIF_GROUPS_Exists, GISIF_Groups = getMatrixCache(context, mesh,
'GISIF_Groups')
if (not k_exists):
setMatrixCache(context, mesh, 'WKS_k', K)
if (not WKS_L_Exists):
WKS_L = getWKSLaplacianMatrixCotangent(context, mesh)
print('GETTING GISIF LAPLACIANS :')
setMatrixCache(context, mesh, 'WKS_L', WKS_L)
if (not WKS_VORONOI_Exists):
print('GETTING GISIF VORONOI :')
WKS_VORONOI, __ = getMeshVoronoiAreas(context, mesh)
setMatrixCache(context, mesh, 'WKS_VORONOI', WKS_VORONOI)
if (cache_k != K or not WKS_EVA_Exists or not WKS_EVE_Exists):
print('GETTING GISIF EIGENS : ', '%s = %s' % (cache_k, K),
WKS_EVA_Exists, WKS_EVE_Exists)
WKS_EVA, WKS_EVE = getWKSEigens(mesh, WKS_L, WKS_VORONOI, K)
mesh.spectral_soft_update = True
#Find the standard deviation between the eigenvalues and apply
mesh.gisif_threshold = np.std(WKS_EVA)
threshold_ratio = mesh.gisif_threshold
mesh.spectral_soft_update = False
setMatrixCache(context, mesh, 'WKS_k', K)
setMatrixCache(context, mesh, 'WKS_eva', WKS_EVA)
setMatrixCache(context, mesh, 'WKS_eve', WKS_EVE)
if (GISIF_Threshold != threshold_ratio or not GISIF_THRESHOLD_Exists):
print('GETTING GISIF GROUPS :')
GISIF_Groups = getGISIFGroups(mesh, WKS_EVA, WKS_EVE, threshold_ratio)
setMatrixCache(context, mesh, 'GISIF_Threshold', threshold_ratio)
setMatrixCache(context, mesh, 'GISIF_Groups', GISIF_Groups)
print('SELECTING GISIF GROUPS :', WKS_EVA)
show_group_index = min(show_group_index,
len(GISIF_Groups) - 1)
linear_gisifs = []
if (linear_gisif_iterations > 0):
linear_gisif_iterations = linear_gisif_iterations + 1
max_linear_gisifs = min(show_group_index + linear_gisif_iterations,
len(GISIF_Groups))
iterations_count = (max_linear_gisifs - show_group_index)
linear_gisifs = np.zeros((GISIF_Groups[0][1].shape[0]))
uselabel = None
print('ITERATIONS COUNT ', show_group_index, iterations_count,
len(GISIF_Groups))
for i in range(iterations_count):
label, evectors_group = GISIF_Groups[show_group_index + i]
if (i == 0):
uselabel = label
eve = (evectors_group**2)
gisifs = np.sum(eve, axis=1)
linear_gisifs = gisifs - linear_gisifs
return linear_gisifs, K, uselabel
else:
label, evectors_group = GISIF_Groups[show_group_index]
eve = (evectors_group**2)
gisifs = np.sum(eve, axis=1)
print('DOING GISIF COMPUTATION :')
print('FINISHED AND RETURNING THE COMPUTED GISIF VALUES :')
# gisifs = gisifs/np.max(gisifs);
return gisifs, K, label
def getHKSColors(context,
mesh,
K=5,
HKS_T=20.0,
HKS_CURRENT_T=20,
HKS_LOG_START=0.1,
HKS_LOG_END=10.0):
K = min(len(mesh.data.vertices) - 1, K)
k_exists, cache_k = getMatrixCache(context, mesh, 'WKS_k')
WKS_L_Exists, WKS_L = getMatrixCache(context, mesh, 'WKS_L')
WKS_VORONOI_Exists, WKS_VORONOI = getMatrixCache(context, mesh,
'WKS_VORONOI')
WKS_EVA_Exists, WKS_EVA = getMatrixCache(context, mesh, 'WKS_eva')
WKS_EVE_Exists, WKS_EVE = getMatrixCache(context, mesh, 'WKS_eve')
hks_t_exists, cache_hks_t = getMatrixCache(context, mesh, 'HKS_T')
hks_log_start_exists, cache_hks_log_start = getMatrixCache(
context, mesh, 'HKS_LOG_START')
hks_log_end_exists, cache_hks_log_end = getMatrixCache(
context, mesh, 'HKS_LOG_END')
hks_matrix_exists, HKS_MATRIX = getMatrixCache(context, mesh, 'HKS_MATRIX')
if (not k_exists):
setMatrixCache(context, mesh, 'WKS_k', K)
if (not WKS_L_Exists):
print('GETTING HKS LAPLACIANS :')
# HKS_L = getLaplacianMatrixCotangent(context, mesh, []);
WKS_L = getWKSLaplacianMatrixCotangent(context, mesh)
setMatrixCache(context, mesh, 'WKS_L', WKS_L)
if (not WKS_VORONOI_Exists):
print('GETTING WKS VORONOI :')
WKS_VORONOI, __ = getMeshVoronoiAreas(context, mesh)
setMatrixCache(context, mesh, 'WKS_VORONOI', WKS_VORONOI)
if (cache_k != K or not WKS_EVA_Exists or not WKS_EVE_Exists):
print('GETTING HKS EIGENS : ', '%s = %s' % (cache_k, K),
WKS_EVA_Exists, WKS_EVE_Exists)
# HKS_EVA, HKS_EVE = getHKSEigens(mesh, HKS_L, K);
WKS_EVA, WKS_EVE = getWKSEigens(mesh, WKS_L, WKS_VORONOI, K)
setMatrixCache(context, mesh, 'WKS_k', K)
setMatrixCache(context, mesh, 'WKS_eva', WKS_EVA)
setMatrixCache(context, mesh, 'WKS_eve', WKS_EVE)
if (cache_hks_t != HKS_T or cache_hks_log_start != HKS_LOG_START
or cache_hks_log_end != HKS_LOG_END or not hks_t_exists
or not hks_matrix_exists or not hks_log_start_exists
or not hks_log_end_exists):
HKS_MATRIX = get_hks(WKS_EVA,
WKS_EVE,
WKS_VORONOI,
num_times=HKS_T,
log_start_value=HKS_LOG_START,
log_end_value=HKS_LOG_END)
setMatrixCache(context, mesh, 'HKS_T', HKS_T)
setMatrixCache(context, mesh, 'HKS_MATRIX', HKS_MATRIX)
print('GETTING HKS COLOR VALUES')
heat = HKS_MATRIX[:, min(int(HKS_T - 1), HKS_CURRENT_T)]
print('FINISHED AND RETURNING THE COMPUTED HKS VALUES :')
return heat, K
def funcmap_correspondences(context,
source,
target,
n_eigen=30,
spectral_steps=100,
coeffsmode='wks'):
# verS, verT, triS, triT = getMeshVPos(source), getMeshVPos(target), getMeshFaces(source), getMeshFaces(target);
n_eigen = min(
len(source.data.vertices) - 1,
len(target.data.vertices) - 1, n_eigen)
#%% 1. LapBel Operator & Basis (eigenfunc)
__, matMS = getMatrixCache(context, source, 'WKS_VORONOI')
__, matCS = getMatrixCache(context, source, 'WKS_L')
__, matMT = getMatrixCache(context, target, 'WKS_VORONOI')
__, matCT = getMatrixCache(context, target, 'WKS_L')
s_k_exists, s_cache_k = getMatrixCache(context, source, 'WKS_k')
WKS_EVA_Exists, WKS_EVA = getMatrixCache(context, source, 'WKS_eva')
WKS_EVE_Exists, WKS_EVE = getMatrixCache(context, source, 'WKS_eve')
if (not s_k_exists):
setMatrixCache(context, source, 'WKS_k', n_eigen)
if (s_cache_k != n_eigen or not WKS_EVA_Exists or not WKS_EVE_Exists):
eivalS, eivecS = getWKSEigens(source, matMS, matCS, n_eigen)
eivalT, eivecT = getWKSEigens(target, matMT, matCT, n_eigen)
setMatrixCache(context, source, 'WKS_k', n_eigen)
setMatrixCache(context, target, 'WKS_k', n_eigen)
setMatrixCache(context, source, 'WKS_eva', eivalS)
setMatrixCache(context, target, 'WKS_eva', eivalT)
setMatrixCache(context, source, 'WKS_eve', eivecS)
setMatrixCache(context, target, 'WKS_eve', eivecT)
else:
__, eivalS = getMatrixCache(context, source, 'WKS_eva')
__, eivalT = getMatrixCache(context, target, 'WKS_eva')
__, eivecS = getMatrixCache(context, source, 'WKS_eve')
__, eivecT = getMatrixCache(context, target, 'WKS_eve')
# eivalS = eivalS[:-1]
# eivecS = eivecS[:,:-1]
# eivalT = eivalT[:-1]
# eivecT = eivecT[:,:-1]
#%% 2. Function Representation (HKS & WKS) & its Coefficient
if (coeffsmode == 'hks'):
basisS = get_hks(eivalS, eivecS, matMS, spectral_steps)
basisT = get_hks(eivalT, eivecT, matMT, spectral_steps)
coefS = get_coef(eivecS, matMS, basisS)
coefT = get_coef(eivecT, matMT, basisT)
elif (coeffsmode == 'wks'):
basisS = get_wks(eivalS, eivecS, num_steps=spectral_steps)
basisT = get_wks(eivalT, eivecT, num_steps=spectral_steps)
coefS = get_coef(eivecS, matMS, basisS)
coefT = get_coef(eivecT, matMT, basisT)
elif (coeffsmode == 'p2p'):
assert len(source.data.vertices) == len(target.data.vertices)
basisS = identity(len(source.data.vertices), dtype=np.float)
basisT = identity(len(target.data.vertices), dtype=np.float)
coefS = get_coef(eivecS, matMS, basisS)
coefT = get_coef(eivecT, matMT, basisT)
else:
raise NotImplementedError(
'The mode %s not known and has not been implemented')
funcMap = get_funcMap(coefS, coefT, eivalS, eivalT)
eivecS_mapped = (funcMap.dot(eivecS.T)).T
return FunctionalMapResult(eivecS, eivecT, eivecS_mapped, funcMap,
coeffsmode, coefS, coefT, basisS, basisT)