Worked on labels on meshes and on curved cellularized structures.

data/cellcomplex_production.py

-from copy import deepcopy
 import numpy as np
-from numpy import linalg as lng
-#import matplotlib as mpl
-#from matplotlib import pyplot as plt
 
 from cellcomplex.property_topomesh.analysis import compute_topomesh_property
 from cellcomplex.property_topomesh.example_topomesh import circle_voronoi_topomesh
-from cellcomplex.property_topomesh.io import save_ply_property_topomesh, read_ply_property_topomesh
-#from cellcomplex.property_topomesh.utils.matplotlib_tools import mpl_draw_topomesh
+from cellcomplex.property_topomesh.io import save_ply_property_topomesh
+
+from bvpy.templates.domains import FaceCellularDomain
+from bvpy.utils.visu import plot
+from bvpy.utils.io import save
+
 
 # ##############################################################################
 # ##############################################################################
@@ -36,21 +36,6 @@ def cell_normal(points, cell):
     return np.array(nrl).mean(axis=0)
 
 
-def plot_points(points, vids):
-    fig = plt.figure()
-    axe = fig.add_subplot(111, projection='3d')
-
-    points = np.array(points)
-    for vid in vids:
-        axe.scatter(points[vid, 0],
-                    points[vid, 1],
-                    points[vid, 2],
-                    marker='o',
-                    label=f'{vid}')
-    plt.legend()
-    plt.show()
-
-
 def approx(x, n):
     '''Approximates a float to a given order.
 
@@ -103,10 +88,10 @@ def read_tissue_text_file(path):
 # ##############################################################################
 # ##############################################################################
 # -- Creating a "tissue-like" property topomesh.
-cvmsh = circle_voronoi_topomesh(size = 5,
-                                voxelsize = 1.,
-                                circle_size = 100.,
-                                z_coef = 0)
+cvmsh = circle_voronoi_topomesh(size=5,
+                                voxelsize=1.,
+                                circle_size=100.,
+                                z_coef=0)
 
 prop_2_compute = {1: ['borders'],
                   2: ['oriented_vertices', 'oriented_borders', 'borders'],
@@ -116,20 +101,30 @@ for deg, names in prop_2_compute.items():
     for name in names:
         compute_topomesh_property(cvmsh, name, degree=deg)
 
+
 path = '/Users/oali/Documents/Work/Research/Devlp/bvpy/data/test_flat.ply'
 save_ply_property_topomesh(cvmsh, path)
 
 
+# -- Defining the epithelial cells on the structure
+epithelium = {cid: 0 for cid in cvmsh.wisps(2)}
+
+for cid, eids in cvmsh.wisp_property('borders', 2).items():
+    for eid in eids:
+        if cvmsh.nb_regions(1, eid) == 1:
+            epithelium[cid] = 1
+            break
 
 # -- Getting the vertex positions
 points = []
 cells = []
+labels = []
 lbl_2_idx = {}
 for idx, (vid, pos) in enumerate(cvmsh.wisp_property('barycenter', 0).items()):
     points.append(list(pos))
     lbl_2_idx[vid] = idx
 
-# -- Forming the cells with their vertex index (in the list of position vectors)
+# -- Writing cells with their vertex index (in the list of position vectors)
 for cid, eids in cvmsh.wisp_property('borders', 2).items():
     oriented_vids = []
 
@@ -152,12 +147,13 @@ for cid, eids in cvmsh.wisp_property('borders', 2).items():
     assert(oriented_vids[0] == oriented_vids[-1])
     oriented_vids.pop()
     cells.append(list(map(lambda x: lbl_2_idx[x], oriented_vids)))
+    labels.append(epithelium[cid])
 
 
 # -- Harmonizing the orientation of all cells.
 oriented_cells = []
 for cell in cells:
-    if  cells.index(cell) == 0:
+    if cells.index(cell) == 0:
         oriented_cells.append(cell)
     else:
         vids_2_switch = [[idx0, idx1]
@@ -171,7 +167,8 @@ for cell in cells:
                 reversed = True
                 break
 
-        if not reversed: oriented_cells.append(cell)
+        if not reversed:
+            oriented_cells.append(cell)
 
 cells = oriented_cells
 
@@ -179,7 +176,8 @@ cells = oriented_cells
 # -- Recording these list in a text file
 save_path = '/Users/oali/Documents/Work/Research/Devlp/bvpy/data/tissue_example_flat.txt'
 
-def save_points_and_cells(points, cells):
+
+def save_points_and_cells(points, cells, label=None):
     with open(save_path, 'w') as file:
 
         for name, lst in zip(['points', 'cells'], [points, cells]):
@@ -187,18 +185,20 @@ def save_points_and_cells(points, cells):
             for line in lst:
                 file.write(' '.join([str(elmt) for elmt in line])+'\n')
 
-save_points_and_cells(points, cells)
-
-# ##############################################################################
-# ##############################################################################
-# -- Instancing the FaceCellularDomain class from the previously computed lists.
-from bvpy.templates.domains import FaceCellularDomain
+        if label is not None:
+            assert len(label) == len(cells)
+            file.write(f'{len(label)}  cell labels:\n')
+            for line in label:
+                file.write(f'{line} \n')
 
 
-tissue = FaceCellularDomain(points, cells, resolution=.05)
+save_points_and_cells(points, cells, labels)
 
 
-from bvpy.utils.visu import plot
-
+# ##############################################################################
+# ##############################################################################
+# -- Instancing the FaceCellularDomain class from the lists computed above.
+tissue = FaceCellularDomain(points, cells, markers=labels, resolution=.05)
 
+save(tissue, save_path[:-4])
 plot(tissue.mesh)

data/tissue_example_curved.txt

+220  points:
+-2.923961461587178 3.2441482921464946 0.7801906650442335
+-2.7456094236265725 -2.466930913813634 0.5622494154255632
+-2.091260831771032 -2.6691748529984674 0.477701004255513
+-1.9579421531705388 -2.9358177631610896 0.5147433450959479
+0.2315931355235309 -2.580002521593032 0.28807894412092694
+-0.13632602829219237 -3.5087844064051703 0.5050890744460552
+0.7173186125032134 -3.7808861164812573 0.608968001780544
+-2.8838191130713775 -1.7752972685010284 0.47520947935894364
+-2.6532326649384834 -0.4215171411818072 0.31088453329855875
+-2.9627114780816695 -1.7190176426105828 0.4848662020119616
+2.731227573538176 -1.8105909716230562 0.44387422628228357
+0.7500043080288806 -4.2657412763709175 0.7695288468104114
+-0.14082659092836616 -4.48117478335171 0.8156563717900751
+-0.3203203397451169 -3.5824425564961655 0.5313886737203897
+-1.0403201567910731 -3.191746720750457 0.4718261953270593
+-1.196796091387838 -3.2560394469549068 0.5021692598487022
+-1.6834371260608716 -2.0309478933794285 0.29266390818872035
+-2.157158548068202 -1.4616889149277672 0.28482721573168
+-2.016854991444407 -0.869605767367873 0.2134566337769675
+-2.9915733363985817 -3.393273874113334 0.8284966672635223
+-2.431785945265422 -3.692754666649614 0.7961134127102893
+-2.28714203280854 -3.8673459731436557 0.8187323975527314
+2.2154458697642148 -1.4592094696531168 0.2963438625217305
+0.3597252762014928 -0.08922401821826213 0.029997722720615367
+0.830650833139455 -1.2112010199680363 0.11217018231276583
+0.8577137185572346 -1.1409366778686378 0.10698853742079084
+0.6000190701158943 -2.6422934859793115 0.3112852472903743
+1.9443817902712484 -2.7001894279245757 0.46074231069880495
+1.536169729835625 -3.2594550854275974 0.5370427074510234
+1.0550056094397202 -3.300867712371561 0.49879729182060356
+1.5287550198151496 -2.0497065512539865 0.27888224527613925
+1.2744340821588838 -1.985991714968799 0.2410136042623432
+-3.1655907239683763 3.1655907239683754 0.8137910959216875
+-4.4921427842957415 -0.14117127424399922 0.8191417045564249
+-3.692829883072662 2.5096445969987378 0.8100904902735202
+-3.715390981949324 2.297331233136662 0.7798408245181178
+-4.0526783024599755 1.7537505060721321 0.7945470655827411
+-1.3755901395749452 2.0329354612866304 0.2567503485435586
+-0.7787474294966907 2.277912282058063 0.24678816015077845
+-1.6140723989196653 3.1996327701186087 0.5312723291532827
+-0.9246951818506421 3.229961307217646 0.4692259182932207
+-0.8097470320337649 3.32326454669327 0.48552838360618794
+0.8191836643398086 3.4876590172896216 0.5289894382745433
+0.12305595225803471 3.2538740952271126 0.44498751235160044
+-0.14268925203795246 3.425392172143995 0.4901519280724105
+-0.10938339397883559 4.376156771800932 0.7831299214409145
+1.3850930956698748 3.208715478415743 0.5092999525678112
+2.319840370694236 0.9766207324342953 0.2707029957266941
+-2.5454511912044495 3.7455176864580566 0.8300556088735369
+-1.7698894472844506 4.089973195119663 0.8073002083099295
+-1.9351701540386914 3.9152237382052273 0.7800418711850335
+-3.528723525853691 -2.737158539163459 0.8102324804248957
+-3.7339557993989794 -2.5375937408729463 0.8255406044069522
+2.8870377196019987 -3.2656688341294147 0.7779576605765336
+2.761815365452808 -2.132430518139853 0.5004959669992078
+2.42091535567397 -2.6741459723887986 0.5377465230250812
+3.976835184331636 -1.6972335612012976 0.7673449409701453
+3.3462781168214186 -1.3206844203557633 0.5318522732567675
+0.9713163444710654 -4.345419530973405 0.8064429722591954
+0.684310798608313 -4.320568341221707 0.7825931870355707
+2.5275423370673784 -3.7191656078378186 0.8197913556265645
+2.0031518303650513 -3.9087261045476094 0.7878415943052144
+2.2769198714672574 -3.8500612422730067 0.8123433193919768
+-0.41363875003221395 -4.3758409017943505 0.788784079711322
+-0.4202648563807767 -4.371282339925716 0.7875063458300178
+-0.699582350738323 -4.416989126614023 0.8120528280747472
+-1.274616357699903 -1.9819761227045132 0.2373600797348514
+-0.04311004051043313 -2.3378587614874347 0.2399816796645089
+-0.7886528214962382 -2.552863025844461 0.30170972723525075
+-0.016342523747426674 -1.5619430052198642 0.11964953714979
+-2.0523999706928 -4.028061743980153 0.8275277537682705
+-1.7804306468710116 -4.114332470112569 0.8155984951141207
+-0.980539128770731 -4.386679896099403 0.819214505665362
+-1.4560257319293468 -4.117836488974934 0.7803302175470518
+-1.484597287699294 -4.123627601617147 0.7851001608641529
+-1.243323996270323 -4.2795492652770495 0.8072391700979004
+-2.77145396716415 -3.5729369252179293 0.8278968262346935
+-2.5031656314934794 -3.683296374838931 0.8064463526690181
+-1.5237766365387229 -0.7248729311259621 0.13473404410625184
+-0.24498576841177402 -0.30128471647566274 0.02275562338699426
+-0.8495153372307137 -1.1806020532880177 0.10911471303189035
+-0.6108936357493207 -1.146845535606831 0.0928251219101218
+-3.58640024598637 2.781897189234916 0.8334408610358602
+-3.407714097912152 3.0043041061775035 0.8347597079170833
+-4.171807834383529 -1.2281124493847906 0.7747510599498625
+-4.437940409027941 -0.7029007078775348 0.8186807895890421
+-3.5701982182333936 -0.18914497038891745 0.5225933628074508
+-4.426875990463657 -0.3122248071135595 0.8007572467470984
+-4.451000406946939 -0.42074341504679597 0.8116706439139827
+-3.1844252274621376 -0.6278403313238871 0.4441420051504986
+-3.2988236619459865 -0.8973641662301223 0.4869878143227572
+-3.949687163460418 2.0124661273245423 0.7996936376937697
+-3.784790425120287 2.2383188178086386 0.7889235913705748
+-4.07838314525876 1.5650089441492652 0.7796285343014336
+-3.5959887067661906 0.48210334032730995 0.5396793768565458
+-2.934364244611868 2.0428099081842563 0.5265567585491269
+-2.683905563276701 2.956578912545964 0.6505904038828728
+-1.9031421144687735 2.8044476223311627 0.4768187454551748
+-1.8291565024801038 2.253291295830676 0.35556367258702387
+-0.8925420888707429 0.21554197321030727 0.048803616492286615
+-1.3684909047307514 -0.01747712308657467 0.09015444390189943
+-0.7142051428369964 0.9506631644369824 0.0784617944727868
+-1.3004434804538847 1.221962247732215 0.14295469222897433
+-0.1379980033535733 4.391167667301262 0.7881922469084587
+-1.5262981883270323 4.239456309015172 0.822715768633202
+-0.9762727533628694 4.367593229711749 0.8131615528856124
+-1.0616795839465991 4.3113880884841596 0.8015264784486681
+-1.2532148278726345 4.313593730954234 0.8183347349387566
+0.8132610185539921 4.331161960977899 0.7913946249120157
+2.6764565326791536 3.4661509678014735 0.783996833533345
+1.4134880440643005 3.1592898704201273 0.5000571299919098
+2.418514540829085 2.3066847634173935 0.4653265467777987
+2.212521067455357 2.94047014784846 0.5576251096608719
+1.584816125517805 0.07502154842408987 0.11866956635760992
+1.745321494352267 -0.6787642720091159 0.1615781575637076
+2.127727110965321 -0.8624825390634896 0.23278280567132376
+2.316518076251662 0.5155284433295765 0.24171900096622423
+0.390062427995053 -0.030871682283632795 0.030361198145306283
+1.300053940131643 0.23820482343697005 0.08665794332925177
+-2.9072077112961363 3.2975798565038543 0.7891114186181116
+-2.754665337585643 3.551293154382994 0.8192033609646947
+-2.2886061645430633 3.8698216847026345 0.8196715244788592
+-1.997094746559562 3.9195191300869396 0.7899625958904629
+3.1931264056613107 3.1931264056613133 0.8258996825316721
+3.3646603104137975 2.966347086647303 0.8163594377446103
+2.6550239804385316 2.188519618380753 0.4913377967533264
+3.860195652507995 2.282913344972634 0.8160780635999095
+3.73012197722529 2.534988278014194 0.824039636887341
+3.4285627983639206 2.8034729223468178 0.7980296334571819
+3.5332001219920075 2.7406309430671953 0.8119602397562783
+4.551694725686819 0.14304276939755378 0.8384862039441741
+4.322571394476201 0.9662091808790917 0.7993756615313021
+-3.242242793227479 -2.888122814261169 0.7729809733232469
+-3.2676644070117087 -2.880833694824958 0.7773101023930052
+-3.1528842457687047 -3.1528842457687087 0.8081342089606802
+-3.8722509337743665 -2.290042818439223 0.8205079585276821
+-3.9440057763183467 -2.0095713159872313 0.7978527257769195
+-3.9351286541907564 -2.018492885266642 0.7965983514897559
+-4.087612318315574 -1.7688678046617357 0.8062510190515049
+-4.164368915545405 -1.4992650632596984 0.7977226994622845
+3.565598345261624 -2.7657615810518443 0.8249281675467727
+3.977412273106016 -1.721179986722143 0.7703206212133967
+3.923510350165916 -1.9991283747643307 0.79076582681433
+3.806957597512539 -2.2514284470166066 0.796617837334177
+3.6752180611196517 -2.414622648004611 0.7885242350521215
+3.667036001201054 -2.492115092980311 0.8004227565727504
+1.5496110695507574 -4.304210327686697 0.8451887968502911
+1.269571719200521 -4.369894520188944 0.8373369330639637
+0.14165576387974654 -4.50755949447946 0.8239743475062279
+0.4209004623014769 -4.452661793363217 0.812264392099574
+2.8848751993995028 -3.2722485941075243 0.7789852428697712
+2.732910253993309 -3.523246669613925 0.80799701756957
+1.7961962579973505 -4.1507646478456675 0.8283841419657436
+1.9973000160873735 -3.9199219942186847 0.7903455754959323
+-4.516728024508566 0.14194389654366704 0.8269336027056876
+-4.4584475780054635 0.42144737997537796 0.8141177296387904
+-4.347334830219784 -0.9717444645753035 0.8066509576998424
+-4.184742440039853 -1.2157800673374284 0.7776313365223052
+-4.2496220755331 1.2346293439031917 0.7973733078359801
+-4.13638186658373 1.489189105633716 0.788631964276392
+-4.32176247963127 0.6844999315519772 0.7829993131855107
+-4.280607684561837 0.7325379478079735 0.7726217809349615
+-4.2966330309186915 0.9604112697009719 0.7905383542082776
+-3.1312148337193335 1.2257639162327407 0.4656061506094458
+-2.6806453077347823 1.6970750273587278 0.42702052375306726
+-2.561691557564141 1.6868742395924117 0.4002265640001581
+-3.2018059184221506 0.7309873299907772 0.4453006053320993
+-2.4957634766795116 0.25828354037544216 0.2698224763481523
+-2.0621197787962244 0.5426182126886797 0.20129978360861664
+-1.970280405129694 0.9090331744156999 0.20668412586373183
+-0.7057075280634522 4.455661974228183 0.8244300936903268
+-0.4219002472430099 4.463238413275679 0.8155833675142643
+1.2724656764803863 4.379855586482166 0.8406844069587333
+0.9787721653731011 4.3787749562697815 0.8170112360613679
+0.13990766782357622 4.451934176035423 0.8064431070013175
+2.9635548620996945 3.3614931533554127 0.8150388004020811
+2.6875484019349276 3.4647665223208786 0.7857197614732199
+1.8173928984398968 4.072691566468359 0.8080606662825845
+-0.33024786004017603 2.1080398541033043 0.20101729912059432
+0.18729695688866504 2.4902749234918224 0.26785155759380835
+-0.20743145200083685 1.1689434585744032 0.08398250386421842
+0.09573632605869463 1.0491511972379368 0.07034059270405395
+3.27796609742927 -0.9053375386008702 0.47643666128475937
+2.7806915335694704 -0.5141493557377789 0.33862387319078247
+2.8698287078185083 0.031925688808344066 0.3475546893171724
+3.4835765551065245 0.3522430810728789 0.5081451241949908
+4.114962038583597 -0.33484457470516 0.7026441105916569
+3.0542353063757006 1.4945227022693266 0.4870830995587415
+3.053202309549797 1.4872276870614 0.4859568670406754
+3.57781754748919 0.7412674429781807 0.5516625996391786
+4.307426035073525 0.9799270331975094 0.7955162518563801
+4.33162504628007 1.2584534092369926 0.8244168668222529
+4.274037823096053 1.5387482994837438 0.834615395705007
+3.917587216642919 2.000423819682863 0.7898532286622818
+4.491522181359862 0.7113872268999238 0.8364028776017004
+4.570023826593949 0.4319944407655692 0.8504299234392733
+3.16241123094975 -3.1624112309497465 0.812294060490622
+3.3948192682206964 -2.99293578457616 0.829145361858704
+4.4393254201256225 -0.139511421705878 0.8031066242282601
+4.26826384484386 -0.3695550377731951 0.7565424297641234
+4.380616682570783 -0.9791838399756251 0.8172701444275112
+0.6960318369407998 4.39457206474704 0.8049726397213982
+0.4217325352902404 4.461464206138218 0.8148902794674251
+2.526846455494433 3.71814164919813 0.819645666805871
+1.544977369898884 4.29133973177467 0.8406932623770689
+1.7819674535299637 4.117883820763792 0.8170360007251379
+1.2076882458622742 1.078569778975467 0.11975481791072157
+0.6957756949192173 1.2934462631468255 0.10389575489738177
+1.7450791362547156 1.3500422444960398 0.20984759362898792
+1.7619728651013238 1.927921107886479 0.2868131532463147
+1.1281234880864095 2.334959223542988 0.2862600116285005
+0.8295222367211841 2.2208216735498034 0.24227947295431287
+4.134520611354514 1.789166835701551 0.8226141330895783
+3.9214691903980214 1.998088351916107 0.7906886002073145
+4.371383400826033 -0.692359113383798 0.7978879775079433
+4.28755044251587 -0.40529284440279373 0.7629809955064738
+4.169272152473522 -1.5010303371756941 0.7995177312270454
+4.312252304013306 -1.2528251073199486 0.8178466760507257
+2.05752228387434 4.038114849642734 0.8312700019394869
+2.3157620208058587 3.9157397299567984 0.8368090356403438
+61  cells:
+37 98 165 169 102
+54 144 143 142 141 56 57 10
+125 128 124 123 175 176 109 112 111
+5 6 29 26 4
+160 161 94 86 87 33 154 155
+95 96 0 32 83 82 34 35
+47 187 189 185 184 116
+3 20 21 70 71 74 73 15
+131 194 195 130 198 199 186 185 189 190
+113 114 25 23 117 118
+5 13 64 63 12 148 149 59 11 6
+207 211 179 178 180 181
+2 1 132 134 19 76 77 20 3
+9 137 136 138 139 84 90
+39 40 41 106 107 104 49 50
+209 210 211 207 206 208
+26 31 24 69 67 4
+85 88 87 86 89 90 84 157 156
+27 30 31 26 29 28
+38 40 39 97 98 37
+4 67 68 14 13 5
+182 183 184 185 186
+17 18 78 80 66 16
+55 53 196 197 140 145 144 54
+97 96 95 164 165 98
+116 184 183 115 114 113
+116 113 118 206 208 47
+188 193 213 212 192 191 190 189 187
+125 128 129 127 126 193 188
+110 112 109 203 219 218 177 46
+78 100 99 79 81 80
+94 166 167 8 89 86
+65 64 13 14 15 73 75 72
+57 182 186 199 215 214 200 217 216 56
+46 177 205 204 172 173 108 42
+187 188 125 111 209 208 47
+7 1 132 133 51 52 135 137 9
+2 16 66 68 14 15 3
+178 179 43 44 41 40 38
+45 103 171 170 105 106 41 44
+167 168 100 78 18 8
+108 201 202 174 45 44 43 42
+7 9 90 89 8 18 17
+69 81 79 23 25 24
+79 23 117 181 180 101 99
+111 112 110 210 209
+163 166 94 161 162 158 159 93
+164 163 166 167 168 169 165
+7 17 16 2 1
+24 31 30 22 115 114 25
+100 168 169 102 101 99
+101 180 178 38 37 102
+55 54 10 22 30 27
+28 61 62 60 151 150 53 55 27
+92 91 36 93 163 164 95 35
+0 96 97 39 50 122 121 48 120 119
+117 181 207 206 118
+42 43 179 211 210 110 46
+57 182 183 115 22 10
+67 68 66 80 81 69
+29 6 11 58 147 146 152 153 61 28
+61  cell labels:
+0 
+1 
+1 
+0 
+1 
+1 
+0 
+1 
+1 
+0 
+1 
+0 
+1 
+1 
+1 
+0 
+0 
+1 
+0 
+0 
+0 
+0 
+0 
+1 
+0 
+0 
+0 
+1 
+1 
+1 
+0 
+0 
+1 
+1 
+1 
+0 
+1 
+0 
+0 
+1 
+0 
+1 
+0 
+0 
+0 
+0 
+1 
+0 
+0 
+0 
+0 
+0 
+0 
+1 
+1 
+1 
+0 
+0 
+0 
+0 
+1 

src/bvpy/domains/geometry.py

@@ -167,6 +167,7 @@ def normal(domain, scale=1, interior=None, degree=1, name='normal'):
 
     return u
 
+
 def get_boundary_facets(mesh):
     """Selects the boundary elements of a given mesh.
 
@@ -223,13 +224,20 @@ def get_boundary_vertex(mesh):
     return bnd_vertex
 
 
-def boundary_normal(mesh):
+def boundary_normal(domain, scale=1, degree=1, name='normal'):
     """Computes the normal vector field on the boundary of a mesh.
 
     Parameters
     ----------
-    mesh : :class:`Mesh<dolfin.cpp.mesh.Mesh>`
-        The mesh on which the boundary normals should be computed.
+    domain : subclass of :class:`Domain<bvpy.domains.AbstracDomain>`
+        The meshed surface on which we want to compute the normal field.
+    scale : float, optional
+        The amplitude we want to set to this field (the default is 1).
+    degree : int, optional
+        The interpolation degree to use to compute the vector space
+        on the border (the default is 1).
+    name : str, optional
+        the label we want to attach to the normal field.
 
     Returns
     -------
@@ -237,6 +245,11 @@ def boundary_normal(mesh):
         a list of 3D vector defined on the outermost vertices of a mesh.
 
     """
+    if domain.mesh is not None:
+        mesh = domain.mesh
+    else:
+        print('WARNING - (geometry.py - l.84): no mesh on the domain.')
+
     mesh.init()
     bnd_facets = get_boundary_facets(mesh)
     facets_index = [f.index() for f in bnd_facets]
@@ -248,13 +261,15 @@ def boundary_normal(mesh):
                              for f in fe.facets(vtx)
                              if f.index() in facets_index])
             norm = np.sum(norm, axis=0)
-            norm = norm / np.linalg.norm(norm)
+            norm = scale * norm / np.linalg.norm(norm)
             normals[vtx.index()] = norm
 
-    V = fe.VectorFunctionSpace(mesh, 'P', 1, dim=3)
+    V = fe.VectorFunctionSpace(mesh, 'P', degree, dim=3)
     u = fe.Function(V)
     d2v = fe.dof_to_vertex_map(V)
     u.vector().set_local(normals.flatten()[d2v])
 
+    u.rename(name, 'label')
+
     return u
 # geometry.py ends here

src/bvpy/utils/interface.py

@@ -105,7 +105,7 @@ def create_expression(source, functionspace=None, degree=None, **kwargs):
 
 
 class FenicsFunctionConverter(object):
-    """Enables conversion of Fenics objects (???) into other formats.
+    """Enables conversion of fenics Functions into other formats.
 
     Parameters
     ----------

src/bvpy/utils/io.py

 import fenics as fe
+from bvpy import BVP
 
 
-def save(bvp, filename):
+def save(data, filename):
     """Save a fenics mesh or function as pvd or xml.
 
     Parameters
     ----------
-    bvp : BVP
-        the simulation to save.
+    data : BVP or Domain
+        the simulation or the domain to save.
     filename : str
         the path and the name of the recording file.
 
@@ -21,7 +22,10 @@ def save(bvp, filename):
         filename += '.xdmf'
 
     with fe.XDMFFile(fe.MPI.comm_world, filename) as f:
-        f.write(bvp.solution)
+        if isinstance(data, BVP):
+            f.write(data.solution)
+        else:
+            f.write(data.mesh)
 
 
 def read_tissue_text_file(path):
@@ -41,15 +45,25 @@ def read_tissue_text_file(path):
     '''
     points = []
     cells = []
+    labels = []
 
     with open(path, 'r') as file:
         content = file.readlines()
 
         point_nbr = int(content[0][:-8])
+        cell_nbr = int(content[point_nbr+1][:-9])
+
         for line in content[1: point_nbr+1]:
             points.append([float(coord) for coord in line.split(' ')])
 
-        for line in content[point_nbr+2:]:
+        for line in content[point_nbr+2:point_nbr+cell_nbr+2]:
             cells.append([int(pidx) for pidx in line.split(' ')])
 
-    return points, cells
+        if content[point_nbr+cell_nbr+2][-8:-2] == 'labels':
+            for line in content[point_nbr+cell_nbr+3:]:
+                labels.append(int(line))
+
+    if len(labels) == 0:
+        return points, cells
+    else:
+        return points, cells, labels

src/bvpy/vforms/abstract.py

@@ -64,10 +64,10 @@ class AbstractVform(ABC):
         bterm = Zero()
         for ind, t in enumerate(self._bterm):
             if isinstance(t[1], int):
-                bterm += fe.dot(t[0],v)*self.ds(t[1])
+                bterm += fe.dot(t[0], v) * self.ds(t[1])
             elif isinstance(t[1], str):
                 Boundary(t[1])._domain.mark(self.ds.subdomain_data(), ind+1)
-                bterm += fe.dot(t[0],v)*self.ds(ind+1)
+                bterm += fe.dot(t[0], v) * self.ds(ind+1)
 
         return bterm
 

tutorials/bvpy_tutorial_5_linearElasticity_2DFlatCellularizedTissue.ipynb

@@ -19,7 +19,7 @@
     "from bvpy.utils.io import read_tissue_text_file\n",
     "\n",
     "path = '../data/tissue_example_flat.txt'\n",
-    "points, cells = read_tissue_text_file(path)\n",
+    "points, cells, labels = read_tissue_text_file(path)\n",
     "\n",
     "# Definition of the domain of interest.\n",
     "from bvpy.templates.domains import FaceCellularDomain\n",
@@ -41,6 +41,14 @@
     "plot(tissue.mesh)"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Loading the structure with a normal force field\n",
+    "Let's load the flat tissue-inspired structure with a constant force field normal to its surface, similar to the one used in tutorial #4 about thin pressurized elastic shell."
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": null,
@@ -62,52 +70,122 @@
   {
    "cell_type": "code",
    "execution_count": null,
-<<<<<<< HEAD
-=======
    "metadata": {},
    "outputs": [],
    "source": [
-    "type(drchlt)"
+    "# Define the source term as the force field applied everywhere on the domain\n",
+    "from bvpy.domains.geometry import normal\n",
+    "\n",
+    "pressure = 1\n",
+    "p_force = normal(tissue, scale=pressure, name='pressure_force_field', interior=[0, 0, -1])"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
->>>>>>> develop
    "metadata": {},
    "outputs": [],
    "source": [
-    "# Define the source term as the force field applied everywhere on the domain\n",
-    "from bvpy.domains.geometry import normal\n",
+    "# Define the variational form\n",
+    "from bvpy.templates.vforms import LinearElasticForm\n",
     "\n",
-    "pressure = 1\n",
-    "p_force = normal(tissue, scale=pressure, name='pressure_force_field', interior=[0, 0, -1])"
+    "young = 1000 * pressure\n",
+    "\n",
+    "elastic_equilibrium = LinearElasticForm(source=p_force, young=young)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Set the linear elastic\n",
+    "from bvpy import BVP\n",
+    "\n",
+    "pressurized_elastic_tissue_prblm = BVP(domain=tissue, vform=elastic_equilibrium, bc=drchlt)\n",
+    "\n",
+    "# Solve the problem\n",
+    "pressurized_elastic_tissue_prblm.solve()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Solution visualization\n",
+    "sol = pressurized_elastic_tissue_prblm.solution\n",
+    "\n",
+    "plot(sol)"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
-<<<<<<< HEAD
-=======
    "metadata": {},
    "outputs": [],
    "source": [
-    "p_force.vector().get_local().reshape(-1,3)"
+    "# Save the solution to be used by a third party pipeline\n",
+    "from bvpy.utils.io import save\n",
+    "\n",
+    "path = '../data/tutorial_results/solution_tuto5_1.xdmf'\n",
+    "\n",
+    "save(pressurized_elastic_tissue_prblm, path)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Loading the structure with a tangent force field\n",
+    "Let's now consider a fully 2D problem where the 2D tissue-inspired structure is loaded on its border by a force field locally normal to its border and embedded within the same plane as the structure."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# -- Generate a new instance of the same tissue\n",
+    "tissue_2 = FaceCellularDomain(points, cells, resolution=.1)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Define the source term as the force field applied everywhere on the domain\n",
+    "from bvpy.domains.geometry import boundary_normal\n",
+    "\n",
+    "boundary_deformation = boundary_normal(tissue_2,\n",
+    "                                       scale=5e-2,\n",
+    "                                       name='imposed deformation')\n",
+    "\n",
+    "\n",
+    "# Define the correspondning boundary conditions\n",
+    "from bvpy.boundary_conditions import dirichlet\n",
+    "\n",
+    "\n",
+    "drchlt = dirichlet(boundary_deformation, boundary='all')"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
->>>>>>> develop
    "metadata": {},
    "outputs": [],
    "source": [
     "# Define the variational form\n",
     "from bvpy.templates.vforms import LinearElasticForm\n",
     "\n",
-    "young = 1000 * pressure\n",
+    "young = 1000\n",
     "\n",
-    "elastic_equilibrium = LinearElasticForm(source=p_force, young=young)"
+    "elastic_equilibrium = LinearElasticForm(young=young)"
    ]
   },
   {
@@ -119,10 +197,10 @@
     "# Set the linear elastic\n",
     "from bvpy import BVP\n",
     "\n",
-    "pressurized_elastic_tissue_prblm = BVP(domain=tissue, vform=elastic_equilibrium, bc=drchlt)\n",
+    "stretched_elastic_tissue_prblm = BVP(domain=tissue_2, vform=elastic_equilibrium, bc=drchlt)\n",
     "\n",
     "# Solve the problem\n",
-    "pressurized_elastic_tissue_prblm.solve()"
+    "stretched_elastic_tissue_prblm.solve()"
    ]
   },
   {
@@ -132,9 +210,9 @@
    "outputs": [],
    "source": [
     "# Solution visualization\n",
-    "sol = pressurized_elastic_tissue_prblm.solution\n",
+    "sol_2 = stretched_elastic_tissue_prblm.solution\n",
     "\n",
-    "plot(sol)"
+    "plot(sol_2)"
    ]
   },
   {
@@ -146,9 +224,128 @@
     "# Save the solution to be used by a third party pipeline\n",
     "from bvpy.utils.io import save\n",
     "\n",
-    "path = 'solution.xdmf'\n",
+    "path = '../data/tutorial_results/solution_tuto5_2.xdmf'\n",
     "\n",
-    "save(pressurized_elastic_tissue_prblm, path)"
+    "save(stretched_elastic_tissue_prblm, path)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Heterogeneous tissue\n",
+    "Let's now consider that our structure represents a multicellular tissue where cells do not feature the same mechanical properties. For instance the Young's modulus of the outermost cells will be assumed higher than the one of inner cells."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# -- Generate a new instance of the same tissue this time with markers associated to cells.\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import fenics as fe\n",
+    "\n",
+    "tissue_3 = FaceCellularDomain(points, cells, markers=labels, resolution=.1)\n",
+    "\n",
+    "young_moduli = [3000 if tissue_3.cdata[cell.index()] == 1 else 1000 for cell in fe.cells(tissue_3.mesh)]\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "for cell in fe.cells(tissue_3.mesh):\n",
+    "    print(tissue_3.cdata[cell.index()])"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import fenics as fe\n",
+    "\n",
+    "from bvpy.utils.interface import create_expression\n",
+    "from bvpy.domains.geometry import get_boundary_facets\n",
+    "\n",
+    "\n",
+    "# -- useful functions\n",
+    "def get_boundary_cells(mesh):\n",
+    "    \"\"\"Finds the epidermal cells within a tissue.\n",
+    "    \"\"\"\n",
+    "    boundary_facets = get_boundary_facets(mesh)\n",
+    "    \n",
+    "    return [cell for cell in fe.cells(mesh) \n",
+    "            if any([facet in boundary_facets\n",
+    "                    for facet in fe.facets(cell)])]\n",
+    "\n",
+    "\n",
+    "def young_hetero(pos, mesh):\n",
+    "    \"\"\"Gives a specific value to epidermal cells\n",
+    "    \"\"\"\n",
+    "    for cell in fe.cells(pos):\n",
+    "        if cell in boundary_cells(mesh):\n",
+    "            return 3000\n",
+    "        else:\n",
+    "            return 1000\n",
+    "\n",
+    "\n",
+    "\n",
+    "fspace = fe.function.functionspace.FunctionSpace(tissue, 'P', 1)\n",
+    "\n",
+    "yng_modulus = create_expression(young_hetero, fspace, degree=1)\n",
+    "\n",
+    "elastic_equilibrium = LinearElasticForm(source=p_force, young=yng_modulus)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "mesh = tissue.mesh\n",
+    "\n",
+    "\n",
+    "\n",
+    "\n",
+    "\n",
+    "\n",
+    "                \n",
+    "get_boundary_cells(mesh) "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Define the variational form\n",
+    "from bvpy.templates.vforms import LinearElasticForm\n",
+    "\n",
+    "young = 1000 * pressure\n",
+    "\n",
+    "elastic_equilibrium = LinearElasticForm(source=p_force, young=young)"
    ]
   }
  ],
@@ -168,7 +365,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.7.7"
+   "version": "3.7.9"
   },
   "latex_envs": {
    "LaTeX_envs_menu_present": true,