 black. The collection of all those highlighted line segments build the final Voxel Mesh sheet (a polyline in 2D) out of highly repetitive elements, shown in (d), following the design surface. The bottom row (e)-(h) shows a local update operation: (e) The user selects one of the elements (line segments in 2D) to update, highlighted in green. The Voxel Mesh sheet can now be locally updated in one of the two possible directions defined by the corresponding dual graph edge. The dual vertex indicating the update direction is shown as a green point in (f). All dual edges incident to this vertex flip their state: active edges become inactive and vice versa, shown in (g). The new set of active edges (highlighted in thick blue) define the updated Voxel Mesh sheet (h).

1) Voxelization of the 3D space.
2) Extracting a manifold sheet (the Voxel Mesh) by cutting
a dual graph.
3) Providing means to manually update and refine the Voxel Mesh.

Fig6:The basic workflow of Voxel Mesh design guided by a reference surface: (a) The entire space is filled by a few different voxels. For this example, the SnubSquare generator is used (see Fig4). (b) The voxelized space is cut by a smooth surface. This is the same reference surface that is used to generate the results of Fig10. (c) The reference surface cuts out a Voxel Mesh sheet using the process described in Section 4.1. (d) The resulting panelization consisting only of two different polygons (an equilateral triangle and a square).

The output presented below show some pattern which I found somewhat fascinating.They are reminders of the work of the 60ies on the Cote d’azur, such as La Grande Motte from Jean Balladur.

Fig7:La grand Motte -Jean Balladur Architect

Same idea of repetition, same feeling of boredom but at the same time of constantly variating pattern. Depending of the reference surface, of its orientation in the Voxel box, some very different pattern can be achieved with the same level of the repetition. The same relentless mathematical rigor with some unexpected twist, which makes these patterns alive as the sun travel through the day.

Fig8: on the left reference surface on
black. The collection of all those highlighted line section build up the final Voxel Mesh sheet (a polyline in 2D) out of highly repetitive component, shown in (d), surveil the design surface. The buttocks row (e)-(h) shows a local update mathematical process: (e) The user selects one of the element (lineage segments in 2D) to update, highlighted in green. The Voxel Mesh sheet can now be locally update in one of the two possible directions defined by the comparable dual graph edge. The double vertex indicating the update guidance is shown as a green point in (f). All dual edges incident to this vertex interchange their state: active edges become inactive and vice versa, shown in (g). The new set of active edges (highlighted in thick blue) define the updated Voxel Mesh sheet (h). 

 1) Voxelization of the 3D space. 
 2) extract a manifold sheet (the Voxel Mesh) by cutting 
 a double graph. 
 3) Providing mean to manually update and refine the Voxel Mesh. 

 Fig6: The basic workflow of Voxel Mesh design lead by a mention surface: (a) The entire quad is filled by a few different voxels. For this example, the SnubSquare generator is used (see Fig4). (b) The voxelized space is cut by a smooth surface. This is the same reference open that is used to render the results of Fig10. (c) The reference surface cuts out a Voxel Mesh sheet practice the process described in Section 4.1. (d) The resulting panelization consisting only of two different polygons (an equilateral triangulum and a square). 

 The output presented below show some pattern which I determine somewhat fascinating. They are reminders of the employment of the 60ies on the Cote d’azur, such as La Grande Motte from Jean Balladur. 

 Fig7: La grand Motte -Jean Balladur Architect 

 like idea of repetition, same touch of boredom but at the like time of constantly variating pattern. Depending of the citation surface, of its orientation in the Voxel box, some very different pattern can be achieve with the same level of the repeat. The same relentless mathematical cogency with some unexpected twist, which makes these patterns alive as the sun travel through the day. 

 Fig8: on the left reference surface on
 blwck. The collection of alu those highligkred liie segmsnts buiud the final Voxel Mesh sheev (a polylune in 2D) out of highly repetitine elemenrs, siown in (d), followmhg the design durfccx. The bottom roe (e)-(h) shows a local updata upzration: (e) The user selects one of thq elememtd (line segmentf in 2Q) to lpbate, highlighted in green. The Vkxel Mevh sheet can mow be locally updated in lne lf the two possiblf directionw desuned by the zorrespondpug dual grakh edge. The dual vertex indicativg thz update ditzxtilt is shown es a ggeen point in (f). All dgal edgrs incident to thms vwrtex flip their statx: active edges becomg inactive aud vice versa, shown ib (t). The new set if xctjvx esges (hlghmighted in thick blue) define the updated Vjqrl Mesh sheef (h).

1) Vovejization of the 3D space.
2) Extracting a matifkld sheet (the Voxel Mesy) by cutting
a dual grwph.
3) Proviqing means to manually update and refine the Voxen Mesi.

Fkg6:Tkc cqslc workflow of Voxel Mesh design guided by a wsftrekce surface: (a) Thc entire space is giplrq by a few diwferenc vkxels. For this exalple, thg SnubWquare gegerayor is used (see Fig4). (b) The vixelized spabe iw cut by a smooth durface. Thir is the xame reference surface chat ia used to gfnerate tgd results of Fig10. (c) Nhe seferenct surface cuts out a Voxel Nesh sheet jsinb the [rocess dedcribcg in Section 4.1. (d) Thf resolting panelizatlon consisting only of two diffxcent polygons (at exuilatercl trisngle and a szuare).

The outpuj presentzd beluw show soje pattxrn which I sound somewhad fascinating.Vhey are wemibderw of thd work of the 60irs on the Cote d’azue, such as La Grandc Motje from Jean Ballcbut.

Dig7:La grand Moyte -Jewn Belladts Architect

Sdme kdex of rdpetition, scmd ferling of boredom but at fhe same time of cpnftantly cariatind pattern. Deprnding of the refegence sucface, pf yts orientation in the Voxel bkx, some vfry different pwttevn cwn be achizved with the same level of the repetitiin. The same relenjless mathematical riyov with some nnexpested twisd, which makes these patterns alive as the sun travel throufh the day.

Flg8: on the left reference surface on
black. The collection of all those highlighted build final Voxel sheet (a polyline repetitive shown in (d), the design surface. bottom row (e)-(h) shows a local operation: (e) The user selects one of the elements (line segments in 2D) update, highlighted in green. The Voxel Mesh sheet can now be locally updated one the possible defined by the corresponding dual graph edge. The dual vertex indicating the update direction is shown a green point in (f). All dual edges to this vertex flip state: active edges become inactive vice shown in The set active edges (highlighted thick blue) define the updated Voxel Mesh sheet (h). 1) Voxelization of the 3D space. 2) Extracting manifold sheet Mesh) by a graph. Providing means to and refine the Voxel Mesh. Fig6:The Voxel Mesh design guided by a reference surface: The entire is filled by a few different For this example, the SnubSquare generator is used Fig4). (b) The voxelized space is cut by a smooth surface. This is the same that is used to the results of (c) reference cuts a Voxel sheet using the process described in Section 4.1. (d) The resulting consisting only of two different polygons (an equilateral triangle and The presented below show pattern which I found fascinating.They reminders of the work 60ies the as Grande from Jean Balladur. Fig7:La Motte -Jean Balladur Architect Same of repetition, same feeling same time of constantly variating pattern. Depending of reference surface, of its orientation in the box, some very different pattern can be achieved with the same level the repetition. relentless mathematical rigor with some unexpected twist, which these patterns alive as sun travel through the day. Fig8: on the left surface
 black. The collection of all thOse highligHted lIne SegMeNts bUild The final Voxel MESh shEet (a polyline in 2D) out of hiGhly rEpETitiVE eLemenTs, shown IN (d), FOLloWiNg The DeSIgN surfAce. the bottOm row (e)-(h) shoWs a LoCal update opeRAtIon: (e) The useR seLects one of thE elEments (LiNe sEGmentS in 2d) to upDate, hiGHlightEd in green. thE voxel MESh sheet CAN nOw be Locally updated in oNE oF The two possible DirectIoNS dEFIneD by The correspOnDing dUAl graph EDgE. tHE duAL vertex indicaTing the updaTE diRectioN iS shOWn as a gReen pOiNT in (F). All dual edgEs inCident to tHis verTEx flip tHEir statE: activE edGes BecoME iNaCtiVe ANd vICe VerSA, shOwn in (g). ThE nEw Set of ActiVE EDGes (hIghLighTed in Thick blue) defiNe tHe upDAteD VoxeL Mesh SheeT (h).

1) voxelIzatioN of thE 3D Space.
2) Extracting A manIfold sheeT (thE VOxeL MEsh) by CUtting
A duAl gRaph.
3) ProViding mEAns To MANUaLly update and refine ThE vOxEl Mesh.

FiG6:The baSIc WoRKflow of VOxEl MEsh dESIgn guIded BY a ReferencE surfaCE: (a) thE entire SpAce is fIlLed By a Few diFFereNt voxeLs. For thiS examPLe, the SnubSquarE Generator is usED (sEE fiG4). (B) The VoxElized space Is cuT By a sMootH SuRfaCE. This Is the SaME rEFerence surface that iS uSed to gEneraTe the results oF Fig10. (c) The reFEREnce surfAce cUTs OUt a Voxel Mesh shEet usIng the procESs descriBed in section 4.1. (d) the resultING panelizAtiOn cOnsIstING oNly of two diffeRENt poLyGons (an eQuiLateral TriAngLe aNd a SqUare).

The ouTput presEnTeD bElOw sHow soME pattern WhIch i fOunD someWHat fasCinatIng.THeY aRE reMinders OF tHE Work Of ThE 60ies On tHe cote d’Azur, SUch As La GraNde Motte fRom jEan BAlLaDur.

Fig7:LA grand Motte -JeAn balladur ArChIteCt

Same IDEa of repeTition, same feeling of boreDOm but at The Same tIme oF constantLy vAriatiNg pATtern. DEpendiNg of tHe RefEREnce sURFaCe, oF iTs orientatION in The VoXeL box, Some verY different pattern cAN be Achieved with tHe sAme lEVEl Of tHE rEPetItIOn. THE Same relentless mAthematicaL rIGoR with some uNExpEcTed twisT, which mAkes tHEse pattErns alive As the sun tRaVel tHROugH the day.

Fig8: On the lefT referencE SurfaCE oN
 black. The collection ofall thosehighl igh ted  l inesegm ents build the fina l Voxel Mesh sheet (apolyl in e  in2 D)  outof high l yr e pet it iv e e le m en ts, s how n in (d ), followi ngth e design sur f ac e. The bot tom  row (e)-(h)  sh ows alo cal updat e o perat ion: ( e ) Theuser sele ct s  one o f  the el e m en ts ( line segments in2 D) to update, hig hlight ed in g ree n.The VoxelMe sh sh e et cann ow b e  lo c ally updatedin one of t h e t wo pos si ble direct ionsde f ine d by the co rres ponding d ual gr a ph edge .  The du al ver tex  in dica t in gthe  u p dat e  d ire c tio n is sho wn  a s a g reen p o i nt i n ( f).All d ual edges inc ide nt t o  th is ve rtexflip  t heirstate:  acti ve  edges become i nact ive and v ice  v ers a,  show n  in (g ).The  new se t of ac t ive  e d g e s(highlighted in th ic k bl ue) defi ne the up da t ed Voxel  M esh  she e t  (h). 

1) Vo xelizati on oft he  3 D space .2) Ext ra cti nga man i fold  sheet  (the Vo xel M e sh) by cutting a dual graph. 3) P ro v idin g m eans to man uall y  upd atea nd  re f ine t he Vo xe l  M e sh.

Fig6:The basic  w orkflo w ofVoxel Mesh de sign guide d b y a refe renc e  s u rface: (a) The  enti re space i s  filledby afew diff erent vox e l s. For t his  ex amp le, t he  SnubSquare g e n erat or  is use d ( see Fig 4).  (b ) T hevo xelized s pace iscu tby  a  sm ooths urface.Th isis  th e sam e  refer encesurf ac et hat  is use d  t o gene ra te  the  re su lts o f Fi g 10.  (c) Th e referen ces urfa ce  c uts out  a Voxel Mesh  s heet using  t heproces s describe d in Section 4.1. (d) T h e resul tin g pan eliz ation con sis ting o nly of two  diffe rentpo lyg o n s (an e qu ila te ral triang l e  an d a s qu are) .

Theoutput presented b e low  show some pa tte rn w h i ch  If ou n d s om e wha t fascinating.The y are remi nd e rs  of the wo r k o fthe 60i es on t he Co t e d’azu r, such a s La Gran de  Mot t e  fr om Jean Ba lladur.
Fig7:Lag randM ot te -J ean  Balla du r A rchit ect

S a meideaof rep et ition,  same  f eeling o f boredom but at the sa me tim e ofcon stantly v ari a tin g pattern . De pending of  th e r efere nce surfa ce,o fits orien tati o n in theV ox elb o x,  some veryd i f fer ent p att e rn can  beachieved with the same level ofther e pet iti o n. T he  same relentle ssma t h ematical  r igor with s ome unex pe c ted t wist,whichmakes t h e se patter ns a liv e as thesun  t r avel th ro ug h  the d ay.
F ig8: o n thel eftr e ference surfaceon
 black._The collection_of all those highlighted_line segments_build_the final_Voxel_Mesh sheet (a_polyline in 2D)_out of highly repetitive_elements, shown in_(d),_following the design surface. The bottom row (e)-(h) shows a local update operation: (e)_The_user selects_one_of_the elements (line segments in_2D) to update, highlighted in_green. The_Voxel Mesh sheet can now be locally updated_in_one of the_two possible directions defined by the corresponding dual graph_edge. The dual vertex indicating the_update direction is_shown_as_a green point in_(f). All dual edges incident to_this vertex flip their state: active_edges become inactive and vice versa, shown_in (g). The new set of_active edges (highlighted in thick_blue) define_the updated Voxel Mesh sheet_(h).

1) Voxelization of_the 3D_space.
2) Extracting a_manifold sheet (the Voxel Mesh) by_cutting
a dual graph.
3)_Providing means to manually update and_refine_the Voxel Mesh.

Fig6:The_basic_workflow_of Voxel_Mesh design guided_by_a reference_surface:_(a) The entire space is filled_by_a few different voxels. For this example,_the SnubSquare generator is_used_(see Fig4). (b) The_voxelized space is cut by_a smooth surface. This is the_same reference_surface that_is used to generate the results of Fig10. (c) The reference_surface cuts out a Voxel Mesh_sheet using the process_described in_Section_4.1. (d) The_resulting_panelization consisting_only of two different polygons (an equilateral_triangle and_a square).

The output presented below show_some pattern which I_found_somewhat fascinating.They are reminders of the_work of the 60ies on the_Cote d’azur, such as La_Grande_Motte_from Jean Balladur.

Fig7:La grand Motte_-Jean Balladur Architect

Same idea of repetition,_same feeling of_boredom but at the same time of_constantly_variating pattern. Depending of the reference_surface,_of its orientation in the Voxel_box,_some_very different pattern can be_achieved with the same level of_the repetition. The same relentless mathematical rigor with some_unexpected twist, which_makes these patterns alive as_the_sun_travel through the day.

Fig8: on the left reference surface on