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A Greedy Delaunay Based Surface Reconstruction Algorithm

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(1)A Greedy Delaunay Based Surface Reconstruction Algorithm David Cohen-Steiner, Frank Da. To cite this version: David Cohen-Steiner, Frank Da. A Greedy Delaunay Based Surface Reconstruction Algorithm. RR4564, INRIA. 2002. �inria-00072024�. HAL Id: inria-00072024 https://hal.inria.fr/inria-00072024 Submitted on 23 May 2006. HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés..

(2) INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE. A Greedy Delaunay Based Surface Reconstruction Algorithm David Cohen-Steiner — Frank Da. N° 4564 Septembre 2002. ISSN 0249-6399. ISRN INRIA/RR--4564--FR+ENG. THÈME 2. apport de recherche.

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(147) : ; 5 o8r%: 5 6 7%: ro 5%: r 6 9%: r 6 q%: q!; 9%: 6 4 :9 5 9%: r 4 :4=; 9%: 57r 9%: 6%4 5%: 8 6 9%: r 4 :r 5 5%: 6 8 4 :q 8 q%:4"r 7%: 9 8. q 6 o!6%4 ;<4 4"q 9 7 7!; 9 9 q%497q 7 o!8 8 5!; 8 7%49%49 o!6!; 87r ro7o8ro q%4"q7r 7 47 8 8o 47 8 6o o; 8 7 6 o!9 77r 5 6 5 67r 5%4 7 5!; ; 49 9 9 9 q 6%49o 45!; o7o 4 477r 9 r!;q 5 4"q 5 7 5 o

(148) 49%4 45!;r 8 57q 6 5%4 r7q7r%4 59959 49 9 9 9 5 97r%46 4o!8%45 7!; 67r 9. 4 48 5 7 5 4o!5 5%49 r7r 9 97q 49%48 6 6 6!; 7o!9 5 r%49 6 7 6 8 8%4 4 45 8 57r 9 49 5o!8 5!; 7 9 6 5!;q7q!; 6 5 87r%4 8 9%47 7 5 q 87q7q 7 r7q 7 5 46 6 9 8 4 4=; ; 9!; 57q 7 57q 5 5 77r 9 457q!;q 7 9o!7 8 ; 67q 8 57q 77r7r q%45 9%4 45 8 7 7 7 6 67ro 467r%4 4 o!9!; 57q 5 6 5o!8 ;q 7 8 6. Table 1: Running times. " $XW   ? 

(149) <7lY /H3

(150) 2  !l

(151)  Z l

(152) # %[   7l "(' W   []%El

(153) #. 2V. k7l

(154) 

(155) 7l $ !l%&  %# . ". "('. )*" /. 9 9 o7o!5 q7r!; 9 9 9 9 9 9 9 9 9 9 o. 4 :9 7 497q%: 5 8 7%:46 9%: 9o o;<: 87r ; 9%: 9 5 4 :9 7 9%: 7 7 4 : 9!; 4 : qo 7 7%: 57q 9%: 7 7 o

(156) : o8r 5%: q 8 9%: 9o 9%: 9o 9%B ro. 9 5 9%: 7 8 9%: 9%4 9%: 9 5 6!;<: ;q 48 5%: 5!; 9%: 9%4 9%: 9 7 9%: 9 5 9%: 9 5 9%: q7r 9%: 9%4 9%: 7 6 9%: 9o 9 9 9. 5%: 9 5 5 5 6%: o!5 q%: 67q 5%: 8o 46o

(157) : r 7 7%4"q%: r7q 4 : 8!; 9%: ; o 4 :6 6 5%: 67q ; 5%: 7 8 9%: q 6 8%: ;q q%: q 7 9%: q7r 9%: 9!; 4 B 87r. ; o!8 88 47 6 7 57q%4 7 7 7o 6 5%4 ;q 6 r7r7r ro

(158) 4 o8q7q 5 7%4 5887 ;q 5o r 8!; 59 69 o!6 6 4"r%4 77q7r 6 77q 5o 5o!5 4"r 8 r76 5 8!; ; o 7 8!; q%4"q 7!; o q 7%4. q%: 5!; %r : q 5 7%: 9o o

(159) : o!5 o!6%:45 5%: 7o 7%: 6o q%:47 7%: 67q 4 :o 4 :4"r 4"q%: 6 6 7!;<: o8r 5%: o 9%: 5o 9%: 8 5 q%: 57r 4 : 9o 9%: 6 8 9%: r%4 4 :7 9 9%: 7o 4 :9 7 5%: 6 8 9%: q7r 4 : ;<4 9%: 8o 4 : r7q 4 :5 6 7%: 7 7. 9%: 57q 9%: 9 7 7%: 5 6 9%:48 47%: o!7 9%: 7 7 9%: 9 5 9%: 9 5 9%: 9 5 9%:4=; 9 9%:45 o7o

(160) : q 8 9%:4 4 9 9 9%: 9 7 9 9%: 9%4 9%: 9%4 9%: 97r 9 9%: 9 7 9%: 9 5 9 9%: 9%4 9%: 9%4 9 9%: 97q. 49%: 6 8 45%: r!; 6%: 5!; 8%: ;q 4 46%: o!8 6%: 7 7 5 5%: ; 7 5 9%: 8 5 48%: ; 5 5%: ; o 5%: 5 7 5 9%: 8 7 45 8%: 7 7 r%:4"q 5%: 6 7 4 : q%4 49%: 87r 4 : 6o 5%: 9%4 4 :5 5 5%: q 7 9%: r 4 : 6!; q%: 8 6 4 :4"r 7%: 7o 7%: 8 5 5%: 8 8 r%: o8q r%: o8r. 49 97q. 9. (seconds).. "  W ?  El\ #   3 ? )^" / W    K ?  " $A_ "  _ "('.

(161) [k .

(162)  

(163)  !"$#%&'"()"'()*+&. TUacq.WYeN{bXd)acq%z(Xpw0–˜X|jpkd©r’wX|jHeh`qsk0woAj}kX|{’kUbeioghUSa©k%jHei`8k}mQaf`bqlq0UmQwzŠX|{bghXq%mQkCxsehaf`8kqœ Figure 5: Hand. w X|«jH¬behjH`Xqsz'k0wk.oAafj}`ŠkafkehU`SX UAdce|mQ”q.XH`w%e¥zt(mQehw0ok%`Aeh{b–!mQkw0Ubr’acq%X|qs{'k}gimJmhXik`œ[o{¢X 3_mQ–n`bwwX eiWYW—jqmhœP`¢kU­¢q0X<XeQX ?wXkweJUAack¨EmJacXHq0k%w|UŸ“'kUb­¢kUX obXHqwq0mhXXWYomJW—zbwX dcaf”.`bq0gYUAUbmQXH{bwwXHzŠX `kX|q0Ua©{bk X_ghrŠXqqjmhUAœ WYmhz`bdcgia X`q%g?m?afq%dceQjHk|dcX|“mJXwq0d©z(r¢X`bjHafehmhk%dc©q0rSo`DXjpmQafw.XH`Nkk|U“bX eidco'Xwghq Figure 6: British Museum. k[kml_npo8q7ro.

(164) B& W /b (T/*)/ L. & ' . i7\!&. 

(165) !!. q0'ƒ oobq0wz(z'X|wjpacq0k.af`bkUgid©mQr8k.“acUbq%ei{bdcXoqXlwkXe?WkmhUacX `ªXpac¬b`ªacqskkUX`X¥jHwX XjHehei–!`b¨EqsXHk0w0wroAjpkkUacacei`S`¦{'eQXH–k}mhkacUd q.Xq0”.XU¨EafXpj}w0U¢r£jHdfeimQobwdfgh{¢X`WYeQkleN{bt(XX_dcqq“mhWYmhd©kzUbdcX|ei{ŠoghjHUªehw0kwUXjpXHkr‚d©r8dcœe8eA;§”XdcPqmQWYzdcX|{œ ªX Figure 7: Large models. 7.

(166) [k .

(167)  

(168)  !"$#%&'"()"'()*+&. TjHeiU`8XŠk}mh¤bac`bwqsq%k¥a©k|WYœ eNT{'UXX_dq0acqYX|jHmhei` `{¢X|mQeiqs`br X jacq%mhq0WYXŠeQehw– X q0{bo'aEw0D–KmhjpjHoXŠd©k|”.“AmQa©kqU kUt(XHeiwoX `ac{q.mJ`w0e¥r8“ eht(tNX¨'jacehmhoobqq0X¢q0oAa©k¥jUSacq¥¨EehX|mQdcoqsWYr¦Xlke£–™eh{'wlXHqs¤Ar'`bWYX¢WYmŸXHk0¨Ew0ehr?dfobwWYX|mQXYq0ei”.`bUqœeiq0X¢t(eio`{mJw0r Figure 8: Engine. Figure 9: Hypersheet. Figure 10: Knuckle. _obwwX|jpei`qsk0wojpkacei`SeQ–kUacq.{baEDjpod©k%WYeN{bXdei`bd©r¢Umhq–˜ehobw%t(eiob`A{mJw0rX|{bghXqœ 3. k[kml_npo8q7ro.

(169) B& W /b (T/*)/ L. TmQzAUmJacq.w0k%q0UA–nwmheiz(W#X acq0q.ehWYUAmJX w}{’zbwkeie¥tbgQdcXw}WYmhq0qz)ei“A`’X¨EkXHU`ŠX ”.t(a©eikobU6`Am {'af0 `b¡g?t(¨Ne|afXp¬”œ XH w|“AjHmhdc`Aeh{’q0XHw_a©kq%dce8qemQ;ŠWYq0zUbdceJa `”.g¥q.ackq.UA`mJehk`¢kUobX`q0a©X–˜eQmJwwWSXœ[{b3_obX_obwke¥wX|XHjHw0ehweQ`wqsq%k0waco`¢jpkkacUbeiX `Sqacmhq.WYz(zbXHdcw0af–˜`bXgbjpkœ Figure 11: Tomo.

(170) [k .

(171) Unité de recherche INRIA Sophia Antipolis 2004, route des Lucioles - BP 93 - 06902 Sophia Antipolis Cedex (France) Unité de recherche INRIA Lorraine : LORIA, Technopôle de Nancy-Brabois - Campus scientifique 615, rue du Jardin Botanique - BP 101 - 54602 Villers-lès-Nancy Cedex (France) Unité de recherche INRIA Rennes : IRISA, Campus universitaire de Beaulieu - 35042 Rennes Cedex (France) Unité de recherche INRIA Rhône-Alpes : 655, avenue de l’Europe - 38330 Montbonnot-St-Martin (France) Unité de recherche INRIA Rocquencourt : Domaine de Voluceau - Rocquencourt - BP 105 - 78153 Le Chesnay Cedex (France). Éditeur INRIA - Domaine de Voluceau - Rocquencourt, BP 105 - 78153 Le Chesnay Cedex (France).   

(172).   . ISSN 0249-6399.

(173)

Figure

Figure 1: Valid candidates
Figure 2: Curve reconstruction : edges incident on ! and their radii
Figure 4: A difficult case at first sight
Table 1: Running times
+4

Références

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