1、null null l : 2009- 01- 24; : 2009- 03- 19bnull null “ : Y v null 9 bnull null T e : + (1973- ), 3 , a1 , q ,p V , 1 Z _ :9 m a E C L ; null ( 1938- ), 3 , s , q , 1 Z _ : Y # e a E C L a 8 . ; null / (1982- ), 3 , ,p V 3 , 1 Z _ :D m ) a E C L b c I | : 1001- 9081( 2009) 07- 1901- 05 y T w V j E杨nu
2、ll 军1,诸昌钤2,邢null 琪2(1. Y v , 730070; null 2. 2 Y v S / , 610031)(yangj mai.l lzjtu. cn)K null 1 :针对由点云数据重建的隐式曲面提出一种新的基于粒子系统的可视化算法b首先,基于平行线束的初始化方法在隐式模型表面找到均匀分布的采样点,避免原来粒子系统中的分割-死亡过程;用共轭梯度法替代原来粒子系统中的梯度下降法作为优化算法,将每一个椭圆粒子累进移动到低能量状态,避免了较长的收敛时间和围绕最小值的摆动现象;用贪婪选择法选择能够覆盖整个曲面的且不产生空洞的活动子集;松弛过程进一步改善依赖曲率的各向异性粒子采
3、样b本文的粒子专门为基于 Splats的表示法而设计,可以直接转换为椭圆 Splats而不需要任何改动b因此,本算法可以快速a高质量地绘制出复杂隐式曲面模型b1 o M :粒子采样;曲面 splatting绘制;隐式曲面;点元;各向异性 m s | : TP391null null D S : AA lgorithm for visualization of implicitsurfaces reconstructed from point cloud dataYANG Jun1, ZHU Changnullqian2, XING Qi2(1. School ofMechanicalandEl
4、ectricalEngineering, LanzhouJiaotongUniversity, LanzhouGansu 730070, China;2.School of InformationScienceandTechnology, SouthwestJiaotong University, Chengdu Sichuan 610031, China)Abstract: In this paper, a novel rendering algorithm for implicit surfaceswhich are reconstructed from point cloud datab
5、y using a particle system was presented. First, an alternative initial technique based on bundles ofparallel lineswas used tofind initial points thatwere evenly distributed on the surface. Becauseof its characteristics, the usualsplitnullandnulldeath criterionof particle system was not needed. Secon
6、d, each ellipticalparticlewasmoved towards aprogressively lower energy stateusinga conjugate gradientmethod, which replaced the gradientnulldescent as an optim ization method to avoid very long convergencetime and irreconcilable oscillation around the minimum. Third, a greedy selection strategy was
7、used to choose a subset ofactive particleswhich guarantee a holenullfree approximation. Finally, a relaxation process further improves the curvature drivenanisotropic particlesampling. Theproposed ellipticalparticleswere specially designed for splatnullbased representation and couldbe directly conve
8、rted into elliptical surface Splats without any modification, thus highnullperformance rendering of compleximplicit surfaces can be obtained.Keywords: particle sampling; surface splatting rendering; implicit surface; point element; anisotropic0null 引言 V T m , m 9 7 Ss , 5( b) U bm 5null 0 W b h “ 4
9、V ? b V 0 s , 7 4 0 S = % , “ i 0 s , H 3 0 ,y N , E B V 20 B 0 _ s s b 4 B ? K l K v 0 “ , 9 0 ,i O 1 b H q b 0 0 W 4 , 0 W M l 20, V _ 0 b4null 绘制Surface Splatting E 8 E , 1 X 8 bW Splats( Splats)/ , m bW F t Splats( Splats) V b 4 Surface Splatting E T w , 1 y : 1) y B B e T w “ d bV Splats ,7 O Z
10、 E Splats 1 H L C , y N , V m ;2) 0 V Splats, 1 ,y N ,4 b E 0 pi = (ci, ni, ui, vi) V Splats ti = (ci, ni, ui, vi ), i T m b w + , n 5 , Splats M l B 2D y W i, y f _ f ; Q ,| 2D y M g m bW b B S Ii, g m bW x) y I(x) T (19) bI(x) =2) 0 “ m 1 “ M ,% u , wq M v Z , 0 bW S l 7 O 0 v ,7 u , 1 0 ,7 O 0 bW
11、 S Y v bm 7null T w Igea 0 “ m 8 U i V e V 0 “ bWS , Stanford Bunny T w , D 17 E 3 b l , V 0 s ,M , 0 bW S 9 l b m 8( a) ! 2 10- 3 H , 2464 0 s Stanford Bunny Tw V ,m 8( b) ! 2 10- 4 H , 11877 0 s Stanford Bunny T w V b E V T w V 3 $ 0 “ ,i V m ,7 WnullHZ E ? ) e ,Y ? “ + 0 ,K $ b 1 knull # v l 1 ,7
12、 O , ! B “ bm 8null / 0 “V 1 , E H W , , 0 “ H W 0 S aM 0 ae H W 7 g b 2 10- 4 H , c 11877 Splat 0 s Stanford Bunny T w 101. 4 s( 0 “ 72. 3 s, 29. 1 s) V E ,7 WnullH E + ? b V A , T w Vj E d r bV 1null E H W d 9 0 0 “ H W /s H W /sTours 626 3. 1 4. 5Igea 9322 59. 7 27. 0Stanford Bunny 11877 72. 3 29
13、. 16null 结语 4 B 0 “ SurfaceSplatting T w E , y B B e T w Vj “ d bY V 3 L , V s ( s S “ b w q e _ s “ ,n 5 ,9 0 bW S i l 0 ? f (w q M 1 ), 0 E 0 M ? ; Q , B 4 , 4 ? V K l 0 “ , V 3 b ;K , V B 0 _ s s + b , 0 Splats, SurfaceSplatting E T w b I D :1null LEVOY M, WHITTEDT. Theuseofpoints as displayprimi
14、tive, TR85null022R. University ofNorth Carolina, 1985.2null GROSSMAN J P, DALLYW J. Point sample renderingEB /OL.2008 - 11 - 20. http: /cva. stanford. edu /publications/1998 /psr. ps.3null LORENSONW E, CLINE H F. M arching cubes: A high resolution3D surface construction algorithm J. Computer Graphic
15、s, 1987,21(4): 163- 169.4null WYVILL B, MCPHEETERS C, WYVILLG. Data structure for softobjectsJ. TheVisualComputer, 1986, 2(4): 227& 234.5null SHIRLEY P, TUCKMAN A. A polygonal approximation to directscalar volume renderingJ. ComputerGraphics, 1990, 24(5): 63- 70.6null HALLM, WARREN J. Adaptive polyg
16、onalization of implicitly denullfined surfaces J. IEEE Computer Graphics and Applications,1990, 10(6): 33- 42.7null W ITKIN A P, HECKBERT P S. Using particles to sample and connulltrol implicit surfacesC / Proceedings of the 21stAnnualConfernullence on ComputerGraphics and InteractiveTechniques. New
17、 York:ACM, 1994: 269- 278.8null ZW ICKERM, PFISTERH, BARR J, etal. Surface splattingC /Proceedings of the 28th Annual Conference on Computer Graphicsand InteractiveTechniques. New York: ACM, 2001: 371- 378.9 null BOTSCH M, SPERNAT M, KOBBELT L. Phong splattingEB /OL. 2008- 11 - 20. http: /www. graph
18、ics. rwthnullaachen. de/uploads/media/phong_splatting. pd.f10null SZELISKIR, TONNESEN D. Surfacemodelingw ith oriented parnullticle systemsJ. ACM SIGGRAPH ComputerGraphics, 1992, 26(2): 185- 194.(下转第 1909页)null1905第 7期 杨军等:由点云数据重建的隐式曲面的可视化算法 null null null null T w Z E V , i z B bK , T w ? L ? 4 B ,
19、 s null b Z E ) “ ? 8 9 v , 9 H W v v 9 F , K 9 ? M V H W bT / B T , i E A 5 F E V ,h E H W b I D :1null , k . E ? 3 % 1 J. 3 D , 2003, 20(1): 19- 82.2null S , , 2 .B ? % 3 9 _ J. 3 , 2001, 18(6): 22- 25.3null . , k . % 1 3 “ d _ J.9 _ , 2005, 22(2): 228- 231.4null CLATZO, SERMESANTM, BONDIAU P Y, e
20、tal. Realistic simunulllation ofthe3nullD grow th ofbrain tumors inMR images coupling diffunullsion w ith biomechanical deformation J. IEEE Transactions onM edical Imaging, 2005, 24(10): 1334- 1346.5 null GAN JIANnullHONG, DAI PEInullDONG, PENG QIANG, et al. Thesimulation of benign tumor growth in b
21、lood vessels circumstanceC / 2008 International Conference on Computer Science andSoftware Engineering. New York: IEEE, 2008: 223- 227.6 null SAMET H. Quadtree, Octrees, and Other HierarchicalM ethodsM . New Jersey: AddisonW esley, 1989.7null JACKINS C, TANIMOTO S. Octnulltrees and theiruse in repre
22、sentingthreenulldimensional objects J. Computer Graphics and Image Pronullcessing, 1980, 14(3): 249- 270.8null LORENSON W E, CLINEH F. M arching cubes: A high resolution3D surface construction algorithm J. ComputerGraphics, 1987, 21(4) : 163- 169.9null WYVILL B, MCPHEETERS C, WYVILL G. Data structur
23、e for softobjects J. TheVisualComputer, 1986, 2(4): 227- 234.10null . E # ! 9 D. q : q v , 2002.11null . E J.% 8 , 2004, 25(2): 203-207.12null 4 . 1 E K Z E # L C D. : S / v , 2007.13null + . . y E D. : 2 Yv , 2007.14null SAVCHENKO V V, PASKO A, OKUNEV O G, etal. Functionrepresentation of solids rec
24、onstructed from scattered surface pointsand contoursJ. ComputerGraphics Forum, 1995, 14(4): 181-188.15null TURK G, BRIEN J O. Variational Implicit SurfacesEB/OL.2008 - 11 - 15 . http: /graphics. cs. uiuc. edu/ jch /cs497jch/variationalnullis. pd.f16null GASCUELM PC, DESBRUNM. Animation ofdeformablem
25、odelsusing implicit surfaces J. IEEE Transactions on Visualization andComputerGraphicsc, 1997, 3(1): 39- 50.17null GASCUELM P. An implicit formulation forprecise contactmodelnulling between flexible solidsC / Proceedings of the 20th AnnualConference onComputerGraphics and InteractiveTechniques. NewY
26、ork: ACM, 1993: 313- 320.18 null MOORE M, W ILHELMS J. Collision detection and response forcomputer animationJ. ComputerGraphics, 1988, 22(4): 289-298.19 null BARAFF D. Coping w ith friction for nonnullpenetrating rigid bodysimulationJ. ComputerGraphics, 1991, 25(4): 31- 40.20null BARAFF D. Fast con
27、tact force computation for nonnullpenetrating rignullid bodiesC /ACM SpecialInterestGroup on ComputerGraphicsand InteractiveTechniques. New York: ACM , 1994: 23- 34.21null HEIDELBERGER B, TESCHNERM, KEISER R, etal. Consistnullent penetration depth estimation for deformable collision responseEB/OL. 2
28、008- 11- 15. http: /www. beosi.l com /download /PenetrationDepth_VMV04. pd.f22null ZHU BO, GU LInullXU, ZHANG JINGnullSI. Amethod for collision renullsponse between deformable objects in virtual surgeryC / Pronullceedings of the 6th International Special Topic Conference onITAB. New York: IEEE, 2007
29、: 119- 122.23null FISHER S, LINM C. FastPenetration Depth Estimation ForElasnullticBodiesUsingDeformedDistanceFieldsEB /OL. 2008- 11-15. http: /www. cs. unc. edu/ geom /DDF/(上接第 1905页)11null TURK G. Renull tiling polygonal surfaces J . ACM SIGGRAPHComputerGraphics, 1992, 26(2): 55- 64.12null HART J
30、C, BACHTA E, JAROSZW, et al. Using particles tosample and control more complex implicit surfaces C /International Conference on Computer Graphics and InteractiveTechniques. New York: ACM, 2002: 129- 136.13null MEYERM D, GEORGEL P, WH ITAKER R T. Robustparticlesystems for curvaturedependantsampling o
31、f implicitsurfacesC /Proceedings of the InternationalConference on ShapeM odeling andApplications 2005. W ashington, DC: IEEE Computer Society,2005: 124- 133.14null LEVET F, HADIM J, REUTER P, etal. Anisotropic sampling fordifferentialpoint rendering of implicit surfacesEB/OL. 2008-11 - 20 . http: /
32、iparla. labr.i fr/publications/2005/LHRS05/particleDifferentia.l pd.f15null KALAIAH A, VARSHNEY A. Differentialpoint renderingC /Proceedings of the 12th Eurographics Workshop on RenderingTechniques. London: SpringernullVerlag, 2001: 139- 150.16null PFISTER H, ZW ICKER M, GROSS M. Surfels : surfaceel
33、ements as rendering prim itivesC / Proceedings of the 27thAnnual Conference on Computer Graphics and InteractiveTechniques. New York: ACM, 2000: 335- 342.17null YANG J, WANG Z, ZHU C, etal. Implicitsurface reconstructionfrom scattered pointdataw ith noiseC / Proceedings of the 7thInternational Confe
34、rence on Computational Science. Berlin:SpringernullVerlag, 2007: 57- 64.18null ALEXANDER K . QuasinullMonte Carlo methods for photorealisticimage synthesis D . Kaiserlautert: University of Kaiserlautert,1997.19null DECORETX, DURAND F, SILLION F X, etal. Billboard cloudsfor extreme model simplification J . ACM Transactions onGraphics, 2003, 22(3): 689- 696.20null TURK G. Generating textures on arbitrary surfaces using reactionnulldiffusionJ. ComputerGraphics, 1991, 25(4): 289- 298.1909第 7期 甘建红等:基于元胞自动机的肿瘤生长形态动态模拟 null null null null
