1. College of Computer Science and Technology, Beijing Normal University, Beijing 100875, China 2. College of Art and Communication, Beijing Normal University, Beijing 100875, China 3. School of Electronics Engineering and Computer Science, Peking University, Beijing 100871, China
This paper presents a method for simulating surface crack patterns appearing in ceramic glaze, glass, wood and mud. It uses a physically and heuristically combined method to model this type of crack pattern. A stress field is defined heuristically over the triangle mesh of an object. Then, a first-order quasi-static cracking node method (CNM) is used to model deformation. A novel combined stress and energy combined crack criterion is employed to address crack initiation and propagation separately according to physics. Meanwhile, a highest-stress-first rule is applied in crack initiation, and a breadth-first rule is applied in crack propagation. Finally, a local stress relaxation step is employed to evolve the stress field and avoid shattering artifacts. Other related issues are also discussed, such as the elimination of quadrature sub-cells, the prevention of parallel cracks and spurious crack procession. Using this method, a variety of crack patterns observed in the real world can be reproduced by changing a set of parameters. Consequently, our method is robust because the computational mesh is independent of dynamic cracks and has no sliver elements. We evaluate the realism of our results by comparing them with photographs of realworld examples. Further, we demonstrate the controllability of our method by varying different parameters.
O’Brien J F, Hodgins J K. Graphical modeling and animation of brittle fracture. In: Proceedings of the 26th Annual Conference on Computer Graphics and Interactive Techniques. 1999, 137–146 https://doi.org/10.1145/311535.311550
2
Pfaff T, Narain R, de Joya J M, O’Brien J F. Adaptive tearing and cracking of thin sheets. ACM Transactions on Graphics, 2014, 33(4): 1–9 https://doi.org/10.1145/2601097.2601132
3
Song J H, Belytschko T. Cracking node method for dynamic fracture with finite elements. International Journal for Numerical Methods in Engineering, 2009, 77(3): 360–385 https://doi.org/10.1002/nme.2415
4
Molino N, Bao Z, Fedkiw R. A virtual node algorithm for changing mesh topology during simulation. ACM Transactions on Graphics, 2004, 23(3): 385 https://doi.org/10.1145/1015706.1015734
Melenk J, Babuška I. The partition of unity finite element method: basic theory and applications. Computer Methods in Applied Mechanics and Engineering, 1996, 139: 289–314 https://doi.org/10.1016/S0045-7825(96)01087-0
7
Rabczuk T. Computational methods for fracture in brittle and quasibrittle solids: state-of-the-art review and future perspectives. Applied Mathematics, 2013, 2013: 1–38
8
Lindblad A, Turkiyyah G. A physically-based framework for real-time haptic cutting and interaction with 3D continuum models. In: Proceedings of ACM Symposium on Solid and Physical Modeling. 2007, 421–429 https://doi.org/10.1145/1236246.1236307
9
Chao S. Simulation for cutting deformable model based on X-FEM. In: Proceedings of International Conference on Intelligent Computing and Cognitive Informatics. 2010, 436–439 https://doi.org/10.1109/ICICCI.2010.99
10
Kaufmann P, Martin S, Botsch M, Grinspun E, Gross M. Enrichment textures for detailed cutting of shells. ACM Transactions on Graphics, 2009, 28(3): 50 https://doi.org/10.1145/1531326.1531356
11
Jeřábková L, Kuhlen T. Stable cutting of deformable objects in virtual environments using XFEM. IEEE Computer Graphics and Applications, 2009, 29(2): 61–71 https://doi.org/10.1109/MCG.2009.32
12
Turkiyyah G M, Karam W B, Ajami Z, Nasri A. Mesh cutting during real-time physical simulation. In: Proceedings of SIAM/ACM Joint Conference on Geometric and Physical Modeling. 2009, 159–168 https://doi.org/10.1145/1629255.1629275
Wu J, Westermann R, Dick C. A survey of physically based simulation of cuts in deformable bodies. Computer Graphics Forum, 2015, 34(6): 161–187 https://doi.org/10.1111/cgf.12528
18
Norton A, Turk G, Bacon B, Gerth J, Sweeney P. Animation of fracture by physical modeling. The Visual Computer, 1991, 7(4): 210–219 https://doi.org/10.1007/BF01900837
19
Lloyd B A, Szekely G, Harders M. Identification of spring parameters for deformable object simulation. IEEE Transactions on Visualization and Computer Graphics, 2007, 13(5): 1081–1094 https://doi.org/10.1109/TVCG.2007.1055
20
Natsupakpong S, Çavu ¸soğlu M C. Determination of elasticity parameters in lumped element (mass-spring) models of deformable objects. Graphical Models, 2010, 72(6): 61–73 https://doi.org/10.1016/j.gmod.2010.10.001
21
Liu T T, Bargteil A W, O’Brien J F, Kavan L. Fast simulation of massspring systems. ACM Transactions on Graphics, 2013, 32(6): 214 https://doi.org/10.1145/2508363.2508406
Levine J A, Bargteil A W, Corsi C, Tessendorf J, Geist R. A peridynamic perspective on spring-mass fracture? In: Proceedings of the ACMSIGGRAPH/Eurographics Symposium on Computer Animation. 2014, 47–55
24
O’Brien J F, Bargteil A W, Hodgins J K. Graphical modeling and animation of ductile fracture. ACM Transactions on Graphics, 2002, 21(3): 291–294 https://doi.org/10.1145/566654.566579
25
Bao Z S, Hong J M, Teran J, Fedkiw R. Fracturing rigid materials. IEEE Transactions on Visualization and Computer Graphics, 2007, 13(2): 370–378 https://doi.org/10.1109/TVCG.2007.39
26
Busaryev O, Dey T K, Wang H. Adaptive fracture simulation of multilayered thin plates. ACM Transactions on Graphics, 2013, 32(4): 52 https://doi.org/10.1145/2461912.2461920
27
Matthias M, Gross M, Müller M. Interactive virtual materials. In: Proceedings of Graphics Interface. 2004, 239–246
28
James D L, Pai D K. Artdefo: accurate real time deformable objects. In: Proceedings of the 26th Annual Conference on Computer Graphics and Interactive Techniques. 1999, 65–72 https://doi.org/10.1145/311535.311542
29
Kielhorn L. A time-domain symmetric Galerkin BEM for viscoelastodynamics. Dissertation for the Doctoral Degree. Graz: Graz University of Technology, 2009
30
Zhu Y, Bridson R, Greif C. Simulating rigid body fracture with surface meshes. ACM Transactions on Graphics, 2015, 34(4): 150 https://doi.org/10.1145/2766942
31
Hahn D, Wojtan C. High-resolution brittle fracture simulation with boundary elements. ACM Transactions on Graphics, 2015, 34(4): 151 https://doi.org/10.1145/2766896
32
Müller M, Keiser R, Nealen A, Pauly M, Gross M, Alexa M. Point based animation of elastic, plastic and melting objects. In: Proceedings of ACM SIGGRAPH/Eurographics Symposium on Computer Animation. 2004, 141–151
33
Pauly M, Keiser R, Adams B, Dutré P, Gross M, Guibas L J. Meshless animation of fracturing solids. ACM Transactions on Graphics, 2005, 24(3): 957–964 https://doi.org/10.1145/1073204.1073296
34
Solenthaler B, Schläfli J, Pajarola R. A unified particle model for fluidsolid interactions. Computer Animation and Virtual Worlds, 2007, 18(1): 69–82 https://doi.org/10.1002/cav.162
35
Li C, Wang C B, Qin H. Novel adaptive SPH with geometric subdivision for brittle fracture animation of anisotropic materials. The Visual Computer, 2015, 31(6): 937–946 https://doi.org/10.1007/s00371-015-1117-8
36
Liu N, He X W, Li S, Wang G P. Meshless simulation of brittle fracture. Computer Animation and Virtual Worlds, 2011, 22(2-3): 115–124 https://doi.org/10.1002/cav.412
37
Hesham O. Fast meshless simulation of anisotropic tearing in elastic solids. Dissertation for the Doctoral Degree. Ottawa: Carleton University, 2011
38
Sifakis E, Der K G, Fedkiw R. Arbitrary cutting of deformable tetrahedralized objects. In: Proceedings of ACM SIGGRAPH/Eurographics Symposium on Computer Animation. 2007, 73–80
39
Wang Y T, Jiang C, Schroeder C, Teran J. An adaptive virtual node algorithm with robust mesh cutting. In: Proceedings of ACM SIGGRAPH/ Eurographics Symposium on Computer Animation. 2014, 77–85
40
Glondu L, Marchal M, Dumont G. Real-time simulation of brittle fracture using modal analysis. IEEE Transactions on Visualization and Computer Graphics, 2013, 19(2): 201–209 https://doi.org/10.1109/TVCG.2012.121
41
Hirota K, Tanoue Y, Kaneko T. Generation of crack patterns with a physical model. The Visual Computer, 1998, 14(3): 126–137 https://doi.org/10.1007/s003710050128
42
Hirota K, Tanoue Y, Kaneko T. Simulation of three-dimensional cracks. The Visual Computer, 2000, 16(7): 371–378 https://doi.org/10.1007/s003710000069
43
Gobron S, Chiba N. Crack pattern simulation based on 3D surface cellular automata. The Visual Computer, 2001, 17(5): 287–309 https://doi.org/10.1007/s003710100099
44
Gobron S, Norishige C. Simulation of peeling using 3D-surface cellular automata. In: Proceedings of the 9th Pacific Conference on Computer Graphics and Applications. 2001, 338–347 https://doi.org/10.1109/PCCGA.2001.962890
45
Federl P. Modeling fracture formation on growing surfaces. Dissertation for the Doctoral Degree. Calgary: University of Calgary, 2003
46
Paquette E, Poulin P, Drettakis G. The simulation of paint cracking and peeling. In: Proceedings of the Graphics Interface. 2002, 59–68
47
Valette G, Prévost S, Lucas L, Léonard J. A dynamic model of cracks development based on a 3D discrete shrinkage volume propagation. Computer Graphics Forum, 2008, 27(1): 47–62 https://doi.org/10.1111/j.1467-8659.2007.01042.x
48
Müller M, Chentanez N, Kim T Y. Real time dynamic fracture with volumetric approximate convex decompositions. ACM Transactions on Graphics, 2013, 32(4): 115 https://doi.org/10.1145/2461912.2461934
49
Raghavachary S. Fracture generation on polygonal meshes using voronoi polygons. In: Proceedings of ACM SIGGRAPH Conference on Abstracts and Applications. 2002, 187–187 https://doi.org/10.1145/1242073.1242200
50
Tang Y, Fang K J, Fu S H, Zhang L B. An improved algorithm for simulating wax-printing patterns. Textile Research Journal, 2011, 81(14): 1510–1520 https://doi.org/10.1177/0040517511404596
51
Schvartzman S C, Otaduy M A. Fracture animation based on highdimensional voronoi diagrams. In: Proceedings of the 18th Meeting of the ACM SIGGRAPH Symposium on Interactive 3D Graphics and Games. 2014, 15–22
52
Martinet A, Galin E, Desbenoit B, Akkouche S. Procedural modeling of cracks and fractures. In: Proceedings of Shape Modelling Applications. 2004, 346–349 https://doi.org/10.1109/SMI.2004.1314524
53
Wyvill B, van Overveld K, Carpendale S. Rendering cracks in batik. In: Proceedings of the 3rd International Symposium on Non-photorealistic Animation and Rendering. 2004, 61–149 https://doi.org/10.1145/987657.987667
54
Hsieh H H, Tai W K. A straightforward and intuitive approach on generation and display of crack-like patterns on 3D objects. In: Nishita T, Peng Q S, Seidel H P, eds. Advances in Computer Graphics, Vol 4035. Berlin: Springer Heidelberg, 2006, 554–561 https://doi.org/10.1007/11784203_51
55
Lu J Y, Georghiades A S, Glaser A, Wu H Z, Wei L Y, Guo B N, Dorsey J, Rushmeier H. Context-aware textures. ACM Transaction on Graphics, 2007, 26(1): 3 https://doi.org/10.1145/1189762.1189765
56
Wei L Y, Lefebvre S, Kwatra V, Turk G. State of the art in examplebased texture synthesis. In: Proceedings of Eurographicsthe ACM SIGGRAPH/ Eurographics. 2009, 93–117
57
Glondu L. Physically-based and real-time simulation of brittle fracture for interactive applications. Dissertation for the Doctoral Degree. Cachan: École normale supérieure de Cachan-ENS Cachan, 2012
58
Liu S G, Chen D. Computer simulation of batik printing patterns with cracks. Textile Research Journal, 2015, 85(18): 1972–1984 https://doi.org/10.1177/0040517514561919
Wicke M, Ritchie D, Klingner B M, Burke S, Shewchuk J R, O’Brien J F. Dynamic local remeshing for elastoplastic simulation. ACM Transactions on Graphics, 2010, 29(4): 49 https://doi.org/10.1145/1778765.1778786
61
Koschier D, Lipponer S, Bender J. Adaptive tetrahedral meshes for brittle fracture simulation. In: Proceedings of ACM SIGGRAPH/ Eurographics Symposium on Computer Animation. 2014, 58–66
Ventura G. On the elimination of quadrature subcells for discontinuous functions in the extended finite-element method. International Journal for Numerical Methods in Engineering, 2006, 66(5): 761–795 https://doi.org/10.1002/nme.1570
64
Fung Y C. A First Course in Continuum Mechanics. Englewood Cliffs, NJ: Prentice-Hall, 1994
65
Rusinkiewicz S. Estimating curvatures and their derivatives on triangle meshes. In: Proceedings of the 2nd International Symposium on 3D Data Processing, Visualization, and Transmission. 2004, 486–493 https://doi.org/10.1109/TDPVT.2004.1335277
66
Iben H N. Generating Surface Crack Patterns. Dissertation for the Doctoral Degree. Berkeley: University of California, Berkeley, 2007
