Splitting meshless deforming objects with explicit surface tracking

We present a novel algorithm for efficiently splitting deformable solids along arbitrary piecewise linear crack surfaces in cutting and fracture simulations. The algorithm combines a meshless discretization of the deformation field with explicit surface tracking using a triangle mesh. We decompose the splitting operation into a first step where we synthesize crack surfaces, and a second step where we use the newly synthesized surfaces to update the meshless discretization of the deformation field. We present a novel visibility graph for facilitating fast update of shape functions in the meshless discretization. The separation of the splitting operation into two steps, along with our novel visibility graph, enables high flexibility and control over the splitting trajectories, provides fast dynamic update of the meshless discretization, and allows for an easy implementation. As a result, our algorithm is scalable, versatile, and suitable for a large range of applications, from computer animation to interactive medical simulation.

[1]  Ted Belytschko,et al.  THE ELEMENT FREE GALERKIN METHOD FOR DYNAMIC PROPAGATION OF ARBITRARY 3-D CRACKS , 1999 .

[2]  Markus H. Gross,et al.  Interactive Cuts through 3‐Dimensional Soft Tissue , 1999, Comput. Graph. Forum.

[3]  Markus H. Gross,et al.  A state machine for real-time cutting of tetrahedral meshes , 2004, Graph. Model..

[4]  Ronald Fedkiw,et al.  Fracturing Rigid Materials , 2007, IEEE Transactions on Visualization and Computer Graphics.

[5]  Demetri Terzopoulos,et al.  Modeling inelastic deformation: viscolelasticity, plasticity, fracture , 1988, SIGGRAPH.

[6]  Ted Belytschko,et al.  A finite element method for crack growth without remeshing , 1999 .

[7]  P. Koumoutsakos.  MULTISCALE FLOW SIMULATIONS USING PARTICLES , 2005 .

[8]  L. Guibas,et al.  Meshless animation of fracturing solids , 2005, ACM Trans. Graph..

[9]  Paolo Cignoni,et al.  A Multiresolution Model for Soft Objects Supporting Interactive Cuts and Lacerations , 2000, Comput. Graph. Forum.

[10]  Leonidas J. Guibas,et al.  Deformable spanners and applications. , 2006, Computational geometry : theory and applications.

[11]  H. Matthies,et al.  Classification and Overview of Meshfree Methods , 2004 .

[12]  Paul A. Wawrzynek,et al.  Automated 3‐D crack growth simulation , 2000 .

[13]  Han-Wen Nienhuys,et al.  Combining finite element deformation with cutting for surgery simulations , 2000, Eurographics.

[14]  Stephane Cotin,et al.  A hybrid elastic model for real-time cutting, deformations, and force feedback for surgery training and simulation , 2000, The Visual Computer.

[15]  Gabriel Zachmann,et al.  Proximity Graphs for Defining Surfaces over Point Clouds , 2004, PBG.

[16]  Daniel Vallejo,et al.  OBPRM: an obstacle-based PRM for 3D workspaces , 1998 .

[17]  Takeo Kanade,et al.  Progressive cutting with minimal new element creation of soft tissue models for interactive surgical simulation , 2001 .

[18]  P. Lancaster,et al.  Surfaces generated by moving least squares methods , 1981 .

[19]  Nina Amenta,et al.  The Domain of a Point Set Surface , 2004, PBG.

[20]  Markus H. Gross,et al.  Optimized Spatial Hashing for Collision Detection of Deformable Objects , 2003, VMV.

[21]  Leonidas J. Guibas,et al.  Meshless animation of fracturing solids , 2005, ACM Trans. Graph..

[22]  Markus H. Gross,et al.  Contact Handling for Deformable Point-Based Objects , 2004, VMV.

[23]  Gábor Székely,et al.  Hybrid Cutting of Deformable Solids , 2006, IEEE Virtual Reality Conference (VR 2006).

[24]  Xavier Provot,et al.  Collision and self-collision handling in cloth model dedicated to design garments , 1997, Computer Animation and Simulation.

[25]  Ronald Fedkiw,et al.  A virtual node algorithm for changing mesh topology during simulation , 2004, SIGGRAPH 2004.

[26]  Marc Alexa,et al.  Point based animation of elastic, plastic and melting objects , 2004, SCA '04.

[27]  Mark A Fleming,et al.  Continuous meshless approximations for nonconvex bodies by diffraction and transparency , 1996 .

[28]  Marshall W. Bern,et al.  A new Voronoi-based surface reconstruction algorithm , 1998, SIGGRAPH.

[29]  Ronald L. Rivest,et al.  Introduction to Algorithms , 1990 .

[30]  Subhash Suri,et al.  An Optimal Algorithm for Euclidean Shortest Paths in the Plane , 1999, SIAM J. Comput..

[31]  Takeo Kanade,et al.  Modifying Soft Tissue Models: Progressive Cutting with Minimal New Element Creation , 2000, MICCAI.

[32]  Chee-Keng Yap,et al.  Approximate Euclidean Shortest Paths in 3-Space , 1997, Int. J. Comput. Geom. Appl..

[33]  Stephane Cotin,et al.  A hybrid elastic model for real-time cutting, deformations, and force feedback for surgery training and simulation , 1999, Proceedings Computer Animation 1999.

[34]  Martin Wicke,et al.  Untangling Cloth With Boundaries , 2022 .

[35]  Jonathan Richard Shewchuk,et al.  Delaunay refinement algorithms for triangular mesh generation , 2002, Comput. Geom..

[36]  Paolo Cignoni,et al.  Enabling cuts on multiresolution representation , 2001, The Visual Computer.

[37]  Nadia Magnenat-Thalmann,et al.  Resolving surface collisions through intersection contour minimization , 2006, ACM Trans. Graph..

[38]  Jessica K. Hodgins,et al.  Graphical modeling and animation of brittle fracture , 1999, SIGGRAPH.

[39]  Tony DeRose,et al.  Surface reconstruction from unorganized points , 1992, SIGGRAPH.

[40]  M. Duflot.  A meshless method with enriched weight functions for three‐dimensional crack propagation , 2006 .

[41]  T. Belytschko,et al.  Element‐free Galerkin methods , 1994 .

[42]  James F. O'Brien,et al.  Graphical modeling and animation of ductile fracture , 2002, SIGGRAPH '02.