A Delaunay Approach to Interactive Cutting in Triangulated Surfaces

We present a method for producing cuts in triangulated surfaces. This method keeps the mesh size low and element quality high. We show the method for triangle meshes in two dimensions, and then generalize it to three dimensional curved surfaces, where bifurcations and annihilations of incisions may occur. This method could be applied to simulating surgery of membrane-like structures, such as veins or intestine.

[1]  M. Bro-Nielsen,et al.  VR simulation of abdominal trauma surgery. , 1998, Studies in health technology and informatics.

[2]  Fabio Ganovelli,et al.  Animating cuts with on-the-fly re-meshing , 2001, Eurographics.

[3]  Gábor Székely,et al.  A New Approach to Cutting into Finite Element Models , 2001, MICCAI.

[4]  Septimiu E. Salcudean,et al.  Needle insertion modelling and simulation , 2002, Proceedings 2002 IEEE International Conference on Robotics and Automation (Cat. No.02CH37292).

[5]  Simon Wildermuth,et al.  A survey of interactive mesh-cutting techniques and a new method for implementing generalized interactive mesh cutting using virtual tools , 2002, Comput. Animat. Virtual Worlds.

[6]  Martti Mäntylä,et al.  Introduction to Solid Modeling , 1988 .

[7]  T. A. Thomas,et al.  Simulation of resistance forces acting on surgical needles , 1997, Proceedings of the Institution of Mechanical Engineers. Part H, Journal of engineering in medicine.

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

[9]  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.

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

[11]  L. Paul Chew,et al.  Guaranteed-quality mesh generation for curved surfaces , 1993, SCG '93.

[12]  Olivier Devillers,et al.  On deletion in Delaunay triangulations , 1999, SCG '99.

[13]  Fernando Bello,et al.  Online Multiresolution Volumetric Mass Spring Model for Real Time Soft Tissue Deformation , 2002, MICCAI.

[14]  Jonathan Richard Shewchuk,et al.  A condition guaranteeing the existence of higher-dimensional constrained Delaunay triangulations , 1998, SCG '98.

[15]  Han-Wen Nienhuys,et al.  A Surgery Simulation Supporting Cuts and Finite Element Deformation , 2001, MICCAI.

[16]  Frank Tendick,et al.  Adaptive Nonlinear Finite Elements for Deformable Body Simulation Using Dynamic Progressive Meshes , 2001, Comput. Graph. Forum.

[17]  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.

[18]  Cynthia Bruyns,et al.  Interactive cutting of 3D surface meshes , 2001, Comput. Graph..

[19]  Jim Ruppert,et al.  A Delaunay Refinement Algorithm for Quality 2-Dimensional Mesh Generation , 1995, J. Algorithms.

[20]  Gary L. Miller,et al.  Control Volume Meshes Using Sphere Packing , 1998, IRREGULAR.

[21]  Markus H. Gross,et al.  Interactive simulation of surgical cuts , 2000, Proceedings the Eighth Pacific Conference on Computer Graphics and Applications.