A Survey of Physically Based Simulation of Cuts in Deformable Bodies

• Published in: Computer graphics forum 2015-09, Vol.34 (6), p.161-187
• Main Authors: Wu, Jun, Westermann, Rüdiger, Dick, Christian
• Format: Article
• Language: English
• Subjects: Analysis; Computer simulation; Cutting; deformable bodies; Deformation; Discretization; Finite element method; finite elements; Formability; I.3.5 [Computer Graphics]: Computational Geometry and Object Modelling-Physically based modelling; I.3.7 [Computer Graphics]: Three-Dimensional Graphics and Realism-Animation; I.3.8 [Computer Graphics]: Applications; Image processing systems; Mathematical models; physically based modelling; Rendering; Simulation; Studies; surgery simulation; Topological manifolds; virtual cutting
• ISSN: 0167-7055; 1467-8659
• DOI: 10.1111/cgf.12528

Virtual cutting of deformable bodies has been an important and active research topic in physically based modelling and simulation for more than a decade. A particular challenge in virtual cutting is the robust and efficient incorporation of cuts into an accurate computational model that is used for the simulation of the deformable body. This report presents a coherent summary of the state of the art in virtual cutting of deformable bodies, focusing on the distinct geometrical and topological representations of the deformable body, as well as the specific numerical discretizations of the governing equations of motion. In particular, we discuss virtual cutting based on tetrahedral, hexahedral and polyhedral meshes, in combination with standard, polyhedral, composite and extended finite element discretizations. A separate section is devoted to meshfree methods. Furthermore, we discuss cutting‐related research problems such as collision detection and haptic rendering in the context of interactive cutting scenarios. The report is complemented with an application study to assess the performance of virtual cutting simulators. Virtual cutting of deformable bodies has been an important and active research topic in physically based modelling and simulation for more than a decade. A particular challenge in virtual cutting is the robust and efficient incorporation of cuts into an accurate computational model that is used for the simulation of the deformable body. This report presents a coherent summary of the state of the art in virtual cutting of deformable bodies, focusing on the distinct geometrical and topological representations of the deformable body, as well as the specific numerical discretizations of the governing equations of motion. In particular, we discuss virtual cutting based on tetrahedral, hexahedral and polyhedral meshes, in combination with standard, polyhedral, composite and extended finite element discretizations. A separate section is devoted to meshfree methods. Furthermore, we discuss cutting‐related research problems such as collision detection and haptic rendering in the context of interactive cutting scenarios. The report is complemented with an application study to assess the performance of virtual cutting simulators.