A virtual node algorithm for changing mesh topology during simulation

612

423

Physically based deformable models have been widely embraced by the Computer Graphics community. Many problems outlined in a previous survey by Gibson and Mirtich have been addressed, thereby making these models interesting and useful for both offline and real-time applications, such as motion pictures and video games. In this paper, we present the most significant contributions of the past decade, which produce such impressive and perceivably realistic animations and simulations: finite element/difference/volume methods, mass-spring systems, mesh-free methods, coupled particle systems and reduced deformable models-based on modal analysis. For completeness, we also make a connection to the simulation of other continua, such as fluids, gases and melting objects. Since time integration is inherent to all simulated phenomena, the general notion of time discretization is treated separately, while specifics are left to the respective models. Finally, we discuss areas of application, such as elastoplastic deformation and fracture, cloth and hair animation, virtual surgery simulation, interactive entertainment and fluid/smoke animation, and also suggest areas for future research.

Section: The Finite Element Methodsmentioning

confidence: 99%

Physically Based Deformable Models in Computer Graphics

Nealen

Müller

Keiser

et al. 2006

612

423

“…This can easily create degenerated or very small elements that decrease the numerical stability of deformation, as stated before. The virtual node method [MBF04,SDF07,WJS*14,JZY*15] embeds cut fragments in virtual elements, the former are used for visual display and collision, while the latter are used for deformation. Virtual elements are duplicates of the original uncut elements.…”

Section: Previous Workmentioning

confidence: 99%

CPU–GPU Parallel Framework for Real‐Time Interactive Cutting of Adaptive Octree‐Based Deformable Objects

Jia

Zhang

et al. 2017

A software framework taking advantage of parallel processing capabilities of CPUs and GPUs is designed for the real‐time interactive cutting simulation of deformable objects. Deformable objects are modelled as voxels connected by links. The voxels are embedded in an octree mesh used for deformation. Cutting is performed by disconnecting links swept by the cutting tool and then adaptively refining octree elements near the cutting tool trajectory. A surface mesh used for visual display is reconstructed from disconnected links using the dual contour method. Spatial hashing of the octree mesh and topology‐aware interpolation of distance field are used for collision. Our framework uses a novel GPU implementation for inter‐object collision and object self collision, while tool‐object collision, cutting and deformation are assigned to CPU, using multiple threads whenever possible. A novel method that splits cutting operations into four independent tasks running in parallel is designed. Our framework also performs data transfers between CPU and GPU simultaneously with other tasks to reduce their impact on performances. Simulation tests show that when compared to three‐threaded CPU implementations, our GPU accelerated collision is 53–160% faster; and the overall simulation frame rate is 47–98% faster.

“…An alternative to remeshing is the virtual node algorithm introduced by Molino et al [MBF04]. Instead of actually splitting simulation elements, the element that is to be split is duplicated.…”

Section: Related Workmentioning

confidence: 99%

“…Precise cutting, however, is not possible. Other algorithms duplicate elements, but are still somewhat limited by the initial mesh resolution [MBF04]. Meshless FEM, as suggested recently, avoids the mesh entirely.…”

Section: Introductionmentioning

confidence: 99%

A Finite Element Method on Convex Polyhedra

Wicke

Botsch

Groß

2007

We present a method for animating deformable objects using a novel finite element discretization on convex polyhedra. Our finite element approach draws upon recently introduced 3D mean value coordinates to define smooth interpolants within the elements. The mathematical properties of our basis functions guarantee convergence. Our method is a natural extension to linear interpolants on tetrahedra: for tetrahedral elements, the methods are identical. For fast and robust computations, we use an elasticity model based on Cauchy strain and stiffness warping. This more flexible discretization is particularly useful for simulations that involve topological changes, such as cutting or fracture. Since splitting convex elements along a plane produces convex elements, remeshing or subdivision schemes used in simulations based on tetrahedra are not necessary, leading to less elements after such operations. We propose various operators for cutting the polyhedral discretization. Our method can handle arbitrary cut trajectories, and there is no limit on how often elements can be split.