[Paper Review] VIPER: Volume Invariant Position-based Elastic Rods

Baptiste Angles, Daniel Rebain+9 more|arXiv (Cornell University)|Jun 12, 2019

3D Shape Modeling and Analysis54 references4 citations

TL;DR

VIPER introduces a position-based elastic rod model that enforces volume conservation by adding per-vertex isotropic scaling as a degree of freedom, enabling realistic simulation of muscle-like volumetric deformations. The method achieves real-time performance (140 Hz for 26,000 DOFs) on GPU and provides a compact, skinning-based alternative to tetrahedral meshes for real-time character deformation.

ABSTRACT

We extend the formulation of position-based rods to include elastic volumetric deformations. We achieve this by introducing an additional degree of freedom per vertex -- isotropic scale (and its velocity). Including scale enriches the space of possible deformations, allowing the simulation of volumetric effects, such as a reduction in cross-sectional area when a rod is stretched. We rigorously derive the continuous formulation of its elastic energy potentials, and hence its associated position-based dynamics (PBD) updates to realize this model, enabling the simulation of up to 26000 DOFs at 140 Hz in our GPU implementation. We further show how rods can provide a compact alternative to tetrahedral meshes for the representation of complex muscle deformations, as well as providing a convenient representation for collision detection. This is achieved by modeling a muscle as a bundle of rods, for which we also introduce a technique to automatically convert a muscle surface mesh into a rods-bundle. Finally, we show how rods and/or bundles can be skinned to a surface mesh to drive its deformation, resulting in an alternative to cages for real-time volumetric deformation.

Motivation & Objective

• To model soft-tissue deformations in real-time with volume conservation, particularly for anatomical structures like muscles.
• To overcome the limitation of existing position-based rods, which do not preserve volume during deformation.
• To provide a compact, efficient alternative to tetrahedral meshes and cage-based deformation for real-time character animation.
• To enable automatic conversion of surface muscle meshes into rod bundles for realistic simulation.
• To support skinning of surface meshes to rods for volumetric deformation, replacing traditional cage-based methods.

Proposed method

• Introduces a per-vertex isotropic scale as an additional degree of freedom to model cross-sectional area changes during stretching or compression.
• Derives continuous elastic energy potentials for volume-invariant deformation, enabling position-based dynamics (PBD) updates that conserve volume.
• Uses a hybrid surface representation: vertices are explicitly parameterized by position and scale, but the rod surface is implicitly defined.
• Employs shape-matching constraints to maintain the rest-pose structure of rod bundles, enabling realistic muscle-like behavior.
• Applies linear blend skinning (LBS) to transfer rod deformations to a surface mesh, enabling skin sliding and secondary motion effects.
• Leverages bone transformations at frame start to initialize particle displacements, accelerating solver convergence during fast motion.

Experimental results

Research questions

• RQ1 Can a position-based rod model be extended to preserve volume during deformation while remaining efficient for real-time simulation?
• RQ2 How can a compact, physically plausible representation of muscles be created using rods that capture both shape and volumetric changes?
• RQ3 Can rod bundles be automatically generated from a surface mesh of a muscle with minimal user input?
• RQ4 Can rods be used as a direct alternative to tetrahedral meshes or cages for real-time volumetric deformation of character skins?
• RQ5 How can the simulation of complex anatomical structures be accelerated and made more interactive through multi-resolution and geometric multigrid techniques?

Key findings

• VIPER achieves real-time simulation at 140 Hz for up to 26,000 degrees of freedom using a GPU-accelerated implementation.
• The addition of isotropic scaling per vertex enables accurate modeling of cross-sectional changes during stretching, such as thinning under tension.
• The method successfully simulates realistic muscle deformation, including bulging and contraction effects, through internal forces or fiber shortening.
• An automatic algorithm converts a surface muscle mesh into a rod bundle with minimal user interaction, enabling rapid setup.
• Skinning rods to a surface mesh produces plausible secondary motions like skin sliding, offering a viable alternative to tetrahedral or cage-based deformation.
• The framework supports efficient collision detection and resolution between rods and between muscles, enabling complex anatomical interactions.