Deform, Cut and Tear a skinned model using Conformal Geometric Algebra

TL;DR

This paper introduces a real-time, integrated character simulation framework using Conformal Geometric Algebra that supports cutting, tearing, and deformation of models, overcoming limitations of previous methods.

Contribution

The work presents a novel CGA-based framework enabling real-time cuts and tears in animated models while maintaining deformation topology, addressing key limitations of prior techniques.

Findings

Supports real-time cutting and tearing of models

Maintains deformation topology during complex operations

Provides easy interpolation of deformations within CGA framework

Abstract

In this work, we present a novel, integrated rigged character simulation framework in Conformal Geometric Algebra (CGA) that supports, for the first time, real-time cuts and tears, before and/or after the animation, while maintaining deformation topology. The purpose of using CGA is to lift several restrictions posed by current state-of-the-art character animation & deformation methods. Previous implementations originally required weighted matrices to perform deformations, whereas, in the current state-of-the-art, dual-quaternions handle both rotations and translations, but cannot handle dilations. CGA is a suitable extension of dual-quaternion algebra that amends these two major previous shortcomings: the need to constantly transmute between matrices and dual-quaternions as well as the inability to properly dilate a model during animation. Our CGA algorithm also provides easy interpolation and application of all deformations in each intermediate steps, all within the same geometric framework. Furthermore we also present two novel algorithms that enable cutting and tearing of the input rigged, animated model, while the output model can be further re-deformed. These interactive, real-time cut and tear operations can enable a new suite of applications, especially under the scope of a medical surgical simulation.