  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.
