  Conformal Geometric Algebra (CGA) is a framework that allows the
representation of objects, such as points, planes and spheres, and
deformations, such as translations, rotations and dilations as uniform vectors,
called multivectors. In this work, we demonstrate the merits of multivector
usage with a novel, integrated rigged character simulation framework based on
CGA. In such a framework, and for the first time, one may perform real-time
cuts and tears as well as drill holes on a rigged 3D model. These operations
can be performed before and/or after model animation, while maintaining
deformation topology. Moreover, our framework permits generation of
intermediate keyframes on-the-fly based on user input, apart from the frames
provided in the model data. We are motivated to use CGA as it is the
lowest-dimension extension of dual-quaternion algebra that amends the
shortcomings of the majority of existing animation and deformation techniques.
Specifically, we no longer need to maintain objects of multiple algebras and
constantly transmute between them, such as matrices, quaternions and
dual-quaternions, and we can effortlessly apply dilations. Using such an
all-in-one geometric framework allows for better maintenance and optimization
and enables easier interpolation and application of all native deformations.
Furthermore, we present these three novel algorithms in a single CGA
representation which enables cutting, tearing and drilling of the input rigged
model, where the output model can be further re-deformed in interactive frame
rates. These close to real-time cut,tear and drill algorithms can enable a new
suite of applications, especially under the scope of a medical VR simulation.

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