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.

保形几何代数 (CGA) 是一个框架，它允许将对象（例如点、平面和球体）以及变形（例如平移、旋转和膨胀）表示为统一向量，称为多向量. 在这项工作中，我们通过基于 CGA 的新型集成操纵角色模拟框架展示了多向量使用的优点。在这样的框架中，人们第一次可以在装配好的 3D 模型上执行实时切割和撕裂以及钻孔。这些操作可以在模型动画之前和/或之后执行，同时保持变形拓扑。此外，除了模型数据中提供的帧之外，我们的框架还允许根据用户输入即时生成中间关键帧。我们有动力使用 CGA，因为它是双四元数代数的最低维扩展，它修正了大多数现有动画和变形技术的缺点。具体来说，我们不再需要维护多个代数的对象并在它们之间不断地嬗变，例如矩阵，四元数和双四元数，我们可以毫不费力地应用膨胀。使用这种一体式几何框架可以实现更好的维护和优化，并使所有原生变形的插值和应用更容易。此外，我们在单个 CGA 表示中展示了这三种新颖的算法，它可以对输入绑定模型进行切割、撕裂和钻孔，其中输出模型可以在交互式帧速率中进一步重新变形。这些接近实时的切割、撕裂和钻孔算法可以启用一套新的应用程序，尤其是在医疗 VR 模拟的范围内。使用这种一体式几何框架可以实现更好的维护和优化，并使所有原生变形的插值和应用更容易。此外，我们在单个 CGA 表示中展示了这三种新颖的算法，它可以对输入绑定模型进行切割、撕裂和钻孔，其中输出模型可以在交互式帧速率中进一步重新变形。这些接近实时的切割、撕裂和钻孔算法可以启用一套新的应用程序，尤其是在医疗 VR 模拟的范围内。使用这种一体式几何框架可以实现更好的维护和优化，并使所有原生变形的插值和应用更容易。此外，我们在单个 CGA 表示中展示了这三种新颖的算法，它可以对输入绑定模型进行切割、撕裂和钻孔，其中输出模型可以在交互式帧速率中进一步重新变形。这些接近实时的切割、撕裂和钻孔算法可以启用一套新的应用程序，尤其是在医疗 VR 模拟的范围内。