2021/02/15 by Manos Kamarianakis, Kamarianakis, Manos, George Papagiannakis +1 · 2 citations
Computer Science · Engineering · Mathematics · #68U05 #Advanced Numerical Analysis Techniques #Algebraic and Geometric Analysis #Computer Graphics and Visualization Techniques #FOS: Computer and information sciences #Graphics (cs.GR) #I.3.8
paper · pdf · doi:10.48550/arxiv.2102.07499
openalex publication_date 2021/02/15 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
Conformal Geometric Algebra (CGA) is a framework that allows the\nrepresentation of objects, such as points, planes and spheres, and\ndeformations, such as translations, rotations and dilations as uniform vectors,\ncalled multivectors. In this work, we demonstrate the merits of multivector\nusage with a novel, integrated rigged character simulation framework based on\nCGA. In such a framework, and for the first time, one may perform real-time\ncuts and tears as well as drill holes on a rigged 3D model. These operations\ncan be performed before and/or after model animation, while maintaining\ndeformation topology. Moreover, our framework permits generation of\nintermediate keyframes on-the-fly based on user input, apart from the frames\nprovided in the model data. We are motivated to use CGA as it is the\nlowest-dimension extension of dual-quaternion algebra that amends the\nshortcomings of the majority of existing animation and deformation techniques.\nSpecifically, we no longer need to maintain objects of multiple algebras and\nconstantly transmute between them, such as matrices, quaternions and\ndual-quaternions, and we can effortlessly apply dilations. Using such an\nall-in-one geometric framework allows for better maintenance and optimization\nand enables easier interpolation and application of all native deformations.\nFurthermore, we present these three novel algorithms in a single CGA\nrepresentation which enables cutting, tearing and drilling of the input rigged\nmodel, where the output model can be further re-deformed in interactive frame\nrates. These close to real-time cut,tear and drill algorithms can enable a new\nsuite of applications, especially under the scope of a medical VR simulation.\n