Related papers: Deform, Cut and Tear a skinned model using Conform…
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…
This position paper delves into the transformative role of Geometric Algebra (GA) in advancing specific areas of Computer Graphics (CG) and Extended Reality (XR), particularly in character animation, rendering, rigging, neural rendering,…
We present an algorithm that allows a user within a virtual environment to perform real-time unconstrained cuts or consecutive tears, i.e., progressive, continuous fractures on a deformable rigged and soft-body mesh model in…
What is the best representation for doing euclidean geometry on computers? These notes from a SIGGRAPH 2019 short course entitled "Geometric algebra for computer graphics" introduce projective geometric algebra (PGA) as a modern framework…
In this work, we present an integrated geometric framework: "deep- cut" that enables for the first time a user to geometrically and algorithmically cut, tear and drill the surface of a skinned model without prior constraints, layered on top…
Distributional and neural approaches to natural language semantics have been built almost exclusively on conventional linear algebra: vectors, matrices, tensors, and the operations that accompany them. These methods have achieved remarkable…
Skeleton-based and cage-based deformation techniques represent the two most popular approaches to control real-time deformations of digital shapes and are, to a vast extent, complementary to one another. Despite their complementary roles,…
What symbolic format should an LLM emit for reliable 3D scene editing from natural language, and does algebraic structure help beyond compact syntax? We evaluate Conformal Geometric Algebra (CGA) as a compact symbolic interface against a…
The problem of deforming an artist-drawn caricature according to a given normal face expression is of interest in applications such as social media, animation and entertainment. This paper presents a solution to the problem, with an…
Robotic grinding is widely used for shaping workpieces in manufacturing, but it remains difficult to automate this process efficiently. In particular, efficiently grinding workpieces of different shapes and material hardness is challenging…
We present GALA, a framework that takes as input a single-layer clothed 3D human mesh and decomposes it into complete multi-layered 3D assets. The outputs can then be combined with other assets to create novel clothed human avatars with any…
Choosing how to encode a real-world problem as a machine learning task is an important design decision in machine learning. The task of glacier calving front modeling has often been approached as a semantic segmentation task. Recent studies…
This paper presents a Surface-Aligned Gaussian representation for creating animatable human avatars from monocular videos,aiming at improving the novel view and pose synthesis performance while ensuring fast training and real-time…
Deep learning-based medical image segmentation and surface mesh generation typically involve a sequential pipeline from image to segmentation to meshes, often requiring large training datasets while making limited use of prior geometric…
High-fidelity reconstruction of dynamic scenes is an important yet challenging problem. While recent 4D Gaussian Splatting (4DGS) has demonstrated the ability to model temporal dynamics, it couples Gaussian motion and geometric attributes…
We introduce PICA, a novel representation for high-fidelity animatable clothed human avatars with physics-accurate dynamics, even for loose clothing. Previous neural rendering-based representations of animatable clothed humans typically…
A tutorial introduction to projective geometric algebra (PGA), a modern, coordinate-free framework for doing euclidean geometry. PGA features: uniform representation of points, lines, and planes; robust, parallel-safe join and meet…
We present Drivable 3D Gaussian Avatars (D3GA), a multi-layered 3D controllable model for human bodies that utilizes 3D Gaussian primitives embedded into tetrahedral cages. The advantage of using cages compared to commonly employed linear…
A tutorial of the Mathematica package CGAlgebra, for conformal geometric algebra calculations is presented. Using rule-based programming, the 5-dimensional conformal geometric algebra is implemented and defined functions simplify the…
Physically-based simulation is a powerful approach for 3D facial animation as the resulting deformations are governed by physical constraints, allowing to easily resolve self-collisions, respond to external forces and perform realistic…