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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…

We present Image Sculpting, a new framework for editing 2D images by incorporating tools from 3D geometry and graphics. This approach differs markedly from existing methods, which are confined to 2D spaces and typically rely on textual…

3D scanning is a complex multistage process that generates a point cloud of an object typically containing damaged parts due to occlusions, reflections, shadows, scanner motion, specific properties of the object surface, imperfect…

This demo takes the form of a challenge to the IJCAI community. A physical vault, secured by a 4-digit code, will be placed in the demo area. The author will publicly open the vault by entering the code on a touch-based interface, and as…

We introduce JuliQAOA, a simulation package specifically built for the Quantum Alternating Operator Ansatz (QAOA). JuliQAOA does not require a circuit-level description of QAOA problems, or another package to simulate such circuits, instead…

Sketch-based shape modeling aims to bridge the gap between 2D drawing and 3D modeling by providing an intuitive and accessible approach to create 3D shapes from 2D sketches. However, existing methods still suffer from limitations in…

We have written a Java applet to illustrate the meaning of curved geometry. The applet provides a mapping interface similar to MapQuest or Google Maps; features include the ability to navigate through a space and place permanent point…

This paper is on customization of computer models using the Easy Java Simulation authoring toolkit for the Singapore syllabus, based on real astronomical data, supported with literature reviewed researched pedagogical features. These 4 new…

In recent years two sets of planar (2D) shape attributes, provided with an intuitive physical meaning, were proposed to the remote sensing community by, respectively, Nagao & Matsuyama and Shackelford & Davis in their seminal works on the…

Computational notebooks, while essential for data science, are limited by their one-dimensional interface, which poorly aligns with non-linear developer workflows and complicates collaboration and human-AI interaction. In this work, we…

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…

Soft deployable structures - unlike conventional piecewise rigid deployables based on hinges and springs - can assume intricate 3-D shapes, thereby enabling transformative technologies in soft robotics, shape-morphing architecture, and…

This paper introduces a novel integration of Large Language Models (LLMs) with Conformal Geometric Algebra (CGA) to revolutionize controllable 3D scene editing, particularly for object repositioning tasks, which traditionally requires…

This study starts from the counter-intuitive question of how we can render a conventional stiff, non-stretchable and even brittle material conformable so that it can fully wrap around a curved surface, such as a sphere, without failure.…

3D Gaussian Splatting (GS) is one of the most promising novel 3D representations that has received great interest in computer graphics and computer vision. While various systems have introduced editing capabilities for 3D GS, such as those…

We prove Homological Mirror Symmetry for a smooth d-dimensional Calabi-Yau hypersurface in projective space, for any d > 2 (for example, d = 3 is the quintic three-fold). The main techniques involved in the proof are: the construction of an…

Embedding Human and Articulated Object Interaction (HAOI) in 3D is an important direction for a deeper human activity understanding. Different from previous works that use parametric and CAD models to represent humans and objects, in this…

Generating realistic 3D Human-Object Interactions (HOI) is a fundamental task for applications ranging from embodied AI to virtual content creation, which requires harmonizing high-level semantic intent with strict low-level physical…

Geometric algebra is an optimal frame work for calculating with vectors. The geometric algebra of a space includes elements that represent all the its subspaces (lines, planes, volumes, ...). Conformal geometric algebra expands this…

A skew Calabi-Yau algebra is a generalization of a Calabi-Yau algebra which allows for a non-trivial Nakayama automorphism. We prove three homological identities about the Nakayama automorphism and give several applications. The identities…