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We present the Julia interface Polymake.jl to polymake, a software for research in polyhedral geometry. We describe the technical design and how the integration into Julia makes it possible to combine polymake with state-of-the-art…
Finding Ricci-flat (Calabi-Yau) metrics is a long standing problem in geometry with deep implications for string theory and phenomenology. A new attack on this problem uses neural networks to engineer approximations to the Calabi-Yau metric…
This paper introduces GA-Unity, the first Unity package specifically designed for seamless integration of Geometric Algebra (GA) into collaborative networked applications. Indeed, in such contexts, it has been demonstrated that using…
Previous works leveraging video models for image-to-3D scene generation tend to suffer from geometric distortions and blurry content. In this paper, we renovate the pipeline of image-to-3D scene generation by unlocking the potential of…
Transformers achieve strong performance across diverse domains but implicitly assume Euclidean geometry in their attention mechanisms, limiting their effectiveness on data with non-Euclidean structure. While recent extensions to hyperbolic…
In this paper we introduce an open-source software package written in C++ for efficiently finding solutions to quadratic programming problems with linear complementarity constraints. These problems arise in a wide range of applications in…
3D Scene Question Answering (3D SQA) represents an interdisciplinary task that integrates 3D visual perception and natural language processing, empowering intelligent agents to comprehend and interact with complex 3D environments. Recent…
As 3D models become critical in today's manufacturing and product design, conventional 3D modeling approaches based on Computer-Aided Design (CAD) are labor-intensive, time-consuming, and have high demands on the creators. This work aims to…
In this paper, we introduce a numerical framework designed to solve problems within the emerging field of Waveguide Quantum Electrodynamics (WQED). The framework is based on collision quantum optics, where a localized quantum system…
Articulation modeling aims to infer movable parts and their motion parameters for a 3D object, enabling interactive animation, simulation, and shape editing. In this paper, we present Sketch2Arti, the first sketch-based articulation…
In this paper, we present Code Shrew, a new software platform accompanied by an interactive programming course. Its aim is to teach the fundamentals of computer programming by enabling users to create their own drawings and animations. The…
This article proposes an artistic approach to increase and enrich the understanding of Julia Sets. This approach includes the mathematical, the playful, the artistic and the computational dimensions. It is argued that these four dimensions…
Automated assembly of 3D fractures is essential in orthopedics, archaeology, and our daily life. This paper presents Jigsaw, a novel framework for assembling physically broken 3D objects from multiple pieces. Our approach leverages…
Sculptors often deviate from geometric accuracy in order to enhance the appearance of their sculpture. These subtle stylizations may emphasize anatomy, draw the viewer's focus to characteristic features of the subject, or symbolize textures…
Parametric computer-aided design (CAD) is the dominant paradigm in mechanical engineering for physical design. Distinguished by relational geometry, parametric CAD models begin as two-dimensional sketches consisting of geometric primitives…
The Web Geometry Laboratory, (WGL), is a blended-learning, collaborative and adaptive, Web environment for geometry. It integrates a well known dynamic geometry system. In a collaborative session, exchange of geometrical and textual…
Programming has become an essential component of K-12 education and serves as a pathway for developing computational thinking skills. Given the complexity of programming and the advanced skills it requires, previous research has introduced…
The rapid development of AR/VR brings tremendous demands for 3D content. While the widely-used Computer-Aided Design (CAD) method requires a time-consuming and labor-intensive modeling process, sketch-based 3D modeling offers a potential…
We introduce some new algebraic structures arising naturally in the geometry of Calabi-Yau manifolds and mirror symmetry. We give a universal construction of Calabi-Yau algebras in terms of a noncommutative symplectic DG algebra resolution.…
Kirigami is the art of cutting paper to make it articulated and deployable, allowing for it to be shaped into complex two and three-dimensional geometries. The mechanical response of a kirigami sheet when it is pulled at its ends is enabled…