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Recent advancements in world models have revolutionized dynamic environment simulation, allowing systems to foresee future states and assess potential actions. In autonomous driving, these capabilities help vehicles anticipate the behavior…

During the last ten years, increasing efforts were made to improve and simplify the process from Computer Aided Design (CAD) modeling to a numerical simulation. It has been shown that the transition from one model to another, i.e. the…

3D modeling is becoming a well-developed field of medicine, but its applicability can be limited due to the lack of software allowing for easy utilizations of generated 3D visualizations. By leveraging recent advances in virtual reality, we…

In this work we propose algorithms to explicitly construct a conservative estimate of the configuration spaces of rigid objects in 2D and 3D. Our approach is able to detect compact path components and narrow passages in configuration space…

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…

Understanding 2D cross-sections of 3D structures is a crucial skill in many disciplines, from geology to medical imaging. Cross-section inference in the context of 3D structures requires a complex set of spatial/visualization skills…

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…

Computer-aided design (CAD) is the digital construction of 2D and 3D objects, and is central to a wide range of engineering and manufacturing applications like automobile and aviation. Despite its importance, CAD modeling remains largely a…

We present a novel methodology based on geometric approach to simulate magnification lens effects. Our aim is to promote new applications of powerful geometric modeling techniques in visual computing. Conventional image…

The creation of manufacturable and editable 3D shapes through Computer-Aided Design (CAD) remains a highly manual and time-consuming task, hampered by the complex topology of boundary representations of 3D solids and unintuitive design…

Reversibility is a key issue in the interface between computation and physics, and of growing importance as miniaturization progresses towards its physical limits. Most foundational work on reversible computing to date has focussed on…

Spatial computing is a technological advancement that facilitates the seamless integration of devices into the physical environment, resulting in a more natural and intuitive digital world user experience. Spatial computing has the…

Generative methods for 3D assets have recently achieved remarkable progress, yet providing intuitive and precise control over the object geometry remains a key challenge. Existing approaches predominantly rely on text or image prompts,…

Parametric Computer-Aided Design (CAD) of articulated assemblies is essential for product development, yet generating these multi-part, movable models from high-level descriptions remains unexplored. To address this, we propose ArtiCAD, the…

Multimodal geometry reasoning requires models to jointly understand visual diagrams and perform structured symbolic inference, yet current vision--language models struggle with complex geometric constructions due to limited training data…

Robotic surface-interaction tasks, such as spray painting or welding, require both accurate geometric planning and precise motion execution. While modern motion planners generate valid geometric paths, they often lack the expert motor…

We develop a computational framework that leverages the features of sophisticated software tools and numerics to tackle some of the pressing issues in the realm of earth sciences. The algorithms to handle the physics of multiphase flow,…

Using an interface inserted in a background mesh is an alternative way of constructing a complex geometrical shape with a relative low meshing efforts. However, this process may require special treatment of elements cut by the interface.…

The concept of open weak CAD is introduced. Every open CAD is an open weak CAD. On the contrary, an open weak CAD is not necessarily an open CAD. An algorithm for computing projection polynomials of open weak CADs is proposed. The key idea…

Aiming at automating the different trades intervening in mechanical parts' design activities, one finds the weakest link within the interface linking the computer aided-design trade (CAD) and the process planning trade (CAPP) where a huge…