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Implicit fields have recently shown increasing success in representing and learning 3D shapes accurately. Signed distance fields and occupancy fields are decades old and still the preferred representations, both with well-studied…
Vector fields are one of the fundamental parts of mathematics which are key for modelling many physics phenomena such as electromagnetic fields or fluid and gas flows. Fields found in nature often exhibit complex structures which can be…
Topological abstractions offer a method to summarize the behavior of vector fields but computing them robustly can be challenging due to numerical precision issues. One alternative is to represent the vector field using a discrete approach,…
Vectors fields defined on surfaces constitute relevant and useful representations but are rarely used. One reason might be that comparing vector fields across two surfaces of the same genus is not trivial: it requires to transport the…
In this paper, we investigate vector fields on polyhedral complexes and their associated trajectories. We study vector fields which are analogue of the gradient vector field of a function in the smooth case. Our goal is to define a nice…
Recent advances in image generation have achieved remarkable visual quality, while a fundamental challenge remains: Can image generation be controlled at the element level, enabling intuitive modifications such as adjusting shapes, altering…
This work begins by establishing a mathematical formalization between different geometrical interpretations of Neural Networks, providing a first contribution. From this starting point, a new interpretation is explored, using the idea of…
Vector fields and line fields, their counterparts without orientations on tangent lines, are familiar objects in the theory of dynamical systems. Among the techniques used in their study, the Morse--Smale decomposition of a (generic) field…
Vector graphics are essential in design, providing artists with a versatile medium for creating resolution-independent and highly editable visual content. Recent advancements in vision-language and diffusion models have fueled interest in…
In this work, a new non-stationary multiple point geostatistical algorithm called vector field-based simulation is proposed. The motivation behind this work is the modeling of a certain structures that exhibit directional features with…
Vector fields are a highly abstract physical concept that is often taught using visualizations. Although vector representations are particularly suitable for visualizing quantitative data, they are often confusing, especially when…
Recent neural networks based surface reconstruction can be roughly divided into two categories, one warping templates explicitly and the other representing 3D surfaces implicitly. To enjoy the advantages of both, we propose a novel 3D…
For domains that involve numerical simulation, it can be computationally expensive to run an ensemble of simulations spanning a parameter space of interest to a user. To this end, an attractive surrogate for simulation is the generative…
Textures are a vital aspect of creating visually appealing and realistic 3D models. In this paper, we study the problem of generating high-fidelity texture given shapes of 3D assets, which has been relatively less explored compared with…
One of the most common ways to represent and share visual designs is with vector graphics. Designers working with vector graphics often explore layout alternatives and generate them by moving and resizing elements. The motivation for this…
Vector graphics are widely used in digital art and valued by designers for their scalability and layer-wise topological properties. However, the creation and editing of vector graphics necessitate creativity and design expertise, leading to…
Vector graphics are widely used in digital art and highly favored by designers due to their scalability and layer-wise properties. However, the process of creating and editing vector graphics requires creativity and design expertise, making…
Scalable Vector Graphics (SVGs) are vital for modern image rendering due to their scalability and versatility. Previous SVG generation methods have focused on curve-based vectorization, lacking semantic understanding, often producing…
Deep neural networks (DNNs) are widely applied for nowadays 3D surface reconstruction tasks and such methods can be further divided into two categories, which respectively warp templates explicitly by moving vertices or represent 3D…
Torse-forming vector fields are generalizations of some important vector fields. In this paper, we present some techniques to transform a proper torse-forming vector field into its special cases. Concrete examples are given.