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Local and global illumination were recently defined in Riemannian manifolds to visualize classical Non-Euclidean spaces. This work focuses on Riemannian metric construction in $\mathbb{R}^3$ to explore special effects like warping, mirages,…
We study constructing an algebraic curve from a Riemann surface given via a translation surface, which is a collection of finitely many polygons in the plane with sides identified by translation. We use the theory of discrete Riemann…
We equip dynamic geometry software (DGS) with a user-friendly method that enables massively parallel calculations on the graphics processing unit (GPU). This interplay of DGS and GPU opens up various applications in education and…
Physically meaningful periodic solutions to certain integrable partial differential equations are given in terms of multi-dimensional theta functions associated to real Riemann surfaces. Typical analytical problems in the numerical…
Representing graphs as sets of node embeddings in certain curved Riemannian manifolds has recently gained momentum in machine learning due to their desirable geometric inductive biases, e.g., hierarchical structures benefit from hyperbolic…
In digital painting software, layers organize paintings. However, layers are not explicitly represented, transmitted, or published with the final digital painting. We propose a technique to decompose a digital painting into layers. In our…
Inpainting-based compression methods are qualitatively promising alternatives to transform-based codecs, but they suffer from the high computational cost of the inpainting step. This prevents them from being applicable to time-critical…
We present the algebraic representation and basic algorithms for MultiAspect Graphs (MAGs). A MAG is a structure capable of representing multilayer and time-varying networks, as well as higher-order networks, while also having the property…
A system for live high quality surface reconstruction using a single moving depth camera on a commodity hardware is presented. High accuracy and real-time frame rate is achieved by utilizing graphics hardware computing capabilities via…
A recent development, called isogeometric analysis, provides a unified approach for design, analysis and optimization of functional products in industry. Traditional volume rendering methods for inspecting the results from the numerical…
We present an algorithm for the computation of the topological type of a real compact Riemann surface associated to an algebraic curve, i.e., its genus and the properties of the set of fixed points of the anti-holomorphic involution $\tau$,…
Extended reality is a fast-growing domain for which there is an increasing need to analyze and understand user behavior. In particular, understanding human visual attention during immersive experiences is crucial for many applications. The…
We make a systematic investigation of quadrature properties for quadrics, namely integration of holomorphic functions over planar domains bounded by second degree curves. A full understanding requires extending traditional settings by…
We present a computational approach to general hyperelliptic Riemann surfaces in Weierstrass normal form. The surface is either given by a list of the branch points, the coefficients of the defining polynomial or a system of cuts for the…
Computing occluding contours is a key building block of non-photorealistic rendering, but producing contours with consistent visibility has been notoriously challenging. This paper describes the first general-purpose smooth surface…
The quest for regular models of arithmetic surfaces allows different viewpoints and approaches: using valuations or a covering by charts. In this article, we sketch both approaches and then show in a concrete example, how surprisingly…
The goal of this paper is to exhibit and analyze an algorithm that takes a given closed orientable hyperbolic surface and outputs an explicit Dirichlet domain. The input is a fundamental polygon with side pairings. While grounded in…
This work studies certain aspects of graphs embedded on surfaces. Initially, a colored graph model for a map of a graph on a surface is developed. Then, a concept analogous to (and extending) planar graph is introduced in the same spirit as…
Geometric reconstruction of opaque surfaces from images is a longstanding challenge in computer vision, with renewed interest from volumetric view synthesis algorithms using radiance fields. We leverage the geometry field proposed in recent…
An efficient computer algorithm is described for the perspective drawing of a wide class of surfaces. The class includes surfaces corresponding lo single-valued, continuous functions which are defined over rectangular domains. The algorithm…