Related papers: Optimizing B-spline surfaces for developability an…
We consider a simply supported plate with constant thickness, defined on an unknown multiply connected domain. We optimize its shape according to some given performance functional. Our method is of fixed domain type, easy to be implemented,…
We propose a variational framework for accretive surface growth driven by an optimality principle. Rather than prescribing a kinetic law, the configuration at each time step is obtained, within a time-discrete setting, as the solution of a…
Existing approaches for classifying dynamic graphs either lift graph kernels to the temporal domain, or use graph neural networks (GNNs). However, current baselines have scalability issues, cannot handle a changing node set, or do not take…
Complex systems have motivated continuing interest from the scientific community, leading to new concepts and methods. Growing systems represent a case of particular interest, as their topological, geometrical, and also dynamical properties…
3D Gaussian Splatting (3DGS) has demonstrated impressive performance in 3D scene reconstruction. Beyond novel view synthesis, it shows great potential for multi-view surface reconstruction. Existing methods employ optimization-based…
3D Gaussian Splatting has achieved impressive performance in novel view synthesis with real-time rendering capabilities. However, reconstructing high-quality surfaces with fine details using 3D Gaussians remains a challenging task. In this…
In this paper, we develop a rigorous mathematical framework for the optimization of hip roof house geometry, with the primary goal of minimizing the external surface of the building envelope for a given set of design constraints. Five…
G-splines are a generalization of B-splines that deals with extraordinary points by imposing G^1 constraints across their spoke edges, thus obtaining a continuous tangent plane throughout the surface. Using the isoparametric concept and the…
This manuscript focuses on the construction of compactly supported dual Gabor frames in $L^2(\mathbb{R})$. The performance of the constructed dual frames is analysed for Gabor systems generated by B-splines and exponential B-splines of…
This paper develops a new way to create smooth piecewise polynomial free-form spline surfaces from quad- meshes that include T-junctions, where surface strips start or terminate. All mesh nodes can be interpreted as control points of…
Dynamic scene reconstruction has garnered significant attention in recent years due to its capabilities in high-quality and real-time rendering. Among various methodologies, constructing a 4D spatial-temporal representation, such as 4D-GS,…
Motivated by a number of recent investigations, we define and investigate the various properties of the ruled surfaces depend on three dimensional Lie groups with a bi-variant metric. We give useful results involving the characterizations…
3D Gaussian Splatting (3DGS) has emerged as a transformative method in the field of real-time novel synthesis. Based on 3DGS, recent advancements cope with large-scale scenes via spatial-based partition strategy to reduce video memory and…
Numerical simulation of complex optical structures enables their optimization with respect to specific objectives. Often, optimization is done by multiple successive parameter scans, which are time consuming and computationally expensive.…
We analyze the space of geometrically continuous piecewise polynomial functions or splines for quadrangular and triangular patches with arbitrary topology and general rational transition maps. To define these spaces of G 1 spline functions,…
We elucidate the geometric background of function-theoretic properties for the Gauss maps of several classes of immersed surfaces in three-dimensional space forms, for example, minimal surfaces in Euclidean three-space, improper affine…
We exploit level set topology optimization to find the optimal material distribution for metamaterial-based heat manipulators. The level set function, geometry, and solution field are parameterized using the non-uniform rational B-spline…
We present SplatFace, a novel Gaussian splatting framework designed for 3D human face reconstruction without reliance on accurate pre-determined geometry. Our method is designed to simultaneously deliver both high-quality novel view…
Image extrapolation aims at expanding the narrow field of view of a given image patch. Existing models mainly deal with natural scene images of homogeneous regions and have no control of the content generation process. In this work, we…
Neural rendering methods have significantly advanced photo-realistic 3D scene rendering in various academic and industrial applications. The recent 3D Gaussian Splatting method has achieved the state-of-the-art rendering quality and speed…