Related papers: Free-form Design of Discrete Architectural Surface…

This paper investigates a kind of degenerated circle packings in hyperbolic background geometry. A main problem is whether a prescribed total geodesic curvature data can be realized by a degenerated circle packing or not. We fully…

Existing neural implicit surface reconstruction methods have achieved impressive performance in multi-view 3D reconstruction by leveraging explicit geometry priors such as depth maps or point clouds as regularization. However, the…

3D Gaussian splatting (3DGS) has recently emerged as an alternative representation that leverages a 3D Gaussian-based representation and introduces an approximated volumetric rendering, achieving very fast rendering speed and promising…

We propose conformal generative modeling, a framework for generative modeling on 2D surfaces approximated by discrete triangle meshes. Our approach leverages advances in discrete conformal geometry to develop a map from a source triangle…

A set of control points can determine a Bezier surface and a triangulated surface simultaneously. We prove that the triangulated surface becomes homeomorphic and ambient isotopic to the Bezier surface via subdivision. We also show that the…

We study the problem to provide a triangular form based on implicit differential equations for non-linear multi-input systems with respect to the flatness property. Furthermore, we suggest a constructive method for the transformation of a…

Using a geometric formalism of elasticity theory we develop a systematic theoretical method for controlling and manipulating the mechanical response of slender solids to external loads. We formally express global mechanical properties…

Many applications of geometry modeling and computer graphics necessite accurate curvature estimations of curves on the plane or on manifolds. In this paper, we define the notion of the discrete geodesic curvature of a geodesic polygon on a…

The Gaussian splatting methods are getting popular. However, their loss function only contains the $\ell_1$ norm and the structural similarity between the rendered and input images, without considering the edges in these images. It is…

The accurate reconstruction of dynamic street scenes is critical for applications in autonomous driving, augmented reality, and virtual reality. Traditional methods relying on dense point clouds and triangular meshes struggle with moving…

Direct design of complex functional materials would revolutionize technologies ranging from printable organs to novel clean energy devices. However, even incremental steps towards designing functional materials have proven challenging. If…

This paper studies the problem of estimating physical properties (system identification) through visual observations. To facilitate geometry-aware guidance in physical property estimation, we introduce a novel hybrid framework that…

With the help of hyper-ideal circle pattern theory, we have developed a discrete version of the classical uniformization theorems for surfaces represented as finite branched covers over the Riemann sphere as well as compact polyhedral…

The log-aesthetic curves include the logarithmic (equiangular) spiral, clothoid, and involute curves. Although most of them are expressed only by an integral form of the tangent vector, it is possible to interactively generate and deform…

We survey structure-preserving discretizations of minimal surfaces in Euclidean space. Our focus is on a discretization defined via parallel face offsets of polyhedral surfaces, which naturally leads to a notion of vanishing mean curvature…

We introduce trimmed NURBS surfaces with accurate boundary control, briefly called ABC-surfaces, as a solution to the notorious problem of constructing watertight or smooth ($G^1$ and $G^2)$ multi-patch surfaces within the function range of…

We use computational modeling to investigate the assembly thermodynamics of a particle-based model for geometrically frustrated assembly, in which the local packing geometry of subunits is incompatible with uniform, strain-free large-scale…

Vertex scaling of piecewise linear metrics on surfaces introduced by Luo is a straightforward discretization of smooth conformal structures on surfaces. Combinatorial $\alpha$-curvature for vertex scaling of piecewise linear metrics on…

Recent advancements in 3D Gaussian Splatting(3DGS) have significantly improved semantic scene understanding, enabling natural language queries to localize objects within a scene. However, existing methods primarily focus on embedding…

We propose a new approach for controlling the characteristics of certain mesh faces during optimization of high-order curved meshes. The practical goals are tangential relaxation along initially aligned curved boundaries and internal…