Related papers: Conformal approach to physics simulations for thin…
Models of folding of a triangular lattice embedded in a discrete space are studied as simple models of the crumpling transition of fixed-connectivity membranes. Both the case of planar folding and three-dimensional folding on a…
This paper introduces a new method to stylize 3D geometry. The key observation is that the surface normal is an effective instrument to capture different geometric styles. Centered around this observation, we cast stylization as a shape…
We present an elastic simulator for domains defined as evolving implicit functions, which is efficient, robust, and differentiable with respect to both shape and material. This simulator is motivated by applications in 3D reconstruction: it…
Owing to the computational complexity of electronic structure algorithms running on classical digital computers, the range of molecular systems amenable to simulation remains tightly circumscribed even after many decades of work. Quantum…
We consider the problem of approximating a two-dimensional shape contour (or curve segment) using discrete assembly systems, which allow to build geometric structures based on limited sets of node and edge types subject to edge length and…
A method is presented for constructing closed surfaces out of Euclidean polygons with infinitely many segment identifications along the boundary. The metric on the quotient is identified. A sufficient condition is presented which guarantees…
Physics simulation is paramount for modeling and utilizing 3D scenes in various real-world applications. However, integrating with state-of-the-art 3D scene rendering techniques such as Gaussian Splatting (GS) remains challenging. Existing…
In the process of projecting the surface of a three-dimensional object onto a two-dimensional surface, due to the perspective distortion, the image on the surface of the object will have different degrees of distortion according to the…
This work is concerned with a representation of shapes that disentangles fine, local and possibly repeating geometry, from global, coarse structures. Achieving such disentanglement leads to two unrelated advantages: i) a significant…
This paper proposes direct and inverse results for the Dirichlet and Dirichlet to Neumann problems for complex curves with nodal type singularities. As an application, we give a method to reconstruct the conformal structure of a compact…
Intraoperative observation of tissue internal structure is often difficult. Hence, real-time soft tissue deformation is essential for the localization of tumor and other internal structures. We propose a method to simulate the internal…
We consider smooth bounded surfaces with a smooth boundary and a prescribed background metric g_0. We now consider all metrics g conformal to g_0 which have a prescribed volume M. We now minimize the first eigenvalue of the Laplace operator…
Cutting-edge smart materials are transforming the domains of soft robotics, actuators, and sensors by harnessing diverse non-mechanical stimuli, such as electric and magnetic fields. Accurately modelling their physical behaviour…
For all open Riemann surface M and real number $\theta \in (0,\pi/4),$ we construct a conformal minimal immersion $X=(X_1,X_2,X_3):M \to \mathbb{R}^3$ such that $X_3+\tan(\theta) |X_1|:M \to \mathbb{R}$ is positive and proper. Furthermore,…
Conformal mapping, a classical topic in complex analysis and differential geometry, has become a subject of great interest in the area of surface parameterization in recent decades with various applications in science and engineering.…
In this paper we survey a number of recent results concerning the existence and moduli spaces of solutions of various geometric problems on noncompact manifolds. The three problems which we discuss in detail are: I. Complete properly…
In classical differential geometry, a central question has been whether abstract surfaces with given geometric features can be realized as surfaces in Euclidean space. Inspired by the rich theory of embedded triply periodic minimal…
Modeling arbitrarily large deformations of surfaces smoothly embedded in three-dimensional space is challenging. The difficulties come from two aspects: the existing geometry processing or forward simulation methods penalize the difference…
We describe how to approximate the Riemann curvature tensor as well as sectional curvatures on possibly infinite-dimensional shape spaces that can be thought of as Riemannian manifolds. To this end, we extend the variational time…
Fluid-structure simulations of slender inextensible filaments in a viscous fluid are often plagued by numerical stiffness. Recent coarse-graining studies have reduced the computational requirements of simulating such systems, though have…