Related papers: Repulsive Surfaces
We investigate the behaviour of vertices and inflexions on 1-parameter families of curves on smooth surfaces in the 3-space, which include a singular member. In particular, we discuss the context where the curves evolve as sections of a…
We propose integrating optimal transport (OT) into operator learning for partial differential equations (PDEs) on complex geometries. Classical geometric learning methods typically represent domains as meshes, graphs, or point clouds. Our…
We demonstrate an approach of exploring design spaces to simultaneously satisfy kinematics- and physics-based requirements. We present a classification of constraints and solvers to enable postponing optimization as far down the design…
Immersed boundary methods are extensively used for simulations of dynamic solid objects interacting with fluids due to their computational efficiency and modelling flexibility compared to body-fitted grid methods. However, thin geometries,…
Interlocking interfaces are commonly employed to mitigate relative sliding under shear.Indeed, Their geometry is typically selected on grounds of fabrication convenience rather than analytical optimality. There is no reason to suppose that…
The calculation of potential energy surfaces for quantum dynamics can be a time consuming task -- especially when a high level of theory for the electronic structure calculation is required. We propose an adaptive interpolation algorithm…
3D scene modeling techniques serve as the bedrocks in the geospatial engineering and computer science, which drives many applications ranging from automated driving, terrain mapping, navigation, virtual, augmented, mixed, and extended…
Shape priors have been widely utilized in medical image segmentation to improve segmentation accuracy and robustness. A major way to encode such a prior shape model is to use a mesh representation, which is prone to causing…
Analysis of the 3D Texture is indispensable for various tasks, such as retrieval, segmentation, classification, and inspection of sculptures, knitted fabrics, and biological tissues. A 3D texture is a locally repeated surface variation…
The Closest Point Method for solving partial differential equations (PDEs) posed on surfaces was recently introduced by Ruuth and Merriman [J. Comput. Phys. 2008] and successfully applied to a variety of surface PDEs. In this paper we study…
Dynamic surface reconstruction of objects from point cloud sequences is a challenging field in computer graphics. Existing approaches either require multiple regularization terms or extensive training data which, however, lead to…
Persistence-based topological optimization deforms a point cloud $X \subset \mathbb{R}^d$ by minimizing objectives of the form $L(X) = \ell(\mathrm{Dgm}(X))$, where $\mathrm{Dgm}(X)$ is a persistence diagram. In practice, optimization is…
This paper proposes Separability Membrane, a robust 3D active contour for extracting a surface from 3D point cloud object. Our approach defines the surface of a 3D object as the boundary that maximizes the separability of point features,…
Designing the topology of three-dimensional structures is a challenging problem due to its memory and time consumption. In this paper, we present a robust and efficient algorithm for solving large-scale 3D topology optimization problems.…
Contact algorithm between different bodies plays an important role in solving collision problems. Usually it is not easy to be treated very well. Several ones for material point method were proposed by Bardenhangen, Brackbill, and…
This thesis is devoted to the Differential Geometry of curves and surfaces along with applications in Quantum Mechanics. In the 1st part we introduce the well known Frenet frame. Later, we show that the curvature function is a lower bound…
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…
High-order meshes are crucial for achieving optimal convergence rates in curvilinear domains, preserving symmetry, and aligning with key flow features in moving mesh simulations, but their quality is challenging to control. In prior work,…
Machine learning of multi-dimensional potential energy surfaces, from purely ab initio datasets, has seen substantial progress in the past years. Gaussian processes, a popular regression method, have been very successful at producing…
Designs generated by density-based topology optimization (TO) exhibit jagged and/or smeared boundaries, which forms an obstacle to their integration with existing CAD tools. Addressing this problem by smoothing or manual design adjustments…