Related papers: An Adaptive Lagrangian B-Spline Framework for Poin…

We present a nodal interpolation method to approximate a subdivision model. The main application is to model and represent curved geometry without gaps and preserving the required simulation intent. Accordingly, we devise the technique to…

We present two novel generative geometric deep learning frameworks, termed Flow Matching PointNet and Diffusion PointNet, for predicting fluid flow variables on irregular geometries by incorporating PointNet into flow matching and diffusion…

Local density of point clouds is crucial for representing local details, but has been overlooked by existing point cloud compression methods. To address this, we propose a novel deep point cloud compression method that preserves local…

Establishing a consistent normal orientation for point clouds is a notoriously difficult problem in geometry processing, requiring attention to both local and global shape characteristics. The normal direction of a point is a function of…

In recent years, parametric representations of point clouds have been widely applied in tasks such as memory-efficient mapping and multi-robot collaboration. Highly adaptive models, like spline surfaces or quadrics, are computationally…

Accurate representation of interfaces and flux exchange is vital for coupled multiphysics simulations across a broad range of applications. Currently, coupling approaches are limited by the underlying discretization or to specific physical…

While three-dimensional (3D) building models play an increasingly pivotal role in many real-world applications, obtaining a compact representation of buildings remains an open problem. In this paper, we present a novel framework for…

Most existing point cloud upsampling methods have roughly three steps: feature extraction, feature expansion and 3D coordinate prediction. However,they usually suffer from two critical issues: (1)fixed upsampling rate after one-time…

In this work, we introduce a novel computational framework for solving the two-dimensional Hele-Shaw free boundary problem with surface tension. The moving boundary is represented by point clouds, eliminating the need for a global…

Exploiting fine-grained semantic features on point cloud is still challenging due to its irregular and sparse structure in a non-Euclidean space. Among existing studies, PointNet provides an efficient and promising approach to learn shape…

Most biological tissues grow by the synthesis of new material close to the tissue's interface, where spatial interactions can exert strong geometric influences on the local rate of growth. These geometric influences may be mechanistic, or…

We derive a variational model to fit a composite B\'ezier curve to a set of data points on a Riemannian manifold. The resulting curve is obtained in such a way that its mean squared acceleration is minimal in addition to remaining close the…

Point cloud is the most fundamental representation of 3D geometric objects. Analyzing and processing point cloud surfaces is important in computer graphics and computer vision. However, most of the existing algorithms for surface analysis…

We present a novel approach to learning a point-wise, meaningful embedding for point-clouds in an unsupervised manner, through the use of neural-networks. The domain of point-cloud processing via neural-networks is rapidly evolving, with…

3D point cloud interpretation is a challenging task due to the randomness and sparsity of the component points. Many of the recently proposed methods like PointNet and PointCNN have been focusing on learning shape descriptions from point…

Recently, many methods have been proposed for face reconstruction from multiple images, most of which involve fundamental principles of Shape from Shading and Structure from motion. However, a majority of the methods just generate discrete…

Existing learning-based surface reconstruction methods from point clouds are still facing challenges in terms of scalability and preservation of details on large-scale point clouds. In this paper, we propose the SSRNet, a novel scalable…

In CAGD the design of a surface that interpolates an arbitrary quadrilateral mesh is definitely a challenging task. The basic requirement is to satisfy both criteria concerning the regularity of the surface and aesthetic concepts. With…

Deep learning systems extensively use convolution operations to process input data. Though convolution is clearly defined for structured data such as 2D images or 3D volumes, this is not true for other data types such as sparse point…

We present an arbitrary updated Lagrangian Material Point Method (A-ULMPM) to alleviate issues, such as the cell-crossing instability and numerical fracture, that plague state of the art Eulerian formulations of MPM, while still allowing…