Related papers: An Improved Physically-Based Surface Triangulation…
Triangulations are an ubiquitous input for the finite element community. However, most raw triangulations obtained by imaging techniques are unsuitable as-is for finite element analysis. In this paper, we give a robust pipeline for handling…
Computational technologies for the approximate solution of multidimensional boundary value problems often rely on irregular computational meshes and finite-volume approximations. In this framework, the discrete problem represents the…
This paper presents an efficient approach for the conceptual design of architectural surfaces which are composed of triangular panels. In the free-form design of discrete architectural surfaces, the Gaussian curvature plays an important…
This paper introduces a Delaunay triangulation algorithm based on the external incremental method. Unlike traditional random incremental methods, this approach uses convex hull and points as basic operational units instead of triangles.…
Mesh adaptivity is a useful tool for efficient solution to partial differential equations in very complex geometries. In the present paper we discuss the use of polygonal mesh refinement in order to tackle two common issues: first,…
Manipulating the shape of a liquid droplet is essential for a wide range of applications in medicine and industry. However, existing methods are typically limited to generating simple shapes, such as ellipses, or rely on predefined…
We propose the first GPU algorithm for the 3D triangulation refinement problem. For an input of a piecewise linear complex $\mathcal{G}$ and a constant $B$, it produces, by adding Steiner points, a constrained Delaunay triangulation…
In this paper, we propose a novel gradient-based method to optimize curvilinear masks in optical lithography. The mask pattern is represented by periodic B-spline curves. We apply Delaunay triangulation to discretize the domains circled by…
The application of modern topology optimization techniques to single physics systems has seen great advances in the last three decades. However, the application of these tools to sophisticated multiphysics systems such as fluid-structure…
Video stabilization is essential for improving visual quality of shaky videos. The current video stabilization methods usually take feature trajectories in the background to estimate one global transformation matrix or several…
This work considers gradient-based mesh optimization, where we iteratively optimize for a 3D surface mesh by representing it as the isosurface of a scalar field, an increasingly common paradigm in applications including photogrammetry,…
We introduce a continuous global optimization method to the field of surface reconstruction from discrete noisy cloud of points with weak information on orientation. The proposed method uses an energy functional combining flux-based…
3D printing of surfaces has become an established method for prototyping and visualisation. However, surfaces often contain certain degenerations, such as self-intersecting faces or non-manifold parts, which pose problems in obtaining a 3D…
Image-based 3D reconstruction has increasingly stunning results over the past few years with the latest improvements in computer vision and graphics. Geometry and topology are two fundamental concepts when dealing with 3D mesh structures.…
In this paper, we propose several mathematical models for 3D surface reconstruction and volume estimation from a set of scattered cloud data. Three meshless methods including the interpolation-based method by RBF, PDE-based approach by…
In shape optimisation it is desirable to obtain deformations of a given mesh without negative impact on the mesh quality. We propose a new algorithm using least square formulations of the Cauchy-Riemann equations. Our method allows to…
We introduce a smoothing algorithm for triangle, quadrilateral, tetrahedral and hexahedral meshes whose centerpiece is a simple geometric triangle transformation. The first part focuses on the mathematical properties of the element…
In the following article we discuss Delaunay triangulations for a point cloud on an embedded surface in $\mathbb{R}^3$. We give sufficient conditions on the point cloud to show that the diagonal switch algorithm finds an embedded Delaunay…
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…
We develop a new optimisation technique that combines multiresolution subdivision surfaces for boundary description with immersed finite elements for the discretisation of the primal and adjoint problems of optimisation. Similar to wavelets…