Related papers: T-Base: A Triangle-Based Iterative Algorithm for S…
High-quality quadrilateral mesh generation is a fundamental challenge in computer graphics. Traditional optimization-based methods are often constrained by the topological quality of input meshes and suffer from severe efficiency…
This paper presents an alternative approach to dehomogenisation of elastic Rank-N laminate structures based on the computer graphics discipline of phasor noise. The proposed methodology offers an improvement of existing methods, where…
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…
This paper presents a complete Pascal interpolation scheme for use in the plane geometry mapping applied in association with numerical methods. The geometry of a domain element is approximated by a complete Pascal polynomial. The…
In this paper we present a new multilevel quasi-interpolation algorithm for smooth periodic functions using scaled Gaussians as basis functions. Recent research in this area has focussed upon implementations using basis function with finite…
In this work we present an algorithm to construct an infinitely differentiable smooth surface from an input consisting of a (rectilinear) triangulation of a surface of arbitrary shape. The original surface can have non-trivial genus and…
Triangulated meshes have become ubiquitous discrete-surface representations. In this paper we address the problem of how to maintain the manifold properties of a surface while it undergoes strong deformations that may cause topological…
In the present paper, an integrated paradigm for topology optimization on complex surfaces with arbitrary genus is proposed. The approach is constructed based on the two-dimensional (2D) Moving Morphable Component (MMC) framework, where a…
We unify and extend previous bijections on plane quadrangulations to bipartite and quasibipartite plane maps. Starting from a bipartite plane map with a distinguished edge and two distinguished corners (in the same face or in two different…
We propose a two-level structural optimization method for obtaining an approximate optimal shape of piecewise developable surface without specifying internal boundaries between surface patches. The condition for developability of a…
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…
Motivated by learning problems including max-norm regularized matrix completion and clustering, robust PCA and sparse inverse covariance selection, we propose a novel optimization algorithm for minimizing a convex objective which decomposes…
Given a finite set of points $P$ sampling an unknown smooth surface $\mathcal{M} \subseteq \mathbb{R}^3$, our goal is to triangulate $\mathcal{M}$ based solely on $P$. Assuming $\mathcal{M}$ is a smooth orientable submanifold of codimension…
Mesh optimization procedures are generally a combination of node smoothing and discrete operations which affect a small number of elements to improve the quality of the overall mesh. These procedures are useful as a post-processing step in…
This work presents a novel framework for spherical mesh parameterization. An efficient angle-preserving spherical parameterization algorithm is introduced, which is based on dynamic Yamabe flow and the conformal welding method with solid…
This paper presents a lowest-order immersed Raviart-Thomas mixed triangular finite element method for solving elliptic interface problems on unfitted meshes independent of the interface. In order to achieve the optimal convergence rates on…
This paper discusses the dimensions of the spline spaces over T-meshes with lower degree. Two new concepts are proposed: extension of T-meshes and spline spaces with homogeneous boundary conditions. In the dimension analysis, the key…
One approach to achieving correct finite element assembly is to ensure that the local orientation of facets relative to each cell in the mesh is consistent with the global orientation of that facet. Rognes et al. have shown how to achieve…
We suggest a novel shape matching algorithm for three-dimensional surface meshes of disk or sphere topology. The method is based on the physical theory of nonlinear elasticity and can hence handle large rotations and deformations.…
An exact conservative remapping scheme requires overlaps between two meshes and a reconstruction scheme on the old cells (Lagrangian mesh). While the are intensive discussion on reconstruction schemes, there are relative sparse discussion…