Related papers: Connectivity-Preserving Cortical Surface Tetrahedr…
We introduce a new technique to create a mesh of convex polyhedra representing the interior volume of a triangulated input surface. Our approach is particularly tolerant to defects in the input, which is allowed to self-intersect, to be…
Geometric rounding of a mesh is the task of approximating its vertex coordinates by floating point numbers while preserving mesh structure. Geometric rounding allows algorithms of computational geometry to interface with numerical…
Surfaces are typically represented as meshes, which can be extracted from volumetric fields via meshing or optimized directly as surface parameterizations. Volumetric representations occupy 3D space and have a large effective receptive…
Swept volume computation, the determination of regions occupied by moving objects, is essential in graphics, robotics, and manufacturing. Existing approaches either explicitly track surfaces, suffering from robustness issues under complex…
This paper presents a hybrid algorithm that combines features form both Sqrt(3) and Loop Subdivision schemes. The algorithm aims at preserving sharp features and trim regions, during the surfaces subdivision, using a set of rules. The…
Electromagnetic simulations of complex geologic settings are computationally expensive. One reason for this is the fact that a fine mesh is required to accurately discretize the electrical conductivity model of a given setting. This…
This paper describes a method for fast simplification of surface meshes. Whereas past methods focus on visual appearance, our goal is to solve equations on the surface. Hence, rather than approximate the extrinsic geometry, we construct a…
Point cloud reconstruction from raw point cloud has been an important topic in computer graphics for decades, especially due to its high demand in modeling and rendering applications. An important way to solve this problem is establishing a…
Converting a three-dimensional medical image into a 3D mesh that satisfies both the quality and fidelity constraints of predictive simulations and image-guided surgical procedures remains a critical problem. Presented is an image-to-mesh…
We introduce a fast and invertible approximation for data simulated as 2D planar meshes with connectivities along the poloidal dimension in deforming 3D toroidal (donut-like) spaces generated by fusion simulations. In fusion simulations,…
Skinning is a popular way to rig and deform characters for animation, to compute reduced-order simulations, and to define features for geometry processing. Methods built on skinning rely on weight functions that distribute the influence of…
In this paper, we present a surface remeshing method with high approximation quality based on Principal Component Analysis. Given a triangular mesh and a user assigned polygon/vertex budget, traditional methods usually require the extra…
Mesh deformation plays a pivotal role in many 3D vision tasks including dynamic simulations, rendering, and reconstruction. However, defining an efficient discrepancy between predicted and target meshes remains an open problem. A prevalent…
An elastic surface model is investigated by using the canonical Monte Carlo simulation technique on triangulated spherical meshes. The model undergoes a first-order collapsing transition and a continuous surface fluctuation transition. The…
Many tasks in geometry processing are modeled as variational problems solved numerically using the finite element method. For solid shapes, this requires a volumetric discretization, such as a boundary conforming tetrahedral mesh.…
Connectivity maintenance is an essential aspect to consider while controlling a multi-robot system. In general, a multi-robot system should be connected to obtain a certain common objective. Connectivity must be kept regardless of the…
Deciding realizability of a given polyhedral map on a (compact, connected) surface belongs to the hard problems in discrete geometry, from the theoretical, the algorithmic, and the practical point of view. In this paper, we present a…
Standard PolyCube-based hexahedral (hex) meshing methods aim to deform the input domain into an axis-aligned PolyCube volume with integer corners; if this deformation is bijective, then applying the inverse map to the voxelized PolyCube…
We describe the implementation of a topological constraint in finite element simulations of phase field models which ensures path-connectedness of preimages of intervals in the phase field variable. Two main applications of our method are…
Given a tetrahedral mesh and objective functionals measuring the mesh quality which take into account the shape, size, and orientation of the mesh elements, our aim is to improve the mesh quality as much as possible. In this paper, we…