204,956 research outputs found
Error-Bounded and Feature Preserving Surface Remeshing with Minimal Angle Improvement
The typical goal of surface remeshing consists in finding a mesh that is (1)
geometrically faithful to the original geometry, (2) as coarse as possible to
obtain a low-complexity representation and (3) free of bad elements that would
hamper the desired application. In this paper, we design an algorithm to
address all three optimization goals simultaneously. The user specifies desired
bounds on approximation error {\delta}, minimal interior angle {\theta} and
maximum mesh complexity N (number of vertices). Since such a desired mesh might
not even exist, our optimization framework treats only the approximation error
bound {\delta} as a hard constraint and the other two criteria as optimization
goals. More specifically, we iteratively perform carefully prioritized local
operators, whenever they do not violate the approximation error bound and
improve the mesh otherwise. In this way our optimization framework greedily
searches for the coarsest mesh with minimal interior angle above {\theta} and
approximation error bounded by {\delta}. Fast runtime is enabled by a local
approximation error estimation, while implicit feature preservation is obtained
by specifically designed vertex relocation operators. Experiments show that our
approach delivers high-quality meshes with implicitly preserved features and
better balances between geometric fidelity, mesh complexity and element quality
than the state-of-the-art.Comment: 14 pages, 20 figures. Submitted to IEEE Transactions on Visualization
and Computer Graphic
Optimizing the geometrical accuracy of curvilinear meshes
This paper presents a method to generate valid high order meshes with
optimized geometrical accuracy. The high order meshing procedure starts with a
linear mesh, that is subsequently curved without taking care of the validity of
the high order elements. An optimization procedure is then used to both
untangle invalid elements and optimize the geometrical accuracy of the mesh.
Standard measures of the distance between curves are considered to evaluate the
geometrical accuracy in planar two-dimensional meshes, but they prove
computationally too costly for optimization purposes. A fast estimate of the
geometrical accuracy, based on Taylor expansions of the curves, is introduced.
An unconstrained optimization procedure based on this estimate is shown to
yield significant improvements in the geometrical accuracy of high order
meshes, as measured by the standard Haudorff distance between the geometrical
model and the mesh. Several examples illustrate the beneficial impact of this
method on CFD solutions, with a particular role of the enhanced mesh boundary
smoothness.Comment: Submitted to JC
An Alternating Mesh Quality Metric Scheme for Efficient Mesh Quality Improvement
AbstractIn the numerical solution of partial differential equations (PDEs), high-quality meshes are crucial for the stability, accuracy, and convergence of the associated PDE solver. Mesh quality improvement is often performed to improve the quality of meshes before use in numerical solution of the PDE. Mesh smoothing (performed via optimization) is one popular technique for improving the mesh quality; it does so by making adjustments to the vertex locations. When an inefficient mesh quality metric is used to design the optimization problem, and hence also to measure the mesh quality within the optimization procedure, convergence of the optimization method can be much slower than desired. However, for many applications, the choice of mesh quality metric and the optimization problem should be considered fixed. In this paper, we propose a simple mesh quality metric alternation scheme for use in the mesh optimization process. The idea is to alternate the use of the original inefficient mesh quality metric with a more efficient mesh quality metric on alternate iterations of the mesh optimization procedure in order to reduce the time to convergence, while solving the original mesh quality improvement problem. Typical results of using our application scheme to solve mesh quality improvement problems yield approximately 40-55% improvement in comparison to the original mesh optimization procedure. More frequent use of the efficient metric results in greater speed-ups
Incremental Visual-Inertial 3D Mesh Generation with Structural Regularities
Visual-Inertial Odometry (VIO) algorithms typically rely on a point cloud
representation of the scene that does not model the topology of the
environment. A 3D mesh instead offers a richer, yet lightweight, model.
Nevertheless, building a 3D mesh out of the sparse and noisy 3D landmarks
triangulated by a VIO algorithm often results in a mesh that does not fit the
real scene. In order to regularize the mesh, previous approaches decouple state
estimation from the 3D mesh regularization step, and either limit the 3D mesh
to the current frame or let the mesh grow indefinitely. We propose instead to
tightly couple mesh regularization and state estimation by detecting and
enforcing structural regularities in a novel factor-graph formulation. We also
propose to incrementally build the mesh by restricting its extent to the
time-horizon of the VIO optimization; the resulting 3D mesh covers a larger
portion of the scene than a per-frame approach while its memory usage and
computational complexity remain bounded. We show that our approach successfully
regularizes the mesh, while improving localization accuracy, when structural
regularities are present, and remains operational in scenes without
regularities.Comment: 7 pages, 5 figures, ICRA accepte
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