Abstract
In numerical modeling tasks that use surface meshes, remeshing is often required. However, while remeshing, distortion can occur. The accumulation of distortions can lead to the collapse of the solution. Smoothing algorithms are used to maintain the quality of the mesh during the calculation. When performing smoothing using methods that shift the mesh nodes, the border nodes are usually fixed to avoid distortion. However, simply fixing the nodes can lead to more severe distortion. This paper presents methods for working with boundary nodes to control such nodes during the smoothing process. Algorithms for working with pseudo-3D surface meshes, which are of particular interest, are also considered.
Highlights
This article discusses computational geometry problems concerning surface unstructured triangular meshes. Such meshes are often used in issues of numerical modeling and computational geometry
The article discusses working with the boundary nodes of an unstructured triangular mesh when smoothing the mesh
The proposed methods are based on the analysis of the mutual arrangement of the surface mesh elements and allow the user to control the behavior of the boundary nodes
Summary
This article discusses computational geometry problems concerning surface unstructured triangular meshes. Such meshes are often used in issues of numerical modeling and computational geometry. In the process of developing programs for numerical modeling, a problem arises: mesh smoothing techniques (Laplace, Taubin smoothing [1], methods that preserve mesh features [2–4]), turn out to be unsuitable for working with meshes that are not closed surfaces. Boundary nodes move towards the body, causing uncontrolled compression of the surface. This feature is unacceptable since the task of preserving the boundaries of the mesh and its geometric features is critical. The work was done in JSCC RAS within the framework of the state assignment on the topic 0580-2021-0016
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