Abstract
Mesh (pre)processing remains an important issue for obtaining useful meshes used in mechanical engineering, especially for finite element calculations. An efficient and robust combination of constrained mesh smoothing together with global optimization based algorithm is presented. In contrast to other “popular” mesh smoothing algorithms that use only local diffusion approaches to smoothing we propose Lagrange-Newton Sequential Quadratic Optimization (LNO) with constraints that can satisfy local and global cost functions, respecting posed constraints. Local cost function is modeled with local average edge length, while global cost function includes barycenter and global average edge length. Experiments with triangular, quadrilateral, and mixed meshes show flexibility of the proposed method to achieve near ideal elements for given input meshes. Convergence is presented for several 2D and 3D meshes. Various additional goals can be mixed over the area of interest with applied weights. In contrast to other methods, unconstrained meshes still preserve their global shape while improving local quality.
Highlights
Mesh optimization methods are used in mechanical engineering applications areas such as solid and fluid dynamics, heat transfer, material science etc
At the beginning the results of this optimization method with two different cost functions applied to many different data sets, ranging from small sets sampled from simple mesh structures to complex models with many vertices, are showed
Initial, b) local optimized after 4 iterations, and c) global optimized after 3 iterations meshes a) initial, b) local optimized after 5 iterations, and c) global optimized after 4 iterations meshes a) global cost functions after 3 iterations
Summary
Mesh optimization methods are used in mechanical engineering applications areas such as solid and fluid dynamics, heat transfer, material science etc. The majority of virtual reality applications use triangular meshes as their fundamental modeling and rendering is primitive Such meshes can be the result of the modeling software, or may be an output of a scanning device. Moving (or shifting) vertices can have a drastic effect on the quality of a mesh and it is more efficient than refinement and collapsing vertices especially when the translation amplitudes are small. Such mesh relaxation can be regarded as mesh smoothing as it results in a visually pleasing mesh that follows some local or global rules. Our mesh optimization problem is an indirect optimization technique using the method of sequential quadratic programming
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