Variational method for untangling and optimization of spatial meshes

Variational method for untangling and optimization of spatial meshes

A variational method that can provably construct 3D quasi-isometric mappings between domains of a complex shape is introduced. A localmaximumprinciple for polyconvexmesh element distortion measures is formulated. It allows us to control the invertibility and distortion bounds for non-simplicial elements in the minimization process. A simple and efficient technique for construction of boundary o...

Local Optimization-Based Untangling Algorithms for Quadrilateral Meshes

Gradient projection based optimization methods for untangling and optimization of 3d meshes in implicit domains

Definition of complex domain as zero isosurface of scalar function resembling signed distance function is powerful and flexible mechanism of geometric modeling. Signed implicit functions can be constructed using surface triangulation, point clouds, set of planar cross-sections, “soup” consisting of disjoint edges and faces, and can be combined with analytical definitions and primitives using bo...

Robust Untangling of Curvilinear Meshes

This paper describes a technique that enables to generate high order / curvilinear meshes in a robust fashion. Accurate estimates of jacobian bounds are used for deriving an unconstrained optimization procedure. Both 2D and 3D valid high order meshes are presented that demonstrate the efficiency of the new technique.

Simultaneous untangling and smoothing of tetrahedral meshes

The quality improvement in mesh optimisation techniques that preserve its connectivity are obtained by an iterative process in which each node of the mesh is moved to a new position that minimises a certain objective function. The objective function is derived from some quality measure of the local submesh, that is, the set of tetrahedra connected to the adjustable or free node. Although these ...