Link Conditions for Simplifying Meshes with Embedded Structures

Abstract

Abstract-Interactive visualization applications benefit from simplification techniques that generate good quality coarse meshes from high resolution meshes that represent the domain. These meshes often contain interesting substructures, called embedded structures, and it is desirable to preserve the topology of the embedded structures during simplification, in addition to preserving the topology of the domain. This paper describes a proof that link conditions, proposed earlier, are sufficient to ensure that edge contractions preserve topology of the embedded structures and the domain. Excluding two specific configurations, the link conditions are also shown to be necessary for topology preservation. Repeated application of edge contraction on an extended complex produces a coarser representation of the domain and the embedded structures. An extension of the quadric error metric is used to schedule edge contractions, resulting in a good quality coarse mesh that closely approximates the input domain and the embedded structures.

Digital body preservation: Technique and applications

“…This step Pisa, Italy) using quadratic based edge collapse with preservation of texture coordinates (Cignoni et al, 2008). The quadric error metric (QEM) approach is one of the most popular simplification algorithms that can handle non-manifold meshes, due to its speed and accuracy (Thomas et al, 2011;Wi et al, 2020). Non-manifold geometry occurs when any edge is shared by more than two faces.…”

Multi-material adaptive volume remesher

“…While this method allows preserving boundary surfaces using a volume based error metric, 1-and 0-junctions are not taken into account. To the best of our knowledge, only [37,38] account for 1-and 0-junctions. The authors propose link conditions defining if an edge can be collapsed without changing the topology of the features of different degrees.…”

“…Therefore, following [36][37][38], we define feature-aware rules and conditions depending on the feature complex hierarchy. Indeed, our rules assign a priority when processing the mesh elements based on their type which defines a so-called hierarchy.…”

Efficient Data Structure for Representing and Simplifying Simplicial Complexes in High Dimensions

“…In this section, we give a local condition on the link of an edge ab in a simplicial complex K under which the contraction of the edge ab preserves the homotopy type of K. This condition, called the link condition, was introduced in [4] to characterize edge contractions that permit a homeomorphic modification when the simplicial complex K is the triangulation of a 2-manifold or a 3-manifold. Unlike previous works [4,15], we make no assumptions on the simplicial complex K. In particular, we do not require that K triangulates a manifold.…”