Controlling Quadric Error Simplification with Line Quadrics

This work presents a method to control the output of mesh simplification algorithms based on iterative edge collapses. Traditional mesh simplification focuses on preserving the visual appearance. Despite still being an important criterion, other geometric properties also play critical roles in diffe...

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Vydáno v:Computer graphics forum Ročník 44; číslo 5
Hlavní autoři: Liu, Hsueh‐Ti Derek, Rahimzadeh, Mehdi, Zordan, Victor
Médium: Journal Article
Jazyk:angličtina
Vydáno: Oxford Blackwell Publishing Ltd 01.08.2025
Témata:
Apexes
CCS Concepts
Computing methodologies → Mesh models
Control methods
Errors
Graph theory
Simplification
Triangles
ISSN:0167-7055, 1467-8659
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Shrnutí:This work presents a method to control the output of mesh simplification algorithms based on iterative edge collapses. Traditional mesh simplification focuses on preserving the visual appearance. Despite still being an important criterion, other geometric properties also play critical roles in different applications, such as triangle quality for computations. This motivates our work to stay under the umbrella of the popular quadric error mesh simplification, while proposing different ways to control the simplified mesh to possess other geometric properties. The key ingredient of our work is another quadric error, called line quadrics, which can be seamlessly added to the vanilla quadric error metric. We show that, theoretically and empirically, adding our line quadrics can improve the numerics and encourage the simplified mesh to have uniformly distributed vertices. If we spread the line quadric adaptively to different regions, it can easily lead to soft preservation of feature vertices and edges. Our method is simple to implement, requiring only a few lines of code change on top of the original quadric error simplification, and can lead to a variety of user controls.
Bibliografie:ObjectType-Article-1
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content type line 14
ISSN:0167-7055
1467-8659
DOI:10.1111/cgf.70184