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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| Veröffentlicht in: | Computer graphics forum Jg. 44; H. 5 |
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Blackwell Publishing Ltd
01.08.2025
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| Abstract | 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. |
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| AbstractList | 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. |
| Author | Liu, Hsueh‐Ti Derek Rahimzadeh, Mehdi Zordan, Victor |
| Author_xml | – sequence: 1 givenname: Hsueh‐Ti Derek surname: Liu fullname: Liu, Hsueh‐Ti Derek organization: Roblox – sequence: 2 givenname: Mehdi surname: Rahimzadeh fullname: Rahimzadeh, Mehdi organization: Roblox – sequence: 3 givenname: Victor surname: Zordan fullname: Zordan, Victor organization: Roblox |
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| Cites_doi | 10.1201/b10688 10.1142/S0218654303000097 10.1145/1057432.1057457 10.1145/3592396 10.1145/1061347.1061350 10.1145/1073204.1073236 10.1016/S0925-7721(99)00030-9 10.1016/0024-3795(94)90493-6 10.1145/1015706.1015817 10.1111/j.1467-8659.2009.01374.x 10.5194/isprs-archives-XLVIII-2-W8-2024-185-2024 10.1109/5.488703 10.1016/j.cma.2004.11.016 10.1145/2898350 10.1111/cgf.13932 10.1111/1467-8659.00698 10.1111/cgf.13933 |
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| SubjectTerms | Apexes CCS Concepts Computing methodologies → Mesh models Control methods Errors Graph theory Simplification Triangles |
| Title | Controlling Quadric Error Simplification with Line Quadrics |
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