SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
Surface simplification using quadric error metrics
Proceedings of the 24th annual conference on Computer graphics and interactive techniques
Graphical Models
Medial Representations: Mathematics, Algorithms and Applications
Medial Representations: Mathematics, Algorithms and Applications
Proceedings of the twenty-fifth annual symposium on Computational geometry
Discrete scale axis representations for 3D geometry
ACM SIGGRAPH 2010 papers
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The Scale Axis Transform provides a parametric simplification of the Medial Axis of a 3D shape which can be seen as a hierarchical description. However, this powerful shape analysis method has a significant computational cost, requiring several minutes for a single scale on a mesh of few thousands vertices. Moreover, the scale axis can be artificially complexified at large scales, introducing new topological structures in the simplified model. In this paper, we propose a progressive medial axis simplification method inspired from surface optimization techniques which retains the geometric intuition of the scale axis transform. We compute a hierarchy of simplified medial axes by means of successive edge-collapses of the input medial axis. These operations prevent the creation of artificial tunnels that can occur in the original scale axis transform. As a result, our progressive simplification approach allows to compute the complete hierarchy of scales in a few seconds on typical input medial axes. We show how this variation of the scale axis transform impacts the resulting medial structure.