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RIAS: Repeated Invertible Averaging for Surface Multiresolution of Arbitrary Degree
IEEE Transactions on Visualization and Computer Graphics
|February 20, 2020
Summary
This study presents novel surface averaging operators for multiresolution modeling, enabling smooth subdivision and reverse subdivision for arbitrary degree surfaces with enhanced continuity properties.
Area of Science:
- Computer Graphics
- Geometric Modeling
- Applied Mathematics
Background:
- Existing surface subdivision methods often lack the ability to perform reverse subdivision or achieve arbitrary continuity.
- Previous work by Stam, Zorin, and Schröder focused on forward subdivision only.
- Generalizing B-Spline multiresolution to arbitrary topology surfaces remains a challenge.
Purpose of the Study:
- To introduce local surface averaging operators with local inverses.
- To develop a method for surface multiresolution (subdivision and reverse subdivision) of arbitrary degree.
- To achieve enhanced continuity properties for subdivision surfaces.
Main Methods:
- Development of two local surface averaging operators with local inverses.
- Application of these operators to devise a surface multiresolution method.
- Configuration of operators to generalize B-Spline multiresolution to arbitrary topology surfaces.
Main Results:
- The proposed method supports both subdivision and reverse subdivision of arbitrary degree.
- Subdivision surfaces exhibit C^d continuity at regular vertices and C^1 continuity at extraordinary vertices.
- The operators involve only direct neighbors of a vertex, simplifying the process.
Conclusions:
- The introduced method provides a robust framework for surface multiresolution with arbitrary degree and enhanced continuity.
- The operators generalize B-Spline multiresolution to arbitrary topology surfaces.
- Smooth reverse and non-uniform subdivisions are supported, offering flexibility in geometric modeling.
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