Multi-level partition of unity implicits
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- Teacher spread
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- Validation status
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Abstract
We present a new shape representation, the multi-level partition of unity implicit surface, that allows us to construct surface models from very large sets of points. There are three key ingredients to our approach: 1) piecewise quadratic functions that capture the local shape of the surface, 2) weighting functions (the partitions of unity) that blend together these local shape functions, and 3) an octree subdivision method that adapts to variations in the complexity of the local shape.Our approach gives us considerable flexibility in the choice of local shape functions, and in particular we can accurately represent sharp features such as edges and corners by selecting appropriate shape functions. An error-controlled subdivision leads to an adaptive approximation whose time and memory consumption depends on the required accuracy. Due to the separation of local approximation and local blending, the representation is not global and can be created and evaluated rapidly. Because our surfaces are described using implicit functions, operations such as shape blending, offsets, deformations and CSG are simple to perform.
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The record
- Venue
- ACM Transactions on Graphics
- Topic
- 3D Shape Modeling and Analysis
- Field
- Engineering
- Canadian institutions
- —
- Funders
- University of AizuUniversity of British Columbia
- Keywords
- Subdivision surfacePartition of unityPiecewiseSubdivisionPartition (number theory)OctreeMathematicsSurface (topology)Representation (politics)AlgorithmDevelopable surfaceQuadratic equationComputer scienceGeometryPolygon meshMathematical analysis
- Has abstract in OpenAlex
- yes