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Approximating Bounded, Non-orientable Surfaces from Points

Adamson, Anders ; Alexa, Marc (2004)
Approximating Bounded, Non-orientable Surfaces from Points.
International Conference on Shape Modeling and Applications 2004. Proceedings.
Conference or Workshop Item, Bibliographie

Abstract

We present an approach to surface approximation from points that allows reconstructing surfaces with boundaries, including globally non-orientable surfaces. The surface is defined implicitly using directions of weighted co-variances and weighted averages of the points. Specifically, a point belongs to the surface, if its direction to the weighted average has no component into the direction of smallest covariance. For bounded surfaces, we require in addition that any point on the surface is close to the weighted average of the input points. We compare this definition to alternatives and discuss the details and parameter choices. Points on the surface can be determined by intersection computations. We show that the computation is local and, therefore, no globally consistent orientation of normals is needed. Continuity of the surfaces is not affected by the particular choice of local orientation. We demonstrate our approach by rendering several bounded (and non-orientable) surfaces using ray casting.

Item Type: Conference or Workshop Item
Erschienen: 2004
Creators: Adamson, Anders ; Alexa, Marc
Type of entry: Bibliographie
Title: Approximating Bounded, Non-orientable Surfaces from Points
Language: German
Date: 2004
Publisher: IEEE Computer Society Press, Los Alamitos
Event Title: International Conference on Shape Modeling and Applications 2004. Proceedings
Abstract:

We present an approach to surface approximation from points that allows reconstructing surfaces with boundaries, including globally non-orientable surfaces. The surface is defined implicitly using directions of weighted co-variances and weighted averages of the points. Specifically, a point belongs to the surface, if its direction to the weighted average has no component into the direction of smallest covariance. For bounded surfaces, we require in addition that any point on the surface is close to the weighted average of the input points. We compare this definition to alternatives and discuss the details and parameter choices. Points on the surface can be determined by intersection computations. We show that the computation is local and, therefore, no globally consistent orientation of normals is needed. Continuity of the surfaces is not affected by the particular choice of local orientation. We demonstrate our approach by rendering several bounded (and non-orientable) surfaces using ray casting.

Uncontrolled Keywords: Point sampled geometry, Surface representation, Surface reconstruction, Ray casting
Divisions: 20 Department of Computer Science
20 Department of Computer Science > Interactive Graphics Systems
Date Deposited: 16 Apr 2018 09:04
Last Modified: 16 Apr 2018 09:04
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