Adamson, Anders ; Alexa, Marc (2003)
Approximating and Intersecting Surfaces from Points.
Symposium on Geometry Processing. Proceedings.
Konferenzveröffentlichung, Bibliographie
Kurzbeschreibung (Abstract)
Point sets become an increasingly popular shape representation. Most shape processing and rendering tasks require the approximation of a continuous surface from the point data. We present a surface approximation that is motivated by an efficient iterative ray intersection computation. On each point on a ray, a local normal direction is estimated as the direction of smallest weighted co-variances of the points. The normal direction is used to build a local polynomial approximation to the surface, which is then intersected with the ray. The distance to the polynomials essentially defines a distance field, whose zero-set is computed by repeated ray intersection. Requiring the distance field to be smooth leads to an intuitive and natural sampling criterion, namely, that normals derived from the weighted co-variances are well defined in a tubular neighborhood of the surface. For certain, well-chosen weight functions we can show that well-sampled surfaces lead to smooth distance fields with non-zero gradients and, thus, the surface is a continuously differentiable manifold. We detail spatial data structures and efficient algorithms to compute ray-surface intersections for fast ray casting and ray tracing of the surface.
| Typ des Eintrags: | Konferenzveröffentlichung |
|---|---|
| Erschienen: | 2003 |
| Autor(en): | Adamson, Anders ; Alexa, Marc |
| Art des Eintrags: | Bibliographie |
| Titel: | Approximating and Intersecting Surfaces from Points |
| Sprache: | Englisch |
| Publikationsjahr: | 2003 |
| Verlag: | Association for Computing Machinery, New York |
| Veranstaltungstitel: | Symposium on Geometry Processing. Proceedings |
| Kurzbeschreibung (Abstract): | Point sets become an increasingly popular shape representation. Most shape processing and rendering tasks require the approximation of a continuous surface from the point data. We present a surface approximation that is motivated by an efficient iterative ray intersection computation. On each point on a ray, a local normal direction is estimated as the direction of smallest weighted co-variances of the points. The normal direction is used to build a local polynomial approximation to the surface, which is then intersected with the ray. The distance to the polynomials essentially defines a distance field, whose zero-set is computed by repeated ray intersection. Requiring the distance field to be smooth leads to an intuitive and natural sampling criterion, namely, that normals derived from the weighted co-variances are well defined in a tubular neighborhood of the surface. For certain, well-chosen weight functions we can show that well-sampled surfaces lead to smooth distance fields with non-zero gradients and, thus, the surface is a continuously differentiable manifold. We detail spatial data structures and efficient algorithms to compute ray-surface intersections for fast ray casting and ray tracing of the surface. |
| Freie Schlagworte: | Ray tracing, Object representation, Curve representation, Surface representation, Solid representation |
| Fachbereich(e)/-gebiet(e): | nicht bekannt 20 Fachbereich Informatik 20 Fachbereich Informatik > Graphisch-Interaktive Systeme |
| Hinterlegungsdatum: | 16 Apr 2018 09:04 |
| Letzte Änderung: | 16 Apr 2018 09:04 |
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