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On normals and projection operators for surfaces defined by point sets

: Alexa, M.; Adamson, A.

Alexa, M.; Rusinkiewicz, S.; Pfister, H.; Groß, M. ; European Association for Computer Graphics -EUROGRAPHICS-; Association for Computing Machinery -ACM-, Special Interest Group on Graphics -SIGGRAPH-; IEEE Computer Society, Technical Committee on Visualization and Graphics:
Symposium on Point Based Graphics 2004. Proceedings
Aire-la-Ville: Eurographics, 2004
ISBN: 3-905673-09-6
Symposium on Point-Based Graphics <1, 2004, Zürich>
Conference Paper
Fraunhofer IGD ()
shape approximation; solid representation; surface representation; curve representation

Levin's MLS projection operator allows defining a surface from a set of points and represents a versatile procedure to generate points on this surface. Practical problems of MLS surfaces are a complicated non-linear optimization to compute a tangent frame and the (commonly overlooked) fact that the normal to this tangent frame is not the surface normal. An alternative definition of Point Set Surfaces, inspired by the MLS projection, is the implicit surface version of Adamson & Alexa. We use this surface definition to show how to compute exact surface normals and present simple, efficient projection operators. The exact normal computation also allows computing orthogonal projections.