Anisotropic point set surfaces
AFRIGRAPH '06 Proceedings of the 4th international conference on Computer graphics, virtual reality, visualisation and interaction in Africa
ACM SIGGRAPH 2006 Papers
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SPBG'08 Proceedings of the Fifth Eurographics / IEEE VGTC conference on Point-Based Graphics
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We present an approach to surface approximation frompoints that allows reconstructing surfaces with boundaries,including globally non-orientable surfaces. The surface isdefined implicitly using directions of weighted co-variancesand weighted averages of the points. Specifically, a pointbelongs to the surface, if its direction to the weighted averagehas no component into the direction of smallest covariance.For bounded surfaces, we require in addition thatany point on the surface is close to the weighted average ofthe input points. We compare this definition to alternativesand discuss the details and parameter choices. Points onthe surface can be determined by intersection computations.We show that the computation is local and, therefore, noglobally consistent orientation of normals is needed. Continuityof the surfaces is not affected by the particular choiceof local orientation. We demonstrate our approach by renderingseveral bounded (and non-orientable) surfaces usingray casting.