Symposium on Point Based Graphics 04
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Browsing Symposium on Point Based Graphics 04 by Subject "Categories and Subject Descriptors (according to ACM CCS): G.1.2 [Numerical Analysis]: Approximation of surfaces and contours I.3.5 [Computer Graphics]: Curve, surface, solid, and object representations"
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Item On Normals and Projection Operators for Surfaces Defined by Point Sets(The Eurographics Association, 2004) Alexa, Marc; Adamson, Anders; Markus Gross and Hanspeter Pfister and Marc Alexa and Szymon RusinkiewiczLevin 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.Item Proximity Graphs for Defining Surfaces over Point Clouds(The Eurographics Association, 2004) Klein, Jan; Zachmann, Gabriel; Markus Gross and Hanspeter Pfister and Marc Alexa and Szymon RusinkiewiczWe present a new definition of an implicit surface over a noisy point cloud. It can be evaluated very fast, but, unlike other definitions based on the moving least squares approach, it does not suffer from artifacts. In order to achieve robustness, we propose to use a different kernel function that approximates geodesic distances on the surface by utilizing a geometric proximity graph. The starting point in the graph is determined by approximate nearest neighbor search. From a variety of possibilities, we have examined the Delaunay graph and the sphere-of-influence graph (SIG). For both, we propose to use modifications, the r-SIG and the pruned Delaunay graph. We have implemented our new surface definition as well as a test environment which allows to visualize and to evaluate the quality of the surfaces. We have evaluated the different surfaces induced by different proximity graphs. The results show that artifacts and the root mean square error are significantly reduced.