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- Anders Adamson, Marc Alexa
- Symposium on Geometry Processing
- 2003

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… (More)

- Marc Alexa, Anders Adamson
- SPBG
- 2004

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… (More)

- Anders Adamson, Marc Alexa
- 2002

Point set surfaces (PSS) are a smooth manifold surface approximation from a set of sample points. The surface definition is based on a projection operation that constructs local polynomial approximations and respects a minimum feature size. We present techniques for ray tracing PSSs. For the computation of ray-surface intersection the properties of the… (More)

- Anders Adamson, Marc Alexa
- Comput. Graph. Forum
- 2006

Point Set Surfaces define smooth surfaces from regular samples based on weighted averaging of the points. Because weighting is done based on a spatial scale parameter, point set surfaces apply basically only to regular samples. We suggest to attach individual weight functions to each sample rather than to the location in space. This extends Point Set… (More)

- Anders Adamson, Marc Alexa
- SMI
- 2004

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… (More)

- Anders Adamson, Marc Alexa
- ACM Trans. Graph.
- 2006

A piecewise smooth surface, possibly with boundaries, sharp edges, corners, or other features is defined by a set of samples. The basic idea is to model surface patches, curve segments and points explicitly, and then to glue them together based on explicit connectivity information. The geometry is defined as the set of stationary points of a projection… (More)

- Anders Adamson, Marc Alexa
- SMI
- 2004

- Marc Alexa, Anders Adamson
- ACM Trans. Graph.
- 2009

Point set surfaces define a (typically) manifold surface from a set of scattered points. The definition involves weighted centroids and a gradient field. The data points are interpolated if singular weight functions are used to define the centroids. While this way of deriving an interpolatory scheme appears natural, we show that it has two deficiencies:… (More)

- Anders Adamson, Marc Alexa
- Shape Modeling International
- 2003

- Anders Adamson, Marc Alexa, Andrew Nealen
- SI3D
- 2005

We present a sampling strategy and rendering framework for intersectable models, whose surface is implicitly defined by a black box intersection test that provides the location and normal of the closest intersection of a ray with the surface. To speed up image generation despite potentially slow intersection tests, our method exploits spatial coherence by… (More)