We advocate the use of point sets to represent shapes. We provide a definition of a smooth manifold surface from a set of points close to the original surface. The definition is based on local maps from differential geometry, which are approximated by the method of moving least squares (MLS). The computation of points on the surface is local, which results in an out-of-core technique that can handle any point set.

Elliptical weighted average (EWA) surface splatting is a technique for high quality rendering of point-sampled 3D objects. EWA surface splatting renders water-tight surfaces of complex point models with high quality, anisotropic texture filtering. In this paper we introduce a new multi-pass approach to perform EWA surface splatting on modern PC graphics hardware, called object space EWA splatting. We derive an object space formulation of the EWA filter, which is amenable for acceleration by conventional triangle-based graphics hardware. We describe how to implement the object space EWA filter using a two pass rendering algorithm. In the first rendering pass, visibility splatting is performed by shifting opaque surfel polygons backward along the viewing rays, while in the second rendering pass view-dependent EWA prefiltering is performed by deforming texture mapped surfel polygons.

We present a method for interactive rendering of large outdoor scenes. Complex polygonal plant models and whole plant populations are represented by relatively small sets of point and line primitives. This enables us to show landscapes faithfully using only a limited percentage of primitives. In addition, a hierarchical data structure allows us to smoothly reduce the geometrical representation to any desired number of primitives. The scene is hierarchically divided into local portions of geometry to achieve large reduction factors for distant regions. Additionally, the data reduction is adapted to the visual importance of geometric objects. This allows us to maintain the visual fidelity of the representation while reducing most of the geometry drastically. With our system, we are able to interactively render very complex landscapes with good visual quality.

Figure 1: Continuous detail levels of a Buddha generated in vertex programs on the GPU. The colors denote the LOD level used and the bars describe the selected amount of points selected for the GPU (top row) and the average CPU load required for rendering (bottom row). In this paper we present sequential point trees, a data structure that allows adaptive rendering of point clouds completely on the graphics processor. Sequential point trees are based on a hierarchical point representation, but the hierarchical rendering traversal is replaced by sequential processing on the graphics processor, while the CPU is available for other tasks. Smooth transition to triangle rendering for optimized performance is integrated. We describe optimizations for backface culling and texture adaptive point selection. Finally, we discuss implementation issues and show results.

In the last years point-based rendering has been shown to offer the potential to outperform traditional triangle based rendering both in speed and visual quality when it comes to processing highly complex models. Existing surface splatting techniques achieve superior visual quality by proper filtering but they are still limited in rendering speed. On the other hand the increasing availability and programmability of graphics hardware lead to the developement of very efficient hardware-accelerated rendering methods. However, since no filtered splats are used, these approaches trade visual quality for rendering speed.

In this paper we present an algorithm to perform interactive boolean operations on free-form solids bounded by surfels. We introduce a fast inside-outside test to check whether surfels lie within the bounds of another surfel-bounded solid. This enables us to add, subtract and intersect complex solids at interactive rates. Our algorithm is fast both in displaying and constructing the new geometry resulting from the boolean operation. We present a

Point set surfaces 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 point set surfaces. For the computation of ray-surface intersection the properties of the projection operation are exploited: The surface is enclosed by a union of minimum feature size spheres. A ray is intersected with the spheres first and inside the spheres with local polynomial approximations. Our results show that 2--3 projections are sufficient to accurately intersect a ray with the surface.

We present an efficient approach for end-to-end out-of-core construction and interactive inspection of very large arbitrary surface models. The method tightly integrates visibility culling and outof-core data management with a level-of-detail framework. At preprocessing

Efficient and informative visualization of surfaces with uncertainties is an important topic with many applications in science and engineering. In these applications, the correct course of action may depend not only on the location of a boundary, but on the precision with which that location is known. Examples include environmental pollution borderline detection, oil basin edge characterization, or discrimination between cancerous and healthy tissue in medicine. This paper presents a method for producing visualizations of surfaces with uncertainties using points as display primitives. Our approach is to render the surface as a collection of points and to displace each point from its original location along the surface normal by an amount proportional to the uncertainty at that point. This approach can be used in combination with other techniques such as pseudocoloring to produce efficient and revealing visualizations. The basic approach is sufficiently flexible to allow natural extensions; we show incorporation of expressive modulation of opacity, change of the stroke primitive, and addition of an underlying polygonal model. The method is used to visualize real and simulated tumor formations with uncertainty of tumor boundaries. The point-based technique is compared to pseudocoloring for a position estimation task in a preliminary user study.

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 has no component into the direction of smallest covariance. For bounded surfaces, we require in addition that any point on the surface is close to the weighted average of the input points. We compare this definition to alternatives and discuss the details and parameter choices. Points on the surface can be determined by intersection computations. We show that the computation is local and, therefore, no globally consistent orientation of normals is needed. Continuity of the surfaces is not affected by the particular choice of local orientation. We demonstrate our approach by rendering several bounded (and non-orientable) surfaces using ray casting.