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.

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 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

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 a novel multi-resolution point sample rendering algorithm for keyframe animations. The algorithm accepts triangle meshes of arbitrary topology as input which are animated by specifying different sets of vertices at keyframe positions. A multi-resolution representation consisting of prefiltered point samples and triangles is built to represent the animated mesh at different levels of detail. We introduce a novel sampling and stratification algorithm to efficiently generate suitable point sample sets for moving triangle meshes. Experimental results demonstrate that the new data structure can be used to render highly complex keyframe animations like crowd scenes in real-time.

Abstract—We present a novel rendering primitive that combines the modeling brevity of points with the rasterization efficiency of polygons. The surface is represented by a sampled collection of Differential Points (DP), each with embedded curvature information that captures the local differential geometry in the vicinity of that point. This is a more general point representation that, for the cost of a few additional bytes, packs much more information per point than the traditional point-based models. This information is used to efficiently render the surface as a collection of local geometries. To use the hardware acceleration, the DPs are quantized into 256 different types and each sampled point is approximated by the closest quantized DP and is rendered as a normal-mapped rectangle. The advantages to this representation are: 1) The surface can be represented more sparsely compared to other point primitives, 2) it achieves a robust hardware accelerated per-pixel shading—even with no connectivity information, and 3) it offers a novel point-based simplification technique that factors in the complexity of the local geometry. The number of primitives being equal, DPs produce a much better quality of rendering than a pure splat-based approach. Visual appearances being similar, DPs are about two times faster and require about 75 percent less disk space in comparison to splatting primitives. Index Terms—Differential geometry, simplification, point sample rendering, per-pixel shading. æ

Abstract—In this paper, we present Confetti, a novel point-based rendering approach based on object-space point interpolation of densely sampled surfaces. We introduce the concept of a transformation-invariant covariance matrix of a set of points which can efficiently be used to determine splat sizes in a multiresolution point hierarchy. We also analyze continuous point interpolation in objectspace and we define a new class of parameterized blending kernels as well as a normalization procedure to achieve smooth blending. Furthermore, we present a hardware accelerated rendering algorithm based on texture mapping and-blending as well as programmable vertex and pixel-shaders. Index Terms—Point-based rendering, multiresolution modeling, level-of-detail, hardware accelerated blending. 1

This paper introduces a method for converting an image or volume sampled on a regular grid into a space-efficient irregular point hierarchy. The conversion process retains the original frequency characteristics of the dataset by matching the spatial distribution of sample points with the required frequency. To achieve good blending, the spherical points commonly used in volume rendering are generalized to ellipsoidal point primitives. A family of multiresolution, oriented Gabor wavelets provide the frequency-space analysis of the dataset. The outcome of this frequency analysis is the reduced set of points, in which the sampling rate is decreased in originally oversampled areas. During rendering, the traversal of the hierarchy can be controlled by any suitable error metric or quality criteria. The local level of refinement is also sensitive to the transfer function. Areas with density ranges mapped to high transfer function variability are rendered at higher point resolution than

High quality point rendering methods have been developed in the last years. A common drawback of these approaches is the lack of hardware support. We propose a novel point rendering technique that yields good image quality while fully making use of hardware acceleration.

We present an innovative modeling and rendering primitive, called