We describe a simple method for reconstructing regions in the plane from well-distributed point samples. For that, we introduce the sphere-of-influence diagram, a planar diagram extracted from the Delaunay triangulation and the sphere-of-influence graph. The sphere-of-influence diagram is simple to understand and to implement, and supports an intuitive scaling parameter to handle variations in the distribution of samples. We report experiments reconstructing regions from point clouds of varying shape and density. We compare our results with those obtained by α-shapes and by ct-shapes.

We present a massively parallel vector graphics rendering pipeline that is divided into two components. The preprocessing component builds a novel adaptive acceleration data structure, the shortcut tree . Tree construction is efficient and parallel at the segment level, enabling dynamic vector graphics. The tree allows efficient random access to the color of individual samples, so the graphics can be warped for special effects. The rendering component processes all samples and pixels in parallel. It was optimized for wide antialiasing filters and a large number of samples per pixel to generate sharp, noise-free images. Our sample scheduler allows pixels with overlapping antialiasing filters to share samples. It groups together samples that can be computed with the same vector operations using little memory or bandwidth. The pipeline is feature-rich, supporting multiple layers of filled paths, each defined by curved outlines (with linear, rational quadratic, and integral cubic Bézier segments), clipped against other paths, and painted with semi-transparent colors, gradients, or textures. We demonstrate renderings of complex vector graphics in state-of-the-art quality and performance. Finally, we provide full source-code for our implementation as well as the input data used in the paper.

Abstract We show how to use affine arithmetic to represent a parametric curve with a strip tree. The required bounding rectangles for pieces of the curve are computed by exploiting the linear correlation information given by affine arithmetic. As an application, we show how to compute approximate distance fields for parametric curves. ACM CSS: I.3.3 Computer Graphics—Curve, surface, solid, and object representations, G.1.2 Numerical Analysis—Approximation of surfaces and contours, G.1.0 Numerical Analysis—Interval arithmetic

This paper introduces a unified and general tesselation algorithm for parametric and implicit surfaces. The algorithm produces a hierarchial mesh that is adapted to the surface geometry and has a multiresolution and progressive structure. The representation can be exploited with advantages in several applications.

This paper describes Lua, a language for extending applications. Lua combines procedural features with powerful data description facilities, by using a simple, yet powerful, mechanism of tables . This mechanism implements the concepts of records, arrays and recursive data types (pointers), and adds some object-oriented facilities, such as methods with dynamic dispatching. Lua presents a mechanism of fallbacks that allows programmers to extend the semantics of the language in some unconventional ways. As a noteworthy example, fallbacks allow the user to add different kinds of inheritance to the language. Currently, Lua is being extensively used in production for several tasks, including user configuration, general-purpose data-entry, description of user interfaces, storage of structured graphical metafiles, and generic attribute configuration for finite element meshes.

To be added when journal hard copy located (also figct,tabct & refct) (not provided by typesetter)