Direct slicing of CAD models to generate process planning instructions for solid freeform fabrication may overcome inherent disadvantages of using stereolithography format in terms of the process accuracy, ease of file management, and incorporation of multiple materials. This paper will present the results of our development of a direct slicing algorithm for layered freeform fabrication. The direct slicing algorithm was based on a neutral, international standard (ISO 10303) STEP-formatted non-uniform rational B-spline (NURBS) geometric representation and is intended to be independent of any commercial CAD software. The following aspects of the development effort will be presented: (1) determination of optimal build direction based upon STEP-based NURBS models; (2) adaptive subdivision of NURBS data for geometric refinement; and (3) ray-casting slice generation into sets of raster patterns. The development also provides for multi-material slicing and will provide an effective tool in heterogeneous slicing processes.

http://www.pages.drexel.edu/~sunwei/WSUN-Papers/JCAD-Directing%20Slicing-published.pdf

Direct slicing of STEP based NURBS models for layered manufacturing

A system is presented for ray tracing trimmed NURBS surfaces. While approaches to components are drawn largely from existing literature, their combination within a single framework is novel. This paper also differs from prior work in that the details of an efficient implementation are fleshed out. Throughout, emphasis is placed on practical methods suitable to implementation in general ray-tracing programs.

Practical ray tracing of trimmed NURBS surfaces

Ray tracing is a well-known rendering technique for producing high-quality and photorealistic pictures. Spline surfaces are also well known and widely used. Thus, there is the need for fast and robust methods for computing the intersections of rays with these surfaces. In this paper, we discuss and compare three recent geometric algorithms for solving the raypatch intersection problem and present new results that are helpful in dealing with this problem.

Ray tracing of spline surfaces: Bézier clipping, Chebyshev boxing, and bounding volume hierarchy – a critical comparison with new results

Instead of computing intersections along a ray, an algorithm is proposed that determines a point of intersection in object space. The method is based on the classical refinement of a hierarchy of axis-aligned bounding boxes that is computed on the fly. Typical rendering artifacts are avoided by taking into consideration the precision of floating point arithmetic. In addition the method lends itself to a simple solution of the self-intersection problem. Considering the obtained precision the algorithm is efficient, simple to use, and to implement.

/pdf/improving-ray-tracing-precision-by-object-space-intersection-2yuh98b1x8.pdf

Improving Ray Tracing Precision by Object Space Intersection Computation

In the proposed tutorial we would like to highlight the connection between rendering algorithms and sorting and searching as classical problems studied in computer science. We will provide both theoretical and empirical evidence that for many rendering techniques most time is spent by sorting and searching. In particular we will discuss problems and solutions for visibility computation, density estimation, and importance sampling. For each problem we mention its specific issues such as dimensionality of the search domain or online versus offline searching. We will present the underlying data structures and their enhancements in the context of specific rendering algorithms such as ray shooting, photon mapping, and hidden surface removal. c © The Eurographics Association 2006. 2 Havran and Bittner / Efficient Sorting and Searching in Rendering Algorithms Organizers bibliographies Vlastimil Havran is an assistant professor at the Czech Technical University in Prague since February 2006. He defended his Ph.D. dissertation on ray shooting algorithms in 2001 at the Czech Technical University in Prague. Later he joined the computer graphics group at Max-Planck-Institute for Informatics in Saarbruecken. He became a research associate at the same institute in 2003. He has contributed to the topic of sorting and searching by his dissertation on ray shooting algorithms which started the area of interactive ray tracing. In addition to sorting and searching he worked on various other topics in rendering. Jiři Bittner holds a Ph.D. in Computer Science from the Czech Technical University in Prague. His main research interests include visibility preprocessing, occlusion culling, real-time rendering, and computational geometry. He has also been active in development of two commercial products dealing with real-time rendering of large scenes. He is currently affiliated with the Vienna University of Technology and the Czech Technical University in Prague. Organizers contact information Vlastimil Havran Czech Technical University in Prague Karlovo naměsti 13 121 35 Praha 2 Czech Republic Phone:+42

Efficient Sorting and Searching in Rendering Algorithms

Parametric curves and surfaces are powerful and popular modeling tools in Computer Graphics and Computer Aided Design. Ray-tracing is a versatile and popular rendering technique. There is therefore a strong incentive in developing fast, accurate and reliable algorithms to intersect rays and parametric curves and surfaces. We propose and demonstrate the use of Chebyshev basis functions to speed up the computation of the intersections between rays and parametric curves or surfaces. The properties of Chebyshev polynomials result in the computation of better and tighter enclosing boxes. For surfaces they provide a better termination criterion to decide on the limits of subdivision, and allow the use of bilinear surfaces for the computation of the intersection when needed. The efficiency of the techniques used depends on the relative magnitude of the coefficients of the Chebyshev basis functions. We show from a statistical analysis of the characteristics of several thousands surfaces of different origin that these techniques will result most of the time in significant improvement in speed and accuracy over other boxing and subdivision technqiues.

Chebyshev Polynomials for Boxing and Intersections of Parametric Curves and Surfaces

The display of volumetric data is a problem of increasing importance. The display of this data is being studied in texture mapping and volume rendering applications. The goal of texture mapping is to add variation to the surfaces that is not caused by the geometric models of the objects. The goal of volume rendering is to display the data so that the study of this data is made easier.
Three-dimensional texture mapping requires the use of filtering not only to reduce aliasing artifacts but also to compute the texture value which is to be used for the display. Study of two-dimensional texture map filtering techniques led to a number of techniques which were extended to three dimensions: namely clamping, elliptical weighted average (EWA) filters, and a pyramidal scheme known as NIL maps; (NIL stands for nodus in largo, the rough translation of which is knot large).
The use of three-dimensional textures is not a straightforward extension of the use of two-dimensional textures. Where two-dimensional textures are usually discrete arrays of texture samples which are applied to the surface of objects, three-dimensional textures are usually procedural textures which can be applied on the surface of an object, throughout the object, or in volumes near the object. We studied the three-dimensional extensions of clamping, EWA filters, and NIL maps for filtering these textures. In addition to these three techniques a direct evaluation technique based on quadrature methods is presented. The performance of these four techniques is compared using a variety of criteria, and recommendations are made regarding their use.
There are several techniques for volume rendering which can be formulated as filtering operations. By altering these display filters different views of the data can be generated. We modified the NIL map filtering technique for use as a filter-prototyping tool. This extension incorporated transfer functions into the NIL map technique. This allows the manipulation of the transfer functions without requiring the re-computation of the NIL maps. The use of NIL maps as a filter-prototyping tool is illustrated with a series of examples.

Filtering volumetric data

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Chebyshev Polynomials for Boxing and Intersections of Parametric Curves and Surfaces

Filtering volumetric data