Accurate solid modeling using polyhedral approximations

In the past few years there has been a lot of interest and excitement generated by solid modeling. Numerous papers have been presented on the value and benefits of this technology. Many talented individuals have contributed to the state of the art. Solid modeling has played a larger role at SIGGRAPH in the past three years, with tutorials, panel discussions and technical papers. All this material has been presented for the most part by academics, researchers and developers of solid modeling systems. The users of solid modeling systems have yet to be heard from. The reason is that there have been very few of them out there in the past. However, that situation is slowly changing. Now that several CAD/CAM vendors are marketing solid modeling systems, a small cadre of users does exist. This panel will be composed primarily of users of solid modeling systems. They will discuss topics of interest to potential users (and also developers) of solid modelers. Questions to be addressed include: What is the status of solid modeling systems from a user standpoint? Can the present solid modelers be used in a production environment today? Should a solid modeling system replace the present wire frame and surface systems or be integrated with them? What are the problems associated with using a solid modeling system? How good is the user interface? Does the necessary application software exist? The primary intent of this Panel discussion is to give the potential user some idea as to whether the available solid modeling systems are useful for his applications. It is beginning to look like the next generation CAD/CAM system for mechanical design will be a solid modeler. The big question is “when will this occur?”

Solid modeling for optimizing metal removal of three-dimensional NC end milling

The ACM Symposium on Solid and Physical Modeling and Applications is an annual international forum for the exchange of recent research results and applications of spatial modeling and computations in design, analysis and manufacturing, as well as in emerging biomedical, geophysical and other areas. Previous symposia in this series were held in Austin, Texas, 1991; Montreal, Canada, 1993; Salt Lake City, Utah, 1995; Atlanta, Georgia, 1997; Ann Arbor, Michigan in 1999 and 2001; Saarbrucken, Germany, 2002; and Seattle, Washington, 2003, and Genova, Italy, 2004. For additional information, visit www.solidmodeling.org, the home page of the Solid Modeling Association that oversees this symposia series.Since its inception in 1991, the ACM Symposium on Solid Modeling and Applications has been the primary venue for disseminating research results in the design, representation, analysis, visualization, and use of digital models of real or planned solid objects and of their bounding surfaces. At the same time, modeling solids entails not only handling their geometric shape, but also their physical properties and behaviors. To emphasize this broader mission, we have expanded the name of the 2005 Symposium to Solid and Physical Modeling (abbreviated SPM). SPM-05 was held on the MIT campus, in Cambridge, Massachusetts, in plenary sessions (no parallel tracks) from Monday June 13 to Wednesday June 15, and was followed by the <u>Shape Modeling International</u> (SMI) conference. Both SPM and SMI events are part of the <u>2005 Joint Convention on Solids and Shapes</u>, (S&S'05) hosted at MIT and chaired by Nick Patrikalakis. The <u>2004 Joint Convention on Shapes and Solids</u> took place in Genoa Italy.Some sixty technical papers have been submitted and were reviewed by the international program committee and expert reviewers from around the world. At least three to four external reviewers and members of the program committee reviewed and discussed each submission. A total of 22 refereed papers have been selected for plenary presentation and full paper publication in the proceedings. In addition, 6 more papers have been selected as technical sketches for shorter publication and presentation at the conference. The symposium program also includes two keynote presentations invited from leading authorities in their fields: Bruce Donald and James O'Brien. Another new feature in the symposium program was that we had three panel session where recent trends and challenges are discussed. The panel sessions were organized by Dimitris Metaxas (Biomedical Modeling), Michael Wang (Physical Modeling and Simulation), and Jan Vandenbrande (Design, Analysis, and Manufacturing).

PLANT DESIGN ON MICROCOMPUTERS

A three-dimensional stratum model stratum model is a useful auxiliary tool for geotechnical engineering and other exploration work. The existing methods for stratum model construction lack complete topological descriptions of entities, so it is difficult to apply them to 3D geological modeling with complex geometric structures and complex topological relationships between modules. To solve the above problem, in this paper, the boundary representation method is used to represent the arbitrarily-shaped geological entities, and the half winged-edge-face structure topological structure is proposed to describe the topological information of the stratum model for a complex entity. The topological structure can record the topological information of the solid stratum model completely, thereby providing the basis for operations with the model and the applications of various algorithms. Based on this topological structure, the construction process for a 3D solid stratum model is proposed. The reliability and effectiveness of the constructed 3D solid stratum model are verified by an engineering case. The solid stratum model not only solves the geological modeling problem with respect to complex geometric and topological relations, but also provides a new method and idea for 3D geological modeling.

This paper presents a new methodology for resolving visible surface images of solid models derived from Boolean combinations of volumetric building blocks. The algorithm introduced here is an extension of well-established scan-line hidden surface removal procedures, and it integrates knowledge of a Boolean construction tree in the surface resolution process. Several hidden surface coherence properties are discussed in terms of their possible exploitation in the intricate solid model visualization process. While many of the earlier coherence techniques depend on a polygon environment in which surfaces and volumes do not intersect, the Boolean process can not afford that luxury because it is inherently required to handle intersecting volumes and surfaces. Initial tests indicate that substantial performance improvements over previous methods can be achieved with the algorithm described in this paper, and that these improvements increase as model complexity increases.An underlying philosophy of a dual solid modeling system is proposed in this paper. It suggests that two solid modelers are necessary to successfully satisfy both analytical precision requirements and user interface visualization requirements. The visual solid modeling task addressed in this paper provides greatly improved response capabilities, as compared to other systems, by striving to optimize the constructive solid model (CSG) solid model computations specifically for display purposes.

3D imaging has become a standard tool in medical diagnostics and, while software is available to visualize volumetric data sets, we do not yet have software that can efficiently transform 3D scan data to solid models that are useful for engineering design and analysis. Why not? Currently, deriving solid models from 3D scans involves 3 steps: (1) segmentation: identification of voxels associated with the structure; (2) polygonization: computing a set of polygons that approximate the surface of the structure; and (3) repair: removing stray voxels and polygons, specifying connectivity, and establishing consistent orientation. Significant progress has been made on accurate, automated segmentation (recent work by Hu et al. (Image Segmentation and Registration for the Analysis of Joint Motion From 3D MRI,” Proc SPIE 6141, pp. 133–142, Medical Imaging: Visualization, Image-Guided Procedures, &amp; Display, 2006), combining graph cuts with level sets is of particular interest) but effective polygonization cannot be guaranteed. In the worst case, manual repairs are needed to patch holes and remove stray elements. Even if a valid boundary representation (b-rep) model is obtained, accurate models contain so many polygons that modeling operations become unfeasible. Moreover, regardless of accuracy, the surface of a polyhedral model will never be truly smooth. In previous work (Storti, D., et al., Artifact vs. Anatomy: Dealing With Conflict of Geometric Modeling Descriptions,” SAE 2007 Transactions Journal of Passenger Cars: Electronic and Electrical Systems, Paper No. 2007-01-2450, Vol. 116, pp. 813–823, 2007), we proposed overcoming the barriers to creating solid models from 3D scans by employing a new solid modeling description, wavelet SDF-reps, that lies much closer to the native 3D scan format and eliminates polygonization. Here, we focus on the ability to produce models with smooth surfaces that are important for various biomedical simulations. For example, careful studies of joint function involve detailed modeling of ligament wrapping; i.e., connective tissue moving across bone surface as the joint configuration changes. Realistic behavior cannot be obtained if the ligament is snagging on or snapping across convex vertices of a polyhedral model. Similarly, haptic simulation of a catheter navigating through the circulatory system cannot be realistic if the catheter gets stuck in concave vertices of the anatomical model. How can the new modeling format address such issues? Wavelet SDF-reps take advantage of a by-product of the segmentation algorithm (Hue et al.) which converts the raw voxel intensity values to a grid of signed distance values. Applying an appropriate interpolant such as Daubechies wavelets (Daubechies, I., Wavelets, CBMS-NS Series in Applied Mathematics, SIAM Publications, Philadelphia, 1992) then produces an implicit or function-based (f-rep) solid model of the segmented structure. Wavelet SDF-reps are inherently multi-resolution and support significant data compression and medial axis computation. We illustrate the capability of wavelet SDF-reps to support smooth models and enable analysis of curvature features.

NC machine tool path generation from CSG part representations

Switching Functions Based Geometric Modeling Language and its Application to Numerical Control Program Verification

Using dexels to make hollow models for rapid prototyping

Design engineers create models of design artifacts with commercial Computer Aided Design (CAD) solid modeling systems and manage the data files through Product Data Management (PDM) systems. These systems stop short of providing support for querying and retrieving data from “within” the CAD data files. A true CAD query language that allows designers the flexibility to describe queries against single and multiple CAD files would be of great benefit for design engineers. This query language ought to be both datacentric and user-centric in nature. The design exemplar, a datastructure that provides a standard representation of design knowledge based upon a general constraint validation and satisfaction algorithm, is shown here to be a concept upon which a CAD query language may be developed. The first required extension of the design exemplar is the inclusion of logical connectives. Some insights into the different levels at which the extensions may be implemented are discussed. Also, some applications retrieving geometric data using this query language are demonstrated. The query language, as it evolves, is expected to support geometric retrieval across domains and offer an all-purpose approach to geometric retrieval.

A spatially-segmented solids database — justification and design

Parametric 3D finite-element mesh generation

This paper studies the numerical and geometric properties of interval B-splines, a newly developed geometric representation introduced for increased robustness in solid modeling systems and for uncertainty representation in data fitting problems. Interval B-spline curves and surfaces have some unique properties that are different from classical B-splines. The properties discussed in this paper include error propagation in the evaluation of B-spline basis functions using rounded interval arithmetic, width of an interval B-spline curve or surface, transformation of interval B-splines, hodograph of an interval B-spline curve, enveloping curves or surfaces of an interval B-spline curve or surface, variation diminishing property, and knot insertion for interval B-splines.

An approach for the fully automatic generation of three‐dimensional finite element meshes is presented. The method is specifically designed for use with solid modelling systems which provide a complete and unique definition of the geometry of a part. The method follows from the basic concepts of the octree encoding technique with specific modifications made to produce valid, user controllable finite element meshes. Example problems are included to demonstrate the technique.