Steven Spitz

Interactive Boolean operations for conceptual design of 3-D solids

Interactive modeling of 3-D solids is an important and difficult problem in computer graphics. The Constructive Solid Geometry (CSG) modeling scheme is highly attractive for interactive design, due to its support for hierarchical modeling and Boolean operations. Unfortunately, current algorithms for interactive display of CSG models require expensive special-purpose hardware that is not easily available. In this paper we present a method for interactive display of CSG models using standard, widely available graphics hardware. The method enables the user to interactively modify the affine transformations associated with CSG sub-objects. The application we focus upon is that of conceptual design, a stage in the design process in which rapid, interactive visualization of the model and high-level design operations are of crucial importance, while the objects are relatively simple. The method converts the CSG graph to a novel Convex Differences Aggregate(CDA) representation. The CDA utilizes graph re-writing techniques, efficient geometric algorithms on convex objects and a built-in hierarchical acceleration scheme. The CDA rendering algorithm is very simple, takes advantage of standard graphics hardware, and makes efficient use of system resources by splitting the work between the graphics system and the CPU. CR

Accessibility analysis for planning of dimensional inspection with coordinate measuring machines

Computer-controlled dimensional inspection is typically performed with coordinate measuring machines (CMMs), which are very precise Cartesian robots that use touch probes to measure the coordinates of points on a workpieces surfaces. Automatic planning and programming of inspection tasks with a CMM involve spatial reasoning, to determine how to orient the part on the CMM, which probes to use, how to orient the probes, and so on. This paper introduces the notions of accessibility and approachability, which are important for inspection planning, and describes two sets of implemented algorithms for computing accessibility information. One of these sets of algorithms performs exact computations on polyhedral objects and is relatively slow, whereas the other uses discrete approximations and achieves high speed by exploiting standard computer graphics hardware. The discretized algorithm has been tested on real-world parts, and is sufficiently fast for industrial applications.

Multiple-goals path planning for coordinate measuring machines

Path planning is a crucial step in automatic programming of coordinate measuring machines(CMMs). The goal is to generate an efficient and collision-free path for the CMM to inspect a collection of points. Previous research concentrates on path planning between two points, or sequencing the points without regard to obstacles and collisions. In this paper we propose a practical path planner that considers both sequencing and collision avoidance. The main idea is to create a roadmap of free-space, where the measurement points are nodes in the network. Once all the measurement points are in a single connected component of the roadmap, then a tour of the points is found by solving the appropriate traveling salesperson problem. CMM heuristics are used to construct the roadmap in an efficient and robust manner. The planner has been implemented and tested on real-world mechanical parts.

Model for the examination of evolutionary trends in tooth development.

Through the use of serial computerized tomography (C-t) scans, two distinct developmental stages can be identified in mature teeth. C-t scans thus provide a non-destructive method for assessing growth within individual teeth, as well as for comparison of the development of modern and fossil teeth. The second deciduous molar (DM2) and first permanent molar (M1) resemble one another morphologically, despite differences in size and developmental rates. Thus, they provide an excellent model for studying variation in growth within an individual. To test the C-t method, we first examined a recent archaeological sample and then examined teeth from Skhul I. Serial C-t scans were used to compare two distinct developmental stages represented by the dentine-enamel junction (DEJ) and outer enamel surface (OES), respectively, in mandibular DM2 and M1 of 31 archaeological specimens. The difference in form and size between these two surfaces in and between teeth was calculated from intercusp distances measured at the DEJ and OES using the form distance matrix. Intercusp distances at the DEJ and OES of these teeth were then compared to their counterparts in the DM2 and M1 of Skhul I, taken here as representative of early anatomically modern Homo sapiens sapiens. Form differences between paired DM2 and M1 at the DEJ were smaller than those at the OES, supporting the hypothesis that differences between the two teeth increase throughout development. The increase in intercusp distances from the DEJ to OES was found to reflect the angulation of cusps relative to one another, rather than enamel thickness. Form differences between the Skhul DM2 and M1 were smaller than those observed in the recent series, and the recent M1 differed more than the DM2 from its fossil counterpart. The similarities found between the Skhul permanent and deciduous teeth and the recent DM2, may reflect a similar growth pattern. This would contribute to earlier crown completion in the fossil M1.

Accessibility analysis using computer graphics hardware

Analyzing the accessibility of an objects surface to probes or tools is important for many planning and programming tasks that involve spatial reasoning and arise in robotics and automation. The paper presents novel and efficient algorithms for computing accessible directions for tactile probes used in 3D digitization with Coordinate Measuring Machines. The algorithms are executed in standard computer graphics hardware. They are a nonobvious application of rendering hardware to scientific and technological areas beyond computer graphics.

One-dimensional selections for feature-based data exchange

In the parametric feature based design paradigm, most features possess arguments that are subsets of the boundary of the current model, subsets defined interactively by user selection of boundary entities. Any system for feature-based data exchange (FBDE) must support the exchange of such selections. In this paper we describe in detail an algorithm for supporting one-dimensional selections (sets of edges and curves) for FBDE. The algorithm is applicable to a wide class of FBDE architectures, including the Universal Product Representation (UPR) and the STEP parametrics specification.

Two-dimensional selections for feature-based data exchange

Proper treatment of selections is essential in parametric feature-based design. Data exchange is one of the most important operators in any design paradigm. In this paper we address two-dimensional selections (faces and surfaces) in feature-based data exchange (FBDE). We define the problem formally and present algorithms to address it, in general and in various cases in which feature rewrites are necessary. The general algorithm operates at a geometric level and does not require solving the persistent naming problem, which is required for selection support inside a single CAD system. All algorithms are applicable to the Universal Product Representation (UPR) FBDE architecture, and the general algorithm is also applicable to the STEP parametrics specification.

Hierarchical constraint satisfaction for high-level dimensional inspection planning

Coordinate measuring machines (CMMs) are very precise Cartesian robots that are used for dimensional inspection. High-level inspection planning for a CMM involves spatial reasoning, to determine how to orient the part on the CMM, which probes to use, how to orient the probes, and what measurements to perform. Current planners are incomplete or only solve the problem partially. In this work, we map the inspection planning problem to a hierarchical constraint satisfaction problem (CSP). The solutions to the CSP are inspection plans of good quality. We show how to extract approximate solutions using efficient clustering methods, which do not entail search and backtracking as prevalent in other planners. We describe our implemented planner and experimental results.

Spatial modeling and reasoning for automatic dimensional inspection

This paper reports on a system that bridges the gap between computer aided design and metrology activities in the life cycle of a mechanical product. It completely automates the process of programming coordinate measuring machines. Accessibility of surface features to probes is efficiently computed by using computer graphics hardware. This information is used by a high-level planner based on constraint satisfaction techniques to determine setups, probes and probe orientation. High-level plans are refined so as to produces operation sequences and probe paths by using a combination of probabilistic roadmaps and travelling salesperson techniques. Experimental results are presented for industrial parts.