Keynote lecture: shape interrogation

Shape interrogation is the process of extraction of information from a geometric model. It is a fundamental component of CAD/CAM systems. In this lecture, we focus on shape interrogation of geometric models bounded by free-form or sculptured surfaces. Such surfaces are widely used in the bodies of ships, automobiles, aircraft, propeller and turbine blades, and various consumer devices. Our basic thesis is that shape interrogation problems can usually be recast in terms of the solution of a nonlinear system of equations, typically a polynomial system. Much of our work is based on the Interval Projected Polyhedron (IPP) Algorithm, which reduces a continuous shape interrogation problem into the discrete problem of computing convex hulls and their intersections. In this way, a bridge between the largely disparate fields of geometric modeling of free-form shapes (based on numerical analysis and approximation theory) and discrete computational geometry (based on the theory of algorithms and combinatorics) is established. Various applications arising from surface intersections, distance function computations, global differential geometry of curves and surfaces, and offsets are described and are reduced to the same unified solution framework. A discussion of unresolved problems in this area is also provided.Dr. Patrikalakis is the Kawasaki Professor of Engineering at MIT and holds a joint faculty appointment in the Departments of Ocean and Mechanical Engineering at MIT. He received a Diploma in Naval Architecture in 1977 from the National Technical University of Athens, Greece, and a Ph.D. in Ocean Engineering in 1983 from MIT. His research in the last 18 years has focused in the general area of applications of computational geometry, geometric modeling, numerical simulation and software engineering in design, analysis and fabrication of complex systems. He has made important contributions in the areas of surface-to-surface intersections for geometric modeling and CAD/CAM applications; robustness in nonlinear geometric modeling; free-form low-order algebraic surfaces; reliable approximation of high-order and procedural parametric curves and surfaces for accurate data exchange between different CAD systems; approximation of generalized offsets for machining, tolerancing and inspection applications in CAM; topologically reliable meshing; feature recognition based on medial axis transform and global differential geometry to assist automated idealization and finite element discretization of structures for performance evaluation and simulation of manufacturing processes; measured surface localization to assist automated inspection of sculptured mechanical objects; scientific visualization and databases, and underwater visualization and map construction and interrogation. His current research focuses on CAD/CAM for objects with local composition control in solid free-form fabrication (SFF), solid model rectification, and distributed information systems for multidisciplinary large-scale physical system simulation.Prof. Patrikalakis is co-director of the Design Laboratory (http://deslab.mit.edu) and the Fabrication Laboratory (http://fablab.mit.edu), and a member of the 3D Printing Laboratory (http://www.mit.edu/~tdp/). Fourteen Ph.D. and 29 M. Eng., S.M. and Engineer's theses have been completed so far under Dr. Patrikalakis' direction. Prior to his work in geometric modeling, he focused his research on theoretical, numerical, and experimental structural dynamics. For his work in CAD, Dr. Patrikalakis was appointed Doherty Assistant Professor at MIT (1988-1990) and since October 1996 as the Kawasaki Professor of Engineering at MIT. He has published over 130 papers and one textbook (http://deslab.mit.edu/DesignLab/pubs/N-T-Book.html), and has edited 16 journal special issues or conference proceedings. He has received research funding from NSF, ONR, DARPA, NAVSEA, Sea Grant, NOAA, USCG, USACE, NUWC, MMS, NIRO, General Electric, Westinghouse, Chevron, Conoco, Doherty Foundation, Furukawa Electric Company and Toshiba. He has served as consultant to various organizations, sat on committees of several professional societies, and is a member of the board of directors of the Computer Graphics Society. He is a member of ACM, ASME, CGS, IEEE, ISOPE, SIAM, SNAME and TCG, and Associate Editor-in-Chief of IJOPE, and ASME Transactions (JCISE) and participates in the editorial boards of several journals, eg. International Journal of Shape Modeling, The Visual Computer, Computer-Aided Design, Mathematical Engineering in Industry, and Graphical Models. He has served as program chair of Computer Graphics International 1991 (CGI'91), as program co-chair of CGI'98, Pacific Graphics '98, ACM Solid Modeling Symposium 2002, and the 1994 NSF Design and Manufacturing Systems Grantees Conference, and as chair of the 1998 NSF DICPM workshop.