Keynote lecture: shape interrogation

Abstract

Shape interrogation is the process of extraction of informationfrom a geometric model. It is a fundamental component of CAD/CAMsystems. In this lecture, we focus on shape interrogation ofgeometric models bounded by free-form or sculptured surfaces. Suchsurfaces are widely used in the bodies of ships, automobiles,aircraft, propeller and turbine blades, and various consumerdevices. Our basic thesis is that shape interrogation problems canusually be recast in terms of the solution of a nonlinear system ofequations, typically a polynomial system. Much of our work is basedon the Interval Projected Polyhedron (IPP) Algorithm, which reducesa continuous shape interrogation problem into the discrete problemof computing convex hulls and their intersections. In this way, abridge between the largely disparate fields of geometric modelingof free-form shapes (based on numerical analysis and approximationtheory) and discrete computational geometry (based on the theory ofalgorithms and combinatorics) is established. Various applicationsarising from surface intersections, distance function computations,global differential geometry of curves and surfaces, and offsetsare described and are reduced to the same unified solutionframework. A discussion of unresolved problems in this area is alsoprovided. Dr. Patrikalakis is the Kawasaki Professor of Engineering at MITand holds a joint faculty appointment in the Departments of Oceanand Mechanical Engineering at MIT. He received a Diploma in NavalArchitecture in 1977 from the National Technical University ofAthens, Greece, and a Ph.D. in Ocean Engineering in 1983 from MIT.His research in the last 18 years has focused in the general areaof applications of computational geometry, geometric modeling,numerical simulation and software engineering in design, analysisand fabrication of complex systems. He has made importantcontributions in the areas of surface-to-surface intersections forgeometric modeling and CAD/CAM applications; robustness innonlinear geometric modeling; free-form low-order algebraicsurfaces; reliable approximation of high-order and proceduralparametric curves and surfaces for accurate data exchange betweendifferent CAD systems; approximation of generalized offsets formachining, tolerancing and inspection applications in CAM;topologically reliable meshing; feature recognition based on medialaxis transform and global differential geometry to assist automatedidealization and finite element discretization of structures forperformance evaluation and simulation of manufacturing processes;measured surface localization to assist automated inspection ofsculptured mechanical objects; scientific visualization anddatabases, and underwater visualization and map construction andinterrogation. His current research focuses on CAD/CAM for objectswith local composition control in solid free-form fabrication(SFF), solid model rectification, and distributed informationsystems for multidisciplinary large-scale physical systemsimulation. 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. andEngineer'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 experimentalstructural dynamics. For his work in CAD, Dr. Patrikalakis wasappointed Doherty Assistant Professor at MIT (1988-1990) and sinceOctober 1996 as the Kawasaki Professor of Engineering at MIT. Hehas published over 130 papers and one textbook(http://deslab.mit.edu/DesignLab/pubs/N-T-Book.html), and hasedited 16 journal special issues or conference proceedings. He hasreceived 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 andToshiba. He has served as consultant to various organizations, saton committees of several professional societies, and is a member ofthe board of directors of the Computer Graphics Society. He is amember of ACM, ASME, CGS, IEEE, ISOPE, SIAM, SNAME and TCG, andAssociate 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, andGraphical Models. He has served as program chair of ComputerGraphics International 1991 (CGI'91), as program co-chair ofCGI'98, Pacific Graphics '98, ACM Solid Modeling Symposium 2002,and the 1994 NSF Design and Manufacturing Systems GranteesConference, and as chair of the 1998 NSF DICPM workshop.