Solid Shape

Solid Shape gives engineers and applied scientists access to the extensivemathematical literature on three dimensional shapes. Drawing on the author's deep and personalunderstanding of three-dimensional space, it adopts an intuitive visual approach designed to developheuristic tools of real use in applied contexts.Increasing activity in such areas as computer aideddesign and robotics calls for sophisticated methods to characterize solid objects. A wealth ofmathematical research exists that can greatly facilitate this work yet engineers have continued to"reinvent the wheel" as they grapple with problems in three dimensional geometry. Solid Shapebridges the gap that now exists between technical and modern geometry and shape theory or computervision, offering engineers a new way to develop the intuitive feel for behavior of a system undervarying situations without learning the mathematicians' formal proofs. Reliance on descriptivegeometry rather than analysis and on representations most easily implemented on microcomputersreinforces this emphasis on transforming the theoretical to the practical.Chapters cover shape andspace, Euclidean space, curved submanifolds, curves, local patches, global patches, applications inecological optics, morphogenesis, shape in flux, and flux models. A final chapter on literatureresearch and an appendix on how to draw and use diagrams invite readers to follow their own pursuitsin threedimensional shape.Jan J. Koenderinck is Professor in the Department of Physics and Astronomyat Utrecht University. Solid Shape is included in the Artificial Intelligence series, edited byPatrick Winston, Michael Brady, and Daniel Bobrow