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We develop a geometric approach to algebras in congruence modular varieties. The idea of coordination of lines in affine geometry finds an almost perfect analog in the coordination of algebras. The geometry is the congruence class geometry, i.e. the subspaces are the blocks of congruence relations.
From the reviews: " A unique and fascinating blend, which is shown to be useful for a variety of applications, including robotics, geometrical optics, computer animation, and geometric design. The contents of the book are visualized by a wealth of carefully chosen illustrations, making the book a shear pleasure to read, or even to just browse in." Mathematical Reviews
19 papers presented by international experts give a state-of-the-art survey of the relevant problems and issues in modeling, CAD/CAM, scientific visualization, and computational geometry. The following topics are treated: • surface design and fairing • subdivision schemes • variational design • NURBS • reverse engineering • physically-based modelling • medical imaging