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An original motivation for algebraic geometry was to understand curves and surfaces in three dimensions. This title covers theoretical and technological advances in areas such as robotics, computer vision, computer-aided geometric design and molecular biology, together with the increased availability of computational resources.

Spectral techniques to explore point clouds in Euclidean space, with applications to collective coordinates in structural biology.- Rational parametrizations, intersection theory, and Newton polytopes.- Some discrete properties of the space of line transversals to disjoint balls.- Algebraic geometry and kinematics.- Rational offset surfaces and their modeling applications.- A list of challenges for real algebraic plane curve visualization software.- A subdivision method for arrangement computation of semi-algebraic curves.- Invariant-based characterization of the relative position of two...