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Description
An introduction to geometric concepts and tools needed for solving problems of a geometric nature with a computer. It offers theoretical understanding of polynomial curves and surfaces. The focus of this book is on "blossoming"--the process of converting a polynomial to its polar form--as a natural, purely geometric explanation of the behavior of curves and surfaces. The book covers computer graphics and animation, robotics, virtual reality, geometric modeling and design, medical imaging, computer vision and motion planning. Contents Introduction | Basics of Affine Geometry | Introduction to Algorithmic Geometry of Polynomial Curves | Multiaffine Maps and Polar Forms | Polynomial Curves as Bezier Curves | B-Spline Curves | Polynomial Surfaces \ Subdivision Algorithms for Polynomial Surfaces \ Polynomial Spline Surfaces and Subdivision Surfaces | Embedding an Affine Space in a Vector Space | Tensor Products and Symmetric Tensor Products | Appendices Related Topics Geometry, Modeling and Simulation |
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