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By virtue of their special algebraic structures, Pythagorean-hodograph (PH) curves offer unique advantages for computer-aided design and manufacturing, robotics, motion control, path planning, computer graphics, animation, and related fields. This book offers a comprehensive and self-contained treatment of the mathematical theory of PH curves, including algorithms for their construction and examples of their practical applications. Special features include an emphasis on the interplay of ideas from algebra and geometry and their historical origins, detailed algorithm descriptions, and many figures and worked examples. The book may appeal, in whole or in part, to mathematicians, computer scientists, and engineers.

Mathematics. --- Computer graphics. --- Computer-aided engineering. --- Algebra. --- Computer mathematics. --- Geometry. --- Computational intelligence. --- Computer-Aided Engineering (CAD, CAE) and Design. --- Computational Mathematics and Numerical Analysis. --- Computer Imaging, Vision, Pattern Recognition and Graphics. --- Computational Intelligence. --- Intelligence, Computational --- Artificial intelligence --- Soft computing --- Mathematics --- Euclid's Elements --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- Mathematical analysis --- CAE --- Engineering --- Automatic drafting --- Graphic data processing --- Graphics, Computer --- Computer art --- Graphic arts --- Engineering graphics --- Image processing --- Math --- Science --- Data processing --- Digital techniques --- Pythagorean-hodograph curves. --- Hodograph equations. --- Pythagorean theorem. --- Geometry, Analytic. --- Curves --- Computer-aided design. --- Calculus --- Conic sections --- Geometry, Analytic --- Geometry, Differential --- Geometry, Enumerative --- Shapes --- Analytical geometry --- Geometry, Algebraic --- Algebra --- Pythagoras' theorem --- Pythagorean proposition --- Theorem, Pythagorean --- Geometry, Plane --- Equations, Hodograph --- Differential equations, Partial --- Fluid mechanics --- PH curves --- Graphic methods --- Computer aided design. --- Computer science --- Computer vision. --- Engineering. --- Construction --- Industrial arts --- Technology --- Machine vision --- Vision, Computer --- Pattern recognition systems --- CAD (Computer-aided design) --- Computer-assisted design --- Computer-aided engineering --- Design --- Optical data processing. --- Optical computing --- Visual data processing --- Bionics --- Integrated optics --- Photonics --- Computers --- Optical equipment