Basic Theory of Surfaces
Quadric surfaces, especially bodies of revolution such as spheres, cylinders, cones, or also ruled surfaces have been widely used in engineering products. This is because their geometric properties are easily specified by their designers and the shapes are easily manufactured by machines. On the other hand, free-form surfaces have only been used in special cases and their design and manufacture have required special talent and skill. But in recent years their uses have increased because of strong demands for high performance and aesthetic quality in engineering products. And computers have been used for their design and manufacture. Accordingly, various mathematical expressions of free-forms for engineering use have been developed.
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