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Show CHAPTER 2 MATHEMATICAL BASIS OF CURVES AND SURFACES Moving closer, he discerned further complexities, and elaborations on complexities: twists, spires, volutes: disks, saddles, wrenched spheres: t9rsions and flexions: spindles, cardioids, lanciform pinnacles: the most laborious, painstaking and intricate rock-carving conceivable, manifestly no random effort of the elements. Jack Vance, The Eyes Of The Overworld Before beginning a description of algorithms to draw curved surfaces it is worthwhile to look at various means of describing them mathematically. This chapter will review the two basic types of surface representation and several geometric operations necessary to draw pictures of them. Some examples of particular classes of surfaces will then be described and the drawing operations given explicitly for them. Finally, a section is given which reviews some properties of bivariate functions which will come in handy in chapters to follow. of Surface Representation Surfaces are generally described mathematically in one of two ways. They may be described Algebraically as being those points which form solutions to an algebraic equation: |
