The master thesis presents conics as rational Bézier curves of degree 2. Some algebraic and geometric properties of conics, presented in such a form, are discussed. The process of changing the form of a conic, from rational Bézier form to implicit form and vice versa, is described and illustrated. We determine the type of a conic, given in a rational Bézier form, based on its number of singularities. Some special attention goes to circular arcs and circles. We show that the degree of the Bézier curve forming a full circle must be at least 5. Quadrics, presented as rational Bézier surfaces, are also discussed. Special attention goes to the sphere. With the help of the stereographic projection we present the octant of a sphere as a rational triangle Bézier patch and a sixth of a sphere as a rational tensor product Bézier surface.
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