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Delo obravnava stožnice, podane kot racionalne Bézierjeve krivulje stopnje 2. V delu opišemo in ponazorimo algebraične in geometrijske lastnosti stožnic, podanih v taki obliki. Izpeljemo postopek za prehod iz racionalne Bézierjeve oblike stožnice v implicitno obliko in obratno. Na podlagi števila singularnosti stožnice, podane v racionalni Bézierjevi obliki, določimo njen tip. Podrobneje se posvetimo krožnemu loku oz. krožnici in pokažemo, da za predstavitev celotne krožnice potrebujemo racionalno Bézierjevo krivuljo stopnje vsaj 5. Nato se posvetimo še predstavitvi kvadrikov z racionalnimi Bézierjevimi ploskvami. Pri tem se osredotočimo predvsem na sfero. S pomočjo stereografske projekcije predstavimo oktant sfere kot racionalno trikotno Bézierjevo krpo, šestino sfere pa kot racionalno Bézierjevo ploskev iz tenzorskega produkta. 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.

Carnotov izrek nam pove, kdaj šest točk, po dve na vsaki stranici poljubnega trikotnika, leži na isti stožnici. Predstavili in dokazali bomo Carnotov izrek v evklidski in projektivni ravnini ter dve njegovi posledici. Prva posledica je definirana v evklidski ravnini in nam predstavi, kako s pomočjo danega trikotnika in izbrane točke konstruiramo šest točk na nosilkah stranic trikotnika, ki ležijo na isti stožnici. To stožnico imenujemo Cevova stožnica. Druga posledica je definirana v projektivni ravnini in nam pove, da točke na stranicah poljubnega trikotnika - ki jih dobimo tako, da iz vsakega oglišča tega trikotnika narišemo dve tangenti na dano stožnico, nato pa tangenti sekamo z nasprotno stranico - ležijo na isti stožnici. The theorem of Carnot gives us a necessary and sufficient condition for six points, two on each side of a given triangle, to be on a conic. We will explain the theorem in both Evclidean and projective plane and then explain two of its applications. The first one is called the construction of the Cevian conic. It tells us how to construct six points on the sides or the carriers of the sides of a triangle so that they will form a conic, a Cevian conic. The second application is defined in the projective plane and tells us that the tangent lines from the vertices of a given triangle to an arbitrary conic intersect the carriers of the opposite sides of the triangle in six points that are on a conic.