20.500.12556/RUL-120179 Konstrukcija gibanja kamere z uporabo Pitagorejskih krivulj delo diplomskega seminarja Construction of camera motion with Pitagorean curves V delu obravnavamo konstrukcije gibanja kamere okoli fiksnega objekta. Želimo si, da so gibanja opisana z racionalnimi krivuljami. Predstavljeno je, kako to naredimo z uporabo P-krivulj in kvaternionov. Opisani so Bernsteinovi bazni polinomi, pomen kontrolnih točk ter kontrolnega poligona in primerjava zapisa krivulje v Bernsteinovi bazi in standardni bazi. Definirana so prikrojena in usmerjena ogrodja ter razlika med njimi, opisana pa so tudi rotacijsko minimizirajoča ogrodja in pogoji za njihovo konstrukcijo. V zaključku je predstavljen preprost interpolacijski problem za konstrukcijo P-krivulje, ki interpolira začetno in končno točko in se jo da opremiti z rotacijsko minimizirajočim usmerjenim ogrodjem. Rezultati so prikazani na več numeričnih primerih. The present thesis deals with the construction of camera movements around a fixed object. The movements are described by means of rational curves. The thesis presents how that is performed by using P-curves and quaternions. It describes Bernstein basis polynomials, the meaning of control points and the control polygon, and also the comparison of curve representation in Bernstein basis and in standard basis. Adapted and directed frames are defined as well as the difference between them. In addition, rotation minimizing frames and the conditions for their constructions are described. In conclusion, a simple interpolation problem of a P-curve construction is presented, which interpolates the first and the last point and can be equipped with a rotation minimizing directed frame. The results are shown in several numerical examples. Bernsteinovi polinomi P-krivulja ortonormirano ogrodje prikrojeno ogrodje usmerjeno ogrodje konstrukcija gibanja kamere Bernstein polynomials P-curve orthonormal frame adapted frame directed frame construction of camera motion true false false Slovenski jezik Angleški jezik Delo diplomskega seminarja/zaključno seminarsko delo/naloga 2020-09-17 07:16:16 2020-09-17 07:16:20 2024-05-29 14:40:39 0000-00-00 00:00:00 2020 0 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 519.6 110221 58344963 1471.pdf 1471.pdf 1 3217337EB33F0E33B92AA05112C6C91F 7949cebc53eff62bda9610142fe25038c10368a17b4201c0b92a090aa51fb196 0520137d-a1ba-11eb-a523-00155dcfd717 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=134959 Fakulteta za matematiko in fiziko 0 0 0