Prikazi prodora oblih ploha uz pomoć računalne grafike

master's thesis

• Author: Dajana Kovačić
• Mentor: Dora Pokaz (mentor)
• Committee member: Dora Pokaz (predsjednik povjerenstva)
• Committee member: Sanja Varošanec (član povjerenstva)
• Committee member: Tina Bosner (član povjerenstva)
• Committee member: Marko Erceg (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2018-09-27, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

Oble plohe čije smo međusobne prodore promatrali u ovom radu su stožac, valjak i sfera. Spomenute plohe su plohe 2. reda, a njihovim prodorom nastaju prostorne krivulje 4. reda. Razlikujemo prave i raspadnute prostorne krivulje, a kakva krivulja nastaje prodorom dviju ploha ovisi o njihovom međusobnom položaju. Prave prostorne krivulje možemo klasificirati na jednodijelne, dvodijelne te krivulje s dvostrukom točkom. Ukoliko dođe do raspada, prostorna se krivulja 4. reda raspada na krivulje... More nižih redova, ali tako da je zbroj redova tih krivulja jednak 4. Općenito, možemo govoriti o raspadu na četiri pravca, raspadu na dvije krivulje 2. reda, raspadu na krivulju 3. reda i pravac te raspadu na krivulju 2. reda i dva pravca. Projekcije oblih ploha i njihovih prodornih krivulja prikazivali smo pomoću Mongeove metode i aksonometrije u programu za 3D modeliranje Rhinoceros, ali primjenom klasičnih metoda presječnih ravnina. Kod prodora valjaka i/ili stožaca presječne ravnine odabiru se tako da obje plohe sijeku duž njihovih izvodnica dok se kod prodora sa sferom presječne ravnine odabiru tako da su najpogodnije za tu drugu plohu. Premda prikazivanje prodora stožaca, valjaka i sfera izgleda i zvuči komplicirano, njihova primjena je široka, a pronalazimo je u svakodnevnom životu. Jednostavniji primjeri prodora su spajanje cijevi, ograde, loptice... Ozbiljniji i kreativniji primjeri prodora su pojedini svodovi i kupole. Less

Abstract (english)

Curved solids whose intersections have been described in this thesis are a cone, a cylinder and a sphere. Mentioned solids are solids of the 2nd order and their intersection is space curve of the 4th order. We differentiate between proper space curves and degenerated space curves and which one appears depends on the position of solids that we intersect. Proper space curves are classified as one-branch, two-branch and curves with one double point. If there comes to decomposition, a space... More curve of the 4th order is decomposed into curves of lower order but so that the sum of their orders equals 4. Generally, we can talk about following decompositions: four lines, two curves of the 2nd order, a curve of the 3rd order and a line, a curve of the 2nd order and two lines. Projections of curved solids and their intersection have been represented by Monge’s method and axonometry in the program for 3D modeling Rhinoceros but also with classical methods of cutting planes. In case of intersecting cylinders and/or cones, we choose cutting planes that intersect both solids along their generatrices. When one of the two solids is a sphere, we choose cutting planes that cut the other solid in the simplest possible curves. Although intersections of curved solids seem and sound complicated, their application is wide and can be found in everyday life. Here are some simple examples of their application: connecting tubes, fences, balls...Serious and creative examples are some domes and vaults. Less

• Keywords: oble plohe; stožac; valjak; sfera; prostorne krivulje; Rhinoceros; Mongeova metoda; aksonometrija
• Keywords (english): curved solids; cone; cylinder; sphere; space curve; Rhinoceros; Monge’s method; axonometry
• Language: croatian
• URN:NBN: urn:nbn:hr:217:390546
• Study programme: Title: Mathematics Education; specializations in: Mathematics Education; Course: Mathematics Education; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra edukacije matematike (magistar/magistra edukacije matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2019-05-17 12:15:36