Ortogonalna projekcija

Ortogonalna projekcija
Raspored pogleda

Ortogonalna projekcija je glavni način predstavljanja predmeta, delova, objekata, mašina,itd. na tehničkim crtežima.[1] Sa perspektive linearne algebre i funkcionalne analize, projekcija je linearna transformacija P iz vektorskog prostora u sebe tako da je P2 = P. Ona ostavlja sliku nepromenjenu.[2] Mada apstraktna, ova definicija projekcije formalizuje ideju grafičke projekcije.

Pogledi

Kod ortogonalne projekcije sve tačke predmeta projektuju se ortogonalno (normalno-pod pravim uglom - 90°) na tri projekcijske ravni :

  • V - vertikalnu
  • H - horizontalnu
  • P - profilnu

Na ovaj način se dobijaju tri slike koje definišu predmet. Ove slike zovu se pogledi.

Na vertikalnicu se projektuje pogled spreda, na horizontalnicu pogled odozdo, a na profilnicu pogled sleva. Tri profilne ravni čine prostorni koordinatni sistem, koji se zasecanjem po određenoj osi zaokreće i svodi u ravanski. Ortogonalnom projekcijom se u izvesnom smislu prostor pretvara u ravan. Iz tog razloga je ortogonalna projekcija najpogodnija za crtanje predmeta na tehničkim crtežima.

Moguća su šest pogleda, ali se u praksi najčešće koriste tri, gore pomenuta. Predmet se na tehničkom crtežu po pravilu predstavlja samo u dovoljno broju pregleda.

Raspored pogleda

Standard definiše dva rasporeda pogleda: evropski i američki.

Evropski raspored pogleda

  • Pogled s preda-crta se po izboru,
  • Pogled sleva-crta se desno od pogleda spreda,
  • Pogled odozgo-crta se dole,
  • Pogled zdesna-crta se levo,
  • Pogled odozdo-crta se gore,
  • Pogled otpozadi-crta se levo od pogleda zdesna.

Američki raspored pogleda

  • Pogled s preda-crta se po izboru,
  • Pogled zdesna-crta se desno od pogleda spreda,
  • Pogled odozgo-crta se gore,
  • Pogled sleva-crta se levo,
  • Pogled odozdo-crta se dole,
  • Pogled otpozadi-crta se levo od pogleda zdesna.
  • Meyer, C. D. (2000). Matrix analysis and applied linear algebra. Philadelphia: Society for Industrial and Applied Mathematics. ISBN 978-0-89871-454-8. 

Reference

  1. ^ Maynard 2005, стр. 22
  2. ^ Meyer 2000

Literatura

Spoljašnje veze

Ortogonalna projekcija на Викимедијиној остави.

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