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GEOMETRIC MODELLING IN EDUCATION PROCESS

GEOMETRIC MODELLING IN EDUCATION PROCESS. Ivana Linkeová Czech Technical University in Prague Faculty of Mechanical Engineering Division of Geometry linkeova@fsik.cvut.cz http://marian.fsik.cvut.cz/ ~linkeova Karlovo n ám. 13 121 35 Praha 2 – Nové Město Czech Republic.

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GEOMETRIC MODELLING IN EDUCATION PROCESS

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  1. GEOMETRIC MODELLING IN EDUCATION PROCESS • Ivana Linkeová • Czech Technical University in Prague • Faculty of Mechanical Engineering • Division of Geometry • linkeova@fsik.cvut.cz • http://marian.fsik.cvut.cz/~linkeova • Karlovo nám. 13 • 121 35 Praha 2 – Nové Město • Czech Republic International Conference on Engineering Education July 25–29, 2005, Gliwice, Poland.

  2. GEOMETRIC MODELLING IN EDUCATION PROCESS • Role of constructive geometry in mechanical engineering • Surfaces of revolution • Principal meridian • Intersection of surfaces of revolution • Degenerated intersection of two quadrics of revolution • Helicoidal surfaces • Principal meridian • Normal section • Envelope surfaces • Translation • Rotation • Helicoidal motion • Conclusion International Conference on Engineering Education July 25–29, 2005, Gliwice, Poland.

  3. SURFACES OF REVOLUTION • Task setting o2 k2 o1 k1 International Conference on Engineering Education July 25–29, 2005, Gliwice, Poland.

  4. SURFACES OF REVOLUTION • Principal meridian construction o2 S2 m’2 k2 m2 ρ2 p2 k1 S1 o1 σ1 m’1 m1 p1 International Conference on Engineering Education July 25–29, 2005, Gliwice, Poland.

  5. SURFACES OF REVOLUTION • 3D model International Conference on Engineering Education July 25–29, 2005, Gliwice, Poland.

  6. C2 o2 T2 o‘2 k2=k‘2 T1 SURFACES OF REVOLUTION C1 k‘1 o1 o‘1 k1 • Intersection of surfaces of revolutionwith parallel axes ρ2 International Conference on Engineering Education July 25–29, 2005, Gliwice, Poland.

  7. SURFACES OF REVOLUTION • 3D model International Conference on Engineering Education July 25–29, 2005, Gliwice, Poland.

  8. C2 C‘2 o2 o‘2 k2 k‘2 C2 C‘2 C‘1 C1 o2 k‘1 k1 o1 o‘1 o‘2 k2 k‘2 C‘1 C1 k‘1 k1 o1 o‘1 SURFACES OF REVOLUTION • Intersection of surfaces of revolutionwith intersecting axes International Conference on Engineering Education July 25–29, 2005, Gliwice, Poland.

  9. SURFACES OF REVOLUTION • 3D model International Conference on Engineering Education July 25–29, 2005, Gliwice, Poland.

  10. SURFACES OF REVOLUTION • Intersection of surfaces of revolutionwith skew axes International Conference on Engineering Education July 25–29, 2005, Gliwice, Poland.

  11. SURFACES OF REVOLUTION • 3D model International Conference on Engineering Education July 25–29, 2005, Gliwice, Poland.

  12. HELICOIDAL SURFACES • Principal meridian construction t ω International Conference on Engineering Education July 25–29, 2005, Gliwice, Poland.

  13. t ω HELICOIDAL SURFACES • Normal section construction International Conference on Engineering Education July 25–29, 2005, Gliwice, Poland.

  14. HELICOIDAL SURFACES • 3D model International Conference on Engineering Education July 25–29, 2005, Gliwice, Poland.

  15. o2 p2 C2 E2=E’2 k2 E’2 o1 p1 k1 E2 C2 ENVELOPE SURFACES • Translation – characteristic curve construction International Conference on Engineering Education July 25–29, 2005, Gliwice, Poland.

  16. ENVELOPE SURFACES • Rotation – task setting o2 G2 S2 a2 x1,2 G1 S1 a1 o1 k1 International Conference on Engineering Education July 25–29, 2005, Gliwice, Poland.

  17. ENVELOPE SURFACES • Translation – characteristic curve construction International Conference on Engineering Education July 25–29, 2005, Gliwice, Poland.

  18. ENVELOPE SURFACES • Solution International Conference on Engineering Education July 25–29, 2005, Gliwice, Poland.

  19. ENVELOPE SURFACES • 3D model International Conference on Engineering Education July 25–29, 2005, Gliwice, Poland.

  20. ENVELOPE SURFACES • Helicoidal motion – task setting International Conference on Engineering Education July 25–29, 2005, Gliwice, Poland.

  21. ENVELOPE SURFACES • Helicoidal motion – solution International Conference on Engineering Education July 25–29, 2005, Gliwice, Poland.

  22. ENVELOPE SURFACES • Helicoidal motion – characteristic curve construction International Conference on Engineering Education July 25–29, 2005, Gliwice, Poland.

  23. ENVELOPE SURFACES • Helicoidal motion – 3D model International Conference on Engineering Education July 25–29, 2005, Gliwice, Poland.

  24. REFERENCES • Kargerová, M., "Geometry and Graphics", textbook, CTU in Prague Publishing, 2004. • Kargerová, M., Mertl, P. "Konstruktivní geometrie", textbook, CTU in Prague Publishing, 2004 • Kopincová, E., Květoňová, B., "Cvičení z konstruktivní geometrie", textbook, CTU in Prague Publishing, 2003. • Velichová, D., "Constructive Geometry", electronic book, http://www.km.sjf.stuba.sk/Geometria/KOGE/book.html,KM SjF STU, 2003. • Chahly, A., T., "Descriptive Geometry", book, Higher School publishing House, Moscow, 1968. • "Rhinoceros – NURBS Modelling for Windows", User’s guide International Conference on Engineering Education July 25–29, 2005, Gliwice, Poland.

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