Geometric Courses for Architectural and Teacher Students at the TU Graz O. Röschel

1. Geometric Courses for Architectural and Teacher Students at the TU Graz O. Röschel Zagreb, February 2007

2. Geometric Courses for Architectural and Teacher Students at the TU Graz Contents: Geometric courses under new technologies (integration of CAD) I. Courses for Architects in the 1st and 2nd semester II. Courses for Teachers and the Architects in the 2nd year Examples of Geometric Topics (including CAD) III. Conclusions Introduction of: Mathematica, Maple and CAD-packages Here: Restriction to the combination of the geometric education with the use of professional CAD-packages! → Look for geometric problems which can be worked out now!

3. Geometric Courses for Architectural and Teacher Students at the TU Graz Introduction of: Mathematica, Maple and CAD-packages Here: Restriction to the combination of the geometric education with the use of professional CAD-packages! In order to enhance the spatial abilities of students: Direct work in a virtual 3D-space (3D Model space) → Look for geometric problems which can be worked out now!

4. Geometric Courses for Architectural and Teacher Students at the TU Graz • I. Courses for Architects in the 1st and 2nd sem. • „Methods of representation“: • 2 lectures in 1st sem. • 2 exercises in 1st sem. • 2 exercises in 2nd sem. • Joint courses of the institute of geometry and the institute of media in architecture • The aim: Balance between descriptive methods and the use of a CAD-package (AutoCAD)

5. I. Courses for Architectural Students • „Methods of representation“: • (A. Wiltsche, Varaždinske Toplice, 2005) • Winter term:Exercises - 5 homeworks: • 3 drawings by hand: • Axonometry • Perspective • Reconstruction

6. I. Courses for Architectural Students • 2 AutoCAD-works: • Technical drawing (architectural plan) • Solid modelling of a real world‘s object • Summer term: • 6 Homeworks: • Pixel graphics, Rhino3D for surface modelling, animation • Examination at the end of the lecture: Divided into a drawing and an AutoCAD part. • Details….

7. Geometric Courses for Architectural and Teacher Students at the TU Graz • II. Courses for Teachers and Architects (beginning in the 2nd year) • The aim: • Training the experienced use of a professional CAD-package combined with geometric contents • Examples: • „Professional CAD-packages“: 2 proseminary • „3D-constructing with AutoCAD“: 2 hours • Training of teacher students of „Geometry“ (in combination with „Mathematics“)

8. Geometric Courses for Teacher Students and Architects • Professional CAD-packages • MicroStation (or AutoCAD) – proseminary (2 hrs/week) • Combination of teaching and solving of given problems • 5 Units: • Unit 1: (3 weeks) Handling with MicroStation‘s plane features • Unit 2: (3 weeks) 3D-features and solid modelling with volumes • Unit 3: (3 weeks) References and hierarchical block-structures • Unit 4: (3 weeks) Modelling of surface models • Unit 5: (3 weeks) Animations and exchange with other packages (AutoCAD, VRML, …)

9. Professional CAD-packages (for teacher students) Unit 1: Handling with MicroStation‘s plane features Homework 1: 1a. Follow the examples of the lecture and determine a planar band ornament with at least 5-fold rotational symmetry, which contains parts of straight lines and circles. Submit the DGN-Files with the name „Name_arb1a.dwg“ to roeschel@tugraz.at – Subject: „Prof_CAD_Pakete_1“. Deadline: 2.11.2006 A student‘s result:

10. Professional CAD-packages (for teacher students) Unit 2: (3 weeks) 3D-features and solid modelling with volumes Homework 1 (cont.): 1b. Follow the examples of the lecture and determine a volume version of the band ornament from 1a. It shall consist of at least 10 congrent pieces, which stick together without self-intersections.

11. Professional CAD-packages (for teacher students) Homework 1b: A Student‘s work

12. Professional CAD-packages (for teacher students) Unit 2(cont.): 3D-solid modelling with volumes and 2D-output (references) Homework 2: Determine a DGN – File with the following contents: 1) The file shall contain 6 solid models (cube1 to cube6 as modified copies of the default model) with TSCHUPIK-cubes. 2) Use references to generate a layout with axonometric images.

13. Professional CAD-packages (for teacher students) Homework 2: A Student‘s work (Exercise for spatial abilities)

14. Professional CAD-packages (for teacher students) Unit 3: References of spatial objects and star polyhedra Homework 3: Use an hierarchical block structure to implement the action the iscosahedral group. Start with a regular pentagondodecahedron and determine different star polyhedra: The small and the great stellated dodecahedron. Additional: Are you able to generate the other stars of this type, too?

15. Professional CAD-packages (for teacher students) Homework 3: A Student‘s work

16. Professional CAD-packages (for teacher students) Unit 4: Modelling of surface models Homework 4 – spherical pavements: Determine a spherical pavement of the octahedral group, which uses a suitable basic spherical patch. Exercises: Planar pavements and spherical pavements fitting to the tetrahedral group.

17. Professional CAD-packages (for teacher students) Homework 4: A Student‘s work Here with gaps:

18. Professional CAD-packages (for teacher students) Unit 5: Export and Animation Exercise: Generate an animation which simulates the generation of a cube (a dodecahedron) from ist net. The cube:

19. Professional CAD-packages (for teacher students) Unit 5: Export and Animation Homework 5: Generate an animation which simulates the „growth“ of regular pentagondodecahedron to a rhombi-triakontahedron (and to the deltoid-hexakontahedron, resp.). Export the animation into a VRML-File. Example: From the cube to the rhombic dodecahedron to the deltoid-iksositetrahedron.

20. Professional CAD-packages (for teacher students) Homework 5: A Student‘s work Dodecahedron → Deltoid-Hexakontahedron

21. Geometric Courses for Teacher Students B. 3D-constructing with AutoCAD (for all students) AutoCAD –seminary (2 hrs/week) Combination of teaching and solving of given problems 5 Units: Unit 1: (2 weeks) Handling with AutoCAD‘s plane features Unit 2: (3 weeks) 3D-features and regions Unit 3: (3 weeks) 3D-modelling Unit 4: (3 weeks) Fractals using AutoLISP Unit 5: (4 weeks) Constructions using the AutoCAD Calculator

22. 3D-constructing with AutoCAD Unit 1: (2 weeks) Handling with AutoCAD‘s plane features Similar to the topics in „professional CAD-packages“ Homework 1: A band ornament with at least 5-fold rotational symmetry.

23. 3D-constructing with AutoCAD Unit 2: (3 weeks) 3D-features and Regions Topics: 3D-constructions, UCS, … Homework 2: Determine a region model of a regular pentagon-dodecahedron. A student‘s work:

24. 3D-constructing with AutoCAD Topics: Blocks … Implement the action of a poyhedral group → „Band-ornaments“

25. 3D-constructing with AutoCAD „Band-ornaments“

26. 3D-constructing with AutoCAD Unit 3: (3 weeks) 3D-modelling Topics: Solids and BOOLEAN Operations Homework 3: Determine a volume-model of a roman or gothic arch (only the frame).

27. 3D-constructing with AutoCAD Homework 3: A Student‘s work (some screenshots from the documentation) Documentation:

28. 3D-constructing with AutoCAD Unit 4: (3 weeks) Fractals and AutoLISP – iterative geometric transformations in space Exercises: Snowflake – iterative steps:

29. 3D-constructing with AutoCAD Dragon Spatial fractals: Homework 4: Determine a volume-model of spatial fractal.

30. 3D-constructing with AutoCAD Homework 4: A Student‘s work

31. 3D-constructing with AutoCAD Unit 5: (3 weeks) Constructions in space using the AutoCAD calculator Exercises: „Ropes and roles“ → Homework 5

32. 3D-constructing with AutoCAD Homework 5: A Student‘s work

33. Geometric Courses for Architectural and Teacher Students at the TU Graz • Conclusion • Courses for Architects • Courses for Teachers and Architects • Examples of Geometric Topics (with CAD) • Allways: Combine the geometric education with the use of professional CAD-packages! • The introduction of CAD-packages in descriptive geometry offers a big chance! • This will allow to put geometric 3D abilities on a new level!

34. Geometric Courses for Architectural and Teacher Students at the TU Graz A Slide Show of the Geometric Exercises

35. Geometric Courses for Architectural and Teacher Students at the TU Graz A Slide Show of the Geometric Exercises

36. Geometric Courses for Architectural and Teacher Students at the TU Graz A Slide Show of the Geometric Exercises

37. Geometric Courses for Architectural and Teacher Students at the TU Graz A Slide Show of the Geometric Exercises

38. Geometric Courses for Architectural and Teacher Students at the TU Graz A Slide Show of the Geometric Exercises

39. Geometric Courses for Architectural and Teacher Students at the TU Graz A Slide Show of the Geometric Exercises

40. Geometric Courses for Architectural and Teacher Students at the TU Graz A Slide Show of the Geometric Exercises

41. Geometric Courses for Architectural and Teacher Students at the TU Graz A Slide Show of the Geometric Exercises

42. Geometric Courses for Architectural and Teacher Students at the TU Graz A Slide Show of the Geometric Exercises

43. Geometric Courses for Architectural and Teacher Students at the TU Graz A Slide Show of the Geometric Exercises

44. Geometric Courses for Architectural and Teacher Students at the TU Graz Thank you for your attention!

45. I. Courses for Architectural Students Details: Winter term: Ex 1 Ex2 Ex3 Ex4 Ex5 Ex6 Ex7 Ex8 Ex9 Ex10 Ex11 Ex12 Ex13

46. I. Courses for Architectural Students Details: Sommer term: Assignments 1 - 6