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

2 Otto Röschel Institute of Geometry Zagreb, 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! Geometric Courses for Architectural and Teacher Students at the TU Graz

3 Otto Röschel Institute of Geometry Zagreb, 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! Geometric Courses for Architectural and Teacher Students at the TU Graz

4 Otto Röschel Institute of Geometry Zagreb, 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) Geometric Courses for Architectural and Teacher Students at the TU Graz

5 Otto Röschel Institute of Geometry Zagreb, „Methods of representation“: (A. Wiltsche, Varaždinske Toplice, 2005) Winter term: Exercises - 5 homeworks: 3 drawings by hand: a)Axonometry b)Perspective c)Reconstruction I. Courses for Architectural Students

6 Otto Röschel Institute of Geometry Zagreb, AutoCAD-works: a)Technical drawing (architectural plan) b)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…. I. Courses for Architectural Students

7 Otto Röschel Institute of Geometry Zagreb, 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“) Geometric Courses for Architectural and Teacher Students at the TU Graz

8 Otto Röschel Institute of Geometry Zagreb, A.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, …) Geometric Courses for Teacher Students and Architects

9 Otto Röschel Institute of Geometry Zagreb, 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 – Subject: „Prof_CAD_Pakete_1“. Deadline: A student‘s result: Professional CAD-packages (for teacher students)

10 Otto Röschel Institute of Geometry Zagreb, 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. Professional CAD-packages (for teacher students)

11 Otto Röschel Institute of Geometry Zagreb, Homework 1b: A Student‘s work Professional CAD-packages (for teacher students)

12 Otto Röschel Institute of Geometry Zagreb, 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. Professional CAD-packages (for teacher students)

13 Otto Röschel Institute of Geometry Zagreb, Homework 2: A Student‘s work (Exercise for spatial abilities) Professional CAD-packages (for teacher students)

14 Otto Röschel Institute of Geometry Zagreb, 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? Professional CAD-packages (for teacher students)

15 Otto Röschel Institute of Geometry Zagreb, Homework 3: A Student‘s work Professional CAD-packages (for teacher students)

16 Otto Röschel Institute of Geometry Zagreb, 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. Professional CAD-packages (for teacher students)

17 Otto Röschel Institute of Geometry Zagreb, Homework 4: A Student‘s work Here with gaps: Professional CAD-packages (for teacher students)

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

19 Otto Röschel Institute of Geometry Zagreb, 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. Professional CAD-packages (for teacher students)

20 Otto Röschel Institute of Geometry Zagreb, Homework 5: A Student‘s work Professional CAD-packages (for teacher students) Dodecahedron → Deltoid-Hexakontahedron

21 Otto Röschel Institute of Geometry Zagreb, 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 Geometric Courses for Teacher Students

22 Otto Röschel Institute of Geometry Zagreb, 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. 3D-constructing with AutoCAD

23 Otto Röschel Institute of Geometry Zagreb, 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: 3D-constructing with AutoCAD

24 Otto Röschel Institute of Geometry Zagreb, Topics: Blocks … Implement the action of a poyhedral group → „Band-ornaments“ 3D-constructing with AutoCAD

25 Otto Röschel Institute of Geometry Zagreb, „Band-ornaments“ 3D-constructing with AutoCAD

26 Otto Röschel Institute of Geometry Zagreb, 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). 3D-constructing with AutoCAD

27 Otto Röschel Institute of Geometry Zagreb, Homework 3: A Student‘s work (some screenshots from the documentation) Documentation: 3D-constructing with AutoCAD

28 Otto Röschel Institute of Geometry Zagreb, Unit 4: (3 weeks) Fractals and AutoLISP – iterative geometric transformations in space Exercises: Snowflake – iterative steps: 3D-constructing with AutoCAD

29 Otto Röschel Institute of Geometry Zagreb, D-constructing with AutoCAD Dragon Spatial fractals: Homework 4: Determine a volume-model of spatial fractal.

30 Otto Röschel Institute of Geometry Zagreb, Homework 4: A Student‘s work 3D-constructing with AutoCAD

31 Otto Röschel Institute of Geometry Zagreb, Unit 5: (3 weeks) Constructions in space using the AutoCAD calculator Exercises: „Ropes and roles“ → Homework 5 3D-constructing with AutoCAD

32 Otto Röschel Institute of Geometry Zagreb, Homework 5: A Student‘s work 3D-constructing with AutoCAD

33 Otto Röschel Institute of Geometry Zagreb, 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! Geometric Courses for Architectural and Teacher Students at the TU Graz

34 Otto Röschel Institute of Geometry Zagreb, A Slide Show of the Geometric Exercises Geometric Courses for Architectural and Teacher Students at the TU Graz

35 Otto Röschel Institute of Geometry Zagreb, A Slide Show of the Geometric Exercises Geometric Courses for Architectural and Teacher Students at the TU Graz

36 Otto Röschel Institute of Geometry Zagreb, A Slide Show of the Geometric Exercises Geometric Courses for Architectural and Teacher Students at the TU Graz

37 Otto Röschel Institute of Geometry Zagreb, A Slide Show of the Geometric Exercises Geometric Courses for Architectural and Teacher Students at the TU Graz

38 Otto Röschel Institute of Geometry Zagreb, A Slide Show of the Geometric Exercises Geometric Courses for Architectural and Teacher Students at the TU Graz

39 Otto Röschel Institute of Geometry Zagreb, A Slide Show of the Geometric Exercises Geometric Courses for Architectural and Teacher Students at the TU Graz

40 Otto Röschel Institute of Geometry Zagreb, A Slide Show of the Geometric Exercises Geometric Courses for Architectural and Teacher Students at the TU Graz

41 Otto Röschel Institute of Geometry Zagreb, A Slide Show of the Geometric Exercises Geometric Courses for Architectural and Teacher Students at the TU Graz

42 Otto Röschel Institute of Geometry Zagreb, A Slide Show of the Geometric Exercises Geometric Courses for Architectural and Teacher Students at the TU Graz

43 Otto Röschel Institute of Geometry Zagreb, A Slide Show of the Geometric Exercises Geometric Courses for Architectural and Teacher Students at the TU Graz

44 Otto Röschel Institute of Geometry Zagreb, Thank you for your attention! Geometric Courses for Architectural and Teacher Students at the TU Graz

45 Otto Röschel Institute of Geometry Zagreb, Details: Winter term: Ex 1 Ex2Ex3 Ex4 Ex5Ex6 Ex7 Ex8 Ex9 Ex10 Ex11 Ex12 Ex13 I. Courses for Architectural Students

46 Otto Röschel Institute of Geometry Zagreb, Details: Sommer term: Assignments I. Courses for Architectural Students