1

Otto Röschel

Institute of Geometry

Zagreb, 24.2.2007

Geometric Courses for Architectural and Teacher Students at the TU Graz

O. Röschel

Zagreb, February 2007

2

Otto Röschel

Institute of Geometry

Zagreb, 24.2.2007

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, 24.2.2007

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, 24.2.2007

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, 24.2.2007

„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, 24.2.2007

2 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, 24.2.2007

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

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Otto Röschel

Institute of Geometry

Zagreb, 24.2.2007

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, 24.2.2007

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:

Professional CAD-packages (for teacher students)

10

Otto Röschel

Institute of Geometry

Zagreb, 24.2.2007

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)

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Otto Röschel

Institute of Geometry

Zagreb, 24.2.2007

Homework 1b: A Student‘s work

Professional CAD-packages (for teacher students)

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Otto Röschel

Institute of Geometry

Zagreb, 24.2.2007

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)

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Otto Röschel

Institute of Geometry

Zagreb, 24.2.2007

Homework 2: A Student‘s work

(Exercise for spatial abilities)

Professional CAD-packages (for teacher students)

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Otto Röschel

Institute of Geometry

Zagreb, 24.2.2007

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)

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Otto Röschel

Institute of Geometry

Zagreb, 24.2.2007

Homework 3: A Student‘s work

Professional CAD-packages (for teacher students)

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Otto Röschel

Institute of Geometry

Zagreb, 24.2.2007

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)

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Otto Röschel

Institute of Geometry

Zagreb, 24.2.2007

Homework 4: A Student‘s work

Here with gaps:

Professional CAD-packages (for teacher students)

18

Otto Röschel

Institute of Geometry

Zagreb, 24.2.2007

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)

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Otto Röschel

Institute of Geometry

Zagreb, 24.2.2007

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)

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Otto Röschel

Institute of Geometry

Zagreb, 24.2.2007

Homework 5: A Student‘s work

Professional CAD-packages (for teacher students)

Dodecahedron → Deltoid-Hexakontahedron

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Otto Röschel

Institute of Geometry

Zagreb, 24.2.2007

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

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Otto Röschel

Institute of Geometry

Zagreb, 24.2.2007

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

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Otto Röschel

Institute of Geometry

Zagreb, 24.2.2007

Unit 2: (3 weeks) 3D-features and RegionsTopics: 3D-constructions, UCS, …

Homework 2: Determine a region model of a regular pentagon-dodecahedron.

A student‘s work:

3D-constructing with AutoCAD

[Nur für akademischen Bereich]

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Otto Röschel

Institute of Geometry

Zagreb, 24.2.2007

Topics: Blocks …

Implement the action of a poyhedral group→ „Band-ornaments“

3D-constructing with AutoCAD

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Otto Röschel

Institute of Geometry

Zagreb, 24.2.2007

„Band-ornaments“

3D-constructing with AutoCAD

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Otto Röschel

Institute of Geometry

Zagreb, 24.2.2007

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

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Otto Röschel

Institute of Geometry

Zagreb, 24.2.2007

Homework 3: A Student‘s work(some screenshots from the documentation)

Documentation:

3D-constructing with AutoCAD

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Otto Röschel

Institute of Geometry

Zagreb, 24.2.2007

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, 24.2.2007

3D-constructing with AutoCAD

Dragon

Spatial fractals:

Homework 4: Determine a volume-model of spatial fractal.

p1 p1

p2

30

Otto Röschel

Institute of Geometry

Zagreb, 24.2.2007

Homework 4: A Student‘s work

3D-constructing with AutoCAD

31

Otto Röschel

Institute of Geometry

Zagreb, 24.2.2007

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, 24.2.2007

Homework 5: A Student‘s work

3D-constructing with AutoCAD

33

Otto Röschel

Institute of Geometry

Zagreb, 24.2.2007

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, 24.2.2007

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, 24.2.2007

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, 24.2.2007

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, 24.2.2007

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, 24.2.2007

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, 24.2.2007

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, 24.2.2007

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, 24.2.2007

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, 24.2.2007

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, 24.2.2007

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, 24.2.2007

Thank you for your attention!

Geometric Courses for Architectural and Teacher Students at the TU Graz

45

Otto Röschel

Institute of Geometry

Zagreb, 24.2.2007

Details:

Winter term:

Ex 1 Ex2 Ex3 Ex4 Ex5 Ex6

Ex7 Ex8 Ex9 Ex10 Ex11 Ex12 Ex13

I. Courses for Architectural Students

46

Otto Röschel

Institute of Geometry

Zagreb, 24.2.2007

Details:

Sommer term:

Assignments 1 - 6

I. Courses for Architectural Students