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

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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

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Otto Röschel


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!


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Otto Röschel


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!


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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)


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„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

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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….


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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“)


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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

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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 [email protected] – Subject: „Prof_CAD_Pakete_1“.Deadline: 2.11.2006

A student‘s result:

Professional CAD-packages (for teacher students)

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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.


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Homework 1b: A Student‘s work


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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.


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Homework 2: A Student‘s work

(Exercise for spatial abilities)


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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?


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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.


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Here with gaps:


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Unit 5: Export and Animation

Exercise: Generate an animation which simulates the generation of a cube (a dodecahedron) from ist net.

The cube:


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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.


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Dodecahedron → Deltoid-Hexakontahedron

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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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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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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:


[Nur für akademischen Bereich]

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Topics: Blocks …

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


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„Band-ornaments“


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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).


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

Documentation:


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Unit 4: (3 weeks) Fractals and AutoLISP – iterative geometric transformations in space

Exercises: Snowflake – iterative steps:


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Dragon

Spatial fractals:

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

p1 p1

p2

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Unit 5: (3 weeks) Constructions in space using the AutoCAD calculator

Exercises: „Ropes and roles“

→ Homework 5


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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!


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A Slide Show of the Geometric Exercises


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Thank you for your attention!


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Details:

Winter term:

Ex 1 Ex2 Ex3 Ex4 Ex5 Ex6

Ex7 Ex8 Ex9 Ex10 Ex11 Ex12 Ex13


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Details:

Sommer term:

Assignments 1 - 6


Documents

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