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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
8
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 [email protected] – 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)
11
Otto Röschel
Institute of Geometry
Zagreb, 24.2.2007
Homework 1b: A Student‘s work
Professional CAD-packages (for teacher students)
12
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)
13
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)
14
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)
15
Otto Röschel
Institute of Geometry
Zagreb, 24.2.2007
Homework 3: A Student‘s work
Professional CAD-packages (for teacher students)
16
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)
17
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)
19
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)
20
Otto Röschel
Institute of Geometry
Zagreb, 24.2.2007
Homework 5: A Student‘s work
Professional CAD-packages (for teacher students)
Dodecahedron → Deltoid-Hexakontahedron
21
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
22
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
23
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]
24
Otto Röschel
Institute of Geometry
Zagreb, 24.2.2007
Topics: Blocks …
Implement the action of a poyhedral group→ „Band-ornaments“
3D-constructing with AutoCAD
25
Otto Röschel
Institute of Geometry
Zagreb, 24.2.2007
„Band-ornaments“
3D-constructing with AutoCAD
26
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
27
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
28
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