Transcript Supplementary Courses in Descriptive Geometry

Institute of
Geometry
Geometric Courses for Architectural and
Teacher Students at the TU Graz
O. Röschel
Zagreb, February 2007
Otto Röschel
Zagreb, 24.2.2007
1
Institute of
Geometry
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!
Otto Röschel
Zagreb, 24.2.2007
2
Institute of
Geometry
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!
Otto Röschel
Zagreb, 24.2.2007
3
Institute of
Geometry
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)
Otto Röschel
Zagreb, 24.2.2007
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Institute of
Geometry
I. Courses for Architectural Students
„Methods of representation“:
(A. Wiltsche, Varaždinske Toplice, 2005)
Winter term: Exercises - 5 homeworks:
3 drawings by hand:
a) Axonometry
b) Perspective
c) Reconstruction
Otto Röschel
Zagreb, 24.2.2007
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Institute of
Geometry
I. Courses for Architectural Students
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….
Otto Röschel
Zagreb, 24.2.2007
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Institute of
Geometry
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“)
Otto Röschel
Zagreb, 24.2.2007
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Institute of
Geometry
Geometric Courses for Teacher Students
and Architects
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, …)
Otto Röschel
Zagreb, 24.2.2007
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Institute of
Geometry
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
[email protected] – Subject: „Prof_CAD_Pakete_1“.
Deadline: 2.11.2006
A student‘s result:
Otto Röschel
Zagreb, 24.2.2007
9
Institute of
Geometry
Professional CAD-packages
(for teacher students)
Unit 2: (3 weeks) 3Dfeatures 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 selfintersections.
Otto Röschel
Zagreb, 24.2.2007
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Institute of
Geometry
Professional CAD-packages
(for teacher students)
Homework 1b: A Student‘s work
Otto Röschel
Zagreb, 24.2.2007
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Institute of
Geometry
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.
Otto Röschel
Zagreb, 24.2.2007
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Institute of
Geometry
Professional CAD-packages
(for teacher students)
Homework 2: A Student‘s work
(Exercise for spatial abilities)
Otto Röschel
Zagreb, 24.2.2007
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Institute of
Geometry
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?
Otto Röschel
Zagreb, 24.2.2007
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Institute of
Geometry
Professional CAD-packages
(for teacher students)
Homework 3: A Student‘s work
Otto Röschel
Zagreb, 24.2.2007
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Institute of
Geometry
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.
Otto Röschel
Zagreb, 24.2.2007
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Institute of
Geometry
Professional CAD-packages
(for teacher students)
Homework 4: A Student‘s work
Here with gaps:
Otto Röschel
Zagreb, 24.2.2007
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Institute of
Geometry
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:
Otto Röschel
Zagreb, 24.2.2007
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Institute of
Geometry
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 rhombitriakontahedron (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.
Otto Röschel
Zagreb, 24.2.2007
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Institute of
Geometry
Professional CAD-packages
(for teacher students)
Homework 5: A Student‘s work
Dodecahedron → Deltoid-Hexakontahedron
Otto Röschel
Zagreb, 24.2.2007
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Institute of
Geometry
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
Otto Röschel
Zagreb, 24.2.2007
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Institute of
Geometry
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.
Otto Röschel
Zagreb, 24.2.2007
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Institute of
Geometry
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:
Otto Röschel
Zagreb, 24.2.2007
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Institute of
Geometry
3D-constructing with AutoCAD
Topics: Blocks …
Implement the action of a poyhedral group
→ „Band-ornaments“
Otto Röschel
Zagreb, 24.2.2007
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Institute of
Geometry
3D-constructing with AutoCAD
„Band-ornaments“
Otto Röschel
Zagreb, 24.2.2007
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Institute of
Geometry
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).
Otto Röschel
Zagreb, 24.2.2007
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Institute of
Geometry
3D-constructing with AutoCAD
Homework 3:
A Student‘s work
(some screenshots
from the documentation)
Documentation:
Otto Röschel
Zagreb, 24.2.2007
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Institute of
Geometry
3D-constructing with AutoCAD
Unit 4: (3 weeks) Fractals and AutoLISP – iterative
geometric transformations in space
Exercises:
Snowflake
– iterative steps:
Otto Röschel
Zagreb, 24.2.2007
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3D-constructing with AutoCAD
Institute of
Geometry
Dragon
p1
p1
p2
Spatial fractals:
Homework 4: Determine a volume-model of spatial fractal.
Otto Röschel
Zagreb, 24.2.2007
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Institute of
Geometry
3D-constructing with AutoCAD
Homework 4:
A Student‘s work
Otto Röschel
Zagreb, 24.2.2007
30
Institute of
Geometry
3D-constructing with AutoCAD
Unit 5: (3 weeks) Constructions in space using the
AutoCAD calculator
Exercises:
„Ropes and roles“
→ Homework 5
Otto Röschel
Zagreb, 24.2.2007
31
Institute of
Geometry
3D-constructing with AutoCAD
Homework 5:
A Student‘s work
Otto Röschel
Zagreb, 24.2.2007
32
Institute of
Geometry
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!
Otto Röschel
Zagreb, 24.2.2007
33
Institute of
Geometry
Geometric Courses for Architectural and
Teacher Students at the TU Graz
A Slide Show of the Geometric Exercises
Otto Röschel
Zagreb, 24.2.2007
34
Institute of
Geometry
Geometric Courses for Architectural and
Teacher Students at the TU Graz
A Slide Show of the Geometric Exercises
Otto Röschel
Zagreb, 24.2.2007
35
Institute of
Geometry
Geometric Courses for Architectural and
Teacher Students at the TU Graz
A Slide Show of the Geometric Exercises
Otto Röschel
Zagreb, 24.2.2007
36
Institute of
Geometry
Geometric Courses for Architectural and
Teacher Students at the TU Graz
A Slide Show of the Geometric Exercises
Otto Röschel
Zagreb, 24.2.2007
37
Institute of
Geometry
Geometric Courses for Architectural and
Teacher Students at the TU Graz
A Slide Show of the Geometric Exercises
Otto Röschel
Zagreb, 24.2.2007
38
Institute of
Geometry
Geometric Courses for Architectural and
Teacher Students at the TU Graz
A Slide Show of the Geometric Exercises
Otto Röschel
Zagreb, 24.2.2007
39
Institute of
Geometry
Geometric Courses for Architectural and
Teacher Students at the TU Graz
A Slide Show of the Geometric Exercises
Otto Röschel
Zagreb, 24.2.2007
40
Institute of
Geometry
Geometric Courses for Architectural and
Teacher Students at the TU Graz
A Slide Show of the Geometric Exercises
Otto Röschel
Zagreb, 24.2.2007
41
Institute of
Geometry
Geometric Courses for Architectural and
Teacher Students at the TU Graz
A Slide Show of the Geometric Exercises
Otto Röschel
Zagreb, 24.2.2007
42
Institute of
Geometry
Geometric Courses for Architectural and
Teacher Students at the TU Graz
A Slide Show of the Geometric Exercises
Otto Röschel
Zagreb, 24.2.2007
43
Institute of
Geometry
Geometric Courses for Architectural and
Teacher Students at the TU Graz
Thank you for your attention!
Otto Röschel
Zagreb, 24.2.2007
44
I. Courses for Architectural Students
Institute of
Geometry
Details:
Winter term:
Ex 1
Ex2
Ex3
Ex4
Ex5
Ex6
Ex7
Ex8
Ex9
Ex10
Ex11
Ex12
Otto Röschel
Ex13
Zagreb, 24.2.2007
45
Institute of
Geometry
I. Courses for Architectural Students
Details:
Sommer term:
Assignments 1 - 6
Otto Röschel
Zagreb, 24.2.2007
46