Short Information on
the three CDROMs
It is the intention of these CDROMs to show to the
user the beauty of geometry and to animate him into creating geometrical
figures on his own.
All three CDROMs were widely reviewed in computer
journals, weekly journals and daily newspapers. In 199697 the Beauty
of Geometry and the Fascination of Interactive Computer Graphics
were shown in the Deutsches Museum in Munich on the occasion of
the exposition Digital Worlds. In addition the three CDROMs are
also on permanent show in the Digital Workshop of the Heinz Nixdorf
Museum in Paderborn.
Beauty of Geometry, Science and Aesthetics
This CDROM represents a multimedia collection of 620 pages with
innumerable hyperlinks. It is divided into two chapters:
Software for Geometry
This chapter contains vector graphics as a direct
application of the Software for Geometry. In 2Dgraphics a variety
of classical curves such as astroids, rosettes, cycloids, etc. are discussed.
Furthermore families of those curves are formed. In 3Dgraphics planes,
rotational surfaces (sphere, cone and cylinder) and Platonic and Archimedic
bodies are introduced, leading to many surprising motifs. All surfaces
can be cut out in complex forms with the curves introduced in 2Dgraphics.
At the same time it is possible to paint these surfaces with families of
these curves, also with very sophisticated ornamentation.
There are 400 different motifs which can be seen.
In addition all these motifs are saved as vector graphics and can be loaded
and run. This is especially interesting because it shows the genesis of
a motif giving insight also into the geometrical construction. During the
drawing of such a motif one can change colors, the width of the pen and
other parameters. There are also 10 demos showing the history of the Software
for Geometry and various application in Differential Geometry.
Ray Tracing
This chapter gives an application of the Software
for Geometry to ray tracing. Although the technique of ray tracing
is completely different to that of vector graphics, the methods of the
Software for Geometry are used to create very complex photo realistic
images. There are sections on illumination models, acceleration techniques
and 2D and 3Dtextures. In each of these sections a theoretical introduction
is also given. All this leads to 220 motifs, including fractal motifs,
SierpinskyTetrahedron, scenes with chessmen and glasses, still lives,
etc.
One of the chessmen scenes won the Computer Graphics
Forum cover photograph prize competition in 1995.
Fascination of Interactive Computer Graphics
In 1995 the appearance of Borland’s Delphi made it
possible to create interactive programs with the Software for Geometry
very easily. The CDROM Fascination of Interactive Computer Graphics
includes 30 interactive programs for 2D and 3Dgraphics. Here the user
is able to realize his own artistic ideas. He can change the geometrical
scene, the type of ornamentation on the surfaces or the background, the
kind of curves used on the surfaces, the colors, the width of the pen and
many more parameters. With simple movements of the mouse he can arbitrarily
change the perspective. Furthermore he can save the results as bitmaps
and HPGLFiles.
The graphical user interface of the CDROM starts
with an introduction and a user’s guide. In a short and not always completely
serious manner a brief introduction is given to the history of Euclidean
Geometry and Analytic Geometry. Among the demos there is a demo on the
Beauty of Geometry and 7 demos of applications to Differential Geometry.
Furthermore there are various articles on the „Software for Geometry„ and
references to the literature. In 2Dgraphics various interactive programs
on families of curves are presented. In 3Dgraphics there is a brief theoretical
introduction to the representation of planes, rotational surfaces and Platonic
bodies. Many interactive motifs using these elements are presented. The
background can be formed with 12 different kinds of ornamentations.
The Fascination of Interactive Computer Graphic"
was awarded the German Education Software Prize digita 96
at the 1996 book fair in Frankfurt.
Wunderworld of Interactive Computer Graphics
With this CDROM the authors have tried  even more
than in the preceding CDROM  to lead the user in an intuitive way through
handling the interactive programs. There are 53 interactive programs with
44 variations. The idea of the variations is to give an impression of how
different the results can be obtained from the same program by simply altering
a few parameters .
Now there are 20 kinds of ornamentations that can
be used for the background as well as for the surfaces. Each change of
a parameter can be tested immediately! This is very important because most
of the programs are very complex. Again the perspective can be changed
by simple movements of the mouse and the results can be saved as bitmaps
and HPGL files.
As a new feature, a guided tour has been created
as an insight in the workshop revealing some of the programming secrets.
Among the demos one finds a demo on the CDROMs Beauty of Geometry
and Fascination of Interactive Computer Graphics as well as 7 demos
of applications to Differential Geometry.
In the chapter on ornamentations a new type of fillornamentation
is introduced serving as a prototype for tiling surfaces. As applications
of Platonic and Archimedic bodies there are interesting applications such
as Eurofootball, Adeno virus and the C60 molecule. There are also five
Impossible Figures à la Escher and a gallery of 11 even more
complex scenes.
Downloads from the Homepage
Recently there have been three initiatives of the
Software for Geometry to the Internet. The purpose is to establish
a public computer graphics forum for the three CDROMs and the Software
for Geometry.
Picture of the month
Under this title a new interactive program for generating
complex pictures is presented each month. The interactive executable can
be downloaded and permits almost an infinite number of variations. The
style of the programs follows those of the interactive CDROMs. Hence the
newly created motifs can be saved as bitmaps or HPGL files.
Gallery
Under this title one can enter a gallery of complex
motifs created using the programs of the month and the programs on the
three CDROMs. The pictures are commented, they can be enlarged and of
course downloaded
Program of the Month
Porting TurboPascalPrograms to DelphiProjects
All three CDROMs have been created with the Software
for Geometry, which has been developed over a period of eight years
at the Mathematical Institute of the JustusLiebigUniversity in Giessen
(Germany). It has been published in two volumes. These books are in German,
however the source code is entirely in English.
The Software for Geometry was presented at
the Cebit ´93 and the Cebit ´95 at the booth of the University
of Giessen. In 1993  at the occasion of the UniversityComputerForum
in Berlin  it was awarded the GermanAustrian UniversitySoftware Prize
as Best Teaching Software in Mathematics.
Meanwhile TurboPascal with all its glorious merits
has been followed by Borland’s Delphi, an interactive development environment
for creation of graphical user interfaces for MSWindows. This software
contains many more features and is logically much more complicated than
even the most advanced versions of TurboPascal. Therefore the transition
has to be considered a big and complicated step. Now two master projects
can be downloaded – for 2DGraphics and 3DGraphics – which allow the fast
port of all objectoriented TurboPascal programs of the Software for
Geometry to Delphi projects. In addition every month there can be downloaded
a TurboPascal program for porting to a Delphi project.
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