Virtual Sculptures

Herbert W. Franke

The method of computer graphics makes it possible to visualize ideas for sculptures before its production with material. Here are to consider the physical and technical conditions for the realization, for instance for the stability. Used in this way the method brings advantages for planning, preparing and describing the shape, and especially also by the production: It is possible to transform the program code so that an application for computer controlled milling and cutting machines is possible.

This is a new method for realize art works, it is possible to produce the sculptures very rapidly with high precision, but the results correspond to the classical type of sculpture. Otherwise the most interesting purpose by using the computer as a tool of art in general is the possibility to enlarge the repertoire of art works. The question is: Could the computer lead us also in new areas of sculptures? A way to find an answer is to ignore the mentioned conditions for physical realization and try to design not realizable 3D-forms. It is remarquable that the computer graphic systems allow us to generate pictures also of such objects. What can be the reason that an object could not practically realized? Here I give a little list of items:

    mechanical instability,
    ignorance of the gravitation,
    irrealistic movements,
    change of shapes,
    permeations,
    not realizable effects of light and colors
    and so on.

A good way to illustrate these ideas is to show some examples.

To evoke the animated objects, load the free Mathematica Reader from internet!

Examples

The program code for the virtual sculptures is written in Mathematica 4.1. For download click at the names listed below. If you have a Mathematica version higher than 3.0 it is possible to calculate the picture series for the animation and let it run. During the endless run you can change the rate and the directions 'forward' and 'backward' - use the menu strip below. You can also change the picture parameters arbitrarily and calculate different series of pictures. This is useful to get higher resolution or a better approach to the mathematical descripted shapes. The animation is particularly remarkable in full screen mode.

1. Spindle

The basis of this example is a helical twisted spindle - an interesting object because of his optical irritating qualities: Showed in rotation it gives the impression of a screw movement up or down. I show a superposition of two spindles, rotating in opposite directions. This leads to an object with selfpermeation, principially not to realize.

2. Snail

This example concerns to an object on the basis of the ENNEPER minimal surface. His form is changed by introduction of further terms into the formula. The movement is a combination of rotation und variation with help of changing variable parameters in the introduced terms. Also here it is to constate a selfpermeation with wandering cutting lines.

3. Donut

The principle of this object is morphing between three mathematical forms of surfaces, the first based on a sphere and the second and third based on a transformed toroid. The result is an unusual movement of pulsation and torsion.

4. Wheel

The object is build up with two parts. The extension is changing during the rotation and also the colors depend on the angle.

5. Chain

The object in the form of a chain is put together with little cubes. Two of such chains are moving so that one sequence of cubes grasp into the other without touch. The 3-dimensional process should be presented in stereo view. The animation is to view with crossing visual angles (- a little glass of whisky is helpful !).

Summary

The results of this experiments have a strange position between reality and irreality.In spite of the impossibility of the physical realisation they have a concrete 3-dimensional form.The medium for presentation is the animation on the monitor or on the television screen.Also a 3-dimensional presentation is possible with help of stereo view or also with a holographic output device.Because the virtual reality will become increasing meaning in the art of tomorrow,the question of construction with material will become negligible.Cyberspace sceneries are good places to use it,but they could also be used in web design-as moving emblemes or simply as eye catcher.And also in internet galleries the possibility of physical production is not weigthy.The virtual sculpture,as discussed in this contribution,could lead far away from the classical type of sculpture in direction to abstract films or to the mobile art objects.But,and this is my opinion,it should-after all the transformations and movements-remain an uniform object,for instance based on the conception of cyclic processes or on random controlled deviations from the prototype.In the art the theoretical discussions should not have decisive meaning for the evaluation,the question,if the results are innovative and aesthetically relevant is more important.Without doubt the ignorance of physical and technical conditions opens a door to never seen objects and movements,and the occupation with this is stimulating for the creator and interesting for the spectator-especially as consequence of confrontation with new spatial structures.In the large field of computer art the virtual sculpture will be only a little facette,but here can originate fascinating results.

Bibliography

Herbert W.Franke:"Animation with Mathematica",Springer-Verlag Heidelberg,2001
Stephen Wolfram:"The Mathematica Book",Wolfram Media,Champaign,Il.,and Cambridge University Press,Cambridge,UK,1999

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Converted by Mathematica October 15, 2004