Visual Thinking through Constructive Function-based Shape Modelling
Valery Adzhiev and Alexander Pasko
Visual thinking or human operating with mental images is strongly imposed in modern culture
through education, media, and entertainment. On the other hand, computer support of visual
thinking remains on the ideology platform built more than 30 years ago. Computer graphics
as the basis of this support was originally oriented to producing eye pleasing pictures.
Nowadays real and synthetic worlds not only exist in parallel, but interact and interpenetrate
each other. This challenge has to be adequately addressed by new generation computer
technologies, which require re-thinking of the entire process (“pipeline”) starting from real
objects, their mental visualization and abstraction, mathematical description, computer
representation, interactive manipulation with the model, generation of images, fabrication and
utilization of new tangible objects thus creating augmented worlds. These worlds including
real and virtual components can be experienced, explored, and modified. There is a need for a
new paradigm for computer graphics in terms of both its mathematical and representational
basis, and applications.
We characterize technical problems of conventional computer graphics, where a computer is
practically used as a fast calculator processing a huge number of simple, mainly polygonal,
objects. Visualization in cultural heritage and virtual surgery give examples of using outdated
technologies applied for achieving new goals. Polygonal models provide not enough accuracy
to reach the goals of such critical applications. Another issue is preservation, reconstruction,
re-building, recreation, fabrication of real world objects from their computer models. Models
have to be precise enough to operate with them on the level close to real world operation. For
example, a constructive model of the Japanese temple Sazaedo made by our group can serve
not only for visual inspection but includes all the information necessary for its physical rebuilding.
The need for compact precise models with unlimited complexity has lead to the newly
emerging paradigm of procedural modeling and rendering. One of the possibilities to
represent an object procedurally is to evaluate a real function representing the shape and other
real functions representing object properties at the given point. Our research group proposed a
constructive approach to development of such function evaluation procedures. The main idea
of this approach is the creation of complex models from functionally defined simple ones
using various operations. Its complexity is concealed by its constructive nature and rather
elementary mathematics of primitive bricks (at least at the introductory steps). It is simple
enough to be mastered by a non-qualified user with minimal preparation time.
We applied this general paradigm in education, where it is very much in the spirit of a
constructionism theory. The main principle of this theory is active learning when learners
gain knowledge actively constructing artifacts external to themselves. For instance, research
at the MIT Media Laboratory has led to the LEGO MindStorms robotics kits allowing
children to build their own robots using “programmable bricks” with electronics embedded
inside. We have been developing not physical but virtual modeling and graphics tools that
make it possible to use an extensible suite of “bricks” with a possibility to modify them or to
introduce new ones on the fly. These tools are developed within an international free and
open source software project HyperFun. We illustrate our educational practice by examples of
courses for school and university students and by some creative projects with participation of
children, students, and artists. For instance, within the Augmented Sculpture Project students
from Moscow created models of real existing sculptures of a Russian artist, animated them
and produced new shapes using a metamorphosis operation, then students in Tokyo
manufactured one of the new models using 3D printing equipment. We are planning an
artistic installation combining virtual and real sculptures (both initial and newly generated) in
an augmented reality environment, where visitors can interact with all the artifacts and even
create new ones on the fly.
Another direction of this new paradigm development is combining it with the Empirical
Modeling principles developed at the Warwick University. This allows for extending
constructive shape modeling with the possibility of implementation of realistic behaviors of
shape models situated in multi-agent environments, providing open ended exploration and
experimentation with shared models. Specific software tools supporting such a combination
include HyperJazz and EmpiricalHyperFun. One of the prospective applications is the newly
emerging “serious computer games”.
We believe and present some evidence that constructive function-based shape modeling
coupled with new interactive techniques is a promising way to support visual thinking
through non-conventional computing.
References
1. A. Pasko, V. Adzhiev, A. Sourin, V. Savchenko, "Function Representation in Geometric Modeling:
Concepts, Implementation and Applications", The Visual Computer, 1995, Vol.11, No.8, pp.429-446.
http://www.hyperfun.org/TVC95.pdf
2. V. Adzhiev, A. Pasko, A. Sarkisov, "'HyperJazz' Project: Development of Geometric Modelling
Systems with Inherent Symbolic Interactivity", in book: "CSG'96: Set-Theoretical Solid Modelling
Techniques and Applications", Proceedings of the International Conference, Winchester, UK, 1996, pp.
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http://www.hyperfun.org/Adzhiev96HyperJazz.pdf
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Models, Academic Press, 2001, Vol. 63, No. 6, pp. 413-442.
http://www.hyperfun.org/GMOD02.pdf
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pp. 19-24.
VALERY ADZHIEV (vadzhiev@bournemouth.ac.uk) is a senior research fellow at the National Centre
for Computer Animation, Media School, Bournemouth University, Poole, UK.
ALEXANDER PASKO (apasko@bournemouth.ac.uk) is a professor at the National Centre for Computer
Animation, Media School, Bournemouth University, Poole, UK.