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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 Visualization in cultural heritage and virtual surgery give examples of using outdated technologies applied for achieving new goals.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 re-building. 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 ЬЧаФTV 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.  HYPERLINK "http://www.hyperfun.org/TVC95.pdf" 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. 183-198.  HYPERLINK "http://www.hyperfun.org/Adzhiev96HyperJazz.pdf" http://www.hyperfun.org/Adzhiev96HyperJazz.pdf 3. A. Pasko, V. Adzhiev, B. Schmitt, C. Schlick, “Constructive Hypervolume Modelling”, Graphical Models, Academic Press, 2001, Vol. 63, No. 6, pp. 413-442.  HYPERLINK "http://www.hyperfun.org/GMOD02.pdf" http://www.hyperfun.org/GMOD02.pdf 4. V. Adzhiev, P. Comninos, A. Pasko, “Augmented Sculpture: Computer Ghosts of Physical Artefacts”, Leonardo journal, MIT Press, 2003, Vol.36, No.3, pp.211-219.  HYPERLINK "http://www.hyperfun.org/ASP_Leonardo.pdf" http://www.hyperfun.org/ASP_Leonardo.pdf 5. C.  HYPERLINK "http://www.u-aizu.ac.jp/%7Evilb/" Vilbrandt, G.  HYPERLINK "mailto:%20gip@tokyo.com" Pasko, A.  HYPERLINK "http://www.k.hosei.ac.jp/%7Epasko/" Pasko,  HYPERLINK "mailto:%20p.fayolle@free.fr" P.-A. Fayolle, T.  HYPERLINK "mailto:%20turlif@turlif.org" Vilbrandt, J. R.  HYPERLINK "mailto:%20jan@pollux.csustan.edu" Goodwin, J. M.  HYPERLINK "http://www.cs.ucla.edu/%7Ejmg/jmg.html" Goodwin, T. L.  HYPERLINK "http://www.kunii.com" Kunii, "Cultural heritage preservation using constructive shape modeling", Computer Graphics Forum, 2004, Vol. 23, No.1, pp. 25-41.  HYPERLINK "http://hyperfun.org/CGF_003[024-041].pdf" http://hyperfun.org/CGF_003[024-041].pdf 6. R. Cartwright, V. Adzhiev, A. Pasko, Y. Goto, T. Kunii,“Web-based Shape Modeling with HyperFun”, IEEE Computer Graphics and Applications, 2005, Vol. 25, No. 2, pp. 60-69.  HYPERLINK "http://www.hyperfun.org/Cartwright_CGAprefinal.pdf" http://www.hyperfun.org/Cartwright_CGAprefinal.pdf 7. A. Pasko, V. Adzhiev, Y. Goto, C. Vilbrandt, “Function-based Shape Modeling Framework in Multilevel Education”, Proc. 26th Annual Conference of the Europian Association for Computer Graphics EUROGRAPHICS’2005, Education papers, Dublin, ed. by J.J.Bourdin and H.McCabe, 2005, pp. 19-24. 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