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Modern education technologies are destined to reflect the realities of a modern digital age. The juxtaposition of real and synthetic (computer-generated) worlds as well as a greater emphasis on visual dimension are especially important characteristics that have to be taken into account in learning and teaching. We describe the ways in which an approach to constructive shape modelling can be used to advancing creative visual thinking in artistic and technical education. This approach assumes the use of a simple programming language or interactive software tools for creating a shape model, generating its images, and finally fabricating a real object of that model. It can be considered an educational technology suitable not only for children and students but also for researchers, artists, and designers. The corresponding modelling language and software tools are being developed within an international HyperFun Project. These tools are easy to use by students of different age, specialization and abilities, and can easily be extended and adapted for various educational purposes in different areas. We applied the theoretical framework and software tools at different levels of education starting from elementary schools to doctoral thesis research in various areas related to artistic design and animation, computer graphics, programming languages, software development, and experimental and theoretical physics. In the process, the students learn how rather abstract mathematical expressions result in creating visually and meaningfully appealing computer-generated artefacts of a different nature that can eventually be fabricated as real objects using 3D printing means. Several application case studies in various areas of art, design, and technical education from different educational institutions and countries are presented. The obtained practical experience shows that this approach can be mastered and appreciated by students at different levels of education as an activity stimulating and supporting their creative thinking. The social context of the learning process allowing for collaborative work is also worth of noting. The presented case-studies demonstrate that seemingly complex modern means of geometric modelling and fabrication can easily be mastered not only by students oriented toward computer specialties but also by children (including those with disabilities) and artists.

This paper deals with 2D image transformations from a perspective of a 3D heterogeneous shape modeling and computer animation. Shape and image morphing techniques have attracted a lot of attention in artistic design, computer animation, and interactive and streaming applications. We present a novel method for morphing between two topologically arbitrary 2D shapes with sophisticated textures (raster color attributes) using a metamorphosis technique called space-time blending (STB) coupled with space-time transfinite interpolation. The method allows for a smooth transition between source and target objects by generating in-between shapes and associated textures without setting any correspondences between boundary points or features. The method requires no preprocessing and can be applied in 2D animation when position and topology of source and target objects are significantly different. With the conversion of given 2D shapes to signed distance fields, we have detected a number of problems with directly applying STB to them. We propose a set of novel and mathematically substantiated techniques, providing automatic control of the morphing process with STB and an algorithm of applying those techniques in combination. We illustrate our method with applications in 2D animation and interactive applications. [ABSTRACT FROM AUTHOR]

This article deals with creating artistic shapes in a cubist style. The authors propose adding cubist features to (or cubification of) time-variant sculptural shapes. A new concept of a 4D cubist camera is introduced for multiple projections from 4D space-time to 3D space, and 3D printing for stop-motion animation is applied. [ABSTRACT FROM AUTHOR]

The SHIVA project was designed to provide virtual sculpting tools for young people with complex disabilities, allowing them to engage with artistic and creative activities that they might otherwise never be able to access. Their creations are then physically built using 3D printing. To achieve this, the authors built a generic, accessible GUI and a suitable geometric modeling system and used these to produce two prototype modeling exercises. These tools were deployed in a school for students with complex disabilities and are now being used for a variety of educational and developmental purposes. This article presents the project's motivations, approach, and implementation details together with initial results, including 3D printed objects designed by young people with disabilities. [ABSTRACT FROM AUTHOR]

The paper presents a novel technique based on extension of a general mathematical method of transfinite interpolation to solve an actual problem in the context of a heterogeneous volume modelling area. It deals with time-dependent changes to the volumetric material properties (material density, colour, and others) as a transformation of the volumetric material distributions in space-time accompanying geometric shape transformations such as metamorphosis. The main idea is to represent the geometry of both objects by scalar fields with distance properties, to establish in a higher-dimensional space a time gap during which the geometric transformation takes place, and to use these scalar fields to apply the new space-time transfinite interpolation to volumetric material attributes within this time gap. The proposed solution is analytical in its nature, does not require heavy numerical computations and can be used in real-time applications. Applications of this technique also include texturing and displacement mapping of time-variant surfaces, and parametric design of volumetric microstructures. [ABSTRACT FROM PUBLISHER]

Enabling animators to smoothly transform between animated meshes of differing topologies is a long-standing problem in geometric modelling and computer animation. In this paper, we propose a new hybrid approach built upon the advantages of scalar field-based models (often called implicit surfaces) which can easily change their topology by changing their defining scalar field. Given two meshes, animated by their rigging-skeletons, we associate each mesh with its own approximating implicit surface. This implicit surface moves synchronously with the mesh. The shape-metamorphosis process is performed in several steps: first, we collapse the two meshes to their corresponding approximating implicit surfaces, then we transform between the two implicit surfaces and finally we inverse transition from the resulting metamorphosed implicit surface to the target mesh. The examples presented in this paper demonstrating the results of the proposed technique were implemented using an in-house plug-in for Maya™. [ABSTRACT FROM AUTHOR]

In this paper we describe an approach to computer-aided sculpting concerned with the creation and modification of digital models based on physical abstract sculptures. We begin by presenting a survey of current methods for the creation of computer-aided sculptured artefacts. Then we proceed to present some original methods and tools based on the function representation of geometric models. We introduce a specialized computer language, named HyperFun, which facilitates the modelling of complex objects. As well as presenting computer-generated animated models of pre-existing sculptures by Russian artist Igor Seleznev, we also show how some interesting novel shapes can be generated using the HyperFun system. Finally we outline two advanced projects concerned with creating a sculpture-based augmented reality which allows for the interactive participation of the observer. In this paper, we present experimental results, which hopefully have some artistic appeal. These results were produced by an international team of researchers and students collaborating through the Internet. Copyright © 2005 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]