Research and development work on functionally-based geometric modeling has been lasting for more than 10 years. A comprehensive information about the theme can be found on F-rep Home page that presents descriptions of selected research topics, list of publications, images and animation. Here, I would like to emphasize R&D concerned with two themes I am especially interested in: user-related problems and multidimensionality in the context of functionally-based modeling systems.
Our approach to "User Interface" matters stems from the conviction that users need flexible high-level tools to do modeling work. Besides, we think that there are different categories of users having different level of expertise and working in a variety of application fields. All of them can require their own modeling system, perhaps with a particular suite of geometric objects, transformations and relations. We believe that such the system can easily be built on a base of universal "F-rep Kernel Geometric Modeling System" that is made extendible to be adapted to different application domains with customizing for needs of particular users. To implement such technology, the basic set of API procedures should be provided as well as a high-level geometric programming language.
We have no doubt that modern geometric modeling systems should have GUI enabling the user to specify the model using direct manipulation and other conventional interactive techniques. However, we see principal drawbacks of GUI, in particular its limited design vocabulary. That is why we attach great importance to "symbolic" user interface based on a high-level geometric programming language. Such a language can serve not only as a suitable instrument for describing functionally-based geometric model but allows to introduce textual definitions of new objects, transformations and relations that can be stored in the system's library. It means that the user can extend the system "in a symbolic manner" to form his/her personal modeling system. We have an intention to develop a technology of creating geometric systems with combining "symbolic" interface with extendible GUI. Another direction of our research concerned with the symbolic definition of a functional-based geometric model is applying genetic programming techniques for generating new symbolic geometric model on the base of initial one.
Personally, I was a designer and (to some extent) implementor of a few geometric languages; the first of them - "CALAN" was built in "HyperSurf" modeling system that has been used in student's exercises within Computer Graphics course both in MEPhI and University of Aizu for many years. Currently, we are working on a few modeling systems of a new generation that are based on a novel high-level geometric language HyperFun . Another geometric language HyperJazz based on principles of definitive programming paradigm is intended to be built in an interactive geometric environment within Empirical Modeling framework.
Multidimensional point sets (shapes) appear in different areas such as:
Multidimensional shapes within F-rep framework are defined with continuous function of several coordinate variables. On the other hand, a multimedia object can be treated as a multidimensional object with Cartesian, visual, audio, haptic and other "multimedia coordinates". These two worlds presently coexist without much interaction. The known areas bridging this gap are computer animation and multidimensional visualization. Time-dependent 3D shapes can be treated in animation as 4D objects. Multidimensional visualization represents discrete multidimensional points and voxel data as image sets.
We propose an approach to more close integration of multidimensional spaces of shape modeling and multimedia by introducing a space mapping between abstract coordinate variables and multimedia coordinates. The essence of the mapping is setting correspondence between intervals each coordinate variable takes and variation intervals that multimedia coordinates have (time interval means life time of the multimedia object, color varies inside color space, such as RGB cube etc. ). Such mapping establishes correspondence between the multidimensional shape and the multimedia object and allows for:
The approach is supported by a suite of tools oriented towards an end user. High-level language HyperFun is the user's instrument for describing a multidimensional model within a hybrid (multirepresentational) modeling system with F-rep in its core. Recently, our team (A. Pasko, V. Adzhiev, E. Fausett) has produced animation "Homotopic Fun in 5D space" that was awarded a prize at Dream Centenary CG Grand Prix 99 held in Japan. This prestigious international contest has attracted more than 500 submissions from 25 countries (Oscar winner of 1999, animation "Bunny" has won the Grand Prix). Our animation was also shown at Eurographics'99 Audiovisual and Multimedia Show (Milano, Italy, September, 1999).
Empirical Modeling (EM) offers both a broad foundational perspective on computing and a novel practical approach to modeling. Central to the EM perspective is an emphasis on the power of the computer to represent state which is easily interpretable, preferably in "real-world" terms. The choice of the epithet "empirical" reflects the fact that EM methods are rooted in observation and experiment. EM is supposed to deal with the systems that are inherently concurrent, and where behaviour, concurrency, agency, dependency, action, state are notions that can most appropriately be formulated with reference to the interaction between a person (or person-like intelligent agent) and the world.
In the Empirical Modeling context, both human participants and inanimate components are represented as agents. Observation-oriented modeling is used to describe the interaction between agents with help of special LSD ("Language for Specification and Description") notation. An LSD analysis is intended to capture the basic features of the initial conceptualisation (or mental picture) of a subject by a modeller. It is therefore initially a provisional, subjective, personal analysis. It will typically represent one or more viewpoints (via the agents identified) on the subject. LSD model is built of agents that act in parallel, interact with each other and with the modeller. We propose an underlying coordination model based on a generative communication scheme relying upon a message queue as a common communication channel and a multi-level priority mechanism as a means for forming and handling computational threads.
We are currently developing "LSD- engine" - an interactive tool for empirical modeling of agent-based systems with concurrent behaviour. As to application area, it is Software and Systems Development in a quite broad sense. EM can help to model the systems where people cooperatively work and interact with each other as well as with devices of diverse nature. In particular, LSD-engine that is suitable for rapid prototyping can be especially useful at the early stages of design and model development. There can be such prospective areas as: Communicating Agents Systems (e.g., telephone networks), Engineering Design (e.g., vehicle cruise control simulation), Educational Technologies (e.g., rapid building models of physical phenomena), Shape Modeling with Behaviour (e.g., simulation of growth of a biological cells colony). More information about Empirical Modeling Project can be found on Empirical Modeling Page maintained by Empirical Modeling Group (Department of Computer Science, University of Warwick, UK).
The system is being implemented on Silicon Graphics workstations with user's manual to be available on the Web. Several students' exercises are implemented on the basis of:
The system is being implemented on Windows NT platform. The user will have possibilities:
The system named "LSD-engine" is being implemented on PC under MS Windows. The system allows:
All these projects are being developed in cooperation with professors Alexander Pasko and Vladimir Savchenko (Shape Modeling Lab, University of Aizu), Dr. Meurig Beynon (University of Warwick, Coventry, England), Mr. Anatoli Ossipov, Mr. Alexander Rikhlinsky, Mr. Alexey Bataev, and Mr. Roman Korovyatsky (students, Moscow Engineering Physics Institute).