In this cloud computing era, great amount of business application system data of various kinds are processed in the `cloud' as circumstances evolve. But if there is no proper data modeling methodology, data in cloud will be beyond understanding and controllable. We consider the Incrementally Modular Abstraction Hierarchy (IMAH), which is an effective and rigid data model-centered concept of topological modeling that reflects such instant changes in information worlds, to be the most suitable, and we implemented the model as a computing system which is called the Cellular Data System (CDS). In this paper, we take up some examples of BOM (Bill of Materials) information management to demonstrate how to simplify business application data modeling by the use of CDS.

In this big data era, if there is no proper data modeling methodology, big data in cloud will be beyond understanding and controllable. We consider the Incrementally Modular Abstraction Hierarchy (IMAH) to be able to model the world of big data as it is. In this paper, we focus on graph data modeling based on IMAH. Internet of Things (IoT), which is the hottest topic in cloud computing research, always includes graph data connecting information of things on the Web. The graph data model, which deals with nodes and edges, is considered a special case of a topological space dealing with subsets as an element mathematically. We exemplify the designed applied geometrical functions in the case study of a route detection application to verify their effectiveness.

In the era of cloud computing, data is processed in a Cloud, and data and its dependencies between systems or functions progress and change constantly within the cloud, as a user's requirements change. Such information worlds are called cyber worlds. We need a more powerful mathematical background which can model the cyber worlds as they are, and a finite automaton for implementing it as a computer system. We consider the Incrementally Modular Abstraction Hierarchy (IMAH) to be most appropriate to model the cyber worlds. We have developed a data processing system called the Cellular Data System (CDS) implementing IMAH. In this paper, we introduce a position information formula, which identifies the relative position of a specified factor in a formula, and its processing map, which obtains a sub-formula using the position information formula in CDS. This function is inevitable in the development of business applications where data have a fixed form, such as parts list data. We show the effectiveness of the formula by taking up a case study of component configuration information management in car manufacturing. In the case study, it is demonstrated that design component configuration information and manufacturring component configuration information are consistently managed even when component configuration frequently changes.

Homotopy type theory has been developed by us for over two decades and is applied to big data to eliminate the inevitable bottleneck of big data implementation originating from inherent combinatorial explosion. An incrementally modular abstraction hierarchy, IMAH in short, is used in 7 layers starting from homotopy, then type, and ending with presentation. Big data is in cyber worlds that are being formed in cyberspaces as computational spaces. Now cyberspaces are rapidly expanding on the Web either intentionally or spontaneously, with or without design. It is quite different in its emphasis of homotopy type theory as recently reported with emphasis on mathematical proof automation and computer verification. Widespread and intensive local activities are melting each other on the web as big data globally to create cyber worlds. The major key players of big data in cyber worlds include e-finance that trades a GDP-equivalent a day and e-manufacturing that is transforming industrial production into Web shopping of product components and assembly factories. Lacking proper theory and design, big data has continued to grow chaotic and are now out of human understanding and control. This research first presents a generic theoretical framework as an incrementally modular abstraction hierarchy, based on homotopy type theory, provides an axiomatic approach to theorize the potentials of big data in cyber worlds, and shows that the incrementally modular abstraction hierarchy automate big data application development and eliminates the need for design verification and validation. It also makes the systems developed secure from the all sort of attacks.

In the era of "Big Data", a large amount of unstructured and diverse data is being stored, and data and its dependencies between systems or functions progress and change constantly, as users' requirements change. Such information worlds are called cyber worlds. We need a more powerful mathematical background which can model the cyber worlds as they are. We consider the Incrementally Modular Abstraction Hierarchy (IMAH) to be most appropriate for modeling the dynamically changing cyber worlds by descending from the most abstract homotopy level to the most specific view level, while preserving invariants. In our research, we have developed a data processing system called the Cellular Data System (CDS) based on IMAH. In this paper, firstly we introduce an aggregation function, positioned as an applied function of the attachment function. Secondly, we deal with matrix-structured data for parts information management by CDS, solving the difficulty arising from the complexity of information about parts and combinations of parts.

Category theory, which has been applied to various fields of computer science and information technology, now provides a mathematical foundation for the development of information systems. The Meiji restoration, which is characterized by a flexible structure where making and breaking alliances among politicians were common and policy migrations of the politicians occurred dynamically in accordance with the progress of the restoration, is analyzed using category theory. Four political goals, which were initiated at the beginning of the Meiji restoration, were achieved by politicians who sometimes cooperated with each other, other times opposed each other, and still other times changed their policy in consideration of the political and financial environments. It is valuable for computer science to describe a dynamically changing system formally using conceptual mathematics. This paper clarifies the dynamic relationship changes of politicians using category theory. In particular, alliance changes of politicians between incidents are represented using functorial databases that are a recent and useful application of category theory.

Homotopy type theory, which generalizes equivalence relations at the most abstract level, is a leading edge science in mathematics and computer science. We have revised our design and modeling method using homotopy type theory. The previously proposed method, which is called the incrementally modular abstraction hierarchy (IMAH), has been applied in many fields of computer science and information technologies. IMAH uses set theory on the second highest abstraction level to clarify sets and their components in a developing system. The clarification of sets and components is more accurately accomplished using homotopy type theory because equivalence relations among components are defined more formally and specifically using the homotopy type. The revised IMAH is applied to clay flower creation. Descending the abstraction hierarchy, the process of clay flower creation is embodied by adding additional concrete properties. Functorial databases are generated in conjunction with defining the clay flower creation processes at each abstraction level.

Information worlds are constantly developing in cloud. In data management, the overlapping of data often brings about a lack of data consistency. We consider the attaching function by an equivalent relation in the Incrementally Modular Abstraction Hierarchy to be quite effective to solve the data overlap problem. In this paper, we design a metadata centralized space, a data centralized space, and their Interco version maps using Formula Expression. We then apply them to file data management, where data oftentimes becomes unexpectedly overlapped in metadata schema-centered management. These help users to arrange dynamic worlds from a data-centric viewpoint.

Incrementally modular abstraction hierarchy (IMAH) based on algebraic topology is a general design method that is applicable to many fields including computer science, information technology and software engineering. Despite the fact that many development examples using IMAH have been announced in a variety of application fields, the number of researchers utilizing IMAH in their application fields is still limited because homotopy theory is a difficult concept for non-mathematical people to gasp. In this paper we utilize push outs and pullbacks instead of homotopy theory to explain how IMAH can be employed to develop systems. Push outs and pullbacks are general concepts encompassing set theory, homotopy theory, and category theory. We describe utilization of IMAH with push outs and pullbacks in the environment of a divide-and-conquer method, where a complicated system is divided into two simple subsystems. When dividing a system or integrating two subsystems, the mathematical concepts of pushout and pullback can be employed. Push outs and pullbacks are also utilized in descending and ascending an abstraction hierarchy, which is an essential power of IMAH. We design a chair, a concurrent system, and Google maps using IMAH to illustrate its utility.

In this "cloud" computing era, various kinds of values are being created in cyber worlds at every moment, causing the worlds to become increasing complex and making it difficult for us to recognize the whole. Consequently, we need a more powerful mathematical background that can accurately model the cyber worlds in the "cloud" as they are. We consider the Incrementally Modular Abstraction Hierarchy to be appropriate for modeling the dynamically changing cyber worlds by descending from the most abstract homotopy level to the most specific view level, while preserving invariants. We have developed a data processing system called the Cellular Data System based on IMAH. In this paper, we introduce basic geometrical design into CDS, and apply CDS to develop the core logic of a route search system, used in most traffic industries but costly due to its complexity, to verify its effectiveness.

In the era of cloud computing, data is processed in a gCloudh, and data and its dependencies between systems or functions progress and change constantly within the cloud, as a user's requirements change. Such information worlds are called cyber worlds. We need a more powerful mathematical background which can model the cyber worlds in the "cloud" as they are. We consider the Incrementally Modular Abstraction Hierarchy (IMAH) to be appropriate for modeling the dynamically changing cyber worlds by descending from the most abstract homotopy level to the most specific view level, while preserving invariants. We have developed a data processing system called the Cellular Data System (CDS) based on IMAH. In this paper, we introduce numerical value identifier processing into condition formula processing, which is the main search function of CDS, as an applied function on the presentation level of IMAH. This function is effective in business application development because subsets, including numerical values from formulas, can be taken out and be calculated by the map. We show its effectiveness through examples of a calculation system for a Bill of Materials (BOM), solving the difficulty arising from the changes of component configration and inconsistent spelling of parts.

Extreme diversities, versatility and dynamism of cloud computing applications with its high availability through smart devices such as smart phones and media are shown to be supported by the cyber world modeling in an incrementally modular abstraction hierarchy (IMAH) with homotopy extension property (HEP) and homotopy lifting property (HLP), as a transparent and highly universal modeling of smart cloud computing businesses to overcome combinatorial explosion of smart computing. It works to realize cost effective and visible businesses with high social impacts, both globally and locally, contributing to clarify smart cloud computing in the smart cloud imagery business.

The theoretical procedure for making a three dimensional landscape sketch is proposed in this paper. At the first stage, the critical points such as summits, ravine bottoms and passes are allocated by a user. These critical points construct fundamental properties of the mountain that a user tries to draw. Applying Morse theory to these critical points, the landscape of the mountain is defined as a sequence of a CW-complex that explains how the surface structure of the mountain changes when the mountain is formed from the bottom to the top step by step. The CW-complex is then concreted by obtaining skeletons from the Reeb graph of the mountain. The skeleton consisting of contour lines is modified without changing its topological structure by giving ranges and ravines. These lines constitute a series of continuous critical points and become invariants as well as summits, ravine bottoms and passes. At the final step, the system automatically generates a proposed landscape from the skeleton using Nurbs lines and surfaces or polygon meshes. By rendering the landscape, a user can change its shape by modifying ranges and ravines until the user satisfies it.

In the era of cloud computing, data is processed in a "Cloud", and data and its dependencies between systems or functions progress and change constantly within the cloud, as a user's requirements change. Such information worlds are called cyber worlds. We need a more powerful mathematical background which can model the cyber worlds in the "cloud"as they are. We consider the Incrementally Modular Abstraction Hierarchy (IMAH) to be appropriate for modeling the dynamically changing cyber worlds by descending from the most abstract homotopy level to the most specific view level, while preserving invariants. We have developed a data processing system called the Cellular Data System (CDS) based on IMAH. In this paper, we introduce numerical value calculation, exponential calculation and the processing maps on the presentation level of IMAH into CDS. This function is quite effective in business application development because numerical values and exponential identifiers can be put into formulas and be calculated. We show its effectiveness through examples of core processing of a cellular phone charge calculation system using numerical value and exponential calculations.

In the era of cloud computing, data is processed in "Cloud", and data and its dependencies between systems or functions progress and change constantly within the cloud, as auser's requirements change. Such information worlds are called cyber worlds. We need a more powerful mathematical background which can model the cyber worlds in the "cloud"as they are. We consider the Incrementally Modular Abstraction Hierarchy (IMAH) to be appropriate for modeling the dynamically changing cyber worlds by descending from the most abstract homotopy level to the most specific view level, while preserving invariants. We have developed a data processing system called the Cellular Data System (CDS) based on IMAH. In this paper, we introduce into CDS the applied functions for calculating numerical values, and apply CDS to develop the core logic of an estimate system, used in most industries but costly due to its complexity, to verify its effectiveness.

Visualization is effective to understand complicated and sophisticated phenomena. Joiner, which joints pieces of woods and has complex process of jointing, is analyzed and modeled for visualization using homotopy theory and attaching maps. Joining the two pieces of woods changes their structures differently, which depends on jointing techniques. The paper describes difference between the tenon-mortise and lap joints in the fundamental group of homotopy. As the properties of the fundamental group are invariants, they are preserved through modeling from the abstract level to the specific one. When describing the process of jointing, two piece of woods are indirectly connected through a virtual attaching space using an attaching map, which avoids unnecessary consideration of piece relations. Using these concepts of homotopy, the process of jointing two pieces of woods are modeled from the abstract level in homotopy to the middle level of cellular structured spaces, to the specific one of physical presentation.

Emergence of cloud computing combined with its high availability through smart devices such as smart phones and media is requiring a transparent and highly universal modeling of the worlds in cloud computing to overcome combinatorial explosion of computing, that are actually cyber worlds. Hence, appropriate scalable modeling of cyber worlds meets the requirements effectively. Extreme diversities, versatility and dynamism of cloud computing applications are shown to be supported by the cyber world modeling in an incrementally modular abstraction hierarchy (IMAH) with homotopy extension property (HEP) and homotopy lifting property (HLP).

A new approach for designing and modeling enterprise systems is described. The homotopy lifting property (HLP) is used to design an enterprise system in a bottom up way. As an example, task changes in a department are designed and implemented by our approach: the incrementally modular abstraction hierarchy (IMAH) starting at the most abstract level of homotopy and ending at the most concrete level of program codes. At first, the HLP is constructed as the most abstract level. Then, task changes and a state transition diagram, which constitute of two spaces of the HLP are defined from an abstract level to a concrete level. Then, agent diagrams are obtained in a bottom-up way. The agent diagrams are transformed from an abstract level to a concrete level until program codes written by the C-like programing language are implemented on an event-driven and multi-thread processor XMOS. While carrying out these procedures, invariants are preserved to avoid unnecessary testing, which usually consumes a large amount of time and cost in the traditional approaches. The established method is also effective in modeling an designing cyber worlds.

In designing dynamic situations such as cyberworlds, we consider the Incrementally Modular Abstraction Hierarchy (IMAH) to be an appropriate mathematical background to model dynamically changing cyberworlds by descending from the most abstract homotopy level to the most specific view level, while retaining invariants. One of the distinctive features of IMAH is to define an adjunction space (an attaching space) level. Cyberspaces are then attached by an equivalence relation, where the attached areas of the spaces are equivalent. The cellular data system (CDS) we developed based on IMAH is equipped with an automatic attaching function defined on the adjunction space level, and in this paper we have applied the function to organizational file permission information management. The function helps a user to search for the data he/she wants from data storage attaching spaces automatically.

Cyberworld systems are characterized by distributed functions and mobile communication. The pi-calculus gives theoretical background for designing and modeling such systems. In this paper, an original method for designing mobile communication systems executed in parallel in the cyberworlds theoretically and systematically is discussed using homotopy theory in the most modern field of mathematics. Homotopy theory gives computer science the theoretical back ground of designing and modeling in the most general way. The homotopy lifting property and homotopy extension property categorizing topological spaces in mathematics are effective in bottom-up / top-down development in computer science. By applying it for designing and modeling complicated systems in the cyberworlds, the paper shows incrementally modular abstraction hierarchy starting with homotopy theory and ending with program codes makes a system development theoretical and systematical.

Cyberworlds are information worlds where data and its dependencies are always changing and may evolve unpredictably, just like living things. Thus far, it has been difficult to model cyberworlds with higher freedom using the existing model because of its complexity. We believe that Incrementally Modular Abstraction Hierarchy (IMAH), which has an abstraction hierarchy preserving invariants from the abstract to the concrete level, and which was invented by one of the authors (T. L. Kunii), makes it possible. We have developed a data processing system called Cellular Data System (CDS) based on IMAH. With CDS, you can express any space, with forms or not, and attach or divide spaces by an equivalence relation to output information like you do in your head. In this paper we have designed and implemented wide-use algebra called unit calculation algebra on the presentation level in IMAH as an application function of CDS, and we have shown its effectiveness through examples.

The mathematical structure of cyberworlds is clarified based on the duality of homology lifting property and homotopy extension property. The duality gives bottom-up and top-down methods to model, design and analyze the structure of cyberworlds. The set of homepages representing a cyberworld is transformed into a state finite machine. In development of the cyberworld, a sequence of finite state machines is obtained. This sequence has homotopic property. This property is clarified to map a finite state machine to a simplicial complex. Wikipedia, bottom-up network construction and top-down network analysis are described as examples.

Currently, in the development of business applications, difficulties occasionally arise between the customer side and the supplier side, causing delays and higher development costs. To deal with this, we propose a new development method for business applications to validate them by invariant preservation based on equivalence relations. We have realized it by designing an algebraic expression called formula expression and applying the algebra to the design of each space in the cellular model. The system is called a cellular data system (CDS). It can become a common tool for both sides to make agreements efficiently in the future. Moreover, because you can manage data which has any form by using CDS, it is appropriate when dealing with data not only in business application development but in the cyberworld where no data manager exists

The incrementally modular abstraction hierarchy, which specifies architecture and modeling of cyberworlds and defines the most general invariants at the higher levels and preserving them at the lower levels, are applied to software development to show that its linear increment of modules prevents combinatorial explosion of design- and test-processes

Abstract An incrementally modular abstraction hierarchy is known to effectively linearize cyberworlds and virtual worlds, which are combinatorially exploding and hardly managed. It climbs down from general level to specific model preserving the higher level modules as invariants. It not only prevents the combinatorial explosion but also benefits the reuse, development, testing and validation of cyberworld resources. By applying this incrementally modular abstraction hierarchy to a kaleidoscope animation, its architecture and modeling is also specified in this paper as a typical case of cyberworlds. In particular, a homotopy lifting property and a homotopy extension property, which satisfy a duality relation, are also described to show how a kaleidoscope world is systematically created top‐down from the whole system and bottom‐up from the components. Copyright © 2006 John Wiley & Sons, Ltd.

The globalization of the real world we live has been almost exploding in its speed and scale spatiotemporally in all the key aspects including business, economy, industry, education and culture, making it hard for human beings to cognize what's going on and deal with them . Thus the links between the real world and conceptual world is getting weaker. The globalization is mainly driven by the Web-based activities in their cyberspaces creating cyberworlds as seen in e-business, e-commerce, e-manufacturing and cultural heritages through the Web and on the Web. Thus the links between the real world and cyberworlds are ever becoming tighter nonlinearly in time and space. It is now crucial to find a way to automatically integrate the dynamically changing worlds, namely the real world, cyberworlds and conceptual worlds, fast enough to cope with the rapid changes. It is a hard task owing to the vast complexity of the worlds to be integrated, and it requires an advanced abstraction modeling. This is an interim progress report on it, presenting the outline based on the previous works on the abstraction hierarchy modeling of cyberworlds to realize an incrementally modular hierarchical modeling of cyberworlds via attaching spaces as quotient spaces and attaching maps. Attaching spaces are also for unique integration of the worlds that are real, cyber, and/or conceptual. They also guarantee liner interoperability of the integrated worlds to eliminate the combinatorial explosion of the computing in their complexity

In the current information society, open-source software products such as Linux have attracted considerable attention due to their widespread public and private use. Information Technology-oriented firms tend to employ open-source software as a part of their business strategy, and as a result conventional business behaviors and customs have begun to break down. Such software has hitherto been discussed mainly in relation to software development, politics, economics, and sociology, but it can and should also be investigated from educational aspects as a means for solving some of the problems affecting society. In this paper, therefore, we explore the potential of open-source learning from the point of view of cyberworlds. We propose here an open-source learning model named the Biotope model on the basis of legitimate peripheral participation and scale-free networks as a potential contribution to the improvement and evolution of our society

for cyberworlds' sessions of the conference.

Considering the increasingly large impacts and potentials of cyberworlds as seen in e-financing that trades GDP equivalent in a day, we human beings living in the real world are at the stage of needing to firmly identify the nature of cyberworlds. It is clear that if we continue to deal with cyberworlds as we have been, they grow chaotic beyond human understanding and control, endangering the real world. In an effort to make cyberworlds an academic discipline to overcome the critical situation, we axiomatize cyberworlds and then theorize them as Euclid did in identifying shapes in the real world.

We apply topological analysis to functionally based shape metamorphosis. Functionally based methods have two problems: shape interpolation is applied without defining the topological information and the time moments of topological changes are not known. Thus, it is difficult to identify the time intervals for key frames of shape metamorphosis animation. Moreover, information on the types of the topological changes is missing. We present a method of the critical points detection based on the Morse theory and classification using the Hessian matrix for solving these problems. The defining function of the linear metamorphosis is treated as a height function. By analyzing how the critical points are changing at a particular height level, we detect the critical points of the metamorphosis process. The critical points can be used for ease in/ ease out effects in animation. In addition, we classify the detected critical points into maximum point, minimum point, and saddle point types. Using the type of the critical points and the sign of the function time derivative at the critical points, we can define the topological information for the shape metamorphosis. We illustrate these methods using shape metamorphosis in 2D and 3D spaces.

We apply topological analysis to functionally based shape metamorphosis. The time-dependent shape is defined using homotopy. The advantage of this method is the automatic generation of the intermediate shapes between the key shapes of different topology types. To complete the method, we have to find a way to automatically detect the critical points on the time axis while the shape undergoes topological changes. These critical points can be later used for generation of non-linear time steps distribution along the time axis, for example, for providing ease-in/ease-out effects in animation. We present a new method for analysis of shape metamorphosis based on the Morse theory, oriented to analysis of a height function. Although we analyze the shape in an N-dimensional space, the height function is defined in the N+2 dimensional space with N point coordinates and two additional coordinates of the defining function and time values. We can analyze how the critical points are changing in the given height level, which takes only zero value of the shape defining function. In this paper, we present this method in comparison with typical Morse theory analysis using simple objects in 2D and 3D spaces.

We further develop a new approach to shape metamorphosis using bounded blending operations in space-time. The key steps of the metamorphosis algorithm are: dimension increase by converting two input kD shapes into half-cylinders in (k+1)D space-time, applying bounded blending union with added material to the half-cylinders, and making cross-sections for getting intermediate shapes under the transformation. This approach is extended here in two directions. First, the problem of "jump" in animation or the rapid transition between shapes in the given interval is solved using "smoothed" versions of half-cylinders which undergo bounded blending. Second, the approach is extended to 3D initial and final shapes with the bounded blending union operation applied to the corresponding "smoothed" 4D space-time half-cylinders.

Abstract Issues of digital preservation of shapes and internal structures of historical cultural objects are discussed. An overview of existing approaches to digital preservation related to shape modeling is presented and corresponding problems are considered. We propose a new digital preservation paradigm based on both constructive modeling reflecting the logical structure of the objects and open standards and procedures. Constructive Solid Geometry (CSG) and Function Representation (FRep) are examined and practically applied as mathematical representations producing compressed yet precise data structures, thus providing inter‐operability between current and future computer platforms crucial to archiving. Examples of CSG reconstruction of historical temples and FRep modeling of traditional lacquer ware are given. We examine the application of fitting of a parameterized FRep model to a cloud of data points as a step towards automation of the modeling process. Virtual venues for public access to cultural heritage objects including real time interactive simulation of cultural heritage sites over the Web are discussed and illustrated.

Abstract Shape transformation between objects of different topology and positions in space is an open modelling problem. We propose a new approach to solving this problem for two given 2D or 3D shapes. The key steps of the proposed algorithm are: increase dimension by converting two input kD shapes into half‐cylinders in (k+1)D space–time, applying bounded blending with added material to the half‐cylinders, and making cross‐sections for getting intermediate shapes under the transformation. The additional dimension is considered as a time coordinate for making animation. We use the bounded blending set operations in space–time defined using R‐functions and displacement functions with the localized area of influence applied to the functionally defined half‐cylinders. The proposed approach is general enough to handle input shapes with arbitrary topology defined as polygonal objects with holes and disjoint components, set‐theoretic objects, or analytically defined implicit surfaces. The obtained unusual amoeba‐like behaviour of the shape combines metamorphosis with the non‐linear motion. Copyright © 2004 John Wiley & Sons, Ltd.

We present an interactive painting system for generating high quality and artistic calligraphy characters and black ink paintings. The system is based on our original algorithm that is unique in physically simulating the dynamic diffusion of liquid ink into absorbent painting paper. The algorithm creates remarkably realistic strokes efficiently. For rendering 20 strokes in different size, it takes only 30 seconds on a personal computer, fast enough for interactive performance. By using this system, the users can create realistic strokes with delicate "Nijimi"-rendering, "kasure"-rendering effects, which are essential to black ink painting and modern calligraphy.

New top-down eLearning tools for hardware logic design courses using the cellular methods are presented that enable students to keep focusing on their primary interests so that they can achieve complex logic circuits design successfully. In a modern logic design classroom, hardware description languages such as VerilogHDL are mostly used to describe circuits for FPGAs. The circuit in each module is described in VerilogHDL and the entire circuit is implemented by combination of designed modules. These HDL descriptions are wrapped in XML and enriched by a specially extended XML vocabulary, in order to share designed modules among learners on the Web. Although XML gives us a common and convenient Web framework, it becomes difficult to verify, validate, and maintain conformance among designed modules if the system becomes very large. To overcome this problem, we employed the cellular models that ensure the consistency among design modules and support a top-down design methodology. The proposed top-down eLearning tools can generate these circuit design data, distribute them to the learner, and manage the design database. The circuit design data wrapped in XML vocabulary are offered to the learner as a self-learning material of the courseware using the top-down (i.e. goal-oriented) method, according to the demand.

The diversity of cyberworlds makes it hard to see consistency in terms of invariants. The consistency requires for us to abstract the most essentials out of the diversity, and hence the most abstract mathematics. It has been true in science in general, and in the theory of universe in particular. What are the most essential invariants in modeling cyberworlds? A branch of the most abstract mathematics is topology. For topology to be computable, it has to be algebraic. So, the searches have been for over two decades in algebraic topology for cyberworld invariants. Equivalence relations define invariants at various abstraction levels. The paper solely serves as an initial summary of algebraic topological resources for studying cyberworlds starting from the very elementary set theoretical level. High social impact application cases of e-financing and emanufacturing are presented at the end. 0. Prologue: What are cyberworlds? Cyberworlds are being formed in cyberspaces as computational spaces. My discovery of cyberworlds goes back to 1969 [4]. Now cyberspaces are on the web either intentionally or spontaneously, with or without design. Widespread and intensive local activities are melting each other on the web globally to create cyberworlds. The major key players of cyberworlds include e-finance that trades a GDP-equivalent a day and e-manufacturing that is transforming industrial production into Web shopping of product components and assembly factories. Without proper modeling, cyberworlds have continued to grow chaotic and are now out of human understanding and control. A novel information model we named “an adjunction space model ” serves to globally integrate local models. As an information model, it is also applicable to the category of irregular data models that capture spatiotemporal aspects of information worlds. Mathematically

Very large databases on the Web have been changing dynamically and have become complicated today. This research aims at helping users' understanding of database changes by database animation. As a case study, animating budget management of one company is researched It shows clearly that database animation help understand the flow of plans and the distribution of the whole budget. Furthermore, it has shown that reverse animation by preserved homotopy realizes the effective reuse of databases.

Metamorphosis between 3D objects is often the transformation between a pair of shapes that have the same topology. This paper presents a new model using Reeb graphs and their contours to create morphing between 3D objects having different topology. The proposed method specifies the correspondence between of the input objects by using the graph isomorphic theory. Then the super Reeb graph, which has the equivalent topological information to the Reeb graphs of the two input objects, is constructed and used to conduct the sequence of the morphing. The evolutions of the topology that occur during the morph can be specified by the transformation of the Reeb graphs and their contours of the input objects. Reeb graph-based modeling allows the users precisely and intuitively control the morph because the topological information of the objects, represented by the structures of the Reeb graphs, is explicit and easy to understand Moreover, the contours of the Reeb graphs also represent the geometrical information of the objects. The examples of morphing between different topological shapes are demonstrated.

Cyber graphics as an emerging technology has been playing key roles as human interfaces of cyber worlds. With the ever increasing roles of cyber worlds in the real world, as seen in e-financial trading that deals the GDP equivalent in a day, understanding of cyber graphics is becoming essential. To this end, scientific research has been conducted to grasp the foundation as invariants. Cellular modeling has been found to be of key importance. The adjunction spaces and cell attaching functions of cyber graphics are investigated through a variety of examples to find the invariants successfully.

After we sketch the design of a product on the Web, we can obtain each part of the product applying a cell decomposition to the sketched design based on the cellular model operations and then applying the homotopy theory to it. When we perform cell decomposition, we can specify the manufacturing procedures of a product as homotopy invariants based on the homotopy theory. Using the parts and the manufacturing procedures of a product, and cell attaching functions accumulated in the cellular design database while these procedures are applied. We show first that we can perform the real design of soft objects, the shapes of which are constantly changing. We then show that the cellular model also can uniformly specify varied sizes. Thus, the cellular model is far more powerful than existing geometric models. The design of bags is taken as an example of soft object and varied sized object design.

New analytical formulations of bounded blending for functionally defined set-theoretic operations are proposed. The blending set operations are defined using R-functions and displacement functions with the localized area of influence. The shape and location of the blend is defined by control points on the surfaces of two solids or by an additional bounding solid. The proposed blending using a bounding solid can be applied to a single selected edge or a vertex. We introduce new types of blends such as a multiple blend with the disconnected bounding solid and a partial edge blend. It is shown to have versatile applications in interactive design.

To transform a three-dimensional object or map texture to its surface, it is necessary to introduce a coordinate system. If the surface can be cut and developed, it is easy to identify each point on the surface with the coordinate values. According to a theory in topology, any closed polygonized two-dimensional surface can be represented by a canonical development. However, no efficient algorithm to actually develop a given surface has been presented, and the theory sounds abstract. This paper proposes a method to develop an arbitrary polygonized closed surface and to establish the correspondence between each point on the surface and a point on a regular polygon. Educational software is developed using the algorithm that visualizes the coordinate system by texture mapping or by allowing a user to paint on the surface.

Abstract The paper presents a skeleton‐based approach for robust detection of perceptually salient shape features. Given ashape approximated by a polygonal surface, its skeleton is extracted using a three‐dimensional Voronoi diagramtechnique proposed recently by Amenta et al. [ 3 ]. Shape creases, ridges and ravines, are detected as curvescorresponding to skeletal edges. Salient shape regions are extracted via skeleton decomposition into patches.The approach explores the singularity theory for ridge and ravine detection, combines several filtering methodsfor skeleton denoising and for selecting perceptually important ridges and ravines, and uses a topological analysisof the skeleton for detection of salient shape regions. ACM CSS: I.3.5 Computational Geometry and Object Modeling

We research the defects of geometric modeling in representing object attachments. It is difficult to represent different types of object attachments such as glueing or fusing in current computer graphics. We consider two types of different attachments such that an object is "put" on the top of another object, and an object is "fused" to the top of another object. To represent the relationships of object attachments, we assume a hypothesis such that we can represent the information of object attachments in computer graphics based on the cellular models, and consider the real implementation in computer graphics for proving that the cellular model of object attachments meet the hypothesis. The results of our research are expected to influence major applications including computer integrated manufacturing (CIM).

Inverse kinematics is one of the most popular method in computer graphics to control 3D multi-joint characters. In this paper, we propose an inverse kinematics algorithm that takes the characteristics of human bodies into account. The mausculoskeletal model is used to solve the redundancy of the human body. Using our method, feasible human body motion can be obtained simply by specifying the motion of several end effectors or body segments. Since muscle dynamics is taken into account, the configuration space of the human body is automatically calculated, and unrealistic postures can be avoided. It is also possible to tune the motion by changing the external load applied to the muscles. Using our method, the amount of work by the animators is reduced to create natural human animation.

The paper proposes an approach for stable extraction of the skeleton of a polygonal surface and detection of surface features, ridges and ravines, corresponding to skeletal edges. The approach adapts the three-dimensional Voronoi diagram technique for skeleton extraction, explores the singularity theory for ridge and ravine detection, and combines several filtering methods for skeleton denoising and for selecting perceptually salient ridges and ravines. Rather than extract the skeleton as a CW-complex, we approximate it with a two-sided surface. It allows us to use standard mesh editing tools for skeleton denoising and achieve stable extraction of the ridges and ravines.

There is a growing need to be able to accurately and efficiently search visual data sets, and in particular, 3D shape data sets. This paper proposes a novel technique, called Topology Matching, in which similarity between polyhedral models is quickly, accurately, and automatically calculated by comparing Multiresolutional Reeb Graphs (MRGs). The MRG thus operates well as a search key for 3D shape data sets. In particular, the MRG represents the skeletal and topological structure of a 3D shape at various levels of resolution. The MRG is constructed using a continuous function on the 3D shape, which may preferably be a function of geodesic distance because this function is invariant to translation and rotation and is also robust against changes in connectivities caused by a mesh simplification or subdivision. The similarity calculation between 3D shapes is processed using a coarse-to-fine strategy while preserving the consistency of the graph structures, which results in establishing a correspondence between the parts of objects. The similarity calculation is fast and efficient because it is not necessary to determine the particular pose of a 3D shape, such as a rotation, in advance. Topology Matching is particularly useful for interactively searching for a 3D object because the results of the search fit human intuition well.

Introduces a new method of shape modeling using homotopy and object-oriented modeling. Homotopy is a kind of topology that gives more general ideas of presenting invariant properties of geometrical objects and is further expanded to conceptual objects. The conventional shape modeling method, using polygonalization, has serious difficulties in preserving invariant properties, leading to the necessity of a massive amount of data. On the other hand, the combination of homotopy and object-oriented modeling, which uses class hierarchy, helps to preserve invariant properties at all abstraction levels. We explain how our new method helps us to preserve invariant properties, which keeps the amount of data to the minimum possible level, using an example of a tennis ball rolling on a slope.

Geometric modeling and computational representations of shapes have been subject to intense research for more than three decades. Interestingly, these subjects are still at the heart of a continuous activity of research and development in computer graphics, virtual environments, image-based rendering, computer-aided geometric design and physical simulations. Currently, geometric and physically-based modeling still face two main challenges: (1) the identification of topological features, and (2) the representation of the modes of interaction between them, both in static and dynamic environments. Current methods have offered many different forms of associating abstract structures with analytical expressions. The variety of modeling tools, from combinational methods to analytic algebraic geometry, not only reflects the richness of ideas in this domain of study but also the desire to improve, enhance and simplify. It is within this realm that we introduce a new framework, called holorgraphic geometric modeling (HGM). This framework combines the advantages of the graph-theoretic representation of combinatorial structures with the analytical flexibility, expressional power and scalability of higher-order, multi-dimensional variables and operators in the form of holors. HGM not only complements the combinatorial structures in geometric modeling but also enhances and reveals new concepts and ideas in the process of developing robust, flexible and scalable domains of formulation for simplicial complexes, cellular spaces, and homotopy in general.

Introduces two new theoretical tools - homotopy and cellular structured spaces - for visualization. Any object is represented by a filtration space, which is a sequence of skeletons that are topological spaces. Using an attaching function that attaches n-1 dimensional balls to the boundaries of n-dimensional balls, a filtration space is composed inductively and step-by-step, by increasing the dimensions. The space obtained by this process is called a cellular structured space, which is composed of cells. The cellular structured space preserves invariant properties of entities. On the other hand, traditional polygonalization has difficulty in preserving invariant properties. A change from one situation represented by a cellular structured space to another situation of a cellular structured space is represented by a homotopy if the change is continuous. Using homotopy and cellular structured spaces, invariant properties are preserved while very large data compression is achieved.

Ever increasing software complexity requires serious consideration to make software as a whole into sustainable social infrastructure. Abstraction hierarchies realized as incrementally modular hierarchies of software are shown to be the strong candidates to reduce software complexity. The program construct of Java is used as a test case to demonstrate the power of cellular modeling and we show how cellular modeling serve as a rapid prototyping tool and a validation tool as well by showing abstracted Java program structures without complexity.

As the scientific ground to support what is believed to be the largest business in the 21/sup st/ century called cyberbusiness, homotopy modeling has been explored and developed. Because of the scale and the growth rate beyond any existing social systems, cyberbusiness imposes challenging requirements for modeling, design, development and operation. Homotopy modeling is based on novel space-time modeling with cellular spatial structures. The paper discusses homotopy modelling as the architectural foundation of cyberworlds.

Computer graphics lacks scientific foundation to make it an academic discipline. Science has been in search of invariants through various changes to identify the scientific truth to build theories on the invariants. A hierarchy of invariants is presented for computer graphics having cellular spatial structures as the core. Same application examples are shown for illustrative purposes.

A computationally valid shape model has been sought so that we can share shapes among varied applications for extensive reuse. Current shape models are targeted at presentations and lack validity in their shape properties, such as topological, geometrical and visual equivalence. Based on cellular structured space modeling (cellular modeling for short), valid shape modeling is formulated and examples are shown to demonstrate its effectiveness.

There is a great demand for data on the mobility and strength capability of the human body in many areas, such as ergonomics, medical engineering, biomechanical engineering, computer graphics (CG) and virtual reality (VR). This paper proposes a new method that enables the calculation of the maximal force exertable and acceleration performable by a human body during arbitrary motion. A musculoskeletal model of the legs is used for the calculation. Using our algorithm, it is possible to evaluate whether a given posture or motion is a feasible one. A tool to visualize the calculated maximal feasibility of each posture is developed. The obtained results can be used as criteria of manipulability or strength capability of the human body, important in ergonomics and human animation. Since our model is muscle-based, it is possible to simulate and visualize biomechanical effects such as fatigue and muscle training. The solution is based on linear programming and the results can be obtained in real time. Copyright © 1999 John Wiley & Sons, Ltd.

The construction and maintenance of large, high-quality software projects is a complex, error-prone and difficult process. Tools employing software database metrics can play an important role in the efficient execution and management of such large projects. In this paper, we present a generic framework to address this problem. This framework incorporates database and knowledge-base tools, a formal set of software test and evaluation metrics, and a suite of advanced analytic techniques for extracting information and knowledge from available data. The proposed combination of critical metrics and analytic tools can enable highly efficient and cost-effective management of large and complex software projects. The framework has the potential for greatly reducing venture risks and enhancing production quality in the domain of large-scale software project management.

Surface creases provide us with important information about the shapes of objects and can be intuitively defined as curves on a surface along which the surface bends sharply. Our mathematical description of such surface creases is based on a study of extrema of the principal curvatures along their curvature lines. On a smooth generic surface we define ridges to be the local positive maxima of the maximal principal curvature along its associated curvature line and ravines to be the local negative minima of the minimal principal curvature along its associated curvature line. The ridges and ravines are important for shape analysis and possess remarkable mathematical properties. For example, they correspond to the end points of shape skeletons. In this paper we derive formulas to detect the ridges and ravines on a surface given in implicit form. We also propose an algorithm for obtaining piecewise linear approximation of ridges and ravines as intersection curves of two implicit surfaces.

We present our approach to volume modelling which combines volume representations by voxel data and by continuous real functions. We discuss the main differences between direct volume visualization and modelling with voxel data, questions of conversion between two representations including volume reconstruction from contour data. We illustrate the approach by several advanced operations on a volumetric object: set-theoretic operations, sweeping, hypertexturing, feature-based sculpting, splitting, spatial and temporal transformations.

We present a method of stable extraction of curvature features from a scattered data obtained by measuring a Noh mask shape. First, since the Noh mask shape can be represented as the graph of a function, we obtain a height function representation of the data. Then, we smooth the height function data by a Gaussian filter and by an iterative nonlinear filter. Finally we compute curvature features using finite-difference approximations. We test our approach detecting convex/concave, saddle, cylindrical, and plane regions on the Noh mask scattered data.

In this paper, a method for recognizing plant species by the shapes of the leaves is presented. The recognition is based on a hierarchical representation of shape features. First, the structures of the shapes of leaves are analyzed and the shapes of components are extracted in detail. The structures and detailed shapes of leaves are approximated by polygons whose vertices are critical points of curvature of contours of leaves. The method also takes variations of shapes of leaves of the same species into account. Experimental results using a number of species in the family of Acer (Maple) indicate that structures of leaves and shapes of their components can be considered as landmarks to recognize the species of plants.

Fashion is an influential medium in multimedia, leading social trends internationally. A typical case of fashion, that of dress, is modeled by cellular spatial structures to show that such algebraic topological modeling can allow a variety of dress designs to be produced from one basic fashion mode, inheriting design characteristics. The basic architecture is a three layered model consisting of a topological layer to specify the basic fashion mode, a geometrical layer to produce varieties of shapes inheriting the topological characteristics, and a visualization layer to implement real dress in wide range of media such as costumes, TV picture content, and publications.

A new method for visual and interactive topology is presented. While many classical and modern textbooks on topology contain beautiful illustrations for learners, and much excellent video software has been produced for animating geometrical phenomena, they are all based on static scenarios. This means their geometrical presentations fail to meet the demand for interactivity. With the progress of multimedia technology, dynamic scenarios, which enable learners to make mathematical experiments as many times as they like, are now well within reach. However, an appropriate methodology for interactive mathematical visualization is still lacking. The authors present a dual visualizer method in which the operational visualizer and the geometrical visualizer play complementary roles. The process graph is a key technique in the operational visualizer The method illuminates crucial factors to be considered in the methodology.

Due to the rapid progress of computer hardware, handling large volume data is getting easier. Although a number of methods have been developed for rendering volumetric datasets, very few have been proposed for shape modeling of such datasets. The paper describes a multiresolution structure for shape modeling with volume data, and the voxel interaction method capable of modeling shapes at arbitrary resolution level. In the voxel interaction method, each voxel acts in a similar way to a cellular automaton. The shape of an object is represented by the internal variables in the voxels. Unlike cellular automata, the interacting voxels can change the speed of the information propagation by selecting an appropriate resolution in the hierarchical structure, which plays an important role in modeling the rigidity of objects in our method. For the acceleration of rendering for 2D image generation, the sampling ratio along the eye-ray in the volume space is determined according to the resolution of the volume data. Experimental results include the examples of shape deformation of human CT data.

Current graphics models suffer from inconsistencies in many ways. Neither homotopical nor topological properties have been inherited in the shapes of graphical objects in particular, and usually continuity and singularity properties are not inherited either. For example, since the most of the shape modeling in computer graphics has polygonalization as the underlying display structures and data structures, the topological properties as well as the shape smoothness properties and singularities are almost always lost, which makes them unrecoverable. We present initial research on shape modeling for computer graphics to remedy this situation, based on a homotopical framework and cellular spatial structures.

This paper proposes a novel method for matching images. The results can be used for a variety of applications: fully automatic morphing, object recognition, stereo photogrammetry, and volume rendering. Optimal mappings between the given images are computed automatically using multiresolutional nonlinear filters that extract the critical points of the images of each resolution. Parameters are set completely automatically by dynamical computation analogous to human visual systems. No prior knowledge about the objects is necessary The matching results can be used to generate intermediate views when given two different views of objects. When used for morphing, our method automatically transforms the given images. There is no need for manually specifying the correspondence between the two images. When used for volume rendering, our method reconstructs the intermediate images between cross-sections accurately, even when the distance between them is long and the cross-sections vary widely in shape. A large number of experiments has been carried out to show the usefulness and capability of our method.

The need for capturing human body motions has been increasing recently for making movies, sports instruction systems and robots that can simulate human motions. The paper proposes a method to facilitate motion capturing using inexpensive video cameras. In our system, a few cameras are used to obtain multiple views of a human body and a three dimensional (3D) volume consistent with the views is created. A model of the human body is then fitted to the volume to obtain the configuration of the human body. We also propose a method to analyze the stability of human postures. We have analyzed a technique of the traditional Chinese martial art, Shorinji Kempo, based on stability to show the effectiveness of our method.

Recent advances in multimedia has necessitated us to look for an effective search method of images. Most of the contemporary indexing methods are based on color distribution in the images. When the users do not remember the colors clearly, however, it has been difficult to retrieve the desired images. The paper proposes an indexing method based on shapes contained in an image. We characterize an image by the half planes that contain the objects in it. We also propose a method to characterize images by the vanishing points of parallel lines contained in an image. The vanishing points represent how three dimensional (3D) objects are projected onto the 2D image.

The paper presents a method of designing curves and surfaces by solving the constraints imposed on the shapes at multiresolution levels. In this method, the curves and surfaces are represented by endpoint interpolating B splines and their corresponding wavelets. At each resolution level, the shape is determined by minimizing the energy function subject to the deformation of the shape while preserving the given constraints. Constraints at a low resolution level are converted to those at a high resolution level using wavelet transforms in order to associate all the constraints with the common basis functions. The constraints at multiresolution levels are then solved recursively from low to high resolution levels. Design examples are also presented.

The authors present an approach to manage evolutionary changes that take place over time in an object-oriented software metrics database schema. The framework is based on the entity-relation (E-R) model and uses a recursive graph structure, known as R-graph, to support the views of software quality and risk. The fundamental mechanism for abstracting views is the introduction of two semantic operators for the R-graph. These operators are proposed based on graph-based predicates and Petri-net based predicate formalism for view abstraction.

We propose fast algorithms for the detection of view independent ridges on surfaces given by graphs of functions. The ridges are defined via extrema of the principal curvatures along the associated principal direction. These algorithms have the advantage to be fast and it appears that the so defined ridges deserve as a characteristic feature of the shape of the surface. Results on analytic surfaces and on real data are shown and discussed.

The paper proposes a system that recognizes three dimensional (3D) objects while measuring them. The system consists of a liquid crystal (LC) projector and a video camera. Our system can be applied to moving objects. The system itself can also move while measuring the objects to obtain the data of a whole scene. In our system, range data is registered on the fly.

There is an increasing demand for human body motion data. Motion capture and physical animation have been used to generate such data. It is, however, apparent that such methods cannot automatically generate arbitrary human body motions. A human body is a redundant multi‐linked body controlled by a number of muscles. For this reason, the muscles must work appropriately and cooperatively for controlling the whole body. It is well‐known that the human body control system is composed of two parts: The open‐loop feed‐forward control system and the closed‐loop feedback control system. Many researchers have investigated the characteristics of the latter by analyzing the response of a human body to various external perturbations. However, for the former, very few studies have been done. This paper proposes an open‐loop feed‐forward model of the lower extremities which includes postural control for accurate animation of a human body. Assumptions are made here that the feed‐forward controller minimizes a certain objective value while keeping the balance of the body stable. The actual human motion data obtained using a motion capturing technique is compared with the trajectory calculated using our method for verification. The best criteria which is based on muscle dynamics is proposed. Using our method, dynamically correct human animation can be created by merely specifying a few key postures.

Pacific Graphics '95, the third international conference on Computer Graphics and its Applications, was held on 21-24 August 1995, in Seoul, Korea.Following on the success of the two previous conferences: Pacific Graphics '93 (Seoul, Korea) and Pacific Graphics '94 (Beijing, China), we received 62 submissions from 22 different countries all over the world and, after peer review, selected 24 papers for publication in the conference proceedings: Computer Graphics and Applications, published by World-Scientific, Singapore.(The proceedings also include 10 invited papers.)The four papers presented in this special issue were judged by the programme committee members to be the best of the 24 selected papers presented at the conference.Each of the four papers was further reviewed by experts in the respective research area and the papers were further improved on the basis of comments received.The first paper, by Kim and Elber, presents a symbolic approach to generate blending surfaces between two polynomial and/or rational surfaces.Using a purely symbolic technique, the authors demonstrate how to compute various cross boundary tangent vector fields on each rail curve and represent the blending surfaces as polynomial or rational surfaces.The next paper, by Sun, Wang and Chin, presents a 3D morphing algorithm which transforms one polyhedral model into another.Considering each polyhedron as a graph representing vertex adjacencies, the authors develop a simple and elegant method which generalizes the 2D polygonal morphing algorithms of Sederberg to a 3D polyhedral morphing algorithm.The third paper, by Lee and Shin, presents an efficient ray casting algorithm for terrain rendering from DTMs (digital terrain models).The authors introduce a formal analysis to vertical ray coherence.Based on this analysis, they propose a new technique which covers the entire image plane with non-parallel ray lines.This

Dental CAD/CAM requires appropriate modelling of human jaw motion in contact with the opposite jaw. Such modelling is necessary for planning orthodontic treatment and robust design of dental restorations, especially their occlusal surfaces which must fit the existing articulation patterns. We propose a fast and purely geometrical approach to model sliding of the lower jaw over the surface of the upper, fixed jaw. For every discrete step of the motion, a new position and orientation of the sliding object is found by maximizing its displacement toward the fixed object, to obtain stable contact without interpenetrations. We impose constraints on the range of rotation angles to justify simplifications of our linear model handling the distance from the fixed object to chosen points on the surface of the sliding object as a function of its configuration. In such formulation, we reduce the complexity of the problem of object placement in contact to that of a linear optimization task. Expensive multi-point collision detection and distance computation are handled by rasterizing graphics hardware, which supports generation of valid configurations for complex objects at stable and interactive speeds. Our model of human jaw sliding compares favourably with experimental motion data. © 1997 John Wiley & Sons, Ltd.

This research addresses the issue of human visual cognitive capability to identify an object irrespective of object orientation throughout the course of object movement in computer animation. The identification is by cognizing the shape characteristics that are independent of the object orientation as invariants. Taking a simple case of a silhouette cartoon animation and having a dolphin as a popular example of an object that changes the orientation while swimming and also jumping up into the air, we show that the orientation independent invariants are the critical points, namely the peaks of the convex portion of the object and the pits of concave portions, and that they are derived from a graph of the curvature change along the boundary of the object.

As the key visual display- and processing- element of information super highway nodes, computer graphics is advancing into dynamic and higher dimensional visual worlds. So is visual algorithms to program visual worlds as the contents of information super highways. This research presents a drastic approach in designing visual algorithms to construct visual worlds. The address is on the most critical phase of conceptual design that has been conducted ad hoc in designers' mind. Conceptual visual algorithms make mental design processes and design results explicitly represented in a computer executable form after interactive machine translation. Hence, they are explicitly validatable against the design requirements. Taking a popular case of human performance design including dramas, music performance and sporting, recreational skiing algorithm design in particular as an example of visual world design, we show a requirement-driven approach to conceptual visual human algorithm design produces a truly effective skiing method to meet wide varieties of recreational requirements.

Modeling of the occlusal surface of teeth is an important problem in computer-aided design of dental restorations. The designed shape must fit the existing jaw articulation. Also, the design process must be fast to be practical in clinical applications. In this paper we present techniques for automatic adjustment of the occlusal surface of restorations based on the results of articulation simulation. The shape of restorations is changed to avoid interpenetrations with the opponent teeth during functional jaw movements. The 3-D space mapping method is used which guarantees the surface smoothness and preservation of the main topological features of the occlusal surface. To speedup calculations we use rasterizing graphics hardware for computationally involved collision detection between complex surfaces of teeth.

A metrics based project management system (MPMS) integrates software metrics data, management queries based on the software metrics data, as well as their responses in a single location. Given the variations in projects, queries, metrics and physical databases to be used, MPMSes should be flexible from a user point of view, and also generic from a designer point of view. Two important steps in the design of an MPMS involve the determination of typical queries that may be posed by users, as well as the selection of the physical database for storing metrics and other project related knowledge. The paper discusses the relative advantages and drawbacks of three selected physical database models, namely the relational data model, object oriented data model, and graph data model, based on a variety of classes of metrics based queries. We conclude that the choice of data model varies according to the class of queries, and has strong implications on the ease and efficiency with which metrics based queries may be posed and executed.

The VC-1 is a parallel graphics machine for polygon rendering based on image composition. This paper describes the architecture of the VC-1 along with a parallel polygon rendering algorithm for it. The structure of the VC-1 is a loosely-coupled array of 16 general-purpose processors, each of which is equipped with a local frame buffer. The contents of the local frame buffers are merged in real time for generating the final image. The local frame buffers are virtualized with a demand-paging technique, by which the image memory capacity for each local frame buffer is reduced to one eighth of full-screen capacity. Polygons are rendered in either pixel parallel or polygon parallel depending on the on-screen area of each polygon. The real performance of the VC-1 as well as estimated performance for systems with up to 256 processors is shown. CR

Computer-aided diagnosis of occlusal disorders and design of dental restorations requires an automated evaluation of jaw occlusion and chewing ability. This requires simulation of the motion of the jaws and characterization of contacts between the surfaces of teeth. We propose approaches to evaluation of the load on teeth and of the grinding process. These characteristics are derived in interactive time, and are based on distance maps and topological structure of the contact zones. The proposed approaches are general and usable in applications where modeling of contact between objects with complex geometry is required.>

The multidimensional diffusion model for computer animation of diffuse ink painting opens up a new dimension in painting. In diffuse painting final image is a result of ink diffusion in absorbent paper. A straight-forward diffusion model however is unable to provide very specific features of real diffuse painting. In particular, it can not explain the appearance of certain singularities in intensity of color in the image which are very important features of diffuse ink painting. In our previous work, a model based on physical analysis of paper structure was proposed. Although this model provided an adequate simulation of many diffuse ink painting properties, it was still insufficient to explain the singularities of intensity distribution precisely. Now we solve this problem. A multidimensional diffusion model which we propose proves to provide exactly the same intensity distribution as in real images. The method was applied to animate ink diffusion 'Nijimi' of traditional Japanese ink painting 'Sumie'.>

Abstract This paper presents a novel approach to the reconstruction of geometric models and surfaces from given sets of points using volume splines. It results in the representation of a solid by the inequality f(x,y,z) ≥ 0. The volume spline is based on use of the Green's function for interpolation of scalar function values of a chosen “carrier” solid. Our algorithm is capable of generating highly concave and branching objects automatically. The particular case where the surface is reconstructed from cross‐sections is discussed too. Potential applications of this algorithm are in tomography, image processing, animation and CAD for bodies with complex surfaces.

Abstract Researchers in the fields of computer graphics and geographical information systems (GISs) have extensively studied the methods of extracting terrain features such as peaks, pits, passes, ridges, and ravines from discrete elevation data. The existing techniques, however, do not guarantee the topological integrity of the extracted features because of their heuristic operations, which results in spurious features. Furthermore, there have been no algorithms for constructing topological graphs such as the surface network and the Reeb graph from the extracted peaks, pits, and passes. This paper presents new algorithms for extracting features and constructing the topological graphs using the features. Our algorithms enable us to extract correct terrain features; i.e., our method extracts the critical points that satisfy the Euler formula, which represents the topological invariant of smooth surfaces. This paper also provides an algorithm that converts the surface network to the Reeb graph for representing contour changes with respect to the height. The discrete elevation data used in this paper is a set of sample points on a terrain surface. Examples are presented to show that the algorithms also appeal to our visual cognition.

We introduce a new concept of ridges, ravines and related structures (skeletons) associated with surfaces in three-dimensional space that generalizes the medial axis transformation approach. The concept is based on singularity theory and involves both local and global geometric properties of the surface; it is invariant with respect to translations and rotations of the surface. It leads to a method of hierarchic description of surfaces that yields new approaches to shape coding, rendering and design. The extraction of the features is based on differential geometry of surfaces with consequent segregation via multiscale analysis. Terrain feature recognition, dental shape reconstruction and medical imagery are a partial list of applications.>

Abstract Computer animation and visualization can facilitate communication between the hearing impaired and those with normal speaking capabilities. This paper presents a model of a system that is capable of translating text from a natural language into animated sign language. Techniques have been developed to analyse language and transform it into sign language in a systematic way. A hand motion coding method as applied to the hand motion representation, and control has also been investigated. Two translation examples are also given to demonstrate the practicality of the system.

Abstract A new translucent display algorithm is proposed for grey‐scale images represented by G‐octrees. The algorithm generates a special triangle quadtree as the display image for the isometric projection of a G‐octree, while traversing the G‐octree from front to back, with respect to the viewpoint. A method of using the translucent effect to analyse the interiors of three‐dimensional objects is also described, together with its implementation results.

The development of a multimedia broadband local area network (LAN) system named CrossoverNet using a intelligent head-end is presented. This head-end provides two-way digital/analog communication with dynamic channel exchange and network configuration control. Based on these functions, the head-end exchanges analog information in a manner similar to digital circuit exchange. Digital and analog information are transmitted separately over the same broadband cable and integrated in audiovisual protocol layers. To provide these facilities, a LAN architecture conforming to the Open Systems Interconnection (OSI) basic reference model is designed using broadband and CATV network technologies. The result, CrossoverNet, can control, operate, and manage a variety of audiovisual devices that are attached to it in a consistent manner. A prototype experiment illustrates the versatility of the system.>

No abstract available.

This paper discusses inputing three dimensional solid object data by means of a two dimensional tablet. This method involves refining an object by gradually generalizing a class of 'permissible' objects. The design of an object is first limited to an octree, which is a set of cubes. At this step, a single selection can create, divide or destroy a cube. It is expected that after this rough design step has been completed, the designer can go on to the next step in which the target object is a polyhedron. The advantages of using this octree design method are: 1. the designer always has a valid three dimensional object, 2. few selections are required for generating a rough design, and 3. each displayed candidate cube serves as a menu for guiding the designer in making decisions. A technique for displaying objects and experimental designs is illustrated.

Recent progress in Japanese computer-integrated manufacturing (CIM) includes the integration of computer graphics, database management systems, local area networks, robotics and software engineering technology. This panel will discuss advanced CAD, CAM CAT (computer-aided testing) and FMS (flexible manufacturing systems) available in Japan.

The logic named PICCOLO for a picture database computer and its implementation is presented. The logic is shown to have three major advantages. One advantage is that the computer design based on this logic can handle a universal variety of pictorial data structures. Another advantage is that a set of data generated by rules such as texture distribution rules is stored in the picture computer efficiently. The third advantage is that this logic can serve as the basis of a logic for parallel processing machines. For implementation of the logic, a new methodology named architecture engineering is introduced as an architecture/design oriented methodology. Implementation case studies show the usefulness of the methodology. Two implementations on an abstract machine that are also on a parallel LISP machine are reported.

Recursive graphs (R-graphs) are modified for use Is a formalism to represent evolving drawings spanning various levels of detail, and store them in a database. A separation of the structural information and the physical image information is advocated. To guarantee maximum flexibility, the physical image information is represented in relational form, and for consistency and ease of manipulation, the R-graphs containing the structural information are mapped into normalized relations. Major design aspects for implementation are considered, such as, the feasibility of a mapping into binary associations and the drawing generation strategy. Binary associations are an adequate model to express conceptual schemata and are often used as input format for existing computer aided database dsesign packages. As an illustration of the propose formalism, the evolution through three levels of detail in nested drawings handled during the design of chemical process plants is demonstrated.

Software design process is formalized based on the concept of the recursive graphs. The proposed formalization defines design schemas by the recursive graphs and design operations by the recursive graph operations. An architecture of a computer aided design process based on this formalization is presented. An example is shown for a buffer system design. It is expected that this formalization reduces software life cycle cost by utilization and machine verification of past design results as well as past design processes.

This paper presents a general and computationally inexpensive algorithmic scheme that falls in a region detection category. In the scheme, a minimal spanning tree is used as a path of a sequential region grower. The algorithm traverses the spatially adjacent graph while maintaining the structural organization of an image. The graph-theoretical evaluation of heuristics is described and examples of implementation are given.

This paper establishes a general principle that all devices and computers embedded in a system should be considered equal from the viewpoint of the simulation design of a computer controlled system. This principle is a formal and general approach to simulation design especially for debugging aids and provides an excellent simulation technique offering generality, simplicity and flexibility. In addition a new, simple, and efficient time flow mechanism is presented. This mechanism can be widely applied to other kinds of programming whenever time management is necessary. For demonstrating and testing the new techniques, the simulation of a minicomputer system is implemented which is used for the purpose of developing and debugging real programs, especially those including input/output control instructions or sensitivity to input/output interrupt timing. This simulation technique can also be applied to a large computer system to debug programs or investigate its behaviour.

We outline herein an approach to evolutionary database systems design and evolutionary database design which is intended to lower the total costs of maintaining, developing and executing application programs against a database. The premise is that it should be possible to have an evolutionary database system which executes efficiently while providing explicit support for changes in application usage. The key concepts are: hierarchical layering of a database specification, inclusion of static/dynamic characteristics in specification of the database, and a hybrid compile/interpret system for the execution phase of the data management system itself.

This paper describes an application of a color graphic display system "INFADS" to a fashion design process using man-machine conversation. One of the main characteristics of the system is the interactive design facility created by combining a color picture processing system with a data base system. Another important characteristic is the introduction of a new recursive concept of "picture" and "texture". Some advantages of describing fashion data in a relational data base are discussed in connection with the need for data independence and the need for the semantic retrieval of pictorial data via a data description scheme.