**Journal for Geometry and Graphics**

**Volume 2 (1998)
Abstracts**

M. Hoffmann, L. Varady: Free-form Surfaces for Scattered Data by Neural Networks, 2 (1998) 001--006- The handling of scattered spatial points is an important question in computer graphics and there are several methods to construct surfaces from these type of data. The aim of our paper is to present a new method which produces standard free-form surfaces from the scattered data. Earlier methods normally construct a triangular control grid from the data however NURBS or Bezier surfaces originally use quadrilateral control grid. In this paper a new approach is presented, where first an artificial neural network is used to order the data and form a grid of control vertices with quadrilateral topology, hence after this step the original, well-known free-form methods can be applied to construct the surface. Another advantage of this method that it can handle arbitrary set of points as well as very few data.

A. Karger: Classical Geometry and Computers, 2 (1998) 007--016- We show that the present stage of development of computer hardware and software enables to solve many elementary and non-elementary problems of classical geometry, which in the past could not be solved for the complexity of involved equations or the degree of the problem. Demonstrative examples are given, including corresponding MAPLE session record.

R. Koch, C. Engelhart: Closed Space Curves of Constant Curvature Consisting of Arcs of Circular Helices, 2 (1998) 017--032- A closed regular curve of class
*C*(^{r}*r*>=2) in the Euclidean 3-space having constant curvature*kappa*_{0}>0 is called closed*kappa*_{0}-curve. We present various examples of nonplanar closed*kappa*_{0}-curves of class*C*, which are composed of^{2}*n*arcs of circular helices. The construction of*c*starts from the spherical image (= tangent indicatrix)*c**of*c*, which then has to be a closed regular curve of class*C*on the unit sphere^{1}*S*consisting of^{2}*n*circular arcs and having the center*O**of*S*as its center of gravity. The case when^{2}*c**is a subset of the intersection of*S*and^{2}*Pi*is studied in detail, assuming that*Pi*is a cube, or, more generally, a regular polyhedron the edges of which are tangent to*S*. In order to describe and to visualize the curves^{2}*c**and*c*, and to derive*c*from*c**, projection methods of Descriptive Geometry are used.

M. Szilvasi-Nagy: Almost Curvature Continuous Fitting of B-Spline Surfaces, 2 (1998) 033--044- An algorithm is presented for the fitting of a tube shaped B-spline surface of (3,2) degrees to another surface along a given connection curve. Satisfying prescribed first and second order boundary conditions at a finite number of interpolation points on the connection curve several vertices of the control net of the bordering patches are computed from a fairness condition. The resulting B-spline surface joins the second surface with almost curvature continuity at those common points in which the tangent planes and the normal curvatures in one prescribed direction of both surfaces coincide.

T. Watanabe: Revision of Inconsistent Orthographic Views, 2 (1998) 045--054- Many algorithms for the generation of solid objects from two-dimensional (2D) orthographic views have bottom-up procedures which generate 3D segments, form 3D faces and construct polyhedrons. When they accept a set of consistent view drawings, they present at least one solid object. However, when the input views are not consistent, contradictions appear during the process in each step of the bottom-up approach. We examine incoherences found in each step of the bottom-up approach in these cases. Then we introduce a method which reveals the sources of incoherences in input views and suggests consistent views. Three kind of sources are considered: extra segments, improper designations of line types (visible lines or hidden lines) and missing segments. Extra segments and improper designations of line types are found by projecting the solid object constructed from subset of 2D segments onto view planes. Probable missing 3D segments are generated not from three views but from two views among three views. Some heuristic rules are proposed in order to select more probable missing segments and make the process efficient. The present method can be used to detect operator's mistakes in input views or misunderstandings of drawing recognition systems.

T. Araki: Basic Education of CAD/CAM Through Multimedia and Network Aid, 2 (1998) 055--064- In the Department of Mechanical Engineering, Tsukuba College of Technology, multimedia is used for presentation using computers as visually interactive intelligent teaching methods for hearing-impaired persons. In another multimedia method, the system is developed and used in education by visual sensing and bodily sensing for teaching materials suitable for hearing-impaired persons. In order to carry out the guidance on the education of "Machine Design and Drawing" and "CAD/CAM" for them smoothly and so as to be easily understandable, various devices have been made. At the same time, when used with a multimedia network system, the communication method is expanded in education, to broaden students' social horizon, and their desire to improve themselves. Furthermore collaborations with a sister school in the US and other schools in Japan by utilizing a network also creates opportunities. Sending and receiving CAD and multimedia data with visual communication on the computer screen via the internet is useful for the basic CAD/CAM education. The development and the study of a visually interactive education system, with the multimedia and teaching materials suitable for hearing-impaired students by using networks, and the results of the practice on education, are reported on.

J. Chen: Kernel Problems of the Modernization of Engineering Graphics Education, 2 (1998) 065--070- The innovation in graphics education lying ahead of us is not only a problem of arranging the contents or selecting the focal points. The divergent opinions are actually controversies about didactic problems with philosophical profundity. At the moment, the main direction of the world education reform is to reinforce the foundation and to develop the ability -- despite the bright coloring of its outer appearance due to modern graphics technique. And the kernel of foundation and ability is intelligence. So, one should take care of the right balance between theory and practice, between the basic concepts of Descriptive Geometry in updated form and the design work with all the powerful tools available on the market. One of the basic problems is still the transformation between 2D and 3D and vice versa.

G. Gittler, J. Glueck: Differential Transfer of Learning: Effects of Instruction in Descriptive Geometry on Spatial Test Performance, 2 (1998) 071--084- An important question in educational research is whether the imparting of knowledge and skills also improves pupils' intelligence. This aspect of transfer of learning is difficult to study within the framework of educational research. The longitudinal study presented here shows, based on sophisticated test materials and methods of analysis, that courses in Descriptive Geometry improve pupils' spatial ability, a primary dimension of intelligence. Also, sex differences that were clearly present at the first testing disappeared during "training" in Descriptive Geometry.

N. Hayata, S. Ino: The Differences in Eye Movements and Visual Impressions in Response to Static Versus Motion Picture Imagery of Streetscapes, 2 (1998) 085--092- This research investigates techniques of urban environment visualization using computer graphics, and the effectiveness of this medium as an evaluative tool for streetscape simulations from a human/environment perspective. In this field, single static pictures and successive static pictures taken at regular intervals are the typical method by which townscape simulations are evaluated. However, by tracking eye movements, we found considerable difference in the visual processes when subjects looked at a still image compared to a motion picture. In a moving environment, visual attention tends to focus on a more limited area which is consistent with the sequential view and continuously reorients itself with the direction of movement. When viewing static images, because the field of vision is not limited by motion, visual attention is dispersed over the whole picture. This gives evidence that perceptions of single static and successive static pictures as sequential environment are different from perceptions of motion pictures which are much closer to real sequential environment.

K. Irie, S. Nagae, D. R. Short, N. Ohtsuki, T. Ezaki: View Variation and their Effect on Student Solution to Transformation Problems -- Part 2: On the Effect of Right Side View, 2 (1998) 093--100- By an experimental method the authors determined in which way different view combinations influence the students' understanding of multiview projection drawings. The students had to produce an isometric projection view drawing from a set of displayed orthographic views. The effect of view variation was examined for three combinations of orthographic views: Front and Top view; Front, Top, and Right Side view; and Top and Right Side view presentation. The instrument selected for this experiment was a CAI (Computer Aided Instruction) system that the authors developed for instruction in graphic transformation problems. The means of time-on-task and the correct response rate (CRR) confirmed the apparent preference of Front and Top view pairing by students.

M. Takahashi, H. Sato, K. Kondo, S. Shimada: A Manual to Teach Computer Graphics by JAVA, 2 (1998) 101--108- Techniques of computer graphics are used in various fields; education, business, science and so on. It is difficult to edit a conventional manual about the computer graphics related with texts and pictures. We developed a system to make students understand the complicated concepts of computer graphics through a screen aided by the manual. The computer network is expected to communicate with many distributed people by texts, pictures, sounds, etc. through the World Wide Web (WWW). JAVA is one of such utilities to help the virtual machine environment on WWW that can manage computer network accessibility. In order to teach computer graphics at the department of computer sciences, a local network is applied as similar as Internet.

J. Lang, H.-P. Schroecker: Edge-Orthogonal Patches through a Given Rational Bezier Curve, 2 (1998) 109--122- Applications in computational fluid dynamics (CFD) have led to the
problem of finding a rational Bezier patch with a given edge parameter line
*k*the way that the parameter lines of the other type intersect*k*orthogonally. This is what we call an orthogonal continuation of*k*. The variety of solutions to the problem is being investigated and a very geometric way for the construction of the solutions is being offered. Using some fundamental features of polynomials we can establish a link between the properties of the weight polynomial and the elevation of degree which is necessary to find non-trivial orthogonal continuations. For some cases which turn out to be unsolvable, and for cases where the solution existing has a very high degree, we can describe a Monte Carlo method providing surprisingly good approximations. This method is even capable of coping with tasks where the right angle is replaced by some arbitrary angle function.

E. Knoll: Developing a Procedure to Transfer Geometrical Constraints from the Plane into Space, 2 (1998) 123--132- In this paper at the interface between geometry and art design the relationship between planar and spatial geometry will be explored as a design element. The question will be answered whether it is possible, starting with a 2-dimensional system of design parameters, to construct a 3-dimensional object based on the spatial equivalents of the initial parameters. To illustrate this process, H. Hinterreiter's painting "Opus 84" will be geometrically analyzed and re-interpreted in space.

V. Y. Mikhailenko, M. I. Yakovlev: Geometric Prerequisites for the Creation and Aesthetization of Trademark Shapes in Graphic Design, 2 (1998) 133--140- In graphic design the creation of trademark shapes has gained specific importance. These identifying symbols for products or companies should integrate features like emotional imagery, logic-motivated originality, simplicity, structural clarity and ease of visual perception. This paper focusses on the geometric prerequisites for these compositions and presents examples of geometrically remarkable designs.

N. Miljkovic, G. M. Ercegan, R. B. Stulic, Z. B. Jandric: Computer Aided Evaluation of Total Hip Prosthesis Stability, 2 (1998) 141--150- To obtain a stable total hip prosthesis it is of crucial importance that a prosthesis is well positioned and well orientated. In order to evaluate the position and orientation of the prosthesis one must determine at least four angles from the postoperative radiograph of the operated hip: inclination of the cup, anteversion of the cup, anteversion of the femoral part and valgus of the femoral part. If the measurement of these angles is carried out by a human himself, some mistakes caused by subjectivity of the person may frequently occur as well as the fact that this information is not useful intraoperative, since the measurement of these angles is usually done after the operation, when there is no way to correct the position and orientation of the prosthesis without another operation. The aim of this paper is to create an algorithm and a program for computer aided evaluation of total hip prosthesis stability in order to gain the most objective and sufficiently fast information which could greatly help the surgeon during the operation, before closing the wound, to decide whether the prosthesis is stable or not.

H. Stachel: New Applications of Geometry, 2 (1998) 151--160- Two problems from different areas are presented in order to
demonstrate the applicability of geometry. In both cases the solutions are
based on results that are beyond the topics we usually teach engineering
students.

(i) For a compliance element to be used in robotics, a mechanism has been developed which produces a "centerless rotation". The presented solution consists of an infinitesimally movable structure.

(ii) The geometry behind panoramic radiographies is analysed. The aim is to make measurements on this important diagnostic tool in dentistry and to use panoramic X-rays in medical imaging for a image fusion with a live video image.

R. A. Wiggs: Form Evolution: From Nature to Polyhedra to Sculpture, 2 (1998) 161--168- This paper written by a sculptor describes a polyhedral generating process from primitive line units that inspires forms of art: A collection of slides and sketches of natural patterns had its beginning more than thirty years ago as a visual aid for teaching drawing and sculpture. As the collection grew, cataloguing became necessary. Spatial patterns were detected that repeated themselves even though a wide range of materials were represented - a drying mud puddle cracked like a turtle's back - like pine tree bark - like cloud systems. These patterns have become a source of information for generating families of polyhedra and for producing many pieces of sculpture.

R. E. Barr, D. Juricic, T. J. Krueger, L. S. Wall, B. H. Wood: The Freshman Engineering Design Graphics Course at the University of Texas at Austin, 2 (1998) 169--180- This paper discusses the course on Engineering Design Graphics (EDG) that has evolved at The University of Texas at Austin in conjunction with developments in the modern practice of engineering design. In particular, the course focuses on solid modeling, which is the new methodology for developing and conveying engineering design ideas. To this end, a curriculum model was developed in which solid modeling serves as the starting point for design representation and for all laboratory exercises, from visualization, through analysis and manufacturing, and to final engineering documentation. The class each week includes a formal lecture, manual sketching assignments, and a computer lab exercise. The lecture and laboratory topics can be subdivided into four parts: 1. introduction to design and computer-aided design; 2. geometric and solid modeling; 3. application to analysis and manufacturing; and 4. engineering documentation. Each of these parts will be detailed in the paper, and some examples of student exercises will be included.

G. R. Bertoline: Visual Science: An Emerging Discipline, 2 (1998) 181--188- The emergence of computer graphics as a powerful medium to communicate information is one of the primary reasons graphics is playing a larger role in engineering, science, and technology. Such a powerful medium has emerged from many sources. The author suggests that there is a philosophical foundation and a unique body of knowledge necessary for a discipline called visual science. This emerging discipline has as its foundation spatial cognition, imaging, and geometry. These three areas when combined provide the knowledge base for visual science. The applications for visual science can be grouped into two areas: artistic an*d technical. It is only through the development of this emerging discipline that all graphics related activities will be viewed within the context of a common discipline: visual science. All those professionals and practitioners in the many graphics related fields can, for the first time, share their common interests. It is hoped that an international effort can be started to further define and validate the emerging discipline of visual science.

E. N. Wiebe (ed.): The Taxonomy of Geometry and Graphics, 2 (1998) 189--196- At the Eighth International Conference on Engineering Computer Graphics and Descriptive Geometry (August, 1998) an international panel was organized to discuss the taxonomy of 'Geometry and Graphics' and its relation to the interests of the International Society for Geometry and Graphics (ISGG). This is a summary of this discussion with the panel members J.E. Baker (Australia), L. Cocchiarella (Italy), I. Kalcic (Slovenia), P.I. Nauk (Russia), K. Suzuki (Japan), G. Weiss (Germany), and E.N. Wiebe (USA).