**Journal for Geometry and Graphics**

**Volume 3 (1999)
Abstracts**

Z. Bancsik, I. Juhasz: On the Arc Length of Parametric Cubic Curves, 3 (1999) 001--016- We are seeking cubic parametric curves whose arc length can be expressed in a closed form. Based on the control points of a Bezier representation of parametric cubics, we provide a criterion to determine whether their arc length has a closed form or not.

D. Agbodan, D. Marcheix, G. Pierra: A Data Model Architecture for Parametrics, 3 (1999) 017--038- In recent years, history-based, constraint-based and
feature-based CAD systems (often gathered under the generic name of
parametrics), appeared as a major progress both to express and to capture
conceptual designs and design intents. This deployment raise two major
issues. The first one is to define a data model that provides for exchange
capabilities between heterogeneous CAD systems and for archiving. The second
one is the well known "topological naming" problem.

The goal of this paper is to propose an unified modeling framework for parametric data, that addresses these two issues. This framework, defined in the object-flavored EXPRESS data specification language, involves a three layers architecture. Gathering the complete definition of a parametric object in the same data model permits both to simplify the data-management, and to define a neutral description of parametrics, enabling exchange between heterogeneous CAD systems.

H. K. Ault: Using Geometric Constraints to Capture Design Intent, 3 (1999) 039--046- With the use of geometric constraints, parametric and variational solid modeling systems enable designers to incorporate relationships between geometric entities into the geometric model and thereby control potential changes in geometry. The objective of developing these constraints or relations is to capture the intent of the designer and restrict changes that may be made by other users of the model. This paper will describe methods and strategies for constraining geometric models and show how these models capture design intent.

F. P. Birra, M. J. Prospero: SiPaViS -- A Toolkit for Scientific Visualization and Simulation, 3 (1999) 047--056- This paper introduces a new approach for scientific visualization and simulation based on a particle system. The main characteristics of the toolkit we designed and implemented at the New University of Lisbon are presented. Along with particles, fields, and particle sources, the central concept of the framework introduces the interaction as the fourth primary class of objects. The result is that a large diversity of techniques for data visualization and simulation can easily be integrated. A user of the toolkit can write a relatively short script in order to build a specific application program. This script is interpreted by SiPaViS (the name of this toolkit) according to the rules of a given grammar and on the basis of the existent re-usable classes. However, a programmer can always extend the set of predefined classes by writing the corresponding code in a common programming language. Some examples are given in the paper under the scope of application areas such as volume rendering through ray-casting implementation and also visualization of vector fields.

A. Conci, F. R. Aquino: Fractal Image Coding by Multi-Scale Selection Based on Block Complexity, 3 (1999) 057--066- Since the conception of automatic fractal image compression, the research on this topic has grown rapidly. This work is intended to provide a new vision on this automatic process by introducing the idea of multi-scale domain-pool classification based on the complexity of the image to be compressed. A preprocessing analysis of this image identifies the complexity of each image block computing its local fractal dimension. The performance of this proposition, evaluated by means of fidelity versus encoding time and amount of compression, is compared with two well-known image compression methods.

M. J. Keil, J. Rodriguez: A Method for Generating Compound Spring Element Curves in Contact with Cylindrical Surfaces, 3 (1999) 067--076- This paper describes a method for enhancing the initial design process, as well as the transfer of data, for the geometry of compound contact springs. A force-length constrained model is developed around a cantilever beam section which has short (less than 10% of the beam's length) structural elements to facilitate proper positioning. The short elements are often considered insignificant in deflection analysis, but are shown to contribute an additional 26% to the structure's deflection. Once this is done, a mount position constrained model is developed which must be solved iteratively. The resulting geometry is smooth, precise, and can be readily transferred to CAD to complete a robust design process.

H. Yamazaki, K. Kondo: A Method of Changing a Color Scheme with Kansei Scales, 3 (1999) 077--084- The purpose of this research is to propose a method of changing a color scheme with Kansei scales. "Kansei" is a Japanese word that means the capability that feels an impression, such as "pathos", "feeling" and "sensitivity. "Kansei" also has meanings such as "sense", "sensibility", "sentiment", "emotion" and "intuition". A method of changing a color scheme with Kansei scales can easily change the color scheme of an image by using Kansei words such as "warm" and "dark". An impression of an image can be changed by it. We constructed a system in accordance with the method. There are three main features of our system. The first is that the system can change any color scheme of an image, because numerical expressions change a color scheme. The second is that the system can change a color scheme colorfully by five Kansei scales. The third is that the system can easily pick up the index colors from the original image, though a well experienced inspector has to decide color species comparing it with a color-catalogue.

D. K. Lieu: Using Interactive Multimedia Computer Tutorials for Engineering Graphics Education, 3 (1999) 085--092- Since the fall semester of 1996, the freshman engineering graphics class at UC Berkeley, with an annual enrollment of 300, has been using an interactive multimedia computer compact disk (CD) entitled "Graphics Interactive." It was assigned, in addition to a conventional text book, as required review material for the class. The CD assisted in visualizing the principles of orthogonal projection and sectioning in engineering drawing, geometric dimensioning and tolerancing, the geometric relationships involved in descriptive geometry, and other engineering graphics topics. The CD presented classical engineering graphics topics using a combination of animation, audio description, and interactive excercises. Results of surveys indicate that the new presentation media was extremely well received and helped with the understanding of the course material.

J. Pretorius: The Future or Graphical Communication Education in the New South Africa, 3 (1999) 093--098- This paper discusses the course in Graphical Communication at the Rand Afrikaans University. Not only the teaching method and the course and lecturer evaluation are presented in detail, but also an outlook on future possibilities concerning research, teacher education and curriculum development is given. One of the main educational problems is the very low level of spatial perception in the historically disadvantaged communities in South Africa.

K. Takeyama, R. Maeguchi, K. Chibana, K. Yoshida:: Evaluation of Objective Test Using a Pair of Orthographic Projections for Descriptive Geometry Education, 3 (1999) 099--110- This paper shows the results of tests that evaluate the effects of the education in orthographic projection. One of them is the "Objective Test" that was developed at Osaka University in 1994. The others are traditional pencil-and-paper tests. We have applied these two kinds of tests to students at Setsunan University from 1995 to 1997. The contents of the education at Setsunan University are different from those of Osaka University. The lectures and workshops at Setsunan University were carried out by pencil-and-paper, while those of Osaka University were carried out by 2D CAD. The results of the objective test have been very stable for three years. Two points to be improved are found out in the process of teaching. The objective test is useful for improving the education in Descriptive Geometry at the Setsunan University. The results of other courses related to Descriptive Geometry as workshops of architectural drawings are also discussed in this paper.

E. Tsutsumi, K. Shiina, A. Suzaki, K. Yamanouchi, T. Saito, K. Suzuki: A Mental Cutting Test on Female Students Using a Stereographic System, 3 (1999) 111--120- A stereographic mental cutting test (hereafter SMCT) was conducted to analyze 3D spatial abilities evaluated by a standard mental cutting test (hereafter MCT). The results of the analysis indicated that the MCT mainly reflects the abilities in making and manipulating three-dimensional mental images. The results also indicated that the subjects came to recognize 3D shapes more easily by using stereograms. However, the stereograms did not have any effect on complicated mental image processing tasks such as transformation of a section to a true shape view. Also, low scoring subjects in this study could not recognize the test solid and its cutting plane well, and they were unable to form correct images of objects, even when they used stereograms.

G. Glaeser: Reflections on Spheres and Cylinders of Revolution, 3 (1999) 121--140- In computer graphics, it is often an advantage to calculate reflections directly, especially when the application is time-critical or when line graphics have to be displayed. We specify formulas and parametric equations for the reflection on spheres and cylinders of revolution. The manifold of all reflected rays is the normal congruence of an algebraic surface of order four. Their catacaustic surfaces are given explicitly. The calculation of the reflex of a space point leads to an algebraic equation of order four. The up to four practical solutions are calculated exactly and efficiently. The generation of reflexes of straight lines is optimized. Finally, reflexes of polygons are investigated, especially their possible overlappings. Such reflexes are the key for the reflection of polyhedra and curved surfaces. We describe in detail how to display their contours.

C. Maeurer, B. Juettler: Rational Approximation of Rotation Minimizing Frames Using Pythagorean--Hodograph Cubics, 3 (1999) 141--160- This article is devoted to the rotation minimizing frames that are
associated with spatial curves. Firstly we summarize some results concerning
the differential geometry of the sweeping surfaces which are generated by
these frames (the so-called profile or moulding surfaces). In the second
part of the article we describe a rational approximation scheme. This scheme
is based on the use of spatial Pythagorean hodograph (PH) cubics (also called
cubic helices) as spine curves. We discuss the existence of solutions and the
approximation order of
*G*Hermite interpolation with PH cubics. It is shown that any spatial curve can approximately be converted into cubic PH spline form. By composing the rational Frenet-Serret frame of these curves with suitable rotations around the tangent we develop a highly accurate rational approximation of the rotation minimizing frame. This leads to an approximate rational representation of profile surfaces.^{1}

J. Pilnikova, P. Chalmoviansky: Basis of Quartic Splines over Triangulation, 3 (1999) 161--176- The modeling of complex shapes usually requires a well-based space of splines. The aim of this work is to give the construction method of such spline space basis over the chosen class of triangulations. This basis has several useful properties - local minimal support, low degree of polynomials. We also present several problems, that arise in lower-degree polynomials.

L. Varady, M. Hoffmann, E. Kovacs: Improved Free-form Modelling of Scattered Data by Dynamic Neural Networks, 3 (1999) 177--182- The aim of this paper is to improve the method of modelling scattered data by free-from surfaces presented in a former paper. In that method a neural network was used for ordering the data and forming a quadrilateral control grid from the scattered points, hence the standard free-form methods like Bezier-surface or NURBS could be applied to approximate or interpolate the data. Instead of the original artificial neural network, which has been used for ordering the data, now a recent development, the dynamic version of this neural network is applied. Hence the preprocess of ordering the spatial scattered data is based on the neural network, the improvement of the network yields a much faster and more reliable algorithm.

G. Weiss, K. Nestler, G. Meinl: Some Moebius-Geometric Theorems Connected to Euclidean Kinematics, 3 (1999) 183--192- To four positions of an object in the Euclidean plane there exists an infinite set of four-bar linkages interpolating these given positions. The set contains an interpolating slider-crank as a special case. The design of such a mechanism is based on geometric reasoning and the use of elementary geometric theorems. Usually such theorems and geometric mappings are proved by kinematic arguments. But they are also interesting for their own, independently from the kinematic point of view. There occur e.g. configurations of circles and lines related to Miquel's configuration in a (real) Moebius plane. Beginning with their kinematic aspects, some 'elementary' geometric theorems are discussed and generalized.

H. Abe, K. Yoshida: Measurement of Visualization Ability of Architectural Space, 3 (1999) 193--200- The Mental Cutting Test (MCT) is the well-known measurement of visualization ability, but MCT only addresses small objects used in descriptive geometry, not the large objects as buildings and architectural space enveloping the human body. In order to measure the visualization ability of the architectural space, the Plan Interpretation Test (PIT) is developed. To know the features of visualization ability of architectural space, PIT and MCT-J were applied to the 253 Osaka University students at the same time. The average score of PIT and MCT-J with standard deviation are 23.9 plus/minus 3.7 points (full score: 30 points), and 19.2 plus/minus 4.5 points (full score: 25 points), respectively. The correlation coefficient between the two is 0.3413. As far as the PIT applied in this experiment is concerned, the average score of the problems on the interior space is higher than that of exterior space. Moreover, the average score of the problems on the interior space enclosed in one floor is higher than the interior space open for two floors or more.

B. W. Field: A Course in Spatial Visualisation, 3 (1999) 201--210- One of the higher level skills required of engineers is that of spatial visualisation. A common measure of spatial visualisation is the Mental Cutting Test (MCT), where subjects attempt to identify the correct cross section resulting from a cut through a solid object, presented pictorially. When students in Engineering at Monash University were tested by the MCT, it was found that there was no apparent development of the skill over the duration of their course. However, students who had undertaken a special 52 hour course in Spatial Visualisation during 1995, 1996, 1997 or 1998 improved their MCT scores significantly compared to a control group of students. In the latter years, modified forms of the MCT were used: these variants were found to be slightly more difficult for weak visualisers, so their improvement in skill was reflected in a larger increase in MCT score. It was concluded that it was possible to increase the visualisation skills of students, where the MCT is used as the measure of the skill.

K. Shiina, K. Suzuki: Design of Modified Mental Rotations Test and its Error Analysis, 3 (1999) 211--218- A new version of the MRT (M-MRT) was designed by modifying the original MRT (V-MRT) in three ways. 1. The structural questions that may evoke strategies other than mental rotation were excluded. 2. Each part was composed of the same three-dimensional objects. 3. In order to make the difficulty of each part equal, the order of the questions was changed on the basis of the simulation of the data of the V-MRT. The M-MRT was administered to 250 subjects and the data was analyzed. There were significant differences of the mean scores in the M-MRT between sexes and majors. The mean score in the M-MRT was significantly larger than that in the V-MRT as for the low score groups. The larger mean score in the V-MRT in the low score groups might be due to the increase of the solving speed caused by the changes in the design of the M-MRT. The mean points of the complete-subjects were almost the same between questions which belong to different parts but are composed of the same objects. This suggests that the difficulties of each part are almost same. The increase of the mean score is considered to be caused by the higher solving speed for Part 2.

X. Sun, K. Suzuki: Evaluation of Educational Effects of the Solid Simulator, 3 (1999) 219--226- We have been developing computer graphics software, which can be run on a microcomputer and assists teaching and learning in early undergraduate graphics curricula. It is called "Solid Simulator" in which are available the generation, Boolean operations and dynamic projections of any polyhedra. During the academic year 1996 a new courseware of graphic science with a solid simulator as an additional instruction tool was developed and conducted in the University of Tokyo. In order to evaluate the courseware, we administered a set of student opinion questionnaires, a spatial test (MCT) and a term end test. The results of the evaluation showed that the new courseware was of significance in enhancing students' spatial ability and helping them to understand the contents of the course.