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.
- 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.
- A closed regular curve of class Cr (r >=2) in the
Euclidean 3-space having constant curvature kappa0>0 is called closed
kappa0-curve. We present various examples of nonplanar closed
kappa0-curves of class C2, which are composed of
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 C1 on the unit sphere S2 consisting of
n circular
arcs and having the center O* of S2 as its center of gravity.
The case when c* is a subset of the intersection of S2 and Pi is studied in detail, assuming
that Pi is a cube, or, more generally, a regular polyhedron the edges of
which are tangent to S2. In order to describe and to visualize the curves
c* and c, and to derive c from c*, projection methods of
Descriptive Geometry are used.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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).