http://graphics.cs.msu.su
January 19 - 20, 1994
Raytracing 3D Linear Graftals
Ph. Bekaert, Y. D. Willems
Dept. of Computing Science
Katholieke Universiteit Leuven
Celestijnenlaan 200A, 3001 Leuven, Belgium
philippe@cs.kuleuven.ac.be
Many objects in nature, like trees, mountains and
seashells, have a property called selfsimilarity.
Sometimes this property is very pronounced, other
natural phenomena exhibit this property to a lesser
degree. During the past years much attention has been
paid to fractals, purely selfsimilar objects.
We present a formalism, based on the well-known
object-instancing graph, to represent objects which are
not necessarily purely selfsimilar. We show that
Iterated Function Systems and some famous variants can
be described elegantly in this formalism. We also
present an algorithm to raytrace such objects.
Keywords: rendering, fractals, formal languages,
raytracing
Generating Plants for Computer Graphics
Bedrich Benes
CTU, Fac. of Electrical Eng.
Dept. of Computer Science
Karlovo nam.13
121 35 Praha 2
e-mail benes@cslab.felk.cvut.cz
Abstract is not available.
Keywords : Tree, L-system, Rendering,
Computer Graphics
A Mathematical Framework for Global Illumination
Algorithms
Ph.Dutre, E.Lafortune, Y.D.Willems
{philipd, ericl, ydw}@cs.kuleuven.ac.be
Department pf Computing Science
Katholieke Universiteit Leuven
Celestijnenlaan 200A
B-3001 Heverlee, Belgium
This paper describes a mathematical framework for
rendering algorithms. Starting from the rendering
equation and the potential equation, we will introduce
the Global Reflection Distribution Function (GRDF). By
using GRDF, we are able to compute the behaviour of
light in an environment, independent of the initial
lighting or viewpoint conditions. This framework is able
to describe most existing rendering algorithms.
Cubic Monte Carlo Radiosity
Pavol Elias, Martin Feda, Peter Ferschin,
Werner Purgathofer
Department of Applied Mathematics
Faculty of Mathematics and Physics, Comenius University,
842 15 Bratislava, Slovakia
e-mail elias@delta.dcs.fmph.uniba.sk
Institute of Computer Graphics
Technical University of Vienna
Karlsplatz 13/186 A-1040 Vienna, Austria
e-mail elias@eigvs4.una.ac.at
A revised radiosity method for curved surfaces is
proposed, based on the Monte Carlo approach. In
order to improve the accuracy of the solution,
a smoothly reconstructed illumination function with
selected discontinuities is used during the radiosity
computation. The reconstructed function is used as
a random number distribution for position sampling to
overcome the constant radiosity assumption syndrome.
Illumination information stored at the surface control
points is used to preserve continuity of the
illumination across the boundary of adjacent surfaces
and to avoid Mach band effects. Implementation in
Flatland is discussed.
Prehlad normalizovanych grafickych systemov
Andrej Ferko
MFF UK, 842 15 Bratislava, SR
ferko@fmph.uniba.sk
The paper deals with the survey of standardized graphics
systems from the point of view of a course for computer
graphics students. This Comenius University course is
based on a new textbook [ErFe93] on this topic which
seems to be a very useful notional and conceptual tool
for systematic understanding to the functionality and
architecture of any graphics system.
Fractal Based Procedural Modelling
Norbert Filip
Department of Geometry
Faculty of Mathematics and Physics
Comenius University
842 15 Bratislava, Slovakia
e-mail filip@delta.dcs.fmph.uniba.sk
Two different methods for procedurally based modelling
are presented as an alternative to the interactive
modelling. Fractal and graftal techniques are shown to
be the possibilities for modelling of natural phenomena
as terrain shapes and trees. Different issues of
consistency for fractal based terrain modelling are
discussed. Second part of the paper shows several
problems of graftal and L-systems trees modelling.
Attention is focused on modeling of branches, the
problem of "twisted" branches and branch connections are
solved. The paper contains remarks towards the
implementation of presented ideas.
Coherence in scan-line algorithms for CSG
Eduard Gröller, Peter Brunner
Technical University Vienna
Institute for Computergraphics
Karlsplatz 13/186/2
A-1040 Vienna, Austria
Tel.:+43(1)58801-4582
FAX:+43(1)5874932
e-mail groeller@eigvs4.tuwien.ac.at
Scan-line algorithms for visibility calculation exploit
various types of coherence properties. Several scan-line
algorithms for Constructive Solid Geometry (CSG)are
discussed. In one approach CSG primitives are
represented by polygonal approximations. Another
technique processes CSG primitives as general quadric
surfaces. We investigate the handling of frequently
occuring quadric surfaces (cube, cone, sphere, cylinder)
as distinct cases. Thus the differing properties of such
objects can be used more efficiently than a uniform
approach would allow. A so called eBRep (extended
Boundary Representation) is defined for the frequently
occuring quadric surfaces. An eBRep is an exact
representation of of a quadric object and contains
curved edges and faces. For each of the above mentioned
quadric surfaces a different, geometry dependent eBRep
is specified. A comparison between the polygon-based
scan-line algorithm for CSG and our eBRep based approach
is done. eBRep is a storage efficient exact
representation of quadric surfaces, well suited for
scan-line visibility determination.
Keywords: CSG, quadrics, scan-line alghoritm, extended
BRep, curved edges
Graphics Systems PHIGS and PHIGS+
Bohuslav Hudec
Dept. of computers
Electrotechnical Faculty of Czech Technical University
Prague
e-mail hudec@cs.felk.cvut.cz
The PHIGS (Programmer's Hierarchical Interactive
Graphics System) is an international ISO standard of
a functional interface between an application program
and a configuration of graphical input and output
devices. This interface contains basic functions for
dynamic interactive 2D and 3D graphics on wide variety
of graphics equippment.
G2 Continuous Beta-spline Curves Defined
on the Interval <0,1)
Maria Imriskova
Radlinskeho 11, 813 68 Bratislava, SR
e-mail imriskov@cvt.stuba.sk
In this paper, the general and special matrices forms
of the cubic beta-spline curve defined on the interval
<0,1) are described.
Visualisation of the Volume Datasets in Science
Juraj Jankovic
Faculty of Mathematics and Physics
Comenius University,
842 15 Bratislava, Slovakia
Volume visualisation is one of the fast-growing areas in
scientific visualisation. It helps to look at scalar or
vector datasets and understand them more easily. An
overview of basic algorithms used for this purpose, some
of enhancements and optimizations are described here.
Semiregular Grids in 2D and 3D
Alexej Kolcun
Institute of geonics
Academy of Sciences of Czech Republic
Studentska 1768, 70200 Ostrava, Czech Republic
Advantages of grids used in finite element analysis ( FEM ),
which are similar to regular, are described in [5]. We
show posibilities of generation and transformation of
such grids and we make comparison of them in 2D. We show
dificulties arising in 3D.
Creating Convex Hulls in E2 Using Dual Representation
Ivana Kolingerova
Department of Computer Science
University of West Bohemia
Americka 42, 306 14 Plzen
Czech Republic
e-mail kolinger@kiv.zcu.cz
The dual representation of points, lines and polygons
introduced in [Gun88] can also be used for computing
convex hulls of a set of points in E2. The main
principles of the dual representation and a sketch of
the algorithm for convex hull computation are given
in this paper. Algorithm can be used both for statical
and semi-dynamical case. More details can be seen
in [Kol94].
Fractal Volumes
C. Kose, C.P.Willis and D.J.Paddon
Department of Computer Science,
University of Bristol,
Queens Building,
University Walk,
Bristol BS8 1TR, UK.
e-mail derek@compsci.bristol.ac.uk
A Mandelbrot set, in quaternion representation, is used
as a test data set to research the necessary
characteristics of a system that visualises large and
complex data sets. An image space software solution is
developed that uses dynamic data partitioning across
a distributed system of processors. A system
configuration is used that minimised the network
diameter in order to reduce the communications overhead.
Simple Graphic CAM System Controlling the Cutting
Machine
Miloslav Kosek
Department of Electrical Engineering
Fculty of Textile Engineering
Technical University of Liberec, Czech Republic
A CAM system using a personal computer for the control
of a cutting machine is described. The key part of the
system is a database of suits. It contains commands
that areprocessed by a personal computer. The computer
can control a drawing or cutting machine that draws or
cuts contours of style parts. The attention is focused
namely to the transform of standard instructions that
are understood by a tailor to commands that drive the
computer.
X Window System
Ales Limpouch
Department of computers
Faculty of Electrical Engineering
Czech Technical University
e-mail limpouch@cs.felk.cvut.cz
The X Window System has, over the last few years,
become increasingly important and it is now accepted
as THE window system for workstations, mainframes and
supercomputers. It has become the standard means of
providing graphical facilities on UNIX systems. This
paper gives a brief overview of fundamental principles,
concepts and architecture of the X system and describes
in detail essential characteristics of the X server.
Keywords : graphical user interface, window management
system, X Window System, X server
Pouzitie octree struktury na urychlenie metody ray
tracing
Jozef Martinka
Katedra aplikovanej matematiky
Matematicko fyzikalna fakulta Univerzity Komenskeho
842 15 Bratislava, Slovenska republika
e-mail jozef.martinka@st.fmph.uniba.sk
Niektore sposoby urychlenia metody ray tracing vyuzivaju
priestorove rozdelenie sceny a jej reprezentaciu pomocou
octree struktury. Hlavne problemy spojene s pouzitim
octree su: vhodna reprezentacia, efektivny sposob
vytvorenia (rozdelenia sceny na kocky octree) a rychly
"prechod" sledovaneho luca cez strukturu. V clanku su
strucne popisane niektore pristupy k rieseniu tychto
problemov.
Triangular Patches under Tension
F. Schindler
Dept. of Computer Science and Engineering
Slovak Technical University
SK-81219 Bratislava, Slovakia
Given a triangular surface scheme that only approximates
the initial data the resulting surfaces do not reflect
the shape of control vertices as much as the user would
have liked. By supplying tension parameters, or what in
this case might be called "shape" parameters, the user
is able to force the triangular surface patch to folow
the control vertices as close as desired without moving
or introducing additional control point
A revised radiosity method for curved surfaces is
proposed, based on the Monte Carlo approach. In
order to improve the accuracy of the solution,
a smoothly reconstructed illumination function with
selected discontinuities is used during the radiosity
computation. The reconstructed function is used as
a random number distribution for position sampling to
overcome the constant radiosity assumption syndrome.
Illumination information stored at the surface control
points is used to preserve continuity of the
illumination across the boundary of adjacent surfaces
and to avoid Mach band effects. Implementation in
Flatland is discussed.
O(lg N) Line Clipping Algorithm in E2
Vaclav Skala
Department of Informatics and Computer Science
University of West Bohemia
Americka 42, Box 314, 306 14 Plzen Czech Republic
e-mail skala@kiv.zcu.cz
A new O(lg N) line clipping algorithm in E2 against a convex
window is presented. The main advantage of the presented
algorithm is the principal acceleration of the line clipping
problem solution. A comparison of the proposed algorithm
with others shows a significant improvement in run-time.
Experimental results for selected known algorithms are also
shown.
Keywords : Line clipping, Convex polygon, Computer graphics,
Algorithm complexity.
Graf potencialu viditelnosti
Eduard Sojka
Katedra informatiky FEL VSB Ostrava
tr.17.listopadu
708 00 Ostrava-Poruba
e-mail eduard.sojka@vsb.cz
Clanek podava novy pohled na teorii potencialu viditelnosti.
Tento pohled predpoklada, ze na mnozine obrazu dane sceny
lze zavest relaci ekvivalence. Tato relace pak indukuje
rozklad mnoziny obrazu, ktera je nekonecna, na konecny pocet
trid. Take prostor obklopujici scenu je dekomponovan na
tridy. Ze vsech bodu jedne tridy vnima pozorovatel
ekvivalentni obrazy. Graf potencialu viditelnosti zachycuje
informaci o techto tridach a vztazich mezi nimi. Predkladana
teorie umoznuje zasadit publikovane pristupy do jednotneho
ramce. Pouziti teorie je ilustrovano na nekolika prikladech.
Graf potencialu viditelnosti muze byt puzit jako
alternativni nebo doplnkovy model sceny a muze byt uzitecny
pri reseni ruznych problemu jako je napriklad problem
viditelnosti, problem navigace ve scene a problem rozpoznani
trojrozmernych objektu.
Klicova slova: graf potencialu viditelnosti, graf aspektu,
viditelnost.
Parallel Progresive Radiosity with Parallel Visibility
Computations
W. Stürzlinger and C. Wild
Institute for Computer science,
Johannes Kepler University of Linz,
Department for graphical and parallel processing
Altenbergerstrasse 69, A-4040 Linz, Austria
Tel.:+43(732)2468-884
Fax :+43(732)2468-10
e-mail wrzl@gup.uni-linz.ac.at
The radiosity method models the interaction of light
between diffuse reflecting surfaces, thereby accurately
predicting global illumination effects. Due to the high
computational effort to calculate the transfer of light
between surfaces and the memory requirements for the
scene description, a distributed, parallelized version
of the algoritm is needed for scenes consisting of
thousands of surfaces. We present a distributed,
parallel radiosity algoritm, which can subdivide the
surface adaptively. Aditionally we present a scheme
for
paralel visibility calculations. Adaptive load
redistribution is also discussed.
Computer Graphics Hardware
Miroslav Snorek
Dept of Computers, Electrical faculty
Czech Technical University of Prague
Abstract is not available.
An Algorithm for Fast Voxel Scene Traversal
Milos Sramek
Institute of Measurement Science
Slovak Academy of Science
Dubravska cesta 9
842 19 Bratislava
SR
Together with improvement of tomographic method of
scanning 3D data, residing in an increase of
distinguishing ability of the scanners, the quality of
final 3D reconstruction of the data comes into
foreground. An inevitable condition for visualization
of small details, comparable with the voxel size is
application of such algorithms, which enable to define
a surface of the scanned object on subvoxel level.
Comong out from paper published at previous year of
Winter School on Computer Graphics and CAD Systems we
present an algorithm for fast traversal of the voxel
scene, which enables to find a nearest intersection of
a ray with the object surface defined in such way.
High speed of the algorithm utilizes object coherency
of the scene, which means that voxels belonging to the
object are usually grouped in connected regions.
The algorithm consists from two steps :
preprocessing and scene traversal. In the preprocessing
phase we assign to each background voxel of the
segmented scene a value equal to its chessboard
distance from the nearest object voxel, which defines
a cubic macro region with no voxels inside. While
generating a discrete ray, we can jump over this
region, which results in up to 6-fold speed up of the
traversal. The algorithm has no additional demands on
memory, since the distance is stored in originally
"empty" backgroud voxels.
Demonstration Constructive du Theoreme de Pohlke-Schwarz
Svatopluk Zacharias
katedra matematiky Zapadoceske Univerzity
Americka 42
306 14 Plzen, CR
Abstract is not available.
Parallelisation of the Ray Tracing Algorithm
Jiri Zara (zara@cs.felk.cvut.cz)
Ales Holecek (xholecek@sun.felk.cvut.cz)
Jan Prikryl (xprikryl@sun.felk.cvut.cz)
CTU, Fac.of Electrical Eng.
Dept.of Computer Science
Karlovo nam.13
121 35 Praha 2
The two typical methods for distribution of ray tracing
rendering algorithm are presented in this article. The
implementation of a distributed ray-tracer on a network
of UNIX workstations is described in details. The first
results are discussed from the point of view of memory
load, time of computation and cost of communication
among processes.
Keywords: computer graphics, rendering, parallel
algorithm, ray-tracing, PVM
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