EG1988 Proceedings (Technical Papers)

Permanent URI for this collection


Tools for Efficient Photo-Realistic Computer Animation

Stößer, Achim
Schmitt, Alfred
Neidecker, Burkhard
Müller, Heinrich
Maus, Thomas
Leister, Wolfgang

Grafields: Field-Directed Dynamic Splines for Interactive Motion Control

Pintado, Xavier
Fiume, Eugene

IXPHIGS: A Portable Implementation of the International PHIGS Standard

Gorog, Jenö
Krammer, Gergely
Vincze, Arpad

The Development of PHEX, a 3D Graphics Extension to X11

Clifford Jr., William H.
McConnell, John I.
Saltz, Jeffrey S.

COLOUR SECTION

Various

Application Profiles for Computer Graphics Standards - A Touch of Realism

Mumford, Anne M.

An Expert System for Polyhedra Modelling

Martin, Philippe
Martin, Dominique

A Compositional Semantics for Graphics

Pineda, Luis A.

Towards a System for Exploring the Universe of Polyhedral Shapes

Colin, Christian

A Formal Specification of a Boundary Representation

Baumann, Peter

Construction and Animation of a Synthetic Actress

Magnenat-Thalmann, N.
Thalmann, D.

METAVIEWS: A Process-Oriented Approach to CAD and Graphics

Takala, Tapio

Conversion of Boundary Representations to Bintrees

Diehl, Rabanus

Generation of High-Quality Curve and Surface with Smoothly Varying Curvature

Higashi, Masatake
Kaneko, Kohji
Hosaka, Mamoru

Using Algebraic Constraints in Interactive Text and Graphics Editing

Li, Jiarong

Boundary to Constructive Solid Geometry: A Step Towards 3D Conversion

Juan, R.

A Procedural System for the Definition and Storage of Technical Drawings in Parametric Form

Cugini, U.
Folini, F.
Vicini, I.

A New Algorithm for Converting Boundary Representation to Octree

Tang, Zesheng
Lu, Shengkai

Automatic Detection of Closed Parametric Surfaces without Interior

Seidel, Hans-Peter

Conic Beta-Splines with Local Tension Control for Interactive Curve Fitting

Pham, Binh

A Simple Spectral Approach to Stochastic Modelling for Natural Objects

Anjyo, Ken-ichi

Liberation from Rectangles: A Tiling Method for Dynamic Modification of Objects on Raster Displays

Slater, Mel
Davison, Allan
Smith, Mark

A Evalution of Some Three-Color Tiling Patterns

Alt, Paul
Cordonnier, Vincent

An Object-Oriented Approach to Process Monitoring

Hütter, Ronald

Experimenting with a Parallel Ray-Tracing Algorithm on a Hypercube Machine

Priol, Thierry
Bouatouch, Kadi

Free-Form Surfaces Modeling by Evolution Simulation

Lienhardt, Pascal

Animation of Stochastic Model-Based 3-D Textures

Gagalowicz, Andre
Ma, Song D.

Architectures for Mass Market 3D Displays

Winser, Paul
Bonnet, Thierry
Dumont, Dominique
Mathieu, Yves

Fractal Approximation of 2-D Object

Levy-Vehel, J.
Gagalowicz, A.

G1 Smoothing Solid Objects by Bicubic Bezier Patches

Liang, Youdong
Ye, Xiuzi
Fang, Shiaofen

A System for Graphical Interaction on Parametrized Models

Van Emmerik , Maarten J.G.M.

Efficient Adaptive Subdivision of Bezier Surfaces

Clay, Reed D.
Moreton, Henry P.

Outline Phase Control for Character Rasterization

Hersch, R. D.

Pseudo Ordering of CSG-Trees

Cottingham, Marion S.

Form-Factors for General Environments

Shao, Ping-Pine
Peng, Qun-Sheng
Liang, You-Done

The Calculus of the Non-Exact Perspective Projection - Scene-Shifting for Computer Animation

Hofmann, Georg Rainer

A Method for Providing Full Interactive Control of the Shape of 3-D Curves and Surfaces

Cros, Frederic
Brock, Philip J.

An Evaluation of CSG Trees Based on Polyhedral Solids

Badouel, Didier
Hegron, Gerard

Optimal Texture Mapping

De Ma, Song
Lin, Hong

Monte-Carlo Integration Applied to an Illumination Model

Bouville, C.
Dubois, J.L.
Marchal, I.
Viaud, M.L.

Fast Algorithm for Polygon Clipping with 3D Windows

Burkert, Andreas
Noll, Stefan


BibTeX (EG1988 Proceedings (Technical Papers))
@inproceedings{
10.2312:egtp.19881003,
booktitle = {
EG 1988-Technical Papers},
editor = { title = {{
Tools for Efficient Photo-Realistic Computer Animation}},
author = {
Stößer, Achim
and
Schmitt, Alfred
and
Neidecker, Burkhard
and
Müller, Heinrich
and
Maus, Thomas
and
Leister, Wolfgang
}, year = {
1988},
publisher = {
Eurographics Association},
ISSN = {1017-4656},
DOI = {
10.2312/egtp.19881003}
}
@inproceedings{
10.2312:egtp.19881004,
booktitle = {
EG 1988-Technical Papers},
editor = { title = {{
Grafields: Field-Directed Dynamic Splines for Interactive Motion Control}},
author = {
Pintado, Xavier
and
Fiume, Eugene
}, year = {
1988},
publisher = {
Eurographics Association},
ISSN = {1017-4656},
DOI = {
10.2312/egtp.19881004}
}
@inproceedings{
10.2312:egtp.19881001,
booktitle = {
EG 1988-Technical Papers},
editor = { title = {{
IXPHIGS: A Portable Implementation of the International PHIGS Standard}},
author = {
Gorog, Jenö
and
Krammer, Gergely
and
Vincze, Arpad
}, year = {
1988},
publisher = {
Eurographics Association},
ISSN = {1017-4656},
DOI = {
10.2312/egtp.19881001}
}
@inproceedings{
10.2312:egtp.19881002,
booktitle = {
EG 1988-Technical Papers},
editor = { title = {{
The Development of PHEX, a 3D Graphics Extension to X11}},
author = {
Clifford Jr., William H.
and
McConnell, John I.
and
Saltz, Jeffrey S.
}, year = {
1988},
publisher = {
Eurographics Association},
ISSN = {1017-4656},
DOI = {
10.2312/egtp.19881002}
}
@inproceedings{
10.2312:egtp.19881040,
booktitle = {
EG 1988-Technical Papers},
editor = { title = {{
COLOUR SECTION}},
author = {
Various
}, year = {
1988},
publisher = {
Eurographics Association},
ISSN = {1017-4656},
DOI = {
10.2312/egtp.19881040}
}
@inproceedings{
10.2312:egtp.19881000,
booktitle = {
EG 1988-Technical Papers},
editor = { title = {{
Application Profiles for Computer Graphics Standards - A Touch of Realism}},
author = {
Mumford, Anne M.
}, year = {
1988},
publisher = {
Eurographics Association},
ISSN = {1017-4656},
DOI = {
10.2312/egtp.19881000}
}
@inproceedings{
10.2312:egtp.19881018,
booktitle = {
EG 1988-Technical Papers},
editor = { title = {{
An Expert System for Polyhedra Modelling}},
author = {
Martin, Philippe
and
Martin, Dominique
}, year = {
1988},
publisher = {
Eurographics Association},
ISSN = {1017-4656},
DOI = {
10.2312/egtp.19881018}
}
@inproceedings{
10.2312:egtp.19881013,
booktitle = {
EG 1988-Technical Papers},
editor = { title = {{
A Compositional Semantics for Graphics}},
author = {
Pineda, Luis A.
}, year = {
1988},
publisher = {
Eurographics Association},
ISSN = {1017-4656},
DOI = {
10.2312/egtp.19881013}
}
@inproceedings{
10.2312:egtp.19881017,
booktitle = {
EG 1988-Technical Papers},
editor = { title = {{
Towards a System for Exploring the Universe of Polyhedral Shapes}},
author = {
Colin, Christian
}, year = {
1988},
publisher = {
Eurographics Association},
ISSN = {1017-4656},
DOI = {
10.2312/egtp.19881017}
}
@inproceedings{
10.2312:egtp.19881012,
booktitle = {
EG 1988-Technical Papers},
editor = { title = {{
A Formal Specification of a Boundary Representation}},
author = {
Baumann, Peter
}, year = {
1988},
publisher = {
Eurographics Association},
ISSN = {1017-4656},
DOI = {
10.2312/egtp.19881012}
}
@inproceedings{
10.2312:egtp.19881005,
booktitle = {
EG 1988-Technical Papers},
editor = { title = {{
Construction and Animation of a Synthetic Actress}},
author = {
Magnenat-Thalmann, N.
and
Thalmann, D.
}, year = {
1988},
publisher = {
Eurographics Association},
ISSN = {1017-4656},
DOI = {
10.2312/egtp.19881005}
}
@inproceedings{
10.2312:egtp.19881014,
booktitle = {
EG 1988-Technical Papers},
editor = { title = {{
METAVIEWS: A Process-Oriented Approach to CAD and Graphics}},
author = {
Takala, Tapio
}, year = {
1988},
publisher = {
Eurographics Association},
ISSN = {1017-4656},
DOI = {
10.2312/egtp.19881014}
}
@inproceedings{
10.2312:egtp.19881010,
booktitle = {
EG 1988-Technical Papers},
editor = { title = {{
Conversion of Boundary Representations to Bintrees}},
author = {
Diehl, Rabanus
}, year = {
1988},
publisher = {
Eurographics Association},
ISSN = {1017-4656},
DOI = {
10.2312/egtp.19881010}
}
@inproceedings{
10.2312:egtp.19881007,
booktitle = {
EG 1988-Technical Papers},
editor = { title = {{
Generation of High-Quality Curve and Surface with Smoothly Varying Curvature}},
author = {
Higashi, Masatake
and
Kaneko, Kohji
and
Hosaka, Mamoru
}, year = {
1988},
publisher = {
Eurographics Association},
ISSN = {1017-4656},
DOI = {
10.2312/egtp.19881007}
}
@inproceedings{
10.2312:egtp.19881016,
booktitle = {
EG 1988-Technical Papers},
editor = { title = {{
Using Algebraic Constraints in Interactive Text and Graphics Editing}},
author = {
Li, Jiarong
}, year = {
1988},
publisher = {
Eurographics Association},
ISSN = {1017-4656},
DOI = {
10.2312/egtp.19881016}
}
@inproceedings{
10.2312:egtp.19881011,
booktitle = {
EG 1988-Technical Papers},
editor = { title = {{
Boundary to Constructive Solid Geometry: A Step Towards 3D Conversion}},
author = {
Juan, R.
}, year = {
1988},
publisher = {
Eurographics Association},
ISSN = {1017-4656},
DOI = {
10.2312/egtp.19881011}
}
@inproceedings{
10.2312:egtp.19881015,
booktitle = {
EG 1988-Technical Papers},
editor = { title = {{
A Procedural System for the Definition and Storage of Technical Drawings in Parametric Form}},
author = {
Cugini, U.
and
Folini, F.
and
Vicini, I.
}, year = {
1988},
publisher = {
Eurographics Association},
ISSN = {1017-4656},
DOI = {
10.2312/egtp.19881015}
}
@inproceedings{
10.2312:egtp.19881009,
booktitle = {
EG 1988-Technical Papers},
editor = { title = {{
A New Algorithm for Converting Boundary Representation to Octree}},
author = {
Tang, Zesheng
and
Lu, Shengkai
}, year = {
1988},
publisher = {
Eurographics Association},
ISSN = {1017-4656},
DOI = {
10.2312/egtp.19881009}
}
@inproceedings{
10.2312:egtp.19881008,
booktitle = {
EG 1988-Technical Papers},
editor = { title = {{
Automatic Detection of Closed Parametric Surfaces without Interior}},
author = {
Seidel, Hans-Peter
}, year = {
1988},
publisher = {
Eurographics Association},
ISSN = {1017-4656},
DOI = {
10.2312/egtp.19881008}
}
@inproceedings{
10.2312:egtp.19881006,
booktitle = {
EG 1988-Technical Papers},
editor = { title = {{
Conic Beta-Splines with Local Tension Control for Interactive Curve Fitting}},
author = {
Pham, Binh
}, year = {
1988},
publisher = {
Eurographics Association},
ISSN = {1017-4656},
DOI = {
10.2312/egtp.19881006}
}
@inproceedings{
10.2312:egtp.19881023,
booktitle = {
EG 1988-Technical Papers},
editor = { title = {{
A Simple Spectral Approach to Stochastic Modelling for Natural Objects}},
author = {
Anjyo, Ken-ichi
}, year = {
1988},
publisher = {
Eurographics Association},
ISSN = {1017-4656},
DOI = {
10.2312/egtp.19881023}
}
@inproceedings{
10.2312:egtp.19881030,
booktitle = {
EG 1988-Technical Papers},
editor = { title = {{
Liberation from Rectangles: A Tiling Method for Dynamic Modification of Objects on Raster Displays}},
author = {
Slater, Mel
and
Davison, Allan
and
Smith, Mark
}, year = {
1988},
publisher = {
Eurographics Association},
ISSN = {1017-4656},
DOI = {
10.2312/egtp.19881030}
}
@inproceedings{
10.2312:egtp.19881021,
booktitle = {
EG 1988-Technical Papers},
editor = { title = {{
A Evalution of Some Three-Color Tiling Patterns}},
author = {
Alt, Paul
and
Cordonnier, Vincent
}, year = {
1988},
publisher = {
Eurographics Association},
ISSN = {1017-4656},
DOI = {
10.2312/egtp.19881021}
}
@inproceedings{
10.2312:egtp.19881029,
booktitle = {
EG 1988-Technical Papers},
editor = { title = {{
An Object-Oriented Approach to Process Monitoring}},
author = {
Hütter, Ronald
}, year = {
1988},
publisher = {
Eurographics Association},
ISSN = {1017-4656},
DOI = {
10.2312/egtp.19881029}
}
@inproceedings{
10.2312:egtp.19881020,
booktitle = {
EG 1988-Technical Papers},
editor = { title = {{
Experimenting with a Parallel Ray-Tracing Algorithm on a Hypercube Machine}},
author = {
Priol, Thierry
and
Bouatouch, Kadi
}, year = {
1988},
publisher = {
Eurographics Association},
ISSN = {1017-4656},
DOI = {
10.2312/egtp.19881020}
}
@inproceedings{
10.2312:egtp.19881026,
booktitle = {
EG 1988-Technical Papers},
editor = { title = {{
Free-Form Surfaces Modeling by Evolution Simulation}},
author = {
Lienhardt, Pascal
}, year = {
1988},
publisher = {
Eurographics Association},
ISSN = {1017-4656},
DOI = {
10.2312/egtp.19881026}
}
@inproceedings{
10.2312:egtp.19881025,
booktitle = {
EG 1988-Technical Papers},
editor = { title = {{
Animation of Stochastic Model-Based 3-D Textures}},
author = {
Gagalowicz, Andre
and
Ma, Song D.
}, year = {
1988},
publisher = {
Eurographics Association},
ISSN = {1017-4656},
DOI = {
10.2312/egtp.19881025}
}
@inproceedings{
10.2312:egtp.19881022,
booktitle = {
EG 1988-Technical Papers},
editor = { title = {{
Architectures for Mass Market 3D Displays}},
author = {
Winser, Paul
and
Bonnet, Thierry
and
Dumont, Dominique
and
Mathieu, Yves
}, year = {
1988},
publisher = {
Eurographics Association},
ISSN = {1017-4656},
DOI = {
10.2312/egtp.19881022}
}
@inproceedings{
10.2312:egtp.19881024,
booktitle = {
EG 1988-Technical Papers},
editor = { title = {{
Fractal Approximation of 2-D Object}},
author = {
Levy-Vehel, J.
and
Gagalowicz, A.
}, year = {
1988},
publisher = {
Eurographics Association},
ISSN = {1017-4656},
DOI = {
10.2312/egtp.19881024}
}
@inproceedings{
10.2312:egtp.19881027,
booktitle = {
EG 1988-Technical Papers},
editor = { title = {{
G1 Smoothing Solid Objects by Bicubic Bezier Patches}},
author = {
Liang, Youdong
and
Ye, Xiuzi
and
Fang, Shiaofen
}, year = {
1988},
publisher = {
Eurographics Association},
ISSN = {1017-4656},
DOI = {
10.2312/egtp.19881027}
}
@inproceedings{
10.2312:egtp.19881019,
booktitle = {
EG 1988-Technical Papers},
editor = { title = {{
A System for Graphical Interaction on Parametrized Models}},
author = {
Van Emmerik , Maarten J.G.M.
}, year = {
1988},
publisher = {
Eurographics Association},
ISSN = {1017-4656},
DOI = {
10.2312/egtp.19881019}
}
@inproceedings{
10.2312:egtp.19881028,
booktitle = {
EG 1988-Technical Papers},
editor = { title = {{
Efficient Adaptive Subdivision of Bezier Surfaces}},
author = {
Clay, Reed D.
and
Moreton, Henry P.
}, year = {
1988},
publisher = {
Eurographics Association},
ISSN = {1017-4656},
DOI = {
10.2312/egtp.19881028}
}
@inproceedings{
10.2312:egtp.19881031,
booktitle = {
EG 1988-Technical Papers},
editor = { title = {{
Outline Phase Control for Character Rasterization}},
author = {
Hersch, R. D.
}, year = {
1988},
publisher = {
Eurographics Association},
ISSN = {1017-4656},
DOI = {
10.2312/egtp.19881031}
}
@inproceedings{
10.2312:egtp.19881037,
booktitle = {
EG 1988-Technical Papers},
editor = { title = {{
Pseudo Ordering of CSG-Trees}},
author = {
Cottingham, Marion S.
}, year = {
1988},
publisher = {
Eurographics Association},
ISSN = {1017-4656},
DOI = {
10.2312/egtp.19881037}
}
@inproceedings{
10.2312:egtp.19881039,
booktitle = {
EG 1988-Technical Papers},
editor = { title = {{
Form-Factors for General Environments}},
author = {
Shao, Ping-Pine
and
Peng, Qun-Sheng
and
Liang, You-Done
}, year = {
1988},
publisher = {
Eurographics Association},
ISSN = {1017-4656},
DOI = {
10.2312/egtp.19881039}
}
@inproceedings{
10.2312:egtp.19881034,
booktitle = {
EG 1988-Technical Papers},
editor = { title = {{
The Calculus of the Non-Exact Perspective Projection - Scene-Shifting for Computer Animation}},
author = {
Hofmann, Georg Rainer
}, year = {
1988},
publisher = {
Eurographics Association},
ISSN = {1017-4656},
DOI = {
10.2312/egtp.19881034}
}
@inproceedings{
10.2312:egtp.19881035,
booktitle = {
EG 1988-Technical Papers},
editor = { title = {{
A Method for Providing Full Interactive Control of the Shape of 3-D Curves and Surfaces}},
author = {
Cros, Frederic
and
Brock, Philip J.
}, year = {
1988},
publisher = {
Eurographics Association},
ISSN = {1017-4656},
DOI = {
10.2312/egtp.19881035}
}
@inproceedings{
10.2312:egtp.19881036,
booktitle = {
EG 1988-Technical Papers},
editor = { title = {{
An Evaluation of CSG Trees Based on Polyhedral Solids}},
author = {
Badouel, Didier
and
Hegron, Gerard
}, year = {
1988},
publisher = {
Eurographics Association},
ISSN = {1017-4656},
DOI = {
10.2312/egtp.19881036}
}
@inproceedings{
10.2312:egtp.19881033,
booktitle = {
EG 1988-Technical Papers},
editor = { title = {{
Optimal Texture Mapping}},
author = {
De Ma, Song
and
Lin, Hong
}, year = {
1988},
publisher = {
Eurographics Association},
ISSN = {1017-4656},
DOI = {
10.2312/egtp.19881033}
}
@inproceedings{
10.2312:egtp.19881038,
booktitle = {
EG 1988-Technical Papers},
editor = { title = {{
Monte-Carlo Integration Applied to an Illumination Model}},
author = {
Bouville, C.
and
Dubois, J.L.
and
Marchal, I.
and
Viaud, M.L.
}, year = {
1988},
publisher = {
Eurographics Association},
ISSN = {1017-4656},
DOI = {
10.2312/egtp.19881038}
}
@inproceedings{
10.2312:egtp.19881032,
booktitle = {
EG 1988-Technical Papers},
editor = { title = {{
Fast Algorithm for Polygon Clipping with 3D Windows}},
author = {
Burkert, Andreas
and
Noll, Stefan
}, year = {
1988},
publisher = {
Eurographics Association},
ISSN = {1017-4656},
DOI = {
10.2312/egtp.19881032}
}

Browse

Recent Submissions

Now showing 1 - 41 of 41
  • Item
    Tools for Efficient Photo-Realistic Computer Animation
    (Eurographics Association, 1988) Stößer, Achim; Schmitt, Alfred; Neidecker, Burkhard; Müller, Heinrich; Maus, Thomas; Leister, Wolfgang
    The goal of the project “Occursus Cum Novo” was to generate a complex photo-realistic animation of nontrivial length in reasonable time at reasonable cost. Photographic realism comprises complex geometric models as well as the implementation of several optical effects. Both can be achieved by simulation. Simulations guaranteeing high quality, as ray tracing does for rendering, are known to be very time consuming. They require the design of powerful data structures and algorithms taking the abilities of todays hardware into account. The first part of this paper is devoted to rendering, here carried out by the raytracing method. An organizing scheme for a network of work stations is described which enabled us to generate 5-minutes of raytraced animation within 2 months without affecting any regular user of the work stations. The second part is devoted to the simulative modeling tools applied in “Occursus Cum Novo”. The recursive generator WAXI and a motion simulator METAMORPHOSIS are described to some detail. The results of the project are of general interest since they show a way leading to efficient high quality photo-realistic animation synthesis in the future.
  • Item
    Grafields: Field-Directed Dynamic Splines for Interactive Motion Control
    (Eurographics Association, 1988) Pintado, Xavier; Fiume, Eugene
    This paper presents an interactive system for motion control that emphasizes object interaction. The fundamental mechanism provided to support interaction between objects is the field. We present a new technique called dynamic splines which dynamically generates a trajectory under field control. Dynamic splines mimic the kinematic behaviour of a particle moving in a field, yet, it is computationally inexpensive compared to full physical dynamic approaches. We also show how to extend the field approach to specify tracking behaviour.
  • Item
    IXPHIGS: A Portable Implementation of the International PHIGS Standard
    (Eurographics Association, 1988) Gorog, Jenö; Krammer, Gergely; Vincze, Arpad
    This paper describes a "portable" object-oriented implementation of the international standard PHIGS. A rapid prototype has been achieved by making use of earlier developments : the IX-CGI module for graphical input, output and interaction and IX-TAM for the creation of and access to objects of different classes, and thus the creation, manipulation and traversal of graph structures with different classes of leaf objects, The “post” function of PHIGS by definition is applied to structure node objects. For each node, it goes. through the element list of the node and, for each element in the list, it invoker the post function of the appropriate element class. Standard extensions are incorporated into this IX-POST module. The limited capabilities provided by the PHIGS input functions are enhanced by an additional interaction interface module IX-IF. A STRUCture e d i TOR program built on top of the PHIGS application interface serves not only as a demonstration of PHIGS capabilities but also as a turnkey program for the wide class of applicaticans with the task of creating and editing symbolic drawings. IXPHIGS is written in the language C and it is a "full software implementation" of all PHIGS capabilities, even for parts which may he enhanced later by using advanced hardware on some target configurations.
  • Item
    The Development of PHEX, a 3D Graphics Extension to X11
    (Eurographics Association, 1988) Clifford Jr., William H.; McConnell, John I.; Saltz, Jeffrey S.
    Today, many computer applications require both 3 dimensional (3D) graphics and window management. The new ISO PHIGS [1] and GKS-3D [2] standards define functional interfaces for applications needing 3D graphics but do not provide control over windows. The X Windowing System (tm), Version 11 [3], is a de facto standard that provides control over windows but has limited 2D graphics capabilities. A consortium of organizations under the auspices of MIT has developed X3D PEX [4], an extension to the X11 standard, that supports PHIGS and GKS3D. The goal of PEX is to provide the best of both worlds: a high performance foundation for PHIGS and GKS-3D within the heterogeneous, distributed, X11 windowing environment. The underlying concept in PEX is that every X11 window has the capability to be a PHIGS or GKS-3D workstation.
  • Item
    COLOUR SECTION
    (Eurographics Association, 1988) Various
  • Item
    Application Profiles for Computer Graphics Standards - A Touch of Realism
    (Eurographics Association, 1988) Mumford, Anne M.
    Computer graphics standards have become widely used and are now a fact of life. We have reached the stage of reviewing and extending the current standards. There is an important move within the user community which needs to be taken into consideration in these processes. This is the development of application profiles within user groups to make their use of the graphics standards easier and to ensure portability. This paper suggests that this move is important and cannot be ignored by users of standards or those involved with the current standards work.
  • Item
    An Expert System for Polyhedra Modelling
    (Eurographics Association, 1988) Martin, Philippe; Martin, Dominique
    Very often we wish to construct shapes according to some criteria, which are properties we want the object to possess. In this case explicit construction becomes an inadapted way of working. One would wish to obtain the result just by giving the desired properties. This is the approach we try to develop here, limiting the problem, for a start, to a special class of solids: the polyhedra. The aim of this study is to demonstrate the general principles which lead to a definition of solids through their properties, and not through an explicit construction. This leads us to the idea that giving a set of properties is a means to model solids, which allows us to talk about declarative modelling.
  • Item
    A Compositional Semantics for Graphics
    (Eurographics Association, 1988) Pineda, Luis A.
    In this paper a theory for developing "intelligent" interactive graphic systems is detailed. The Fregean compositionality principle is enunciated for graphical representations. Geometrical symbols and relations receive semantic interpretations which are expressed as first order relations in the first order logical language. These interpretations are introduced with the help of deictic expressions. Deictic expressions constitute one associative mechanism between analogical representational systems used in graphics, and functional representational systems commonly used in AI applications. Interpretations of graphical symbols and geometrical relations between them constitute an ontology upon which complex linguistic interpretations are assigned to graphics. A concept of graphical grammar is introduced. Frege's compositionality principle, and the notion of graphical grammar lead to a concept of meaningful drawing. The graphical grammar constitutes a second associative mechanism between the two representational systems that have been mentioned. The truth conditions for relations in the graphical grammar are computed through geometrical knowledge. Computational geometry algorithms are associated with the high level representational system by means of the graphical grammar. Semantic interpretations of graphics are useful in carrying out natural language-like dialogue about graphical representations. Dialogues refer to true facts in particular interactive states, A notion of interactive state as a function of time and situation is then developed. One example of how this theory can be used in linking interactive graphics with AI applications is given. In the example, the semantic interpretation of a geographical map is constructed. This theory has been tested with an experimental program called GRAFLOG. The program is implemented in PROLOG and GKS.
  • Item
    Towards a System for Exploring the Universe of Polyhedral Shapes
    (Eurographics Association, 1988) Colin, Christian
    It is often easier to model a shape by giving its properties rather than describing it explicitly. Thus, we are interested in methods which allow us to create shapes automatically by only giving a set of properties. We propose a certain number of thoughts on the creation of objects achieved by the gluing together of elementary polyhedra. The formal approach that we develop is based on an exploration of the universe of polyhedral shapes. We also discuss techniques to automatically compute viewpoints, which emphasize the properties of the structures which have been created. These methods are one of the advantages of such a modeling.
  • Item
    A Formal Specification of a Boundary Representation
    (Eurographics Association, 1988) Baumann, Peter
    Geometric modellers are used in a wide spectrum of applications in computer graphics. As many other applications use the generated internal representation of solids, semantic correctness is of special importance. On the other hand, the methodology of formal specification offers, in particular, the advantage of ensuring correctness by mathematical means. It is therefore a good idea to formally specify a geometric modeller. This paper describes an abstract data type defining a boundary representation. Special attention is paid to the operations for manipulating solids, i.e. the so-called Euler operations. The operation mfe (make face & edge) is used to show in detail how pre- and post-condition can be derived. Finally, mappings of this abstract data type onto implementations with different data models are discussed.
  • Item
    Construction and Animation of a Synthetic Actress
    (Eurographics Association, 1988) Magnenat-Thalmann, N.; Thalmann, D.
    This paper describes a method for creating and animating a synthetic actress. It emphasizes the methodology used to generate realistic images and motions. In particular, points which are often ignored in the literature are explained in detail: for example, the planning and preparation of models for digitizing, composition, skeleton installation and the animation process itself.
  • Item
    METAVIEWS: A Process-Oriented Approach to CAD and Graphics
    (Eurographics Association, 1988) Takala, Tapio
    A system-theoretic approach to the computer aided design (CAD) process is presented. Dependency network among objects, consisting of design operations - transactions - is formed automatically during design. The derivation process of an object, its history, can be extracted as a metalevel macro object and further edited with metadesign operations. Both top-down and bottom-up strategies are supported with this "design-by-example" method. The process-oriented methodology applies to the configuration of graphics systems also, as demonstrated with the METAVIEWS user interface.
  • Item
    Conversion of Boundary Representations to Bintrees
    (Eurographics Association, 1988) Diehl, Rabanus
    Methods for the conversion from boundary-representations to approximation models (especially the bintree model) are examined. A new algorithm for the conversion to the bintree model is presented. It employs an inheritence mechanism during the subdivision, and reduces the block classification of leaf nodes by taking over the colours of the block corners calculated in advance.
  • Item
    Generation of High-Quality Curve and Surface with Smoothly Varying Curvature
    (Eurographics Association, 1988) Higashi, Masatake; Kaneko, Kohji; Hosaka, Mamoru
    A method for generating curves and surfaces which satisfy constraints of tangent directions and curvature at arbitrary points and which have smoothly varying curvature is introduced. The method is geometrical determination of a Bezier polygon, and quite different from conventional methods such as minimizing the integral of the square of curvature value or the second derivative. This method enables following things : generation of smooth curves by explicitly indicating the characteristic properties of the curves generation of smooth surfaces having not only smooth boundaries but also cross tangent and curvature which change smoothly along the boundary curve, high accurate approximation of intersection curves of surfaces, by satisfying a tangent direction, an osculating plane. and curvature constrained by the surface equations.
  • Item
    Using Algebraic Constraints in Interactive Text and Graphics Editing
    (Eurographics Association, 1988) Li, Jiarong
    In many graphical application areas such as architectural and mechanical design, spatial relationships are vastly used to construct and manipulate complex objects. They are used to describe dependencies between components in objects or between objects and their contexts. These relationships, especially the precise ones, can be represented with algebraic relations and appropriately processed by using constraint programming techniques. Rather than embedding relationships in pre-defined objects, this approach offers possibility to treat relationships explicitly. This paper presents an editing program for presentation materials. The program provides facilities to interactively specify and modify relationships such as alignment, connection and enclosure. The normal editing operations are combined with constraint satisfaction so that an operation on one object may also change the related objects in a chain reaction fashion. A constraint satisfaction algorithm has been implemented in the program. This algorithm is able to solve linear equations.
  • Item
    Boundary to Constructive Solid Geometry: A Step Towards 3D Conversion
    (Eurographics Association, 1988) Juan, R.
    Several solid representation schemes exist today in solid modeling. As none of them has properties that are uniformly better than any other, the need for modeling systems working on two or more different schemes which perform every operation in the most suitable scheme, became evident. Then it is necessary to provide geometric modeling systems with the ability of converting from one scheme into another scheme. As most solid modellers use either, a boundary representation (BR) or a constructive solid geometry representation (CSG), conversion from one into the other appears to be of capital importance. Conversion from CSG into BR has been carefully studied but a few attention has been deserved to the conversion from BR to CSG. This paper presents an algorithm which generates CSG binary trees from BR representations over a restricted class of polyhedra. The tree is optimal in the output size. Unfortunately, the algorithm does not in general warrant a correct conversion and, consequently some open questions and ideas for further research are presented.
  • Item
    A Procedural System for the Definition and Storage of Technical Drawings in Parametric Form
    (Eurographics Association, 1988) Cugini, U.; Folini, F.; Vicini, I.
    The construction of a truly USER-FRIENDLY CAD system requires the acquisition and management of a tremendous amount of information which cannot be. and must not be. directly requested from the user, but which has to be obtained by intelligently interpreting the sequence of operations performed by him. The system described here is out forward as a USERFRIENDLY tool for the definition. storage and modification of technical drawings in parametric form. The system that has been implemented (GIPS Graphic Interactive Parametric System) assists the user during the steps of definition and modification. taking advantage of the abiIity to interpret the procedure the user follows in describing the object he wants to design.
  • Item
    A New Algorithm for Converting Boundary Representation to Octree
    (Eurographics Association, 1988) Tang, Zesheng; Lu, Shengkai
    Conversion algorithms between different object representations have become Increasingly important In soIid modeling system. In this paper, an algorithm for converting boundary representation of 3D object to octree structure is presented. This algorithm Is based on the transformation of Cartesian coordinates of voxels in the object universe to octant addresses or to node addresses of octree. The surface coherence, edge coherence, voxel coherence are used to speed up the transformation. In order to save memory space, Iinear octree Is used and the Intermediate resulting octant addresses are condensed as early as possible. The resolution of octree structure may also be controled by defining the number of levels of octree. This Is the bottom-up algorithm for converting boundary representation of 3D object to octree structure.
  • Item
    Automatic Detection of Closed Parametric Surfaces without Interior
    (Eurographics Association, 1988) Seidel, Hans-Peter
    This paper presents an algorithm for the automatic detection of closed piecewise parametric surfaces without any inside or outside, e.g. a Klein bottle. The algorithm is able to decide whether a given closed surface is orientable or not. If non-orientable, the surface will not divide Euclidean 3-space into two halves. Therefore a non-orientable surface can never serve as the boundary of a solid object. The algorithm is based on results from algebraic topology and thus avoids the computation of derivatives and normal vectors. Several applications of the algorithm to rational tensor product B-spline surfaces are given.
  • Item
    Conic Beta-Splines with Local Tension Control for Interactive Curve Fitting
    (Eurographics Association, 1988) Pham, Binh
    Polynomial Beta-splines were introduced by Barsky as an extension of polynomial B-splines with bias and tension parameters which allow more flexibility in controlling shape in curve fitting. It is possible to show that a quadratic Beta-spline segment is equivalent to a quadratic B-spline segment with suitably modified control vertices. This provides a simple method for evaluating quadratic Beta-splines using De Boor's algorithm for calculating polynomial B-splines. A representation for conic Beta-splines with one tension parameter is introduced and some properties are derived. They form a basis for an efficient algorithm for interactive curve fitting with conic Beta-splines. The results are extended further to cover the case of conic Beta-splines with varying tension where the tension parameter is an interpolating function between the tension values at each end of a segment.
  • Item
    A Simple Spectral Approach to Stochastic Modelling for Natural Objects
    (Eurographics Association, 1988) Anjyo, Ken-ichi
    Stochastic modeling has been widely used in computer graphics to depict natural objects or phenomena. Various techniques are available, depending on what object is to be represented and what extent of realism to be achieved. This paper presents a simple approach to stochastic spectral synthesis for producing a large range of natural objects and scenes at low computational cost. By considering a wide class of power spectra, the method can provide twodimensional stochastic models for various objects, involving terrains, clouds and sea waves. Moreover, some functional operations and parameters for the models are introduced, which can make the models more flexible in describing a three-dimensional complex scene.
  • Item
    Liberation from Rectangles: A Tiling Method for Dynamic Modification of Objects on Raster Displays
    (Eurographics Association, 1988) Slater, Mel; Davison, Allan; Smith, Mark
    When graphics objects (also called segments) are used on raster display hardware, problems arise because of the mismatch between the high level requirements of object manipulation, and the low level representation from which the image is refreshed. This paper describes a tiling algorithm which provides a solution to the problems of damage repair and hit detection. In particular methods for handling object priority are discussed and experimental results showing the performance of the algorithm for a number of cases are presented.
  • Item
    A Evalution of Some Three-Color Tiling Patterns
    (Eurographics Association, 1988) Alt, Paul; Cordonnier, Vincent
    Some new technologies for information display use discrete arrays of cells or picture elements. Each cell displays a single color and the colors do not overlap as they do on a CRT screen. Colored cells are distributed on the two dimension display surface by repeating a basic model called a pattern. Patterns can be evaluated by observing images displayed using them. However, such approaches usually do not give numerical results and depend strongly on the selected images and the observers. In this paper, we suggest and examine some pattern evaluation criteria which relate only to the pattern and its geometrical aspect: Fidelity of color location, the quality of white area and the fidelity of shapes used for lines drawing or characters. Numerical and geometrical approaches are proposed to evaluate the quality of several patterns. The result is a classification of the test patterns. Some of them seem to be better than frequently used patterns. In addition, comments are offered on future pattern design.
  • Item
    An Object-Oriented Approach to Process Monitoring
    (Eurographics Association, 1988) Hütter, Ronald
    Current and future user interface requirements of process monitoring applications are summarized. An object-oriented approach to meet these requirements is described. A special displayfile structure, the socalled object-oriented displayfile as well as some important object types are highligted, to explain the benefits of object orientation in the area of process monitoring user interfaces.
  • Item
    Experimenting with a Parallel Ray-Tracing Algorithm on a Hypercube Machine
    (Eurographics Association, 1988) Priol, Thierry; Bouatouch, Kadi
    A parallel space tracing algorithm is presented. It subdivides the scene into regions. These latter are distributed among the processors of an iPSC hypercube machine designed by Intel company. Each processor subdivides its own region into cells to accelerate the ray tracing algorithm. Processors communicate by means of messages. The pyramidal shape of the regions allows the deletion of the primary ray messages. A method of performing a roughly uniform load distribution is proposed.
  • Item
    Free-Form Surfaces Modeling by Evolution Simulation
    (Eurographics Association, 1988) Lienhardt, Pascal
    We present in this paper a procedural method for modeling free-form, planar surfaces subdivisions, which allows simulating evolutions of such subdivisions. This method is founded on the common principles deduced from corpuscular phenomena modeling method (particle systems), and method for vegetal trees modeling by simulation of evolution. These principles are : - use of a discrete model, which is a set of basic elements, from which time discretization is deduced, -proper activity of basic elements; these methods consists in simulating the behaviour of these elements; - characterization of modelled object evolution, which is achieved by "functions" associated to basic elements; - priority of topology over geometry. A surface is defined as a set of surface elements, supported by a rooted, planar tree. A surface is initially reduced to a point. Surface evolution characterization and control are exclusively exerted through this tree. This method is applied to image synthesis and animation of natural shapes, especially vegetal shapes.
  • Item
    Animation of Stochastic Model-Based 3-D Textures
    (Eurographics Association, 1988) Gagalowicz, Andre; Ma, Song D.
    We have previously shown the validity of a statistical model proposed by us for realistic textures. We have also shown how to use this model to map realistic textures onto a still surface of any shape and extent, maintaining consistency and scaling without producing repeating patterns.The problem we have to solve in this paper is how to use this statistical model in order to produce animated objects while keeping temporal consistency. This problem a priori difficult to solve as our mapping technique is statistical.We propose two different techniques. The first method called the image space method creates texture directly on the image planes. The second one called the object space method performs the texture synthesis on the object surface itself which has to be sampled finelly beforehand.
  • Item
    Architectures for Mass Market 3D Displays
    (Eurographics Association, 1988) Winser, Paul; Bonnet, Thierry; Dumont, Dominique; Mathieu, Yves
    We discuss the specific architecture requirements of real time 3D display systems intended for low cost mass market products of the near future. Vertex transformation and polygon rendering are two processing aspects where hardware acceleration must be used to achieve the performance target. The use of one or more DSP chips as vertex processors is discussed, and two efficient z-buffer implementations described. Antialiasing and texture mapping greatly improve the visual impression at some processing cost.
  • Item
    Fractal Approximation of 2-D Object
    (Eurographics Association, 1988) Levy-Vehel, J.; Gagalowicz, A.
    We present some new techniques for shape approximation with fractals, using Iterated Function System, a powerful method which allows good control on the resulting fractal. The main point discussed here can be stated as follows : given a grey level image A, find a few number of functions and associated probabilities that approximately generate A. Two directions have been explored : the first uses a gradient method, thus it was necessary to define a smooth error function ; the second one is based upon the ideas of simulated annealing. We then generalize the methods to a broader class of functions, and present some results.
  • Item
    G1 Smoothing Solid Objects by Bicubic Bezier Patches
    (Eurographics Association, 1988) Liang, Youdong; Ye, Xiuzi; Fang, Shiaofen
    A general and unified method is presented for generating a wide range of 3D objects by smoothing the vertices and edges of a given polyhedron with arbitrary topology using bicubic Bezier patches. The common solution to the compatibility equations of geometric continuity between two Bezier patches is obtained and employed as the foundation of this new method such that this new solid and surface model is reliable and compatible with the solid modeling and surface modeling system in the most common use. The new method has been embeded in an algorithm supported by our newly developed solid modeling system MESSAGE. The performance and implementation of this new algorithm show that it is efficient, flexible and easy to manipulate.
  • Item
    A System for Graphical Interaction on Parametrized Models
    (Eurographics Association, 1988) Van Emmerik , Maarten J.G.M.
    A system that enables the definition of parametrized solid models by means of graphical interaction is presented. The position, orientation and dimensions of primitive volumes for Constructive Solid Geometry (CSG) are determined by a number of control points. All control points are linked to nodes in a tree of local coordinate systems. The relations between control points is therefore determined by the relations of the nodes in this geometric tree. The user can create nodes and define geometric relations between them by graphical interaction on the geometric tree. With the system described in this paper, it is possible to define relations
  • Item
    Efficient Adaptive Subdivision of Bezier Surfaces
    (Eurographics Association, 1988) Clay, Reed D.; Moreton, Henry P.
    The support of free-form surfaces by modem solid modeling systems has necessitated the development of hardware and algorithms for the interactive display of surface patches. This paper describes an algorithm for the display of multiple surface patches at frame rates capable of providing smooth motion. The algorithm runs on the Silicon Graphics IRIS 4D GT workstation. Real-time motion is achieved by exploiting a microcodable pipeline of floating point processors and existing support for the display of Gouraud shaded Z-buffered polygons. The paper presents tradeoffs in the development of a high performance rendering algorithm. We discuss issues related to hardware support, surface representation, adaptive display, and the minimization of display artifacts such as faceting and cracking. More detailed discussion addresses the choice of Bezier surface patches and subdivision criteria.
  • Item
    Outline Phase Control for Character Rasterization
    (Eurographics Association, 1988) Hersch, R. D.
    Character rasterization on middle-resolution output devices (screens, laser printers) is one of the most difficult tasks in the domain of resolution-independent raster imaging. Low sampling leads to unacceptable low-quality discrete character shapes Better looking shapes can be generated by adapting parts of the shape outline to the sampling grid Grid adaptation of character parts is realized by several outline phase control mechanisms Algorithms have been developed to adapt horizontal and vertical bars as well as curvilinear character parts to the grid. Special phase control mechanisms are used to ensure a uniform appearance of characters over the baseline.
  • Item
    Pseudo Ordering of CSG-Trees
    (Eurographics Association, 1988) Cottingham, Marion S.
    Using Constructive Solid Geometry (CSG) methods, it is usual for primitive object representations to be stored at the leaf nodes of binary trees. The major part of the work involved in generating an image of the object is finding what surface is visible at each pixel in the screen. Using conventional rendering methods this can be simplified by ordering the primitives by their screen positions and by their depths. Using ray tracing techniques this can be achieved by testing if rays intersect with primitives, the number of these intersection tests can be reduced by ordering. However it is not generally possible to order data (in any one direction) in CSG-trees where intersection or difference operators are involved. This paper describes a method that enables 'local' three-way ordering of the data contained in CSG-trees that can be used with either conventional scan-line rendering methods or ray tracing techniques. This is achieved by the introduction of underlying data structures that dynamically change throughout the image generation step. Using this method, the primitive/polygon visible at a particular pixel can usually be accessed directly via pointers.
  • Item
    Form-Factors for General Environments
    (Eurographics Association, 1988) Shao, Ping-Pine; Peng, Qun-Sheng; Liang, You-Done
    A new algorithm, based on the hemi-cube formulation, which calculates the form-factors required by the solution of the rendering equation, is presented. The concept of form-factors of the standard radiosity method is developed, In particular, the concept of specular form-factors is proposed. These new form-factors are also purely geometric terms describing the transfer of energy from one surface to another within a non-diffuse environment. The new form-factor is evaluated by numerical integrations based on the hemi-cube algorithm. The equations of the effective diffuse radiosity are presented and solved by numerical methods. The extension fully develops the characteristic of radiosity method and successfully solves the view-independent energy transfer in a general environment.
  • Item
    The Calculus of the Non-Exact Perspective Projection - Scene-Shifting for Computer Animation
    (Eurographics Association, 1988) Hofmann, Georg Rainer
    This paper shows the principle way to apply the, scene-shiftin technique of the classical film to computer animation. calculus is presented which is a modification of the well-known classical calculus of the perspective projection. However,, a given perspective view (which may be a frame in a computer animated film) of a three-dunensiona! scene does not change homogenous1 when the position of the viewer (i.e. the eyepoint, the location of the camera ... ) changes. So the subject of this paper is to ask for these parts of the frame with only little changes within a tolerance E. Based on the theorems of the presented calculus, a computer animated film as a sequence of single frames may no longer be computed frame by frame, one frame independent from another, and every frame passing through the whole visualization pipeline of the rendering system. In any frame, parts of the preceeding frame may be inserted, if necessary with two-dimensional modifications: scaling, shifting. This will decrease the computing costs for that frame significantly, since for these arts of the frame no new perspective transformahon and rendering is required. It is a shortening of the visualization pipeline. For the sake of the compactness of this paper we will give no detailed proofs of the theorems presented in here. The interested readers may obtain these information directly from the author.
  • Item
    A Method for Providing Full Interactive Control of the Shape of 3-D Curves and Surfaces
    (Eurographics Association, 1988) Cros, Frederic; Brock, Philip J.
    This paper presents a new method for providing an interactive local control on 3-D curves and surfaces. The possibility of interacting directly on the vector tangent to the curve at each control point (e.g. changing its magnitude and direction) gives the user a more intuitive control for shaping a curve than if he has to manipulate "abstract" parameters (like bias or tension). This technique is based on the use of Cardinal-splines and can also provide a means to obtain local control on surfaces.
  • Item
    An Evaluation of CSG Trees Based on Polyhedral Solids
    (Eurographics Association, 1988) Badouel, Didier; Hegron, Gerard
    Set operation on polyhedra is an important component of Geometric Modeling System (GMS) when a Constructive Solid Geometry (CSG) representation with polyhedral solid primitives is used. Output data will be the unique resulting polyhedron which provides an efficient data structure for displaying objects. With no use of spatial coherency, computational complexity of a set operation is quadratic. The new evaluation scheme called Boolean Octree limits set operation evaluation in a ‘minimal space of calculation’ where primitive boundaries intersect each other and where resulting evaluation participates in the construction of the final resulting object. Boolean Octree computes set operations in a local level providing a linear complexity for geometric calculations. During space subdivision, Boolean Octree has a global view on local CSG tree (projection of the CSG tree in local space) taking into account simplifications of the boolean expression. Set evaluation is done in the local volumes containing only two operands the configurations of which are ‘simple’, that is to say for a local description of an object there is only one vertex with any face number, one edge, or one face.
  • Item
    Optimal Texture Mapping
    (Eurographics Association, 1988) De Ma, Song; Lin, Hong
    Texture mapping is one of the most important techniques for highquality image synthesis. It can enhance immensely the visual richness of raster-scan images. We address in this paper the problem of mapping planar texture pattern onto arbitrarily curved surfaces. It is well known that such a mapping will inevitably produce distortion for any undevelopable surface. Although many techniques for texture mapping have been presented in the literature [1], to our knowledge, no general method existed which could control or minimize this distortion. We present in this paper a new method for texture mapping. The main idea is to develop the given curved surface approximately on a two-dimensional plane using an approximate locally isometric mapping while minimizing the distortion by an optimization technique. Our experience has shown that by using this technique, one can reduce considerably the distortion and thus improve the quality of the generated images.
  • Item
    Monte-Carlo Integration Applied to an Illumination Model
    (Eurographics Association, 1988) Bouville, C.; Dubois, J.L.; Marchal, I.; Viaud, M.L.
    The use of Monte-Carlo integration together with stochastic sampling is very useful for dealing with the scattering phenomena that occur in the propagation and reflection of light. In this paper, these techniques have been applied to the implementation of a physicsbased global illumination model. The theoretical basis of this approach is presented briefly and various applications to realistic image rendering are then described. This concerns the rendering of penumbra and scattered reflection effects, antialiasing and accurate color modelling through spectral integration. For all these applications, both theoretical and implementation aspects are developed and it is shown that stochastic techniques can provide very simple and efficient algorithms.
  • Item
    Fast Algorithm for Polygon Clipping with 3D Windows
    (Eurographics Association, 1988) Burkert, Andreas; Noll, Stefan
    Many applications which use 3D graphics, need 3D geometric modeling and hence polygon clipping against 3D Windows or general volumes. The disadvantages of existing clipping algorithms are that they are 2D, slow or produce incorrect results. This paper describes a new 3D clipping algorithm for concave polygons with one contour. The new algorithm is an extension to the algorithm of Liang and Barsky: The necessary condition for the appearance of a corner of the clipping rectangle in the output polygon is replaced by a necessary and sufficient condition and then extended to the three dimensional case. Another advantage of the presented algorithm is the the removal of degenerated edges. The algorithm is useful for implementing the draft international standards GKS-3D and PHIGS and also for 3D Window Systems.