Table Of ContentFreeform Tools in
CAD Systems
Josef Hoschek (Ed.)
Freeform Tools in
CAD Systems
A Comparison
Edited by
Prof. Dr. rer. nat. Josef Hoschek
Technische Hochschule Darmstadt
83
B. G. Teubner Stuttgart 1991
Die Deutsche Bibliothek - CIP-Einheitsaufnahme
Freeform tools in CAD systems: a comparison / ed. by Josef
Hoschek. - Stuttgart: Teubner, 1991
ISBN-13: 978-3-322-86774-2 e-ISBN-13: 978-3-322-86773-5
DOl: 10.1007/978-3-322-86773-5
NE: Hoschek, Josef [Hrsg.]
Das Werk einschlieBlich aller seiner Teile ist urheberrechtlich geschiitzt. J ede Verwer
tung auBerhalb der engen Grenzen des Urheberrechtsgesetzes ist ohne Zustimmung
des VerJages unzulassig und strafbar. Das gilt besonders fUr Vervielfaltigungen, Uber
setzungen, Mikroverfi1mungen und die Einspeicherung und Verarbeitung in elektroni
schen Systemen.
© B. G. Teubner Stuttgart 1991
Softcover reprint of the hardcover 1s t edition 1991
Preface
From 13th-17th May, 1991 the Centre for Applied Mathematics at the
Darmstadt University of Technology and at the University of Kaiserslautern
in cooperation with the European Consortium for Mathematics in Industry
{ECMIl has organized the Workshop: "Practice of Computer Aided Gemetric
Design - What CAD Systems are really capable of". Some of the most im
portant software vendors had been invited to participate in the workshop
and to demonstrate their developments in the area of free form surface
technology. The following systems were presented: CATIA (IBM/Dassault);
EUCLID (Matra); ICEM (CDC); SYRKO (Mercedes-Benzl; STRIM (Cisigraph);
UNIGRAPHICS (McDonnel Douglas) and in addition the visualization system
WAVEFRONT (mental images) was introduced.
The presentations were supposed to focus on the following topics: re
presentation of analytical curves/surfaces; Coons-Eace-Top-Elements;
multisurfs; triangular patches; offset surfaces; volume elements; inter
secting algorithms; operations for combination of curves, surfaces and
volumes; sweeping elements/fillets; blending methods; parametrization of
data; interpolation/approximation of irregular data/NC data; NC control
(three axes, five axes milling). - Demonstrations of the systems were
also given on work stations. Besides, a qUestionnaire should have given a
short overview on the implementations.
Beside these presentations of software systems, the participants had the
opportunity to hear lectures on developments for interfaces.
A panel discussion with some speakers and participants working as software
vendors and as software users closed the workshop. Following themes were
treated in the discussion: mathematical problems; consistency; information
hiding; data exchange and archival; future of CAD systems. Our special
thank goes to Dr. \V6rdenweber for chairing the panel discussion with
ability and for his help in the general organization of this workshop.
The present book contains the written versions of most of the contributions
and a short version of the panel discussion. The questionnaire allows a
direct comparison of the presented systems, the reader can realize what the
systems have really solved and which solutions can be expected in the future.
- Bench marks were not given to the software systems.
would like to thank the software vendors taking part in the workshop
and all the speakers - without their help such an event could not have
taken place. Our thanks also to all the participants (some forty from the
industry and 2S from universities) for their keen questions and their part
icipation in the discussion and also to the software vendors for their (in
general) precise and straight answers.
Darmstadt, July 1991 - Josef Hoschek
Table of Contents
Preface
Table of Contents
3
Presentations of CAD Systems
CA TIA/IBM, Dassault :
P. Moreau, O. Bellart S
Curve and Surface Representation in Catia System
B. Worden weber: 27
A Case for CAD
B. Worden weber, P. Santarelli: 37
Digitising Sculptured Surfaces
ICEM / Control Data:
T. H. Weiss barth 4S
Representations and Operations in the ICEM Systems
D. Bischoff 63
ICEM MESH - A Mesh Generation Tool for Free-Form
Surfaces
STRIM/cisigraph:
J. Lang, A. Massabo, D. Pyzak 79
Practice of Computer Aided Geometric Design
SYRKO/Merces Benz:
R. Klass, B. Kaufmann, B. Kuhn 107
Car Body Design and Manufacturing with SYRKO
UNIGRAPHICS/McDonnel Douglas:
K. Sears, G. Allen 129
Curves and Surfaces in Unigraphics and Parasolid
EUCLID / Matra
F. Le Breton, H. Rybak and J. Wagner: 147
UNISURF IV - The advanced Solids & Surfaces Module
of EUCLID-IS
- 4 -
II Visualisation System
WAVEFRONT - MENTAL RAY/mental images 173
R. Herken, R. Hodleke, T.-M. Thamm-Sehaar, J. Yost,
S. Borae
High Quality Visualization of CAD Data
III Lectures on Developments for Interfaces
R. Anderl 195
The Development Methodology of STEP and its Concept for
Shape Representation
G. Berold, M. Bereovier 207
Integration of Physical "Phenomena" into CAD
H. Grabowski, X. LJ 219
General Matrix Representation for NURBS Curves and
Surfaces for Interfaces
J. Hosehek 233
Approximate Conversion and Merging of Spline
Surface Patches
IV Questionnaire on Curve/Surface/Volume Implementations
247
ANSWERS - Part I (EUCLID, STRIM, ICEM) 249
ANSWERS - Part II (UNIGRAPHICS, SYRKO, CA TIA) 254
V Excerpts of the Panel Discussion 260
CURVE AND SURFACE REPRESENTATION
IN CATIA SYSTEM
Pierre MOREAU
Olivier BELLART
1.0 Introduction
What do CAD/CAM users need?
They want efficient design tools for shorter design cycles and higher produc
tivity.
To reach theses goals, the CIM system must be powerful, user friendly and
easy to use. The available possibilities must satisfy users' needs, masking as
much as possible CAD internal techniques such as mathematics so that end
users can spend all their working time in their speciality.
However modeling shapes and objects needs geometric representations and
CIM systems must handle mathematical concepts. This paper deals with the
following problems: How to choose the most appropriate mathematical con
cepts? Must a CIM system only have a single mathematical representation or
does it need several mathematical representation to satisfy end-user needs?
After a short discussion about advantages and disavantages of some mathemat
ical representations, we demonstrate the necessity of a multi-representation
architecture. We point out the importance of NURBS in CAD today and we
deduce the technical choices of Dassault Systemes for curve and surface repre
sentation in CATIA.
- 6 -
2.0 Does a perfect mathematical representation exist?
To illustrate our discussion, we are going to study in a pragmatical point of
view, the most famous family of concepts: B-splines
2.1 From polynomial to NURBS : a gradual sophistication.
Continuity and not opposition.
It would be an error to set polynomial basis or Bernstein basis against NURBS.
Each of these concepts are a step of mathematical bases evolution. Each new
basis tries to correct deficiencies or to add properties, by elevating the concep
tual level. But, consequently, new difficulties or restrictions may occur.
Sophistication has secondary effects ....
To carry out this objective analysis, we must study each step of this evolution.
The main principles are well known. So, for each concept, we will just point out
the main improvements and the main disadvantages.
Polynomial basis.
The first used.
Mathematics
Remark: Formulas are given for curves. There are no major difficulties to
generalize to surface.
Current point of the curve at parameter u, P(u) is defined by :
End of Mathematics
- 7 -
L
* PI
* P3
* P4
* P2
o
Figure 1. Polynomial basis. arc and its point components
POSITIVE
• Particularly efficient evaluation for any degree with Horner method
• Easy formal derivation
NEGATIVE
• Most of components have no geometric meaning.
• Continuity management is difficult.
• Not homogeneous basis. Stability problems are possible.
... 8 ...
Bernstein basis (Bezier points): a geometrical meaning.
L
---
---------.,t-
--
"-
........"...-. ~
o
Figure 2. Bernstein basis, an arc and the same arc after moving a point
A change of basis.
Mathematics
Current point P(u) can be written as :
2...
n
P(u) = /jBj,n(U)
j = 0
