Design Reuse in Product Shape Modeling:
A Study of Freeform Feature Reuse by Signal
Processing Techniques
Design Reuse in Product Shape Modeling:
A Study of Freeform Feature Reuse by Signal
Processing Techniques
Proefschrift
ter verkrijging van de graad van doctor aan de Technische Universiteit Delft,
op gezag van de Rector Magnificus prof. dr. ir. J. T. Fokkema, voorzitter van het College voor Promoties,
in het openbaar te verdedigen op dinsdag 26 April 2005 te 10.30 uur
door
Chensheng Wang
Master of Science in Mechanical Engineering,
Prof. Dr. P. J. Stappers
Toegevoegd promotor: Dr. J. S. M. Vergeest
Samenstelling promotiecommissie:
Rector Magnificus voorzitter
Prof. Dr. P. J. Stappers Technische Universiteit Delft, promotor Dr. J. S. M. Vergeest Technische Universiteit Delft, promotor Prof. Dr. Ir. F. J. A. M. Van Houten University of Twente
Prof. D. J. van Eijk Technische Universiteit Delft Prof. Dr. Ir. L. J. van Vliet Technische Universiteit Delft Prof. Ir. K. H. J. Robers Technische Universiteit Delft Dr. W. F. Bronsvoort Technische Universiteit Delft
Wang, C.
Design Reuse in Product Shape Modeling: A Study of Freeform Feature Reuse by Signal Processing Techniques,
Ph.D. Thesis, Delft University of Technology. ISBN: 90-5335-051-9
Keywords: CAD/CAM, shape modeling, Fourier transforms, signal processing, shape descriptor.
Copyright © 2005 by C. Wang. All right reserved. No part of the materials protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording or by any information storage and retrieval system, without written permission from the author.
To my parents, Zhihuan and Yonglin, and Zhihuan’s father and mother
Preface
Time is flying. Since the first time I got in touch with Computer-Aided Design (CAD) technology when doing my MSc project, more than fifteen years have past. Eventually, I decided to work for my PhD, regardless of several difficulties I encountered.
Being knowledgeable is a life-long pursuit. Working in the cutting edge of CAD technology is my pleasure. The presented study, characterized by its interdisciplinary nature, is partially inspired by this motivation. As stated in its title, this research is dealing with design reuse, especially Freeform Feature (FFF) reuse, in a shape-modeling environment. FFF reuse has long been recognized as a fundamental problem in fast shape creation in industrial product design. Although the findings are limited, the present study attempts to break through the barrier of conventional CAD technique.
On September 11, 2001, a remarkable day in human history, I joined the Faculty of Design, Engineering, and Production, Delft University of Technology. In three years of research, I have learned a lot from my colleagues. I faithfully believe that honesty, modesty, realism, and creativity are crucial moral characteristics of a scientist, which deserve one to pursue. So will I.
I owe a word of thanks to a number of people for their support throughout this study. First of all, thanks to my supervisor Joris Vergeest for providing me the opportunity to conduct this study. Joris’ kind help from research to daily life made this research become reality. I am grateful to my promotor Pieter Jan Stappers for his kind guidance in conducting scientific research. His scientific spirit has been inspiring me in my academic career.
I thank Wim Bronsvoort for his constructive suggestions for composing this thesis. His scientific spirit and modesty have been an inspiration for me. I would also like to thank Lucas van Vliet for his kind help in proof reading the draft thesis, which resulted in many suggestions for improvements in technical formulations.
Thanks to Aad Bremer for his kind support to overcome many difficulties in research, and Tjamme Wiegers for beneficial discussions in the Dynash Research Group. I am also grateful to my colleagues in the Department of Design Engineering for their friendship, which accompanied me these years. Special thanks go to Astrid Bijkerk for her kind help in daily management.
I owe very much to my parents. I lost my mother in the year 2002. Although she could not read in English, I still wish she could see this text from heaven.
I am grateful to my wife Zhihuan and my daughter Yonglin. They have experienced much difficulty during these years. I would also like to thank Zhihuan’s parents for their continuous support, which assured the final success of the research. I also have to thank my brother and my sister for their efforts in taking care of the family during these years.
Shifting back to the research, I would say that the significance of this research is much more than its outcomes, since the exploration of this new field reveals promising possibilities for the development of computer-assisted technologies in design. I do expect a lot more from future research in this field.
Chensheng Wang Delft, January 8, 2005
Summary
Lack of facilities in supporting design reuse is a serious problem in product shape modeling, especially in computer-aided design systems. This becomes a bottleneck of fast shape conceptualization and creation in consumer product design, which consequently prohibits creativity and innovation. In the past, several efforts have been made in order to improve this situation, with confined methodologies in the spatial domain, following conventional ways of geometrical operations. These domain dependent researches did not yield satisfactory solutions. Looking at the state of the art technologies, to find a better solution, an investigation applying interdisciplinary knowledge has to be conducted.
The present study aimed at finding a systematic approach to support design reuse in shape modeling, especially Freeform Feature (FFF) reuse, by hypothesizing that a better solution could be achieved by applying signal processing techniques. This global goal was further decomposed into a number of concrete objectives, each correlated to a broad spectrum of domain specific knowledge. Investigations on relevant subjects enrich the aggregation of knowledge, especially that concerning computer-assisted technologies in industrial design field.
Solutions of this study functionally extend the capability of shape modeling, and enhance the interchange ability of shape depiction between the spatial and the frequency domain. A number of examples were employed to test the methods and mathematical formulations proposed. The results affirm that the hypothesis works, and the methodology developed in this research are both effective and beneficial.
FFF reuse has long been recognized as one of the significant aspects in design reuse. Despite a number of techniques have been proposed, challenges still remain as that (i) most of the existing techniques works only in the spatial domain, and are confined to specific predefined model representations; (ii) feature distortions imposed by feature interactions during shape modeling process were commonly neglected or incapable to handle by these methods. By studying the signal properties of shapes, the achievements of the present research contributed to the following aspects:
• At the theoretical level, the present study comprehensively investigated the fun-damentals of frequency-based shape representation. The interdisciplinary study involved issues such as Fourier Transforms (FTs) and its representations,
dis-cretization of a continuous function, sampling theorem, computational issues of
Discrete FT (DFT), Fourier Shape Descriptors (FSDs), and correlation of
spa-tial geometry and its spectral components. Typical problems in shape depiction using the FSD were analyzed, and related techniques to depress side effects, such as the Gibbs phenomenon, were provided. And the theoretical principles of representing a regional shape using its frequency components were formu-lated. Applications of high-order surface interpolation and the computation of the Unevenly Spaced Fast FT (USFFT) were revisited. In addition, the compu-tation of surface properties using spectral represencompu-tation was elaborated; • At the methodological level, a framework for FFF reuse was proposed based on
the spectral representation, and the process of FFF reuse was explored. In order to establish the spectral representation of a regional shape, a definition of the
Fourier Shape Model (FSM) was elaborated. Based on the corresponding
rela-tionship of a spatial shape and its spectral components, three methods for re-trieving the signal of FFF in a Region of Interest (ROI) were formulated. One of the innovative points of these methods is that they tend to support the retrieval of a pure FFF in the ROI, either in an exact or in an approximative manner. By applying the principle of signal synthesis, FFF reuse was implemented by a controlled synthesis of signals of both the FFF and the base surface. In addition to general shape synthesis achieved by a direct arithmetic addition of the sig-nals, three types of spectral operators were formulated in the controlled shape synthesis. Issues in a controlled shape synthesis using these spectral operators were explored, such as parameterization, alignment, periodicity of the input dataset, and the validity of shape mapping. In addition, spectral analysis was discussed, and a scheme for shape information abstraction and indexing was elaborated for the purpose of establishing a shape repository. These methodo-logical studies concluded a systematic approach for FFF reuse using signal processing techniques, which appears beneficial in facilitating shape modeling; • At the application level, related knowledge aggregation from both theoretical
and methodological study contribute to a pilot system for FFF reuse, composing a set of application tools. These tools work exclusively for the ROI. The as-sessment results show that the proposed algorithms are efficient, and the tools built on the theoretical formulations are both effective and valid.
Starting from the question ‘How to support FFF reuse in a shape modeling environ-ment, coping with diverse model formats?’ Chapter 1 gives a brief introduction, in which the position of FFF reuse in the stream of design reuse is clarified, and the research domain is specified. Research propositions are raised and a preliminary strategy to achieve the goal is provided.
Chapter 2 reviews relevant technologies in shape modeling and reuse. It covers a broad range of subjects, from shape modeling of scattered data in computer graphics, feature technologies, and techniques for regional shape manipulation in Computer-Aided Design/Industrial Design (CAD/CAID), to shape descriptors and surface frequencies in shape analysis. The literature review reveals that conventional techniques for FFF reuse are inefficient in implementing FFF retrieval, and incapable to cope with multiple model formats. Therefore, an alternative way is required.
In Chapter 3, a systematic approach of shape description using frequency-based techniques is elaborated. The formulation includes continuous function discretization using the sampling theorem, the DFT and its computation, as well as data interpolation at unequally spaced grid using the USFFT. Chapter 3 concludes that a discrete finite dataset
can be depicted by a Fourier shape descriptor using its frequency components. This forms the foundation for further development of the techniques of FFF reuse in the present context. It was identified that the computational efficiency plays a crucial role in this kind of applications.
Chapter 4 describes a framework for FFF reuse, based on signal processing tech-niques. A FSM for representing a regional shape using its frequency spectrum is defined. The pre- and post-processing of the input dataset is discussed in this chapter. By collectively forming the basic concepts, Chapter 4 also provides a guideline for the whole research work.
In Chapter 5, three techniques for FFF retrieval are formulated, namely, the exact method, the minimal surface method, and the shape filtering method. The exact method can deliver an accurate result for FFF retrieval, whereas the other methods approximate solutions. It has been found that to precisely decompose the compound signal of a ROI is difficult. Retrieval of the feature signal by filtering technique works well only under specific conditions; otherwise, a series of approximations will be resulted in. Quality of retrieved feature signal is analyzed in this chapter.
Techniques for FFF reuse are elaborated in Chapter 6, in which several spectral operators are formulated, namely, the spherical mapping operator, the cylindrical mapping operator, and the normal mapping operator. These operators implement the inclusion of a FFF into an existing shape model with diverse representation formats, by means of controlled signal synthesis. They can be thought as a supplementary to the conventional shape mapping methods. Related issues, including the quality of shape synthesis applying these methods are analyzed. In addition, methods for regional shape abstraction are also elaborated in this chapter, based on frequency representations.
Chapter 7 provides some examples of possible applications of the proposed ap-proaches in facilitating product design. It is an extension of the research work that describes how the proposed techniques can enhance fast shape creation, local enrichment, as well as facilitate design knowledge engineering. These examples confirm that the proposed techniques are not only useful, but also advantageous, compared with conventional techniques.
In Chapter 8, the application prototype is explored, including the system architecture, data formats, functional flow, and dialog tools. An assessment is also provided to address three critical issues in the implementation, namely, the computational efficiency of the formulated algorithms, the effectiveness of the proposed methods, as well as the validity of the developed techniques.
Chapter 9 summarizes the research work and concludes the contribution of the scientific exploration. Prospects and suggestions for further research are drawout.
Applying signal processing techniques to facilitate shape modeling is an innovative yet creative exploration, which brings us a number of obvious advantages. The methodologies proposed in our work contribute to the aggregation of knowledge of shape perception and manipulation. However, we would admit that the present research raises more challenges than its solutions. For instance, when treating a shape as signals, to what extent it would be applicable in depicting geometric shapes, and how to deal with morphological topology issues. To answer these questions further investigations are required.
Finally, we believe that the present study is just the beginning, in the sense of open-ing a new field of research in CAD/CAID technologies. We expect that the fusion of knowledge from diverse disciplines may mature the computer-assisted design technology in the near future. By now, to shape designers I would say that let us start to think shapes as signals, and to play shapes with signals.
Chensheng Wang February 2005, Delft The Netherlands
Glossary
AI Artificial Intelligence
BRDF Bidirectional Reflection Distribution Function
B-Rep Boundary Representation
B-Spline Basic Spline
CAD Computer-Aided Design
CAGD Computer-Aided Geometric Design
CAID Computer-Aided Industrial Design
CAM Computer-Aided Manufacturing
CE Concurrent Engineering
CG Computer Graphics
CIMS Computer Integrated Manufacturing System
COM Component Object Model
CSG Constructive Solid Geometry
CSI Cumulative Shape Identity
CW-complex A homotopy-theoretic generalization of the notion of a simplicial complex
DSD Directly Specified Deformation
EFFD Extended Freeform Deformation
FFD Freeform Deformation
FFF Freeform Feature
FFT Fast Fourier Transform
FSD Fourier Shape Descriptor
FSM Fourier Shape Model
FT Fourier Transform
GPU Graphic Processing Unit
HT Hartley Transform
ICAD Intelligent CAD
ICSID The International Council of Societies of Industrial Design
IDEF Integrated Definition, a methodology to describe processes in
enterprises
ISM Intrinsic Shape Model
ISO International Organization for Standardization
MAT Medial Axis Transform
MC Marching Cubes
MLS Moving Least Squares
MNN Minimum Norm Network
MQS Modified Quadratic Shepard
NC Numerical Control
NFFD NURBS-based Freeform Deformation
NFSI Normalized Fourier Shape Identity
NURBS Non-uniform Rational Basic Spline
PCA Principal Component Analysis
PDES Product Data Exchange Specification
PDE Partial Differential Equation
PM Product Model
POU Partition of Unity
RBF Radial Basis Functions
RE Reverse Engineering
RSD Reflective Symmetry Descriptor
SM Shape Modeling
STEP Standard for the Exchange of Product Model Data
STL Stereo-lithography Tessellation Language
SVD Singular Value Decomposition
UI User Interface
UT Uncertainty Theorem
VISC Visualization in Scientific Computing
Legend of Symbols
n
C Computational continuity, generally, n=0,1,2 ' 0, 0 C C ' 1, 1 C C f( )
The feature boundary curve and its projection
The boundary curve on secondary surface and its projection
x Continuous real-valued function in the spatial domain Fourier transformation of f( )x F( )τ s F n G n
The Nyquist frequency
Geometric continuity, generally, =0,1,2 Set of positive integers
`
J Jacobian matrix
,
M N Integer number M N, ∈Ι
The power spectrum of F( )τ P( )τ
Rn n
n
\ n n
-tuple
-Dimensional Euclidian space, =1,2,3 0 S 1 S Χ , , Primary surface Secondary surface Set of functions x y z ℵ ]
Real values variables
Sampling grid Set of integer ω Frequency term Γ Ω ∅ ( , ) k Mapping or function
Area or parameter region Empty set or area
x y
ϕ Radial basis functions ( )
k x
φ Basis functions ( )τ
Lattice area , m n Φ nf xn ∂ ∂ n ⊆ ∪ ∩ ∀ 1 d k k
Order directional derivative
Belong to Union/And Intersection Exists x =
∏
Multiplication of x x1, , , ,2" x kk =1,2, ," d ||| ( ) x x ∆ Dirac function 0− 1P P Euclidian distance between P0 and P 1
f Absolute value of f , and f ≥ 0
Mode of P, 2 2 2 x y z p p p = + + P P
Contents
Preface···I Summary ···III Glossary ··· VII Legend of Symbols···IX Chapter 1. Introduction ··· 1 1.1 Design Reuse ···11.1.1 Studies of Design Reuse···3
1.1.2 Related Disciplines to the Study of Design Reuse ···4
1.1.3 Design Reuse at the Information Level···5
1.2 Shape Reuse···6
1.2.1 Objects of Shape Reuse···7
1.2.2 Data Sources for Shape Reuse···8
1.2.3 Related Issues and Technologies ···10
1.3 Objectives ···14
1.4 Hypothesis ···16
1.5 Strategy···17
1.6 Thesis Contributions···18
1.7 Outline of the Thesis ···19
1.8 Publications···20
Chapter 2. Related Issues in Freeform Feature Reuse: A Literature Review··· 21
2.1 Overview of Shape Modeling Techniques ···22
2.1.1 A Classification of Shape Model Representations ···22
2.1.2 Limitations of Conventional Shape Modeling Methods ···23
2.1.3 Scattered Data Modeling Techniques ···24
2.1.4 Uncertainty Principle ···28
2.1.5 Multiresolution in Approximation ···28
2.2 Local Shape Modifiers in Shape Modeling ···30
2.2.1 Texture Mapping ···31
2.2.2 Bump Mapping ···32
2.2.3 Displacement Mapping ···33
2.3 Feature Technologies in Product Shape Design ···35
2.3.1 Generative Approaches ···36
2.3.2 Feature Recognition ···36
2.3.3 Feature Reuse···37
2.4 Freeform Features ···39
2.4.1 Definition and Representation ···39
2.4.2 Freeform Feature Discrimination and Retrieval ···44
2.4.3 Shape Processing ···49
2.4.4 Freeform Feature Reuse ···51
2.5 Surface Frequency···54
2.5.1 Fourier Method ···54
2.5.2 Spherical Harmonics ···55
2.5.3 Continuous Surface Frequency Method···55
2.6 Summary···56
Chapter 3. Fourier Shape Descriptors ···59
3.1 Definition of Fourier Shape Descriptors ···60
3.1.1 Fourier Transforms and Their Representations ···61
3.1.2 Fourier Sinusoidal Basis···63
3.1.3 Computation of the Discrete Fourier Transforms (DFTs) ···71
3.1.4 Definition of Fourier Shape Descriptors ···79
3.2 High-order Surface Interpolation on Scattered Dataset···84
3.2.1 USFFT (Steidl, 1998) (Kunis, et al. 2003) ···84
3.2.2 Computational Complexity ···87
3.2.3 Error Estimation of the USFFT ···87
3.3 Surface Properties of Fourier Shape Descriptors ···88
3.3.1 Surface Normal···89
3.3.2 Arc Length···89
3.3.3 Surface Area ···90
3.3.4 Curvature ···90
3.4 Summary···91
Chapter 4. A Framework for Freeform Feature Reuse···93
4.1 Fundamentals ···94
4.1.1 Basic Concepts···95
4.1.2 Problem Domain ···96
4.1.3 Shape Parameters ···98
4.1.4 Representation Scope ···99
4.2 Overview of the Framework for Freeform Feature Reuse···99
4.3 Fourier Shape Model ···102
4.3.1 Analysis of Imprecision ···105
4.3.2 Properties of the Fourier Shape Model ···105
4.4 Pre-processing···107
4.4.1 Interactive Specification of the Region of Interest ···107
4.4.2 Localization ···109
4.4.3 Interpolation···111
4.4.4 Resampling ···113
4.5 Post-processing ···114
4.5.1 Points and Normals ···115
4.5.2 Context Adaptation ···116
4.5.3 Continuity in Surface Models···117
4.5.4 Topological Adaptation···118
Chapter 5. Freeform Feature Retrieval by Signal Decomposition ··· 121
5.1 Correspondence between a Spatial Shape and Its Spectrum ···122
5.1.1 Shape Representation in the Frequency Domain···122
5.1.2 Correspondence between A Spatial Shape and Its Spectrum···123
5.2 Freeform Feature Discrimination···124
5.2.1 Feature Fitting Techniques···125
5.2.2 Template Fitting···125
5.3 Spectral Properties of the Frequency Representation ···126
5.3.1 Frequency Response to the Sampling Configurations ···126
5.3.2 Stability Analysis···127
5.4 Freeform Feature Retrieval by Signal Processing···128
5.4.1 Process of Freeform Feature Retrieval···128
5.4.2 Exact Feature Retrieval ···130
5.4.3 Minimal Surface Method ···134
5.4.4 Shape Filtering Method···137
5.4.5 Quality Analysis ···142
5.5 Summary···143
Chapter 6. Freeform Feature Reuse by Signal Synthesis ··· 145
6.1 Freeform Feature Reuse via Shape Synthesis···146
6.1.1 Categories of Shape Synthesis···146
6.1.2 Displacement Mapping in Shape Synthesis ···147
6.2 General Shape Synthesis by Signal Processing ···148
6.2.1 Overview of the Shape Synthesis Process···148
6.2.2 General Shape Synthesis and its Signal Flow ···149
6.3 Spectral Operators for Freeform Feature Reuse ···152
6.3.1 Spherical Mapping Operator ···152
6.3.2 Cylindrical Mapping Operator···154
6.3.3 Surface Normal Mapping Operator ···156
6.3.4 Directional Matrix ···157
6.3.5 Controlling the Style of Displacement Mapping···158
6.4 Issues in Shape Synthesis ···159
6.4.1 Parameterization and Alignment ···159
6.4.2 Validity of Shape Synthesis ···161
6.4.3 Remarks on Periodicity and Boundary Issues···161
6.4.4 Quality Analysis of Shape Synthesis ···162
6.5 Spectral Analysis and Shape Processing ···162
6.5.1 Spectral Analysis and Signal Restoration ···162
6.5.2 Shape Processing ···164
6.6 Shape Information Abstraction ···166
6.6.1 Normalized Fourier Shape Identity···167
6.6.2 Cumulative Shape Identity ···169
6.6.3 Considerations in Shape Information Indexing···171
6.7 Summary ···173
Chapter 7. Applications ··· 175
7.1 Shape Abstraction and Regional Shape Manipulation···176
7.1.1 Shape Abstraction Using the FSM···177
7.1.2 Regional Shape Manipulation Using Spectral Operators···178
7.2 Reinforcing Design Creativity ···180
7.2.1 Bridging the Gap Between Traditional Design Means and Advanced CAD Systems ···180
7.3 Multi-resolution in Regional Shape Representation ···183
7.4 Enriching Regional Appearance ···184
7.5 High-order Surface Design ···185
7.6 Applications in Knowledge Engineering···187
7.6.1 Creating A Shape Repository of FFFs ···187
7.6.2 Facilitating the Reuse of Shape Information ···188
7.7 Summary···189
Chapter 8. Implementation and Assessment···191
8.1 Overview of the Prototype System···192
8.1.1 System Architecture···192
8.1.2 User Interface···197
8.1.3 Kernel Data Structure···199
8.1.4 Data I/O ···205
8.2 Tools for Shape Analysis and FFF Retrieval···206
8.2.1 Dialog of Shape Analysis ···206
8.2.2 Tools for FFF Retrieval···207
8.3 Tools for Effective Shape Control ···208
8.3.1 Controlled Shape Synthesis···208
8.3.2 Implementing Shape Decomposition ···209
8.4 Assessment···210
8.5 Summary···216
Chapter 9. Conclusions and Prospects···217
9.1 Summary of the Research Work ···217
9.1.1 Investigation of the State of the art Technologies ···218
9.1.2 Theoretical Development ···218
9.1.3 Pilot System Implementation and Validity Assessment ···219
9.2 Conclusions···220
9.3 Prospects and Future Work···221
Bibliography···223
Own Publications···237
Samenvatting ···239
1
Introduction
"An implication of what we are saying at the moment, however, 'I pointed out,' is that the capacity for knowledge is present in everyone's mind. If you can imagine an eye that can turn from darkness to brightness only if the body as a whole turns, then our organ of understanding is like that. Its orientation has to be accompanied by turning the mind as a whole away from the world of becoming, until it becomes capable of bearing the sight of real being and reality at its most bright, which we're saying is goodness."--Emerging from the cave.
(Socrates Plato, «The Republic», 518c)
Reuse is a general notion, which means utilizing existing objects with minor or without processing. The reused objects can be intellectual knowledge, experiences, old machinery, or others. Reuse activity widely takes place in our daily lives, bringing us great benefits by exploiting the potential value of objects. Broadly speaking, the progress of science and technology owes not only to new inventions, but also to the aggregation and reuse of past wisdom. For instance, it was proved that, in electronics and software engineering, the reuse of standardized or object-oriented modules could bring significant advantages (Sodhi, 1999).
In the field of industrial design, supporting facilities for reuse are also desirable to promote productivity and efficiency, by maximizing the capacity of using past concentrations of engineering creativity and expertise. Especially, in recent years, the increasing expectation for industrial products with higher quality and lower costs has heightened the needs for computational tools able to reinforce the capability of reuse in a computer-aided design environment.
1.1 Design
Reuse
Design reuse refers to the inclusion of intellectual assets built in previous designs. As a natural strategy, it is, whether consciously or subconsciously, employed by designers in problem solving, by using successful precedents in part or as a whole for new designs (Sivaloganathan, et al. 1999). This makes the building of a new product model cheaper
Figure 1.1 A general process of design with the support of reuse, adapted from Neelamkavil, et al. (2003).
and faster. For instance, in shape modeling, the reused components will not only be already designed, but also tested for reliability and manufacturability.
Generally speaking, a design process is an iteratively evolving procedure, which consists of four phases: (i) planning and clarifying the design problem according to the market and the company needs; (ii) generating and formalizing design concepts with the specifications on cost and manufacturing; (iii) transforming the specification into a concrete design scheme; and (iv) finalizing the design and documentation. In addition, iterations as the intrinsic cycle in approaching solutions are associated with each phase.
Design reuse widely exists throughout the design process through providence of competitive product strategies, alternating design concepts and configurations, and rationalization of design implementations. Figure 1.1 shows a general scenario of design process with the support of design reuses, using an Integrated Definition (IDEF0) graph,
adapted from Neelamkavil, et al. (2003). Some of the input factors in this figure may be considered in an earlier phase, for instance, the aesthetic, ergonomic, or economic constraints sometimes play roles in the conceptual design phase. The input parameters to each phase are not exhaustively enumerated here.
3
D
m
m n≤
3
The reusable design knowledge are constituted by structured information, such as rationalization constraints for design decisions, design rules, past experiences, manufacturability and the criterion for process plan, scientific principles, and product information. In Figure 1.1, D D , and D denote the input of the recursive design processes within or across phases, shown in a forward order (i.e., D to where ). However, propagation may sometimes happen in the reverse order, for instance, some of the factors in detailed design phase (i.e., D ) may request a revision of the embodiment scheme (e.g., to ).
1, 2, 4 D D 4 n D 4
Figure 1.2 A schematic process of design knowledge abstraction. 1.1.1 Studies of Design Reuse
Historically, studies of design reuse are conducted at three levels:
• Firstly, at philosophical level, principles and methodologies for design reuse are developed (Sivaloganathan, et al. 1999). For instance, cognitive study on design reuse aims at developing methodologies for (i) representing; (ii) organizing; (iii) recognizing; and (iv) retrieving design knowledge (Finger, 1998). Clausing (1998) identifies ‘achieving of the best strategic balance between reuse and in-novation’ as a principal objective in product development. Studies at this level discover the abstract guidelines for the implementation of design reuse; • Secondly, at knowledge level, product design, process plan, material choices,
heat-treatment, and other engineering-related information are investigated (Duffy, et al. 1995) (Duffy, et al. 1998). Being structured information, the pro-cedure of engineering processes constitutes design knowledge, which in turn can be further reused. Studies at this level create rules or strategies for captur-ing and codcaptur-ing of the procedural information; and
• Finally, at information level, product shape-related properties and data are plored, such as geometric models of artifacts or components, shape styles ex-pressed by the topological elements, and freeform features depicted by local geometric parameters (Vergeest, et al. 2001) (van den Berg, et al. 2002). Stud-ies at this level generally lead to applicable tools, for instance, in
Computer-Aided Design/Industrial Design (CAD/CAID) systems.
Despite already studied for a long time, challenges at each of these levels still remain. For instance, at the knowledge level, gaining the know-how of design requires capturing the structured information in design processes, which appears to be a sophisticated task. It always needs high-level abstraction of design information based on domain knowledge and specific expertise, by which the engineering information of a product, such as physical model data, descriptive data, and textual documents, can be acquired, extracted,
and abstracted. Figure 1.2 schematically shows the process of abstracting and encoding of design knowledge.
Aspects on the study of design reuse
The following aspects have been recognized as pivot issues in the study of design reuse by Sivaloganathan, et al. (1999): (i) focused innovation; (ii) cognitive issues on design reuse; (iii) computational perspective of design reuse; (iv) reuse of standard components; (v) design reuse tools and methods; (vi) design reuse systems; and (vii) other issues in design reuse. So far, the significance of design reuse was addressed by most of the documented investigations, and new strategies for reuse at the philosophical or knowledge level were proposed. Based on these findings, some frameworks for reusing the procedural or functional knowledge of product design were established.
Reuse versus overuse
There are a number of factors that might hamper design reuse, due to lack of inappropriate levels of reuse. Investigations within engineering organizations have suggested that reuse inhibitors are wide-ranging, falling under five main headings: (i) environmental concerns; (ii) organizational restrictions; (iii) motivational objectives; (iv) cognitive limitations; and (v) engineering causes (Busby, 1998).
Although an appropriate level of design reuse can bring in significant advantages, one should be aware that overuse of design reuse can also kill creativity. Related issues were reported by Lloyd, et al. (1998). For instance, they believe that design fixation can cause overuse, which inhibits innovation. They conducted a field study surrounding the issue of ‘when a designer resorts to starting from the first principles and when he resorts
to using past knowledge’, and concluded that organizational processes that lead to placing
too much emphasis on the integrity of previous design solutions have the problem of design fixation (Lloyd, et al. 1998) (Sivaloganathan, et al. 1999). In this situation, design reuse becomes copying the overall design solution, resulting in an overuse of previous designs.
1.1.2 Related Disciplines to the Study of Design Reuse
The study of design reuse requires specific domain knowledge and application backgrounds. In recent years, the convergence in science and technology has enhanced the interdisciplinary nature of the study of design reuse. There are a number of subjects constituting the study domain, such as cognitive sciences, knowledge engineering (e.g., knowledge discovery and data mining), informatics for information capturing and retrieving, Reverse Engineering (RE), digital image/signal processing, shape modeling, computational geometry and Computer Graphics (CG), as well as CAD/CAID technologies. Based on the level of the study of design reuse, these subjects can be roughly classified into three categories, namely, (i) methodologies, concerning how to conduct reuse, which aim at discovering general rules in design reuse at the philosophical or abstract level; (ii) technologies, related to the theoretical fundamentals for implement-ing reuse, by which computational algorithms and mathematical models are invented; and finally, (iii) applications, regarding computational packages supporting design reuse, including domain-specific frameworks, and computer assisted tools or systems.
Figure 1.3 schematically shows the subjects related to the study of design reuse. The circular arrows represent the cycle of reuse in a CAD/CAID environment, in which the objects of reuse can be design strategies, modeling algorithms, as well as existing product models.
Figure 1.3 Related disciplines to the study of design reuse. 1.1.3 Design Reuse at the Information Level
Design reuse at the information level investigates the reusability of shapes, colors, descriptive texts, and other design information. Due to technological limitations, high-level information is often poorly captured, archived, and managed in existing CAD/CAID systems (Neelamkavil, 2003). For instance, because of lacking sufficient mechanisms for abstraction, currently, there is nearly an absence of reusable high-level parameters in a geometric model. As a consequence, model editing is restricted to manual operations such as local or global geometric deformations, and primitive adding or removing. The reuse of geometric objects is possible only in very specific situations, namely either as a
copy-and-paste operation1 of a regional surface, or via Boolean operations when the geometric
object is relatively simple, such as that for prismatic and analytical geometries. However, it is also known that, for more complex geometric objects, reuse support is strongly required (Vergeest, et al. 2000).
One of the goals of industrial design is to ease people’s life by delivering them high-quality products via a designer’s creative work. Henry Dreyfuss (1904-1972), one of the great industrial designers of the twentieth century, pointed out when he describes the rules of an industrial designer: “If people are made safer, more comfortable, more efficient–or
just plain happier, the designer has succeeded.” In this regard, the shape information of a
product plays an important role, leading to a successful design. Raymond Loewy (1893-1986), an influential industrial designer, said: “Ugliness doesn’t sell.” In fact, the geometric shape of industrial products, as a conveyer for associating various engineering
1 A copy-and-paste operation is developed to implement the reuse of regional geometry like what happens in a word processor. It works on a piecewise surface, and results in a surface editing in a fully automatic way. The pasted geometry is normally implemented as a displacement.
Figure 1.4 The cycles of global and local shape reuse.
attributes, is the core of CAD/CAID systems. Shape information reuse is one of the most important factors in the implementation of supporting tools for design reuse (Duffy 1999).
Existing researches on design reuse appear weak in terms of supporting reuse at the information level, although the expectation for applicable tools facilitating reuse in the geometric modeling process of industrial products is high. As a consequence, there are few publications found in this category, as well as few tools for design reuse in commercial CAD/CAID systems.
1.2 Shape
Reuse
Shape reuse refers to the reuse of geometric information, such as geometric parameters, patterns, and topological configurations. During the past decades, with the widespread application of CAD/CAID systems and digital acquisition equipment, a tremendous amount of design knowledge has been accumulated as repositories of product models on the Internet or within organizations. The exploitation of these valuable resource, especially that of geometric models of products, has become an attractive yet challenging research field to design research community, for its merits leading to saving time and money, and avoiding unnecessary mistakes (Suh, 1990) (Ullman, 2002) (Neelamkavil, at al. 2003). The present study also takes this issue as one of the objectives.
In practice, strategies for shape reuse usually follow one of these two approaches, namely, treating the geometric model of a product either as a whole by using such techniques as Group Technology (GT) (Gallagher, et al. 1973), or as feature compositions (Shah, et al. 1995) (Vergeest, 2001). The former addresses the global properties of product shapes; for instance, by means of the Opitz coding scheme (Bond, et al. 1988) (Allen, et al. 1988), design information can be categorized according to shape characteris-tics and its supplementary properties, such as tolerances, materials, production operation types, sequences, and functions chosen by the manufacturer (Gallagher, et al. 1973) (Dowlatshahi, et al. 1998), whereas the latter exploits local shape properties, such as the characteristics of a regional geometry, Freeform Features (FFFs), and the Region of
Figure 1.5 An example of the shape reuse process and the effects in local enrichment; (a1)~(a5) are the process of
transplanting an existing freeform feature to a target, from Biermann, et al. (2002).
Critical issues in shape reuse have been recognized as: (i) capturing either regional geometry or global shape information; (ii) retrieving the global or local shape parameters of a geometric model; (iii) adapting the retrieved shape parameters to fit into existing modeling contexts (regional), or conducting direct modification on the retrieved model (global); and (iv) documenting the current model either partially or as a whole into a repository, which in turn can serve as the input of reuse in the future. The cycle of shape reuse is schematically shown in Figure 1.4, which consists of two approaches, namely, the global and the local shape reuse.
In fact, shape reuse is one of the greatest interests in RE as well (Ingle, 1994), espe-cially, when the geometric model of a product is reverse-engineered (Várady, et al. 1997). The reverse-engineered physical models usually serve as a starting template for the creation of a new shape, in which partial shape reuse frequently happens. The benefits of supporting shape reuse, whether as a whole or partially, were reported in the fast shape design project by van Dijk, (1994) and van Elsas, (1997), and in cut-and-paste tools for local shape enrichment by Biermann, et al. (2002). Figure 1.5 shows some examples of FFF reuse, in which local geometries are captured and transplanted.
FFFs are widely used high-level shape entities with great significance in industrial design. Figure 1.6 shows the process of FFF reuse in carrying out aesthetical enrichment in detailed design. In Figure 1.6, FFFs from different data sources are retrieved and adjusted to fit into the current modeling context. In fact, being capable of facilitating fast creation and variation of enriched shape models, the supporting tools for FFF reuse are also desirable in shape conceptualization, where a huge unknown design space has to be explored.
By now, we have introduced the concept of design and shape reuse. We have ad-dressed the importance of design reuse at information level, and clarified the position of shape reuse in the stream of the study of design reuse. Techniques for FFF reuse are of particular interest to the present study, which requires comprehensive investigation on issues such as the representation and the analysis of FFF geometry. Further discussions will concentrate on shape reuse, especially the reuse of regional shape information, i.e., FFFs. Developing systematic methodologies and applicable tools to facilitate FFF reuse in shape modeling is the main objective in this research.
1.2.1 Objects of Shape Reuse
As shown in the previous section, one of the straightforward tools for FFF reuse is copying-and-pasting of regional geometry or FFFs (Biermann, et al. 2002) (Dumont, et al. 2003). In fact, most of such methods work in the spatial domain, and are unable to
Figure 1.6 The process of freeform feature reuse in local enrichment; items with dark color typically need human
intervention (part of Figure 1.1).
accommodate with arbitrary data sources, due to limitations of representation adopted in those approaches.
Broadly speaking, any digitized shape models can be the potential data sources for shape reuse. For instance, it can be a solid model, a surface model, a discrete model, or even a physical model, as shown in Figure 1.6. One of the common characters of objects of shape reuse is that it must be a computer-interpretable model. While strategies for global shape reuse emphasize abstract shape characters, approaches for local shape reuse, especially for FFF reuse, typically investigate the detailed parameters of regional geometry. Local shape reuse frequently happens in a multiple-representation environment, to which a unified shape representation, specifically that for regional shapes, has to be established.
1.2.2 Data Sources for Shape Reuse
Date sources for shape reuse include digital and physical models. Depending on their representation, they can be categorized as CAD models that possess complete data and topological structures, such as solid and surface models; discrete models that possess simple data and topological structures, such as that in Stereo Lithography (STL)2 and
StereoLithography Contour (SLC) format3, or that of a point cloud; and physical models
2 STL is a facet-based representation that approximates surface and solid entities only. Entities such as points, lines, curves, and attributes such as layer, color from CAD systems will be ignored during the output process. An STL file consists of a list of facet data. Each facet is uniquely identified by a unit normal (a line perpendicular to the triangle and with unit length) and by three vertices (corners). The normal and each vertex of a facet are specified by three coordinates, so there are in total of 12 numbers stored for each facet.
3 The SLC file format is a “ ” contour representation of a CAD model. It consists of successive cross-sections taken at ascending Z intervals in which solid material is represented by interior and exterior boundary polylines.
1 2 2 D
that can be digitized to a discrete model by means of scanning or sensing. Characteristics of these models are described below:
(i) CAD models. These models can typically be depicted by Boundary
Represen-tation (B-Rep), or Constructive Solid Geometry (CSG) represenRepresen-tation. A local or a
regional shape can generally be represented by Non-Uniform Rational Basic Spline (NURBS) surfaces with the following form:
( )
( )
( )
( )
( )
1 1 , , , , 0 0 1 1 , , , 0 0 B B , B B M N m n m n m k n l m n M N m n m k n l m n w u v u v w u v − − = = − − = = =∑ ∑
∑ ∑
d p (1.1)where form the control point matrix,
topologi-cally in a rectangular region; denote weight factors, where at the corner points and w for the other points;
, , 0,1, , 1; 0,1, , 1 m n m= M− n= N− d " " , m n w , 0 m n≥ 0,0 , w ,wm0,w0,n,wm n, >0
( )
u m , m k B , =0,1, ,"M−1, and( )
,Bn l v n, =0,1, ," N−1 are the B -spline basis functions with order k in u and order in direction, respectively, defined by the knot vectors
l v U=
(
u u0, , ,1"uM k+)
and(
v v0, , ,1 vN l+)
=
V " using the de Boor iteration formula (de Boor, 1978); and p
( )
u v, are the resulting surface points at each( )
u v pair; normally, , u∈[
0,M+k]
, v∈[
0,N k+]
.In a CAD/CAID system, there are always mechanisms to access the underlying dataset of geometry, for instance, by using the pointers in the data structure.
(ii) Discrete models, including mesh and point cloud models. These models are
typically obtained from a scan of physical objects. A discrete model can be interpolated into a continuous model using shape-modeling techniques. For instance, a pointset can be interpolated by a real-valued function as
f :\d→\ , N where
(
f1( )
, ,f( )
)
T N N = ∈ Xf x " x \ and X=
{
x1, ,"xd}
⊂\ are the finite set of dpairwise distinct points; d denotes the dimension of the parameter space; N the
dimension of the function space; \ the N N -dimensional functional space; and \ the
-dimensional parametric space (Iske, et al. 2002). A 3D point cloud is the simplest form of a scattered dataset with representation
d
d
( )
{ }
f x , X⊂\2.A discrete model typically possesses a flattened topological structure; for instance, in a point cloud model all the data are equally stored at the same level without layer information.
(iii) Physical models. Physical models are often used as references in product
design. By means of digitization, a physical model can be interpreted into a digital model with a finite pointset
{ }
3k
= ⊂ \
P p , where k∈ ` denotes the size of the pointset; ` the set of positive integers; and \3 the 3D Euclidian space.
SLC data can be generated from various sources, either by conversion from CAD solid or surface models or more directly from systems that produce data arranged in layers, such as CT-scanners.
In summary, shape reuse, as a focal point in the broad research field of design reuse, concerns the reuse of geometric information. And regional shape reuse, especially FFF reuse, is one of the important aspects in shape reuse, which becomes the target of our study.
1.2.3 Related Issues and Technologies
The study of FFF reuse in shape modeling involves a broad range of subjects in design research, which can be further categorized as:
• CAID and shape modeling techniques, which are relevant to shape creation and topology maintenance;
• Shape descriptors and shape analysis, which are relevant to shape representation and the extraction of shape characteristics;
• Freeform feature technologies, including FFF definition, abstraction, and ma-nipulation, which constitute the fundament to the present study; and
• Techniques for FFF reuse, including feature capturing, extraction, and trans-planting methods.
These issues will be briefly introduced in the following subsections.
CAID and shape modeling techniques
CAID is often thought of as CAD adapted and specialized for aesthetic design. A CAD modeling system addresses model validity and consistency by maintaining a unique representation of the geometric model, whereas a CAID system tends to be more interested in the flexibility of depicting morphological characteristics. Both types of systems are widely used in industrial design. For instance, popular CAD systems include SolidWorks®, CATIA®, UG-II®, and others; and the most commonly used CAID systems
include Alias|Wavefront MAYA®, 3D Max Studio®, and Rhinoceros®. Despite the ability
of handling colors, textures and other visual factors, the ultimate capability of shape morphology manipulation is of most concern in a CAID system, by which the aesthetic aspects, such as styling and profile, are enforced.
In recent years, many a research on highly flexible techniques of shape depiction have been conducted with a focus on basic geometric primitive-based model representa-tions, such as mesh-based models (Kobbelt, et al. 2000) (Desbrun, et al. 2002) (Dey, et al. 2002), and pointset models (Zwicker, et al. 2002) (Frisken, 2000) (Alexa, et al. 2001) (Reuter, et al. 2003). This is sometimes referred as Shape Modeling (SM), in contrast to
the conventional CAD modeling techniques. Unlike in CAD modeling, where the geometric representation and topological information are synchronously generated and maintained during the modeling process, the typical characteristics of shape modeling techniques are:
• Utilizing the simplest geometric primitives, such as points, lines or facets; • Only maintaining the simplest model topology; for instance, in a mesh model,
only vertices and edge adjacency information are kept; and
• Capable of supporting multiresolution visualization, when handling huge data-sets.
To implement FFF reuse in a shape modeling context, issues such as how to acquire and to incorporate the reused feature geometry into the existing modeling framework
become the main concern, which generally requires interrogating the underlying data format.
Shape descriptors and shape analysis
Shape descriptors, as a unique shape representation, have been intensively investigated, for instance, in image processing (Gonzalez, et al. 2002). Based on their mathematical methods, shape descriptors can generally be categorized in two classes: (i) boundary-based descriptors; and (ii) regional-boundary-based descriptors (Wu, 1998). The former represents shapes based on boundary information, such as radius, contour, and chord length; whereas the latter represents shapes by regional information, such as shape metrics based on the relative areas of shape contained in concentric rings located in the shape centroid. There are some other classifications, for instance, on the basis of information preservation, in which methods allowing for accurate reconstruction of a shape from its descriptor are called information preserving, opposite to information non-preserving (Loncaric, 1998).
Shape descriptors are widely used for 2D shape registration, for instance, global and local shape matching metrics, including global statistical approaches based on a method of moments (Belkasim, et al. 1991), Fourier Shape Descriptors (FSDs) (Zhan, et al. 1972)
(Arbter, et al. 1990) (Tello, 1995) (Persoon, et al. 1997), wavelet shape descriptor that takes the local geometric attributes into consideration, such as the curvature and slope, and multi-resolution shape descriptors (Kauppinen, et al. 1995) (Chuang, et al. 1996) (Gonzalez, et al. 2002). FSD and wavelet shape descriptor are often referred to as
frequency-based descriptors, since they transform a shape into a frequency spectrum.
Criteria for the evaluation of shape description methods include (Marr, et al. 1978): • Accessibility, which describes the efficiency to compute a shape descriptor in
terms of memory requirements and computational time;
• Scope, which denotes the coverage of shapes that can be described by the method;
• Uniqueness, which refers to whether a one-to-one mapping exists between a shape and its descriptor; and
• Stability or sensitivity, which measures how sensitive a descriptor is against small changes on a shape.
Shape descriptors are often utilized to characterize the geometric attributes of a shape, such as in the calculation of surface properties. Metrics and some 3D shape descriptors are widely used in conducting spatial shape analysis (Osada, et al. 2002). In recent years, the application of signal-processing techniques has become prevailing in the field of shape analysis and processing (Taubin, 1995) (Persoon, et al. 1997) (Wu, et al. 1998) (Karni, et al. 2001); for instance, methods for describing and processing point-sampled objects using spectral-based operators were reported by Pauly, et al. (2001). Problems of using these methods are that the calculation of a shape identity is either computationally expensive (Wu, et al. 1998) or lack of generality (Funkhouser, et al. 2003).
Frequency-based shape descriptors are potentially useful in terms of coping with diverse data sources, and free of underlying data complexity. In addition, it is possible to utilize these kinds of descriptors to conduct shape analysis, processing, or hopefully FFF retrieving at a lower computational cost.
Features in product shape modeling
Features are referred to as a hyper-class of entities, grouped by engineering relevance. In a CAD system, features are classified as form features and functional features (Bronsvoort, et al. 2001b). Functional features are often utilized to modularize the process of design and to maintain the design intent throughout continuing modifications (Andrews, et al. 1999) (Bronsvoort, et al. 2004), whereas form features serve to characterize the shape properties. A design system applying feature technique is often termed as feature-based design system (Shah, et al. 1995) (Bronsvoort, et al. 2002) (van den Berg, et al. 2002). In
shape modeling, form features are commonly used to construct geometric models. Related topics in this field include form feature recognition and design by features (Finger, et al. 1990) (Shah, et al. 1995) (Bronsvoort, et al. 2001a).
FFF is a specific class amongst various engineering features, which has long been recognized as the pivot entity in shape modeling. As high-level geometric entities, FFFs can provide advantageous mechanism for treating a set of geometric elements as a single entity (Fontana, et al. 1999). This is more convenient than working with low-level constructive elements, since a FFF can be manipulated by means of a limited number of significant parameters, thus enabling fast creation and modification of geometric models (De Martino, et al. 1998). Interestingly, cognitive study also affirmed the significance of FFFs in shape description4 (Stillings, et al. 1987) (Cassirer, et al. 1998).
It has been identified that, from an aesthetic point of view, two categories of FFFs have significant impact on shape appearances (Fontana, et al. 1999):
• Structural features, created in the preliminary phase of design. They are struc-tural entities used for defining the surfaces constituting the product, thus having an important aesthetic impact;
• Detailed features, created in the second modeling phase. They are applied on a surface either for adding aesthetic and functional details, or for enforcing visual effects of the characteristic elements, such as the identity logo, an operational warning, or decorative forms.
Structure features often serve to group connected sets of curves according to their intrinsic meaning, i.e., either contours or character lines, to treat them as a unique entity, and to maintain the relationship among the correspondingly derived surfaces and their validity. They constitute the basis for an easier and more efficient successive modification of the whole product, by varying the parameters of structural elements.
Detailed features are generally created in the posterior modeling phase, which typically corresponds to local modification of a given freeform surface to create objects possessing complex shape details. From a perceptual point of view, detailed features are constituted by relatively higher frequency components, in order to set up the distinction against the domain surface; for instance, a logo on a car or a regional deformation on an object. A detailed feature contributes to the style of a product by enhancing its regional characteristics, without hurting its topological structure globally. Hence, it has limited impact on shape styling.
Despite the advantages of features in shape modeling, caution should be taken when utilizing the feature concept. Since originated and mainly investigated in mechanical design, the concept of feature is often associated with non-geometric attributes in a CAD system (Rossignac, 1990) (De Martino, et al. (1994) (Dumenjo, et al. 1998). For example,
4
In the symbolic system proposed by Cassirer (1874-1945), the representation of content in human cognition happens in three levels, i.e., symbol form, symbol structure and symbol meaning. A corresponding correlation can be derived in the FFF study as: symbol form ↔ detailed feature and, symbol structure ↔ structural feature.
Figure 1.7 A comparison of feature retrieval techniques; (a) a shape with a region of interest where a feature is
located; (b) a hard-copy of the regional geometry, in which the influence of the base surface on the feature is inherited; (c) a pure feature, in which the distortion imposed by the articulated base surface is excluded.
both the procedures and the functions can be treated as features in a CAD system, such as in SolidWorks®. This is partially due to the reason that classical mechanical parts are
defined by canonical geometric entities, and the identification of the association between shapes and functions could easily be achieved.
Within the scope of this research, the geometry of shapes is mostly interested. There-fore, we specify the application domain of the term feature as a set of geometric entities whose main contribution to shape modeling or product styling can be governed either aesthetically or functionally.
Under this constraint, features are always referred to as distinct geometric character-istics on a shape, such as streamlined profiles, functional bumps or cuts, or others (Fontana, et al. 1999).
Techniques for freeform feature reuse
Conventionally, feature reuse is implemented in the spatial domain by transferring a regional geometry from one place to another within a model or across models. Post-processing steps, such as context adaptation and boundary transition, have to be associated with the implementation process in order to incorporate the reused geometry into the new modeling context. For instance, the copy-and-paste method has implemented a FFF reuse by first cutting-and-copying the feature geometry and then pasting it to a specified region on the target surface (Biermann, et al. 2002) (Dumont, et al. 2003). In this context, feature retrieval is implemented by detecting the curvature variation along feature boundary (Kobbelt, et al. 2001). This is rather complicated, and causes that this approach relies heavily on the underlying data structure of the model (Frisken, et al. 2000) (Gonzalez, et al. 2002). These methods may work with all kinds of digitized shape models,
including solid models, surface models, mesh models, and point cloud models. In particular, when working with discrete models, feature-fitting5techniques are always
employed to serve as an auxiliary means to discriminate the parameters of feature geometry and to interpolate it into a continuous representation (Vergeest, et al. 2003). In some cases, feature-fitting techniques are indispensable to the reuse of a regional geometry; for instance, when a scanned model in involved in RE.
In the context of FFF reuse, it is important to make a distinction between features and ROIs. A feature is often referred to the highly articulated geometry in a specified region, whereas a ROI is simply a regional geometry. As shown in Figure 1.7, Figure 1.7-(b) is a ROI, and Figure 1.7 -(c) is called a feature (or pure feature). In order to obtain a pure feature, the influence of the underlying domain shape has to be screened out. However, because of the complexity of both model geometry and its topology, to eliminate the distortion of feature imposed by geometrical interactions during modeling process is hardly achievable in the spatial domain in most cases. This is one of the main drawbacks in existing approaches.
Interdisciplinary studies, such as volume data manipulating by digital signal process-ing techniques, have revealed a new possibility for shape depiction, namely, describprocess-ing shapes in the frequency domain (Anuta 1970) (Hughes 1992) (Malzbender 1993) (Taubin,
1995) (Gonzalez, et al. 2002). Shape representation by using frequency-based descriptors, such as Fourier descriptors and wavelets (Mallat 1989) (Chuang, et al. 1996), seems to be promiseful for separating the feature from a ROI in terms of the frequency threshold. In addition, the tedious efforts of managing model topology and trivial low-level geometric entities can also be avoided by using these descriptors.
The exploration on related techniques of FFF reuse reveals the possibility of con-ducting pure feature retrieval by applying signal processing techniques. This is useful for us to identify the right direction of study.
1.3 Objectives
The literature study and investigations on CAD/CAID technologies show that: (i) there are great demands in promoting the efficiency of shape modeling in industrial design (van Dijk, 1994) (van Elsas, 1997); and (ii) currently there is no sufficient knowledge aggregation contributing to shape understanding and characteristic capturing in product modeling; (iii) commercial CAD/CAID systems lack systematic mechanism to support shape reuse (Biermann, et al. 2002); and (iv) effective manipulation of shape geometry is continuously the greatest concern to the design community, and far from solved (Vergeest, et al. 2001).
Towards these requirements, objectives of the current study can be formulated as
finding a proper mechanism for capturing and reusing FFFs in the context of product shape modeling, and implementing an application prototype.
Our study is application oriented, rather than an invention of new theories. However, to assist technical formulation, related theories will be explored and further developed. The above objectives can further be clarified into three levels, namely, theoretical principles, systematic approaches, and applications, as listed below:
Objective 1: Theoretical principles
5 Feature fitting is a technique, in which a predefined template is used to fit with an existing dataset, normally scattered, retrieving the geometric parameters of the dataset.
In the present research, studies of theoretical principles aim at:
• Exploring the knowledge of how human perceptual system interacts with mor-phological shapes in the physical world, and the possibility of applying this knowledge in the study of CAD technology;
Psychological studies have resulted in a number of valuable findings, which help us to understand the mechanism of human perception to the morphology of objects. The application of this trunk of knowledge may catalyze innovative so-lutions in approaching our research goal.
• Investigating the principles of signal processing, and based on this elaborating methodological strategies to employ these tenets in facilitating information re-use in shape modeling;
This will include (i) studying the theory of Fourier transforms and shape de-scriptors; (ii) exploring the information content of a signal, in an effort to estab-lish the perceptual correspondences between a signal and its spatial shape; and (iii) probing the fundamental principles and rules of geometric shape control us-ing its frequency counterparts.
Objective 2: Systematic Approaches
The efforts of exploring systematic approaches for FFF reuse include the following aspects:
• Establishing a feasible framework for the reuse of design knowledge at informa-tional level in the context of product shape modeling;
• Elaborating applicable computational models for the differentiation of informa-tion content and the discriminainforma-tion of signal attributes;
This computational model should be a kind of interpretation of freeform shapes suitable for (i) conducting shape analysis; (ii) easing signal decomposition; and (iii) facilitating high-level abstraction of the information content of a shape. The trunk of knowledge of proposing such computational models may correlate to a broad range of disciplines, such as that shown in Figure 1.3.
• Formulating dedicated algorithms for retrieving specific information content from a signal spectrum and for implementing the inclusion of information con-tent to a given shape model;
The correct formulation of such algorithms requires (i) investigating technolo-gies for multidimensional signal separation and synthesis; (ii) studying tech-niques for multi-context shape modeling; and (iii) exploring the rules of shape morphology and maintaining the validity of a shape model; as well as (iv) re-searching computing efficiencies.
Objective 3: Application prototypes
Pioneer applications of strategies and formulations will be addressed by demonstrating the advantages of applying the proposed methodologies in facilitating knowledge reuse in the broad range of design activities. For the evaluation of the proposed techniques, a pilot system will be developed, which is constituted by the following work:
• Designing the architecture of a CAD test-bed capable of facilitating the realiza-tion of advanced shape modeling funcrealiza-tions;
