Table Of ContentGeometric Modeling and Reasoning
of Human-Centered Freeform Products
Charlie C. L. Wang
Geometric Modeling
and Reasoning
of Human-Centered
Freeform Products
123
Charlie C.L. Wang
The ChineseUniversity ofHong Kong
Hong Kong
China
ISBN 978-1-4471-4359-8 ISBN 978-1-4471-4360-4 (eBook)
DOI 10.1007/978-1-4471-4360-4
SpringerLondonHeidelbergNewYorkDordrecht
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(cid:2)Springer-VerlagLondon2013
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Dedicated to my family for their endless
love, forbearance and encouragement
Preface
Thisbookcoversthecontentonusinggeometricapproachestodesignthefreeform
shape of products that are worn by human bodies. The recent trend about user-
customized product design requires that the shape of such products be automati-
callyadjustedaccordingtothehumanbodies’shape,sothatpeoplewillfeelmore
comfortable when wearing them.
The motivation of this book is to introduce readers to the newly developed
geometric solution for the design automation of customized freeform objects,
whichcan greatlyimprovetheefficiencyofdesignprocessesinvariousindustries
involving customized products (e.g., garment design, toy design, jewel design,
shoe design, and design of medial devices, etc.). The products in the above
industries are usually composed of very complex geometry shape (represented by
free-form surfaces), and are not driven by a parameter table but a digital human
model with freeform shapes or part of human bodies (e.g., wrist, foot, and head
models). After carefully designing a product around one particular human model,
itisdesirabletohaveanautomatedtoolfor‘‘grading’’thisproducttoothershape-
changedhumanbodieswhileretainingtheoriginalspatialrelationshipbetweenthe
product and human models.
The techniques introduced in this book are based on myresearch conducted in
this area in the past decade, which cover the algorithms of human body recon-
struction, freeform product modeling, constraining and reconstructing freeform
products, and shape optimization for improvingthe manufacturability offreeform
products. Based on these techniques, the design automation problem for human-
centeredfreeformproductscanbefundamentallysolved.Thisbookcanbeusedas
areferencebookforresearchersanddevelopersworkingonproblemsofautomatic
designing of products customized for individuals, and it can also be used as a
referencebookforcoursesincomputer-aidedproductdesignatthegraduatelevel.
My research conducted in this area was initiated during my graduate study.
I would like to thank Prof. Matthew M. F. Yuen, Prof. Kai Tang, Prof. Shana
Smith,Prof.QifuWang,Dr.JinFan,Dr.ZhuangWuandProf.JiansongDengfor
their encouragement and valuable advice at the early stage of my work.
Acknowledgments also go to my collaborators, students, and research staff, in
vii
viii Preface
particular, my collaborators—Prof. Kin-Chuen Hui, Prof. Xiaogang Jin, Prof.
Chih-Hsing Chu, Prof. Alexandre Kung and Dr. Terry Chang, my students and
researchstaff—YunboZhang,Tsz-HoKwok,Siu-PingMok,ShengjunLiu,Yuwei
Meng, Kwan-Chung Chan, Alan Yeung, Samuel Li, Hoi Sheung, Yuen-Shan
Leung, and Ya-Tien Tsai, and all staff at the Department of Mechanical and
Automation Engineering, The Chinese University of Hong Kong (CUHK).
The bulk of this research was supported by the Hong Kong Research Grants
Council under grants CUHK/412405, CUHK/416307, and CUHK/417109, the
Innovation and Technology Commission under the grant of Innovation Technol-
ogyFundITS/026/07,theShunHingInstituteofAdvancedEngineering(SHIAE)
undergrantCUHK/8115022,theindustrialsponsors—TPC(HK)LimitedandTak
Wai Model Clothes Rack Co., and the direct research grants of CUHK.
Shatin, Hong Kong, May 2012 Charlie C. L. Wang
Contents
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Design Automation in Commercial CAD/CAM Systems . . . . . . 1
1.2 Human-Centered Freeform Products . . . . . . . . . . . . . . . . . . . . 2
1.3 Demanded New Technology for Design. . . . . . . . . . . . . . . . . . 4
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2 Digital Human Bodies for Individuals. . . . . . . . . . . . . . . . . . . . . . 9
2.1 Reconstruction of Human Bodies for Individuals. . . . . . . . . . . . 9
2.1.1 Shape Acquisition. . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.1.2 Methods for Surface Reconstruction . . . . . . . . . . . . . . . 10
2.1.3 Orienting Unorganized Points for Surface
Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.1.4 Iterative Consolidation of Unorganized Points . . . . . . . . 19
2.2 Feature Point Extraction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.2.1 Problem Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
2.2.2 Rule-Based Extraction. . . . . . . . . . . . . . . . . . . . . . . . . 32
2.2.3 Bending-Invariant Matching Algorithm . . . . . . . . . . . . . 33
2.3 Optimal Cross-Parameterization . . . . . . . . . . . . . . . . . . . . . . . 42
2.3.1 Patch-Based Cross-Parameterization . . . . . . . . . . . . . . . 44
2.3.2 Construction of Common Base Domains . . . . . . . . . . . . 48
2.3.3 Optimization. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
2.4 Shape Space Analysis of Human Bodies . . . . . . . . . . . . . . . . . 73
2.4.1 Statistical Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
2.4.2 Synthesis-Based Reconstruction . . . . . . . . . . . . . . . . . . 76
2.5 Parametric Design of 3D Human Body . . . . . . . . . . . . . . . . . . 77
2.5.1 Correlation with Semantic Parameters. . . . . . . . . . . . . . 79
2.5.2 Feasibility Check . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
2.5.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
ix
x Contents
3 Geometry of Freeform Products. . . . . . . . . . . . . . . . . . . . . . . . . . 87
3.1 Non-Manifold Data Structure for Freeform Products . . . . . . . . . 87
3.1.1 Topology. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
3.1.2 Data Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
3.1.3 Topological Operators. . . . . . . . . . . . . . . . . . . . . . . . . 92
3.2 Constructive Design. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
3.2.1 Feature Graph. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
3.2.2 Constraint Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
3.2.3 Visible Geometry Specified by Sketch Input . . . . . . . . . 99
3.2.4 Shape Construction. . . . . . . . . . . . . . . . . . . . . . . . . . . 100
3.3 Interactive Design of Tight Products . . . . . . . . . . . . . . . . . . . . 101
3.3.1 Styling Design by Curve Drawing. . . . . . . . . . . . . . . . . 101
3.3.2 Trimming. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
4 Design Automation of Human-Centered Products. . . . . . . . . . . . . 107
4.1 Transformation of Style Design. . . . . . . . . . . . . . . . . . . . . . . . 107
4.2 Shape Warping Based on Free-Form Deformation. . . . . . . . . . . 108
4.2.1 Shape Encoding onto Human Bodies. . . . . . . . . . . . . . . 109
4.2.2 Decoding for Shape Reconstruction. . . . . . . . . . . . . . . . 111
4.3 Design Automation Based on Volumetric Parameterization . . . . 112
4.3.1 Rigid Body Transformation . . . . . . . . . . . . . . . . . . . . . 113
4.3.2 RBF-Based Elastic Function. . . . . . . . . . . . . . . . . . . . . 115
4.3.3 Surface Fitting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
4.3.4 CSRBF Approach for Volumetric Parameterization. . . . . 118
4.3.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
4.4 Realization of Flexible Shape Control . . . . . . . . . . . . . . . . . . . 120
4.4.1 Specifying Features on Product. . . . . . . . . . . . . . . . . . . 123
4.4.2 Shape Matching on Features. . . . . . . . . . . . . . . . . . . . . 124
4.4.3 Sampling and Construction of Local Support. . . . . . . . . 127
4.4.4 Local Shape Encoding. . . . . . . . . . . . . . . . . . . . . . . . . 128
4.4.5 Controlled Reconstruction . . . . . . . . . . . . . . . . . . . . . . 129
4.4.6 Examples. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
5 Manufacturability of Products Fabricated by Planar Materials. . . 133
5.1 Manufacturability Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
5.2 Surface Flattening Based on Energy Model . . . . . . . . . . . . . . . 134
5.2.1 Energy Function and Energy Release . . . . . . . . . . . . . . 135
5.2.2 Triangle Flattening . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
5.2.3 Planar Mesh Deformation . . . . . . . . . . . . . . . . . . . . . . 140
5.3 Geometry Processing for Flattenable Mesh Surface. . . . . . . . . . 141
5.3.1 Flattenable Laplacian Meshes. . . . . . . . . . . . . . . . . . . . 141
5.3.2 Variational Subdivision of FL Meshes. . . . . . . . . . . . . . 149
Contents xi
5.3.3 Local Flattenable Perturbation . . . . . . . . . . . . . . . . . . . 151
5.3.4 Least-Norm Solution for FL Mesh Processing . . . . . . . . 154
5.4 Segmentation for Production. . . . . . . . . . . . . . . . . . . . . . . . . . 162
5.4.1 LPFB Computation. . . . . . . . . . . . . . . . . . . . . . . . . . . 164
5.4.2 Quasi-Developable Mesh Segmentation. . . . . . . . . . . . . 173
5.4.3 Discussion on Limitations . . . . . . . . . . . . . . . . . . . . . . 176
5.5 WireWarping: Surface Flattening with Length-Preserved
Feature Curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177
5.5.1 Preliminary Definitions . . . . . . . . . . . . . . . . . . . . . . . . 178
5.5.2 Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180
5.5.3 LayingOutFeatureCurvesandInteriorMeshVertices. . . 181
5.5.4 Numerical Analysis and Least-Norm Solution . . . . . . . . 183
5.6 WireWarping++: Surface Flattening with Length Control. . . . . . 186
5.6.1 Multi-Loop Optimization Framework . . . . . . . . . . . . . . 187
5.6.2 Shape Error Function. . . . . . . . . . . . . . . . . . . . . . . . . . 189
5.6.3 Topology Processing. . . . . . . . . . . . . . . . . . . . . . . . . . 190
5.6.4 Case Study: Design and Manufacturing of Jeans. . . . . . . 192
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195
6 Compression Products Fabricated by Extensible Materials . . . . . . 199
6.1 Elastic Medical Braces. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199
6.1.1 Woven Model for Elastic Brace . . . . . . . . . . . . . . . . . . 200
6.1.2 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202
6.1.3 Algorithmic Details. . . . . . . . . . . . . . . . . . . . . . . . . . . 208
6.2 A Physical/Geometric Approach for Patterns
of Compression Garment . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211
6.2.1 Physical Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211
6.2.2 Geometric Constraints. . . . . . . . . . . . . . . . . . . . . . . . . 214
6.2.3 Numerical Solution. . . . . . . . . . . . . . . . . . . . . . . . . . . 215
6.2.4 Experimental Results and Verification. . . . . . . . . . . . . . 219
6.3 Material-Related Coefficients . . . . . . . . . . . . . . . . . . . . . . . . . 220
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225
Chapter 1
Introduction
1.1 DesignAutomationinCommercialCAD/CAMSystems
As techniques developed since 1960s, computer-aided design and manufacturing
(CAD/CAM)playsanimportantroleinproductdesignandmanufacturinginmany
industries.CAD/CAMsystemshavebeendemandedbythedesignofnewaircrafts
andautomobiles,whicharemainlyassembledfrommechanicalcomponents.Atthe
beginning,CADsoftwarewasusedtoreplacetheconventionalengineeringdrawing
board so that designers can modify drawings in an easier and more economical
manner in the computer system. The later development of CAD techniques make
a CAD system have components far beyond this primary function [7]. One of the
major components is parametric modeling [1, 4, 5] (or called parametric design
[8]),whichhelpsthedesignautomationofmanyindustrialproductslikemechanical
partsandarchitecture.
Parametricmodelingusesparameters(suchasdimensions)thatcanbemodified
latertodefineamodel.Otherthanthedimensionstoconstructmodels,theconstraints
betweengeometricentitiesarealsoexplicitlyspecifiedinmanycases.Forexample,
planeAmustbeparalleltoplaneB,andthedistancebetweenthemshouldbegreater
than 100mm. The constraints serve as bridges to link the dimensions of a model
together;therefore,therelationshipsbetweenthemarespecified.Allthedimensions
ofadesignedmodelcanthenbecoupledbythesegeometricconstraintstoafewkey
parameters.Changingthevaluesoftheseparametersvariestheshapeofthedesigned
model,whichleadstoafamilyofvariationalmodelsderivedfromtheoriginaldesign
(suchasdescribedin[10]).Animportantfunctionofdesignautomationistoadjust
the shape of a product automatically according to some design purposes (such as
reducing the maximal stress in the product under a fixed loading). In many cases,
theparametricmodelingisbasedonthetechniqueofconstraintsolver(see[3]for
anexample).
Figure1.1 shows the progressive steps to build a gear model in a commercial
CAD/CAM system by parametric modeling, where the thickness and the number
of teeth are chosen as key parameters. In the later phases of the design cycle, a
C.C.L.Wang,GeometricModelingandReasoningofHuman-CenteredFreeform 1
Products,DOI:10.1007/978-1-4471-4360-4_1,©Springer-VerlagLondon2013
