appearance of woven cloth

127 Pages·2007·26.02 MB·English

APPEARANCE OF WOVEN CLOTH
A Dissertation
Presented to the Faculty of the Graduate School
of Cornell University
in Partial Fulfillment of the Requirements for the Degree of
Doctor of Philosophy
by
Piti Irawan
January 2008
(cid:13)c 2008 Piti Irawan
ALL RIGHTS RESERVED
APPEARANCE OF WOVEN CLOTH
Piti Irawan, Ph.D.
Cornell University 2008
The appearance of a particular fabric is produced by variations in both large-scale
reflectance and small-scale texture as the viewing and illumination angles change
across the surface. This thesis presents a study of the reflectance and texture of
woven cloth that aims to identify and model the most important optical features of
cloth appearance. New measurements are reported for a range of fabrics including
natural and synthetic fibers as well as staple and filament yarns. A new scattering
model for woven cloth is introduced that describes the reflectance and the texture
based on an analysis of specular reflection from the fibers. Unlike data-based
models, our procedural model requires no image data. It can handle a wide range
of fabrics using a small set of physically meaningful parameters that describe the
characteristics of the fibers, the geometry of the yarns, and the pattern of the
weave. The model is validated against the measurements and by comparisons to
high-resolution video of the real fabrics.
BIOGRAPHICAL SKETCH
The author was born on January 23, 1980 in Jakarta, Indonesia. From 1998 to
2002 he studied at Purdue University, where he received a bachelor’s degree in
Computer Science with a minor in Asian Studies. He then joined the Computer
Science Ph.D. program at Cornell University and spent much of the time between
2002 and 2007 thinking about Computer Graphics. Out of personal interest, he
pursued a graduate minor in Management.
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for Anita
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ACKNOWLEDGEMENTS
I would like to give my thanks to my advisor, Steve Marschner, for the support and
encouragement he gave me over the course of my graduate study. This dissertation
is the product of his confidence in me and the time he spent guiding me along the
way. I would also like to thank my minor advisor, Wesley Sine, whose fun and
instructive classes broaden my horizon and kept me sane. I am honored to have
excellent people in my committee; Don Greenberg has been like a grandfather
to me and the insights Joe Halpern and Johannes Gehrke brought from outside
computer graphics were invaluable. I would like to thank Kavita Bala for being a
proxy for Johannes and Kelly Patwell and Ganesh Ramanarayanan for helping me
with the forms required by the Graduate School.
I had the pleasure of working with many wonderful people. I thank Jim Ferw-
erda for his guidance during the early years of my stay at Cornell. I thank Bruce
Walter, Steve Westin, Kavita Bala, and Doug James for their feedbacks on my
work. I thank Ken Torrance for lending his laboratory. Thanks to Hurf Sheldon
and Martin Berggren for assisting me with cluster use and keeping my computer
connected and running. Thanks to Cay Wilson for helping me with my Computer
Science account. Thanks to Kelly Patwell, Becky Stewart, Linda Stephenson, and
Peggy Anderson for administrative support. I am deeply indebted to my fellow
students Jon Kaldor and Jon Moon; one Jon created the model of the platform
used in the turntable sequence seen in Chapter 9 and the other helped me countless
times with many aspects of this work. Thanks also to Ganesh Ramanarayanan,
Kamal Aboul-Hosn, and Milind Kulkarni for sharing an office during my first year
at Cornell.
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Special thanks to my undergraduate mentor, Sally Hastings, whose guidance
and kindness I recall whenever I think of Purdue.
I owe my deepest gratitude to my parents and my wife, Anita. Their support,
encouragement, patience, and unconditional love are what kept me going.
This work was supported by the National Science Foundation through the
CAREER grant CCF-0347303 and by an Alfred P. Sloan Research Fellowship.
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TABLE OF CONTENTS
Biographical Sketch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii
Dedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv
Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v
Table of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii
List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix
List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x
List of Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xii
List of Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii
List of Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii
1 Introduction 1
2 Background 3
2.1 Cloth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.1.1 Textile fibers . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.1.2 Production methods . . . . . . . . . . . . . . . . . . . . . . 5
2.2 Structure of Woven Cloth . . . . . . . . . . . . . . . . . . . . . . . 6
2.3 Mathematical Preliminaries . . . . . . . . . . . . . . . . . . . . . . 9
2.3.1 Rotation matrices . . . . . . . . . . . . . . . . . . . . . . . . 9
2.3.2 Trigonometric identities . . . . . . . . . . . . . . . . . . . . 10
2.3.3 Conic sections . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.3.4 Dot and cross products . . . . . . . . . . . . . . . . . . . . . 12
2.3.5 Gauss map and Gauss sphere . . . . . . . . . . . . . . . . . 13
2.3.6 Matrix calculus . . . . . . . . . . . . . . . . . . . . . . . . . 13
3 Prior Work 15
3.1 BRDF and BTF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3.2 Measurements and Studies of Cloth BRDF . . . . . . . . . . . . . . 15
3.3 Modeling Cloth BRDF . . . . . . . . . . . . . . . . . . . . . . . . . 17
3.4 Modeling Cloth Texture . . . . . . . . . . . . . . . . . . . . . . . . 18
3.5 Data-based Approaches to Cloth Modeling . . . . . . . . . . . . . . 19
4 Overview of the Model 20
5 Measurements 22
5.1 Reflectance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
5.2 Texture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
5.3 Turntable Sequences . . . . . . . . . . . . . . . . . . . . . . . . . . 33
6 Geometry 36
6.1 Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
6.2 Geometry of a Yarn Segment. . . . . . . . . . . . . . . . . . . . . . 36
6.2.1 Normal to the yarn surface and fiber tangent on Gauss spheres 40
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6.3 Relation Between a Segment Rectangle and Its Curved Cylinder . . 40
6.4 Spine Curves and Radius of Curvature . . . . . . . . . . . . . . . . 46
7 Reflection 53
7.1 Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
7.2 Scattering from a Yarn Segment . . . . . . . . . . . . . . . . . . . . 54
7.2.1 Scattering integral for a yarn segment . . . . . . . . . . . . . 55
7.2.2 Scattering from specular fibers . . . . . . . . . . . . . . . . . 56
7.3 Finding Ideal Specular Reflection . . . . . . . . . . . . . . . . . . . 59
7.3.1 Ideal specular reflection on Gauss spheres . . . . . . . . . . 61
7.4 Geometry Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
7.5 Phase Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
7.6 Attenuation Function . . . . . . . . . . . . . . . . . . . . . . . . . . 73
8 Reflectance Model and Texture Model 75
8.1 Reflectance Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
8.2 Texture Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
8.2.1 Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
8.3 Computing the Models . . . . . . . . . . . . . . . . . . . . . . . . . 80
8.3.1 Staple yarn . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
8.3.2 Filament yarn . . . . . . . . . . . . . . . . . . . . . . . . . . 83
9 Results 88
9.1 Staple Fabrics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
9.2 Filament Fabrics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
9.3 Modeling New Fabrics . . . . . . . . . . . . . . . . . . . . . . . . . 104
10 Conclusion 106
Bibliography 109
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LIST OF TABLES
2.1 Examples of commonly found woven fabrics. . . . . . . . . . . . . . 8
8.1 All the parameters of the reflectance model. . . . . . . . . . . . . . 81
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