Plain TeX With Postscript

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N

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ISF dS D

Z

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Z Fydydx C

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Q

Z Fydzdx C

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R

Z Fzdxdy

D

ZZ

V

Z@Fx

@x C

@Fy

@y C

@Fz

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Plain TE

X with PostScript

Integrating Plain TEX and PostScript Graphics

Dr William Maguire

Consulting Engineer


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Plain TEX with PostScript

Integrating Plain TEX and PostScript Graphics

Dr William Maguire

Consulting Engineer


4/22

Plain TEX with PostScript

cWilliam Maguire 2011

All rights reserved. No part of this work may be reproduced or transmitted in any form or by

any means, electronic or mechanical, including photocopying, recording, or by any information

storage or retrieval system, without the prior written permission of the copyright owner and

publisher.

Published by William Maguire cWilliam Maguire 2011

TEX R is a trademark of the TEX User Group and PostScript

R is a registered trademark of

Adobe Systems Incorporated. Mac R and OS X R are trademarks of Apple Incorporated and

Windows R is a trademark of Microsoft Corporation. Unix R is a registered trademark of The

Open Group in the United States and other countries.

BBEdit R and TextWrangler R are trademarks of Bare Bones Software Incorporated. Other

propriety names used in the book are registered trademarks, and where possible this is indicated

within the text.

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PREFACE

Part 1 of the book introduces plain TEX, which is a free powerful typesetting suite of

programs available from the TEX User Group at http://www.tug.org.

This book was written to describe and define various TEX templates for producing a range

of document styles with the minimum of coding, to allow typesetting of:

(1) a basic document such as a novel;

(2) an historical treatise;

(3) an engineering or scientific report;

(4) a technical book (including this book);

(5) a letter and an envelope;

(6) curriculum vitae (Resume); and

(7) various tables.

This is a sample of possible documents that should not be taken as the definitive list. For

example, no specific templates are provided for legal documents but the templates that are

provided could be adapted to suit.

Furthermore, the aim was to keep the macro definitions to an absolute minimum and to

provide a facility for incorporating graphic images (including tables, figures and plates,

produced with TEX, PostScript and other programs, into the more demanding document

structures.

More advanced TEX templates should provide the macros or code to:

(a) set the page size;

(b) automatically number chapters, sections, sub-sections and sub-subsections, plates,

figures and tables, and generate a table of contents, including the preface (or fore-

word), the contents and appendices;

(c) produce boxed paragraphs with or without drop shadows;

(d) produce time and date stamps;

(e) define special symbols and characters; and

(f) create X ETEX documents that use any system font.

To keep the number of new macros to a minimum, tried and tested macro packages,

includingEplainandcolortabhave been used.

Part 2 of the book begins with an introduction to PostScript code elements that are used

in subsequent chapters to build up useful plotting routines. Incorporating a graphic image,

no matter what the source, is almost routine in plain TEX but Chapter 12 describes a few

simple techniques for overlaying PostScript graphic images with elements produced in plain


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TEX; this approach plays to the strengths of both systems, which I believe complement and

enhance one another.

Throughout the book, macros and blocks of code have been written in such a way that

they can be reused to produce different document types (TEX) and the development of

multifaceted vector graphics (PostScript).

All too often, computer programs are driven by what a particular programming language

offers rather than what the user desires as a finished product. This is true in the case

of object oriented programming (OOP), that offers the programmer a set of off-the-shelf

building blocks or black boxes that the programmer feels obliged to use in order to meet

his goal.

PostScript is a procedural interpretive language used to build elements of graphics and text

on a page or computer screen; it makes sense to construct procedures or modules that can

be reused in other PostScript programs. With experience and over time, these procedures

can be debugged and further refined to produce more robust and flexible code.

In the days before graphics user interfaces (GUIs) programmers of procedural languagesonly had to learn a few reserved words and the basic language structure, be it Fortran,

Pascal, C or Basic, before setting out to build a program. In contrast today, the OOP

programmer seems to spend a lot of time poring over manuals, trying to work out how to

piece together the building blocks.

It has been said that PostScript was designed with the primary aim of being generated

by other software and indeed it is widely used this way, but its simplicity and flexibility

has attracted programmers who have even written small word-processors, for which it was

probably never intended.

I was first attracted to PostScript when reading about the TEX special definition, which

when used with keywords, such as postscript, postscriptfile or illustration can add PostScriptpictures, PostScript or encapsulated PostScript from separate files. Demonstration examples

usually show how to include mirrored text, which as we shall see in Chapter 6 is one of the

effects that can be obtained by manipulating the PostScript font matrix.

I do not consider 3D graphics in the PostScript part of the book, since this has already been

done by Casselman (2005). PSTricks and Asymptote provide powerful graphics facilities

that use LATEX to typeset labels and equations for high-quality PostScript output. Asymptote,

which runs on all the major operating systems including Unix, Microsoft Windows and

Mac OS X, is a programming language with a powerful C++syntax.

Having tried the various methods of interfacing and incorporating graphics into a TEX

document, I believe that the simplest and most efficient approach is to produce a PDF fileoutside TEX and import it into the master document as a graphics image in the same way as

a JPG digital photograph. I would also suggest, with the exception of simple tabbed lists,

that this is the best way of adding tables to a TEX document.

Rather than using the TEXverbatimmacros to list code extracts, I opened both the TEX and

PostScript files in Bare Bones BBEdit, which allowed fast manipulation of the documents

and saving extracts in PDF format with colored comments. The extracts could then be sized

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and cropped with the Mac Preview program to provide a consistent look before importing

into the books master document.

I have not included any reference to Donald Knuths analogy of the digestive system to

describe the inner working of TEX nor do I mention esoteric stuff such as badness or

naughtiness! Here I will say that lines of text are placed in boxes and itsbadnessis used by

the TEX page-break algorithm. If you are interested or ever need to know about the moreobscure TEX features, I refer you to The TEXbook, (Knuth, 1986) or Salomon (1995).

In essence, it is unnecessary to know how a word-processor works to use it or to be familiar

with its source code; equally it is unnecessary to fully understand the inner workings of

TEX in order to use it with comparable ease and efficacy.

Section 2.16 outlines the steps needed to incorporate babel into plain TEX and gives an

example of specifying German as the working language. Unlike the LATEX babel macros,

we cannot switch between languages, so the polyglots may be disappointed. Although

the babel macros were written to allow plain TEX users access to them, information on

their use in plain TEX is sparce. What we get here though is access to the 40 or so, babel

language hyphenation profiles, which cover most European languages as well as Afrikaansand Bahasa Indonesia, for example.

The table of contents generator requires changing just a few words to work with a babel

language and the modification can be completed in a matter of minutes.

The full listings of the plain TEX preamble used to write this book and the table of contents

generator are presented in Appendix A and involve just 400 lines or so of TEX. Appendix

A also includes the full listings for a plain TEX preamble and table of contents generator

for German, assuming that the corresponding babel hyphenation profile has been installed

previously.

The PostScript code to produce a fancy header in a European language is presented in

Section 6.8, which describes how to override the standard fonts and re-encode the font table

to make use of the ISO 8859-1 Latin fonts. This serves as an example for other tasks.

The MathTime Pro fonts have been used for the mathematical content of the book, for no

reason other than their sheer elegance.

Chapter 10 describes how PostScript may be used to produce high-quality stereographic

projections, using either the equal area (Schmidt) and equal angle (Wulff) stereonet. Sec-

tion 10.8 briefly describes a front-end Objective-C program for the Mac, that automates

producing plots of up to three sets of data lines and intersecting planes. The front-end

program launches C++programs to do the actual building as well as launching a text editor

for viewing the built EPS source code and either of the Mac OS X programs, Preview or

Skim to view and convert an EPS file to PDF format.

In closing I would like to add that I am extremely grateful to Dr Boris Veytsman, who

suggested incorporating access to babel. I would also like to thank Robin Laakso, who

offered words of great encouragement during the drafting of this book and who put me in

touch with Boris. Finally we are all indebted to Professor Donald Knuth for his generosity

in sharing TEX and his considerable contributions to its development and refinement over

the past 30 years, and more.

William Maguire, Chiangrai July 2011

vii


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CONTENTS

PREFACE v

CONTENTS ix

1 INTRODUCTION 3

1.1 TEX 3

1.2 TEX Graph Utilities 4

1.3 PostScript Background 7

2 PLAIN TEX ELEMENTS 11

2.1 TE

X Fonts 11

2.2 Adobe Fonts 11

2.3 MathTime Pro Fonts 12

2.4 Other Fonts 12

2.5 Font Installation 13

2.6 Eplain 14

2.7 Page Layout 16

2.8 Headers, Footers and Footnotes 17

2.9 Rules, Boxes and Drop Shadow Boxes 18

2.10 Creating Openings in Paragraphs 20

2.11 Miscellaneous Definitions 232.12 Columns 25

2.13 Todays Date and Time 25

2.14 System Fonts 26

2.15 Generating Table of Contents 27

2.16 Providing European Language Support with Babel 30

3 TEX TEMPLATES 35

3.1 Basic Preamble 35

3.2 Book 36

3.3 Historical Treatise 363.4 Technical Report 37

3.5 Letter and Envelope 37

3.6 Curriculum Vitae (Resume) 42

4 TEX MATHEMATICS 45

4.1 Stirling Number 45

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Table of Contents

4.2 Zeta and Related Functions 46

4.3 Polynomials 48

4.4 Trigonometrical Functions 49

4.5 Hyperbolic Functions 50

4.6 Definite Integrals 51

4.7 Jacobian 54

4.8 Vectors 55

4.9 Elliptic Integrals 57

4.10 LaPlace Transforms 59

4.11 Nested Sum 62

4.12 Partial Differential Equations 63

4.13 Fourier Series 64

4.14 The Lucida Bright Fonts 1 66

4.15 The Lucida Bright Fonts 2 69

4.16 Additional Mathematics Exercises 70

5 TEX TABLES 71

5.1 Basic Tables 71

5.2 General Tables 72

5.3 Coloring Tables 79

6 POSTSCRIPT BASICS 89

6.1 Page Layout 89

6.2 Fonts 90

6.3 Line Drawing 986.4 Plot Markers 103

6.5 Arrows 108

6.6 Drop Shadow Boxes 111

6.7 Patterns and Shading 112

6.8 Fancy Header 118

6.9 Loops and Conditionals 120

7 LINEAR GRAPHS 123

7.1 Grid Generation 123

7.2 Scaling 1257.3 Plotting Curves and Labelling 127

7.4 Inputting Data 128

7.5 Mathematical Functions 129

7.6 Additional Linear Graph Exercises 145

8 LOGARITHMIC GRAPHS 147

8.1 Log-Linear Plots 147

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Table of Contents

8.2 Rainfall 151

8.3 Particle Size Distribution 153

8.4 Log Log Plots 159

9 POLAR PLOTS 163

9.1 Grid Generation 1639.2 Log Spiral 165

9.3 Lemniscates of Bernoulli 167

9.4 Limacon 169

9.5 Butterfly Curve 171

10 STEREOGRAPHIC PROJECTIONS 173

10.1 Equatorial Projection 173

10.2 The Schmidt and Wulff Stereonets 173

10.3 The Prolog Definitions and Variables 176

10.4 Generating Grids, Labels and Tick Marks 18110.5 Intersection of Planes 183

10.6 Latitude and Longitude 185

10.7 Animation 187

10.8 PSStereonet Front-end for Mac 190

11 SPECIAL POSTSCRIPT 193

11.1 Numbers 193

11.2 Polygons 194

11.3 Penrose Figures 196

12 TEX AND POSTSCRIPT 201

12.1 Namecards 201

12.2 Mathematics in PostScript 203

12.3 The Bessel Functions 206

12.4 The Fresnel Integrals 209

12.5 The Generalized Lissajous 213

12.6 Equations in a Circle 214

12.7 Equations in a Polygon 216

12.8 Overwriting JPEG Images 219

12.9 Adding Finishing Touches to the Book 222

BIBLIOGRAPHY 227

APPENDICES

A Principal TEX Templates 223

B Additional TEX Templates 249

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Table of Contents

C Selected TEX Fonts 259

D PostScript Font Tables 267

E Linear Grid and Polar Plot Programs 275

F Bessel Functions and Fresnel Integrals 291

G Stereonet Ancilliary Programs 307

H Estimating Trend and Plunge 317

I PSStereonet Program 319

J Listings of Additional C++Programs 331

INDEX 343

TABLES

4.1 Relationships Involving LaPlace Transforms 60

4.2 A Few Selected LaPlace Transforms 61

5.1 Information about Selected American States 715.2 The 25 Largest States of America 73

5.3 Aerial Photograph Interpretation 75

5.4 Automatic Rain Gauge 76

5.5 Geology of London Basin 78

5.6 The 25 Largest States of America Shaded 80

5.7 The 25 Smallest States of America Shaded 81

5.8 Geological Eras Pre-Cambrian to Cretaceous 82

5.9 Geological Eras Cenozoic 83

5.10 Summary of Piezometric Groundwater Observations 855.11 Translation of Some Gaelic Phrases 85

10.1 Apple Numbers Spreadsheet to Convert Compass Bearings to Angles 181

FIGURES

1.1 Plots of Trigonometrical Functions Produced with MetaPost 4

1.2 MetaPost Polygon 7

6.1 Example of Boxes Drawn with Dashed Lines 101

6.2 Plots Showing Effect of Bezier Control Points 101

6.3 Cubic and Quintic Polynomials 1026.4 Exponential Functions 103

6.5 Partly Filled Circles 104

6.6 Partly Filled Circles with Crosses 104

6.7 Partly Filled Circles Grays 105

6.8 Partly Filled Circles with Crosses Grays 105

6.9 Arrow Display 109

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Table of Contents

6.10 Constructing Drop Shadow Boxes 111

6.11 Pattern Filled Shapes 113

6.12 Beethoven CD Label 117

7.1 Linear Grid 123

7.2 Limacon Curves with a < b 130

7.3 Cardioid Curves - Special Case of Limacon witha D b 131

7.4 The Catenary 133

7.5 Lemniscate of Bernoulli Three-leaved Rose 135

7.6 Lemniscate of Bernoulli Three-leaved Rose (Rotated) 136

7.7 Lemniscate of Bernoulli Four-leaved Rose 137

7.8 Lemniscate of Bernoulli Four-leaved Rose (Rotated) 138

7.9 Cycloid Cusp at Origin 140

7.10 Cycloid Vertix at Origin 140

7.11 Prolate Cycloid witha < b 141

7.12 Hyperbolic Spiral 1437.13 Slope Stability Section 145

8.1 Log-Linear Grid 149

8.2 Log-Linear Grid with Check Values 149

8.3 Variation of Coefficient of Permeability with Depth 150

8.4 Plot of Maximum Rolling Rainfall 153

8.5 Particle Size Distribution 157

8.6 Comparison of Seismicity Worldwide and in Southern California 158

8.7 Log-Log Grid with 6 6 Cycles 159

8.8 Log-Log Plot of Functions 160

9.1 Radial Grid 164

9.2 The Logarithmic Spiral 166

9.3 The Bernoulli Curves 168

9.4 The Cardioid 170

9.5 The Butterfly Curve 172

10.1 Stereographic Projection 173

10.2 The Schmidt Equal Area Stereonet 174

10.3 Comparison of the Schmidt (upper) and Wulff (lower) Stereonets 175

10.4 Calculating the Trend and Plunge at the Intersection of Two Planes 178

10.5 Reference Grid to Locate Text, Arrows and Drop Shadow Boxes 18010.6 Curtailed Gridlines in Vicinity of North Pole 182

10.7 Stereographic Projection of Maps using Line Drawing 186

10.8 Pages Extracted from Animated PDF File Frames 50 and 95 189

10.9 PSStereonet Front-End Program for Mac OS X 190

10.10Stereonet Plot Three Data Sets Produced using Front-End Program 191

10.11Stereonet Plot Intersecting Planes Produced using Front-End Program 192

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Table of Contents

11.1 20-Sided Polygon 196

11.2 Penrose Triangle 198

11.3 Penrose Square 198

11.4 Penrose Pentagon 199

11.5 Penrose Hexagon 199

11.6 Penrose Octagon 200

11.7 Penrose Square and Octagon 200

12.1 Namecards Produced with TEX and PostScript 202

12.2 Bessel Functions of the First Order 208

12.3 Plot of the Fresnel Integrals,C.x/and S.x/ 210

12.4 Plot of the Euler Spiral using Fresnel Integrals,C.x/and S.x/ 211

12.5 Plot of the Euler Spiral (Mirrored and Rotated) 212

12.6 Plot of the Generalized Lissajous Curve (Translated and Mirrored) 213

12.7 Equations in a Circle 215

12.8 Equations in a Polygon 21712.9 Equations in Dodecagons 218

PLATES

10.1 Brunton 5009 GEO Pocket Transit for Measuring Dips & Strikes 181

12.1 White Bougainvillea (also found in Indonesia, India, Taiwan, Zimbab-we, Vietnam, Malaysia and the Philippines) Photograph taken in 2006

223

12.2 Deep Red Frangipani (Plumeria ruba also found in India, Indonesia,Sri Lanka, Laos, Mexico, Central America and Hawaii) Photograph

taken in 2006

223

12.3 Hong Kong Business District, Exchange Square, Central, Hong KongIsland Photograph taken in 2003

224

12.4 Hong Kong Tram, Johnston Road, Wanchai, Hong Kong Photographtaken in 2003

224

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Chapter 2

Der Rede Einsteins am 22 August 1930

Verehrte An- und Abwesende!

Wenn Ihr den Rundfunk horet, so denkt auch daran, wie die Menschen in den Be-

sitz dieses wunderbaren Werkzeuges der Mitteilung gekommen sind. Der Urquellaller technischen Errungenschaften ist die gottliche Neugier und der Spieltrieb des

bastelnden und grubelnden Forschers und nicht minder die konstruktive Phantasie des

technischen Erfinders.

Denkt an Oersted, der zuerst die magnetische Wirkung elektrischer Strome bemerk-

te, an Reis, der diese Wirkung zuerst benutzte, um auf elektromagnetischem Wege

Schall zu erzeugen, an Bell, der unter Benutzung empfindlicher Kontakte mit seinem

Mikrophon zuerst Schallschwingungen in variable elektrische Strome verwandelte.

Denkt auch an Maxwell, der die Existenz elektrischer Wellen auf mathematischem

Wege aufzeigte, an Hertz, der sie zuerst mit Hilfe des Funkens erzeugte und nachwies.

Gedenket besonders auch Liebens, der in der elektrischen Ventilrohre ein unvergleich-liches Spurorgan fur elektrische Schwingungen erdachte, das sich zugleich als ideal

einfaches Instrument zur Erzeugung elektrischer Schwingungen herausstellte. Ge-

denket dankbar des Heeres namenloser Techniker, welche die Instrumente des Radio-

Verkehres so vereinfachten und der Massenfabrikation anpassten, dass sie jedermann

zuganglich geworden sind.

Sollen sich auch alle schamen, die gedankenlos sich der Wunder der Wissenschaft

und Technik bedienen und nicht mehr davon geistig erfasst haben als die Kuh von der

Botanik der Pflanzen, die sie mit Wohlbehagen frisst.

Denket auch daran, dass die Techniker es sind, die erst wahre Demokratie moglichmachen. Denn sie erleichtern nicht nur des Menschen Tagewerk, sondern machen

auch die Werke der feinsten Denker und Kunstler, deren Genuss noch vor kurzem ein

Privileg bevorzugter Klassen war, der Gesamtheit zuganglich und erwecken so die

Volker aus schlafriger Stumpfheit.

Was speziell den Rundfunk anlangt, so hat er eine einzigartige Funktion zu erfullen

im Sinne der Volkerversohnung. Bis auf unsere Tage lernten die Volker einander

fast ausschlielich durch den verzerrenden Spiegel der eigenen Tagespresse kennen.

Der Rundfunk zeigt sie einander in lebendigster Form und in der Hauptsache von der

liebenswurdigen Seite. Er wird so dazu beitragen, das Gefuhl gegenseitiger Fremdheit

auszutilgen, das so leicht in Misstrauen und Feindseligkeit umschlagt.

Betrachtet in dieser Gesinnung die Ergebnisse des Schaffens, welche diese Ausstel-

lung den staunenden Sinnen des Besuchers darbietet.

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Chapter 4Page ofq50 texPrinted: 6/24/11 2:30:26 PM Printed For: William Maguire%+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

% equation 4.50

%

$$

\PARENS{\matrix{{{\ts\partial A}\over{\ts\partial t}} \cr

\noalign{\vskip4pt}

{{\ts\partial B}\over{\ts\partial t}} \cr \noalign{\vskip4pt}

{{\ts\partial C}\over{\ts\partial t}} \cr}} =

\PARENS{\matrix{{{\ts\partial A}\over{\ts\partial x}} & {{\ts\partial A}\over

{\ts\partial y}} & {{\ts\partial A}\over{\ts\partial z}} \cr \noalign{\vskip4pt}

{{\ts\partial B}\over{\ts\partial x}} & {{\ts\partial B}\over

{\ts\partial y}} & {{\ts\partial B}\over{\ts\partial z}} \cr

\noalign{\vskip4pt}

{{\ts\partial C}\over{\ts\partial x}} & {{\ts\partial A}\over

{\ts\partial C}} & {{\ts\partial C}\over{\ts\partial z}} \cr }}

\PARENS{\matrix{{{\ts\partial x}\over{\ts\partial t}} \cr

\noalign{\vskip4pt}

{{\ts\partial y}\over{\ts\partial t}} \cr

\noalign{\vskip4pt}

{{\ts\partial z}\over{\ts\partial t}} \cr}}

\eqno(4.50)$$

The equation uses \matrix and the MathTime Pro \PARENS for the large brackets. A

shortcut \ts is used to force the elements of the matrix to use \textstyle, which would

otherwise default to\scriptstyle. \noalignadds additional space between the rows.

4.8 Vectors

Gauss Theorem

A scalar flow of a vector function Fthrough a surfaceS(closed surface integral) is equal

to the integral ofr Fover the volume Vbounded byS, the closed volume integral.

ISF dS D

ZV

r Fd V .4:44/

which in cartesian coordinates is:

ISF dS D

Z

P

ZFydy dx C

Z

Q

ZFydz dx C

Z

R

ZFzdx dy

D

ZZ

V

Z@Fx

@x C

@Fy

@y C

@Fz

@z

dx dy dz .4:45/

where,

the subscripts, P, Q and R (signifying surface areas) in the second part of Equation 4.45 arePyz ,

Pzx and

Pxy respectively.

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TEX Mathematics

coefficients of vertical and horizontal permeability differ), the equation to define the problem

is:

@u

@t D cvr

@2u

@r2 C

1

r

@u

@r

!C cv

@2u

@z2 .4:68/

The settlement of a soil, beneath a loaded area is defined by:

D

Z H0n dz D mv

p1H

Z H0

u dz

! .4:69/

where,

mv is the coefficient of volume change, n is an increment of a soil layer with a total

thickness ofH;p1 andu are the pressure and pore water pressure, respectively.

The settlement of a consolidation layer, is defined by the following solution of the differentialEquation 4.70.

D mvp1H

"1

8

2

ND1XND0

1

.2NC 1/2.2NC1/

22Tv=4

# .4:70/

where,

Nis an integer from zero to 1 andTv is a time factor, which is defined in Equation 4.71.

Tv D cv

H2t D k

wmvt

H2 .4:71/

where, w is the density of water, k is the coefficient of consolidation, H is the layer

thickness and t is time. An example of mathematics using the Lucida Bright font is

presented on the next page; it was typeset as a separate document and imported.

4.13 Fourier Series

A Fourier series breaks down a periodic function into the sum of oscillating sine and cosine

or complex exponential functions. They were introduced by the French mathematician and

Physicist, Joseph Fourier (1768-1830), who was investigating problems of heat transferand vibrations. They are also used extensively in electrical engineering.

The Fourier series of an even function f .t/of periodT,

f.t/ D a0 C

1XnD1

an cos

2n

T

t .feven/ .4:72/

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Logarithmic Graphs

Duration (hours)

MaximumR

ollingRainfall(mm)

LEGEND

16/06/199324/07/1994

1-4/07/1997

26/04/1998

24/08/2000

06/07/2001

16/07/2006

07/06/2008

Rolling rainfall at rain

gauge H04 preceding the7 June 2008 landslide

0.01 0.1 1.0 10 100 10000

200

400

600

800

1000

1200

1400

1600

MAXIMUM ROLLING RAINFALL AT RAIN GAUGE H04

FOR MAJOR RAINSTORMS BETWEEN 1993 AND 2008

Figure 8.4 Plot of Maximum Rolling Rainfall

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Stereonet Projections

1020

30

40

50

60

70

80

100

110

120

130

140

150

160170

280

290

300

310

320

330

340350

190200

210

220

230

240

250

260

N

E

S

W

SCHMIDT STEREONET

EQUAL AREA STEREOGRAPHIC PROJECTION

William Maguire April 9, 2011Plotted using PSStereonet

Figure 10.7 Stereographic Projection of Maps using Line Drawing

%++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++% map latitude and longitude and fill land areas

%

enhance mapping exec 0 setlinewidth clip

dataset1 maplines stroke dataset1 maplines closepath fill



stereonet restore % release

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Special PostScript

Figure 11.6 Penrose Octagon

Figure 11.7 Penrose Square and Octagon

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Chapter 12

Equations in Polygon

3

1

apaD

m

.2mC1

/pa

Z =20

cos2m

C1 xdxD

.2m/.2

m 2/

6

4 2

.2m

C1/.2

m 1/

5

3 1D

.2m/

.2mC1

/

dxD

Z =20

cos2m x

dxD.2m

1/.

2m3/

53

1

.2m/.2

m 2/

6

4 2

2

D.2m

1/

.2m/

2

1 x cos2n xdx

D

.2m/.

2n1/

.2m

C2nC

1/D.

mC1/

.nC

12/

2.mCn

C32/

D12B.

mC1;n

C1

2

/

cos2n

C1 xd

xD.2n

/.2m

1/

.2mC2

nC1/

D.n

C1/

.mC

12/

2.mC

nC32/

D12B.

mC12;nC1

/

xD.2m

1/.

2m3/

5

3 1

.2m/.2

m2/

6

4 2

a2m

C2

.2mC2

/2D.2m

1/

.2mC2/

a2m

C2

2

42

1

2amC

1

paD

.2m/

.2mC1

/

2amC

1

Figure 12.8 Equations in a Polygon

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Plain TEX TemplatesPage of reamblegerman texPrinted: 6/24/11 3:17:26 PM Printed For: William Magui

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% BOOK TEMPLATE

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\input ofs [,a35] % the 35 Adobe postscript fonts

\setfonts [Times/10.25pt] %

\fontdef\tt [CMTypewriter/mag0.9]

\fontdef\chapfont [Helvetica/11.00pt]\fontdef\secfont [Helvetica/11.00pt]

\fontdef\hdfont [Helvetica/10.75pt]

\fontdef\ftfont [Helvetica/9.00pt]

\fontdef\tableh [Helvetica/10.0pt]

\fontdef\hv [Helvetica/10.0pt]

\fontdef\note [Times/9.0pt]

\fontdef\pagx [Times/9.75pt]

\fontdef\indexfonts [Times/8.5pt]

% build the Thai Baht symbol

\def\rvbar{\vrule height 1.75ex depth 0.20ex width .125ex}

\def\baht{B\kern -0.375em\lower 0.025ex\hbox{\rvbar}\kern 0.275em}

\def\regsym{$\circ$\kern -0.375em R\kern 0.275em}

% build the Euro symbol

\def\rhbar{{\raise 0.85ex\hbox{\vrule height 0.05em width 1.1ex}}\kern-0.51em

{\raise 0.55ex\hbox{\vrule height 0.05em width 1.1ex}}}

\def\euro{C\kern -0.70em\rhbar\kern0.25em}

\rm\baselineskip=12.05pt % default font and line spacing

\input eplain % input the Eplain macros for graphics etc.

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% set MathType Pro fonts for the mathematical content

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\input mtp2 % load the Mathtype Pro fonts\MTP{10.0pt}{7.7pt}{6pt} % and set sizes for mathematics

\loadbm % bold

\loadmfrak % fraktur

\loadmscript % script

% Definition of nested sum operator lambda

\def\mtplam{\MTP{22.5pt}{7.7pt}{6pt}}

\mathchardef\upnested="1183

\mathchardef\slnested="1103

\def\nestedsum{\mathop{\vcenter{\hbox{\mtplam$\upnested$}}}}

% Definition to left justify and indent equation

\def\leftjusteq#1#2#3{{\color{black}$$\displaylines{\hskip#1{#2}\hfill#3}$$}}% Definition to center equation with left equation

\def\lefteqnocent#1#2{{\color{black}$$\displaylines{#1\hfill{#2}\hfill}$$}}

%\input verbatim/salomonverbatim % David Salomon's powerful verbatim macro

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% code to place an imported image

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Plain TeX With Postscript