text stringlengths 1 1k ⌀ | source stringclasses 12
values |
|---|---|
Next, note that the load impedance creates a voltage
divider with the source (antenna) impedance such that
˜VL =
(
Eile
) ZL
ZA + ZL
(10.141)
c⃝ S. Lally CC BY -SA 4.0 (modified)
Figure 10.20: Equivalent circuit model for an antenna
in the presence of an incident electric field ˜Ei, termi-
nated into a load impedance ZL.... | Electromagnetics_Vol2.pdf |
ZL = Z∗
A = Rrad − jXA. Therefore:
PR,max = 1
2
⏐⏐Eile
⏐
⏐2 Rrad
|ZA + Z∗
A|2
= 1
2
⏐⏐Eile
⏐
⏐2 Rrad
|2Rrad|2
=
⏐⏐Eile
⏐
⏐2
8Rrad
(10.146)
No
w using Equations 10.135, 10.137, and 10.146, we
find:
Ae =
⏐⏐Eile
⏐
⏐2
/8Rrad
|Ei|2 /2η
(10.147)
which
reduces to:
Ae = η|le|2
4Rrad
(10.148)
It
is not surprising that effective ... | Electromagnetics_Vol2.pdf |
198 CHAPTER 10. ANTENNAS
wire antennas. For the electrically-short dipole (ESD)
of length L, le ≈ (L/2) sin θand
Rrad ≈ 20π2 (L/λ)2. Thus, we find the effective
aperture assuming free space (i.e., η= η0) is:
Ae ≈ 0.119λ2 |sin θ|2 (lossless ESD) (10.149)
Remarkably , the effective aperture of the ESD does
not depend on i... | Electromagnetics_Vol2.pdf |
example:
Example 10.10. Ef fective aperture of a
half-wave dipole.
The electrically-thin half-wave dipole exhibits
radiation resistance ∼= 73 Ω and effective length
λ/π. Assuming the dipole is lossless and in free
space, Equation 10.148 yields:
Ae ≈ 0.131λ2 (half-wave dipole, max.)
(10.151)
Again, this is the effective... | Electromagnetics_Vol2.pdf |
No previous experience with thermodynamics is
assumed in this derivation.
Consider the scenario depicted in Figure 10.21. In
this scenario, the antenna is completely enclosed in a
chamber whose walls do not affect the behavior of the
antenna and which have uniform temperature T. The
load (still conjugate matched to the... | Electromagnetics_Vol2.pdf |
and Bis the bandwidth within which Pload is
measured.
Similarly , the antenna is a source of noise power
Pant. Pant can also be interpreted as captured
thermal radiation – that is, electromagnetic waves
stimulated by the random acceleration of charged
particles comprising the chamber walls. These waves
radiate from the... | Electromagnetics_Vol2.pdf |
10.13. EFFECTIVE APER TURE 199
per steradian of solid angle. 5 The total power
accessible to the antenna is one-half this amount,
since an antenna is sensitive to only one polarization
at a time, whereas the thermal radiation is equally
distributed among any two orthogonal polarizations.
PA is the remaining power, obta... | Electromagnetics_Vol2.pdf |
and delivered to the antenna; i.e.,
Pant = Pload (10.155)
Combining Equations 10.152, 10.154, and 10.155, we
obtain:
(kT
λ2 B
)∮
Ae(θ′,φ′) sin θ′dθ′dφ′ = kTB
(10.156)
which reduces to:
∮
Ae(θ′,φ′) sin θ′dθ′dφ′ = λ2 (10.157)
Let ⟨Ae⟩ be the mean effective aperture of the
antenna; i.e., Ae averaged over all possible dire... | Electromagnetics_Vol2.pdf |
isotropic antenna is quite useful as we shall soon see.
Since the effective aperture of an isotropic antenna
must be the same as its mean effective aperture, we
find:
Ae = λ2
4π ≈ 0.080 λ2 (isotropic antenna)
(10.159)
Note
further that this must be the minimum possible
value of the maximum effective aperture for any
ant... | Electromagnetics_Vol2.pdf |
directivity. Directivity is defined in Section 10.7 as
the factor by which a transmitting antenna increases
the power density of its radiation over that of an
isotropic antenna. Let us once again consider the
ESD, for which we previously determined (via the
effective length concept) that Ae ∼= 0.119λ2 in the
direction i... | Electromagnetics_Vol2.pdf |
200 CHAPTER 10. ANTENNAS
presented earlier, or using the reciprocity theorem
developed in Section 10.10.
The fact that effective aperture is easily calculated
from transmit directivity is an enormously useful tool
in antenna engineering. Without this tool,
determination of effective aperture is limited to direct
measur... | Electromagnetics_Vol2.pdf |
characteristic of an antenna that applies in both the
transmit and receive case. Recall that radiation
patterns are used to quantify the way (transmit)
directivity varies with direction. Suddenly , we have
found that precisely the same patterns apply to the
receive case! Summarizing:
As long as the conditions required ... | Electromagnetics_Vol2.pdf |
the directivity of the antenna. There is no new physics
at work here; we are simply taking advantage of the
fact that the concepts of effective aperture and
directivity describe essentially the same characteristic
of an antenna, and that this characteristic is the same
for both transmit and receive operation.
Additiona... | Electromagnetics_Vol2.pdf |
10.14. FRIIS TRANSMISSION EQUA TION 201
10.14 Friis T ransmission
Equation
[m0219]
A common task in radio systems applications is to
determine
the power delivered to a receiver due to a
distant transmitter. The scenario is shown in
Figure 10.22: A transmitter delivers power PT to an
antenna which has gain GT in the dir... | Electromagnetics_Vol2.pdf |
density at range Rfrom the transmitter which radiates
this power through a lossless and isotropic antenna
would be:
PT
4πR2 (10.162)
that
is, total transmitted power divided by the area of
a sphere of radius Rthrough which all the power
must flow . The actual power density Si is this amount
times the gain of the transmi... | Electromagnetics_Vol2.pdf |
Ae = λ2
4πGR (10.165)
Thus,
Equation 10.164 may be written in the
following form:
PR,max = PTGT
( λ
4πR
)2
GR (10.166)
This
is the Friis transmission equation. Summarizing:
The Friis transmission equation (Equa-
tion
10.166) gives the power delivered to a
conjugate-matched receiver in response to a dis-
tant transmitte... | Electromagnetics_Vol2.pdf |
applies; one simply uses the appropriate (and
probably significantly different) value of Lp.
A common misconception is that path loss is equal to
the reduction in power density due to spreading along | Electromagnetics_Vol2.pdf |
202 CHAPTER 10. ANTENNAS
the path between antennas, and therefore this
“spreading loss” increases with frequency . In fact, the
reduction in power density due to spreading between
any two distances R1 <R2 is:
PT/4πR2
1
PT/4πR2
2
=
(R1
R2
)2
(10.169)
which
is clearly independent of frequency . The path
loss Lp, in contr... | Electromagnetics_Vol2.pdf |
by the associated effective apertures, and forms in
which the effects of antenna impedance mismatch
and/or cross-polarization are taken into account.
Example 10.11. 6 GHz point-to-point link.
T errestrial telecommunications systems
commonly aggregate large numbers of
individual communications links into a single
high-b... | Electromagnetics_Vol2.pdf |
λ= c
f
∼
= 3 × 108 m/s
6 × 109 Hz
∼
= 5
.00 cm (10.171)
R= 30 km, and PR ≥ 10−15 W . W e assume
that the height and high directivity of the
antennas
yield conditions sufficiently close to
free space. W e further assume
conjugate-matching at the receiver, and that the
antennas are co-polarized. Under these
conditions, P... | Electromagnetics_Vol2.pdf |
10.14. FRIIS TRANSMISSION EQUA TION 203
Image Credits
Fig. 10.1: c⃝ Offaperry (S. Lally), https://commons.wikimedia.org/wiki/File:Standing W ave Creation.svg,
CC
BY -SA 4.0 (https://creativecommons.org/licenses/by-sa/4.0/).
Fig. 10.2: c⃝ Offaperry (S. Lally), https://commons.wikimedia.org/wiki/File:Electrically-Short D... | Electromagnetics_Vol2.pdf |
https://commons.wikimedia.org/wiki/File:Magnitude of the Radiated Field.svg,
CC
BY -SA 4.0 (https://creativecommons.org/licenses/by-sa/4.0/).
Fig. 10.6: c⃝ Offaperry (S. Lally), https://commons.wikimedia.org/wiki/File:FHplaneMag.svg,
CC BY -SA 4.0 (https://creativecommons.org/licenses/by-sa/4.0/).
Fig. 10.7: c⃝ T . Tru... | Electromagnetics_Vol2.pdf |
Fig. 10.10: Inductiveload, https://commons.wikimedia.org/wiki/File:T wo Port Circuit.svg,
public
domain. Modified.
Fig. 10.11: c⃝ Sevenchw (C. W ang),
https://commons.wikimedia.org/wiki/File:An electromagnetic system consisting of a current distribution
radiating an electric field.svg,
CC
BY -SA 4.0 (https://creativecomm... | Electromagnetics_Vol2.pdf |
204 CHAPTER 10. ANTENNAS
Fig. 10.15: c⃝ Sevenchw (C. W ang),
https://commons.wikimedia.org/wiki/File:Thin straight dipole respond to incident plane wave.svg,
CC
BY -SA 4.0 (https://creativecommons.org/licenses/by-sa/4.0/).
Fig. 10.16: c⃝ Sevenchw (C. W ang),
https://commons.wikimedia.org/wiki/File:Dipole of interest dr... | Electromagnetics_Vol2.pdf |
public
domain. Modified.
Fig. 10.20: c⃝ Offaperry (S. Lally),
https://commons.wikimedia.org/wiki/File:Antenna Equivalent Circuit.svg,
CC
BY -SA 4.0 (https://creativecommons.org/licenses/by-sa/4.0/). Modified.
Fig. 10.21: Chetvorno, https://en.wikipedia.org/wiki/File:Antenna and resistor in cavity .svg,
public
domain. Mod... | Electromagnetics_Vol2.pdf |
Appendix A
Constituti
ve Parameters of Some
Common Materials
A.1 Permittivity of Some
Common Materials
[m0135]
The values below are relative permittivity ǫr ≜ ǫ/ǫ0
for
a few materials that are commonly encountered in
electrical engineering applications, and for which
permittivity emerges as a consideration. Note that
“... | Electromagnetics_Vol2.pdf |
function of temperature. In applications where
precision better than about 10% is required, primary
references accounting for frequency and temperature
should be consulted. The values presented here are
gathered from a variety of references, including those
indicated in “ Additional References. ”
Free Space (vacuum): ǫ... | Electromagnetics_Vol2.pdf |
capacitors exhibit ǫr ranging from about 5 to 50.
Semiconductors commonly appearing in electronics
– including carbon, silicon, geranium, indium
phosphide, and so on – typically exhibit ǫr in the
range 5–15.
Glass exhibits ǫr in the range 4–10, depending on
composition.
Gasses, including air, typically exhibit ǫr ∼= 1 ... | Electromagnetics_Vol2.pdf |
206 APPENDIX A. CONSTITUTIVE P ARAMETERS OF SOME COMMON MA TERIALS
lower end of the range.
Other liquids typically exhibit ǫr in the range 10–90,
with considerable variation as a function of
temperature and frequency . Animal flesh and blood
consists primarily of liquid matter and so also exhibits
permittivity in this r... | Electromagnetics_Vol2.pdf |
and for which µr is significantly different from 1.
These materials are predominantly ferromagnetic
metals and (in the case of ferrites) materials
containing significant ferromagnetic metal content.
Nearly all other materials exhibit µr that is not
significantly different from that of free space.
The values presented here... | Electromagnetics_Vol2.pdf |
which these materials are typically used.
Free Space (vacuum): µr ≜ 1.
Iron (also referred to by the chemical notation “Fe”)
appears as a principal ingredient in many materials
and alloys employed in electrical structures and
devices. Iron exhibits µr that is very high, but which
decreases with decreasing purity . 99.9... | Electromagnetics_Vol2.pdf |
A.3. CONDUCTIVITY OF SOME COMMON MA TERIALS 207
Ferrites include a broad range of ceramic materials
that are combined with iron and various combinations
of other metals and are used as magnets and magnetic
devices in various electrical systems. Common
ferrites exhibit µr in the range 16–640.
Additional Reading:
• CRC H... | Electromagnetics_Vol2.pdf |
instead in terms of resistivity, which is simply the
reciprocal of conductivity .
Conductivity may vary significantly as a function of
frequency . The values below are representative of
frequencies from a few kHz to a few GHz.
Conductivity also varies as a function of temperature.
In applications where precise values ar... | Electromagnetics_Vol2.pdf |
about 5 S/m for seawater (thus, a relatively good
conductor), varying also with temperature and
pressure. T ap water is typically in the range of
5–50 mS/m, depending on the level of impurities
present.
Soil typically exhibits σin the range 10−4 S/m for
dry soil to about 10−1 S/m for wet soil, varying also
due to chemi... | Electromagnetics_Vol2.pdf |
208 APPENDIX A. CONSTITUTIVE P ARAMETERS OF SOME COMMON MA TERIALS
Non-conductors. Most other materials that are not
well-described as conductors or semiconductors and
are dry exhibit σ <10−12 S/m. Most materials that
are considered to be insulators, including air and
common dielectrics, exhibit σ <10−15 S/m, often by
... | Electromagnetics_Vol2.pdf |
Appendix B
Mathematical
Formulas
B.1 T rigonometry
[m0138]
ejθ = cos θ+ jsin θ (B.1)
cos θ= 1
2
(
ejθ + e−j
θ)
(B.2)
sin θ= 1
j2
(
ejθ − e−j
θ)
(B.3)
cos2 θ= 1
2 + 1
2 cos 2θ (B.4)
sin2 θ= 1
2 − 1
2 cos 2θ (B.5)
sin (a± b) = sin acos b± cos asin b (B.6)
cos (a± b) = cos acos b∓ sin asin b (B.7)
Hyperbolic trigonometric... | Electromagnetics_Vol2.pdf |
Gradient
Gradient in Cartesian coordinates:
∇f = ˆx∂f
∂x + ˆy ∂f
∂y + ˆz∂f
∂z (B.10)
Gradient
in cylindrical coordinates:
∇f = ˆρ∂f
∂ρ + ˆφ1
ρ
∂f
∂φ + ˆz∂f
∂z (B.11)
Electr
omagnetics V ol. 2. c⃝ 2020 S.W . Ellingson CC BY SA 4.0. https://doi.org/10.21061/electromagnetics- vol- 2 | Electromagnetics_Vol2.pdf |
210 APPENDIX B. MA THEMA TICAL FORMULAS
Gradient in spherical coordinates:
∇f = ˆr∂f
∂r + ˆθ1
r
∂f
∂θ + ˆφ 1
rsin θ
∂
f
∂φ (B.12)
Di
vergence
Divergence in Cartesian coordinates:
∇ · A = ∂Ax
∂x + ∂Ay
∂y + ∂Az
∂z (B.13)
Di
vergence in cylindrical coordinates:
∇ · A = 1
ρ
∂
∂ρ (ρAρ) + 1
ρ
∂Aφ
∂φ + ∂Az
∂z (B.14)
Di
vergen... | Electromagnetics_Vol2.pdf |
Laplacian
in Cartesian coordinates:
∇2f = ∂2f
∂x2 + ∂2f
∂y2 + ∂2f
∂z2 (B.19)
Laplacian
in cylindrical coordinates:
∇2f = 1
ρ
∂
∂ρ
(
ρ∂f
∂ρ
)
+ 1
ρ2
∂2f
∂φ2 + ∂2f
∂z2 (B.20)
Laplacian
in spherical coordinates:
∇2f = 1
r2
∂
∂r
(
r2 ∂f
∂r
)
+ 1
r2 sin θ
∂
∂θ
(∂f
∂θ sin θ
)
+ 1
r2 sin2 θ
∂2f
∂φ2 (B.21) | Electromagnetics_Vol2.pdf |
B.3. VECTOR IDENTITIES 211
B.3 V ector Identities
[m0140]
Algebraic Identities
A · (B × C) = B · (
C × A) = C · (A × B)
(B.22)
A × (B × C) = B (A · C) − C (A · B) (B.23)
Identities Involving Differential Operators
∇ · (∇ × A) = 0 (B.24)
∇ × (∇f) = 0 (B.25)
∇ × (fA) = f(∇ × A) + ( ∇f) × A (B.26)
∇ · (A × B) = B · (∇ × A... | Electromagnetics_Vol2.pdf |
Appendix C
Ph
ysical Constants
[m0141]
The speed of light in free space (c), which is the
phase velocity of any electromagnetic radiation in
free space, is ∼= 2.9979 × 108 m/s. This is commonly
rounded up to 3 × 108 m/s. This rounding incurs error
of ∼= 0.07%, which is usually much less than other
errors present in ele... | Electromagnetics_Vol2.pdf |
to as the intrinsic impedance of free space.
Boltzmann’s constant is ∼
= 1.381 × 10−23 J/K, the
amount of energy associated with a change of one
degree of temperature. This is typically assigned the
symbol k(unfortunately , the same symbol often used
to represent wavenumber).
Electromagnetics V ol. 2. c⃝ 2020 S.W . Ell... | Electromagnetics_Vol2.pdf |
Index
acceptance
angle, 140
aluminum, 43, 46, 207
Ampere’s law
general form, 7, 8, 26, 34, 105, 146, 154, 155,
159
magnetostatics, 6, 18, 124
antenna
electrically-short dipole (ESD), 155–157, 159,
161, 168–172, 175–177, 198
folded half-wave dipole, 136
half-wave dipole, 136, 159, 161–162, 198
isotropic, 199, 201
micros... | Electromagnetics_Vol2.pdf |
poor, 41–43
cone of acceptance, 140
constitutive relationships, 7
copper, 43, 207
Coulomb force, 21
Coulomb’s law , 18
coupling, 196
critical angle, 88
curl, 210
current, 5, 48
current density
surface, 5, 163
volume, 5, 163
current moment, 20, 150, 152, 162
cutoff frequency , 100, 106, 117, 123
cyclotron motion, 11
dB,... | Electromagnetics_Vol2.pdf |
214 INDEX
English system of units, 2
evanescent waves, see waves
far field, 153, 161, 167
Faraday’s law , 7, 23
ferrite, 207
fiber optics, 88
flux
electric, 7
magnetic, 6, 7
force, 20
FR4, 41, 127, 128, 136, 205
Friis transmission equation, 201–202
gain
power, 39
voltage, 40
Gauss’ law
electric field, 5, 18
magnetic field, ... | Electromagnetics_Vol2.pdf |
isotropy , 9
Jefimenko’s equations, 18
Johnson-Nyquist noise, 198
joule heating, 27
Joule’s law , 27
Kirchoff’s voltage law
electrostatics, 5
Laplace’s Equation, 133
Laplacian (operator), 210
lever arm, 15
linear (media), 9
linearity , 9
Lorentz force, 11
Lorentz reciprocity theorem, 187–188
Lorenz gauge condition, 149
... | Electromagnetics_Vol2.pdf |
motor, 13, 17
mutual coupling, 196
notation, 3
numerical aperture, 140
Ohm’s law , 6, 25, 27, 30, 50
ohmic loss, 27, 34
omnidirectional, 182
optical fiber, 138–143
parallel-plate waveguide, see waveguide, see
waveguide, see waveguide, see waveguide,
see waveguide
path gain, 201
path loss, 201
pattern (radiation), 179–18... | Electromagnetics_Vol2.pdf |
INDEX 215
normalized, 180
permeability , 6
of common materials, 206–207
relative, 6, 206
permittivity , 5
complex-valued, 30, 33–34
effective, 128
of common materials, 205–206
relative, 5, 205
phase velocity , 95–97, 118
in microstrip, 128
phasor, 7
plane of incidence, 70
plane wave relationships, 36, 73, 77, 107, 154,... | Electromagnetics_Vol2.pdf |
radiation resistance, 174, 175
radome, 60, 64
ray-fixed coordinates, 68, 70
Rayleigh-Jeans law , 198
reciprocity , 186–190
rectangular waveguide, see waveguide
reference phase, 67
reference polarization, 67
reflection coefficient, 57
refraction, 81
resistivity , 207
RG-59, 52, 53, 131
right hand rule
magnetostatics, 19, 1... | Electromagnetics_Vol2.pdf |
thermodynamics, 198
time-harmonic, 7, 147
time-invariance (media), 9
torque, 15
total internal reflection, 82, 84, 86, 88–90, 138
transducer, 166
transmission line
analogy for wave propagation, 58, 63
coaxial, 52, 53, 103, 121, 129–135
differential, 121
lossy , 36
lumped-element model, 122, 124
microstrip, see microstri... | Electromagnetics_Vol2.pdf |
216 INDEX
units, 1–2
vector
arithmetic, 211
identity , 211
position-free, 15
vector effective length, 183, 190, 192, 195, 196
water, 205, 207
wave equation
electromagnetic, 36, 147, 149, 150
magnetic vector potential, 149, 150
source-free lossless region, 8
source-free lossy region, 30–32
wave impedance, 8, 37, 42, 154... | Electromagnetics_Vol2.pdf |
VOLUME 2
Electromagnetics, volume 2, by Steven W. Ellingson is a 216-page peer-reviewed open
textbook designed especially for electrical engineering students in the third year of a
bachelor of science degree program. It is intended as the primary textbook for the second
semester of a two-semester undergraduate engi... | Electromagnetics_Vol2.pdf |
at Virginia Tech (https://www.faculty.ece.vt.edu/swe/oem). The project goal is to
create publicly available, no-cost, openly licensed content for courses in engineering
electromagnetics. The project is motivated by two things: lowering the cost of learning
materials for students and giving faculty the freedom to ado... | Electromagnetics_Vol2.pdf |
Advance Praise for Electromagnetics
“I commend the author for the hard work and generosity required to create a
book like this and to make it available for free. The overall format is pleasing and
the material is generally rigorous and complete. Well done. ”
— Karl Warnick, Brigham Young University
“I really liked s... | Electromagnetics_Vol2.pdf |
Algorithms and Data Structures
With Applications to Graphics and Geometry | algorithms and data structures.pdf |
This book is licensed under a Creative Commons Attribution 3.0 License
Algorithms and Data Structures
With Applications to Graphics and Geometry
Jurg Nievergelt
Klaus Hinrichs
Copyright © 2011 Jurg Nievergelt
Editor-In-Chief: Jurg Nievergelt
Associate Editor: Marisa Drexel Ulrich
Editorial Assistants: Jon Durden, Tessa... | algorithms and data structures.pdf |
Table of Contents
Part I: Programming environments for motion, graphics, and geometry.................................7
1. Reducing a task to given primitives: programming motion...................................................9
A robot car, its capabilities, and the task to be performed................................. | algorithms and data structures.pdf |
2. Graphics primitives and environments.................................................................................14
Turtle graphics: a basic environment............................................................................................................. 14
QuickDraw: a graphics toolbox ..................... | algorithms and data structures.pdf |
Part II: Programming concepts: beyond notation....................................................................33
4. Algorithms and programs as literature: substance and form..............................................34
Programming in the large versus programming in the small......................................... | algorithms and data structures.pdf |
Divide-and-conquer expressed as a diagram: merge sort............................................................................. 46
Recursively defined trees................................................................................................................................ 47
Recursive tree traversal........ | algorithms and data structures.pdf |
6. Syntax.....................................................................................................................................53
Syntax and semantics..................................................................................................................................... 53
Grammars and their... | algorithms and data structures.pdf |
7. Syntax analysis.......................................................................................................................62
The role of syntax analysis.............................................................................................................................. 62
Syntax analysis of pare... | algorithms and data structures.pdf |
8. Truth values, the data type 'set', and bit acrobatics.............................................................69
Bits and boolean functions............................................................................................................................. 69
Swapping and crossovers: the versatile exclus... | algorithms and data structures.pdf |
Binary search.................................................................................................................................................. 79
In-place permutation...................................................................................................................................... 82... | algorithms and data structures.pdf |
This book is licensed under a Creative Commons Attribution 3.0 License
Paths in a graph.............................................................................................................................................. 93
Boolean matrix multiplication............................................................. | algorithms and data structures.pdf |
The Euclidean algorithm.............................................................................................................................. 102
The prime number sieve of Eratosthenes..................................................................................................... 103
Large integers........... | algorithms and data structures.pdf |
13. Reals....................................................................................................................................110
Floating-point numbers................................................................................................................................ 110
Some dangers........... | algorithms and data structures.pdf |
Newton's method for computing the square root......................................................................................... 115
14. Straight lines and circles.....................................................................................................119
Intersection..................................... | algorithms and data structures.pdf |
The riddle of the braiding straight lines....................................................................................................... 126
Digitized circles ............................................................................................................................................. 131
Part IV... | algorithms and data structures.pdf |
The halting problem is undecidable............................................................................................................. 139
Computable, yet unknown............................................................................................................................ 140
Multiplication of co... | algorithms and data structures.pdf |
Growth rates and orders of magnitude......................................................................................................... 146
Asymptotics................................................................................................................................................... 147
Summation f... | algorithms and data structures.pdf |
Trees.............................................................................................................................................................. 155
17. Sorting and its complexity..................................................................................................158
What is sorting? How... | algorithms and data structures.pdf |
Quicksort....................................................................................................................................................... 166
Analysis for three cases: best, "typical", and worst...................................................................................... 169
Is it possib... | algorithms and data structures.pdf |
18. What is a data structure?...................................................................................................180
Data structures old and new......................................................................................................................... 180
Algorithms and Data Structures 4 A... | algorithms and data structures.pdf |
The range of data structures studied............................................................................................................ 181
Performance criteria and measures.............................................................................................................. 182
19. Abstract data types... | algorithms and data structures.pdf |
Priority queue............................................................................................................................................... 190
Dictionary....................................................................................................................................................... | algorithms and data structures.pdf |
Implementation of the fixed-length fifo queue as a circular buffer............................................................ 202
Implementation of the fixed-length priority queue as a heap..................................................................... 205
Heapsort .................................................. | algorithms and data structures.pdf |
The fifo queue implemented as a one-way list ............................................................................................ 214
Tree traversal................................................................................................................................................ 214
Binary search t... | algorithms and data structures.pdf |
The special case of small key domains ........................................................................................................ 240
The special case of perfect hashing: table contents known a priori ............................................................ 241
Conventional hash tables: collision resol... | algorithms and data structures.pdf |
A virtual radix tree: order-preserving extendible hashing.......................................................................... 251
23. Metric data structures.......................................................................................................254
Organizing the embedding space versus organizing it... | algorithms and data structures.pdf |
Spatial data structures: objectives and constraints......................................................................................257
The grid file................................................................................................................................................... 259
Simple geometr... | algorithms and data structures.pdf |
Part VI: Interaction between algorithms and data structures: case studies in geometric
computation................................................................................................................................271
24. Sample problems and algorithms............................................... | algorithms and data structures.pdf |
Visibility in the plane: a simple algorithm whose analysis is not................................................................ 279
25. Plane-sweep: a general-purpose algorithm for two-dimensional problems illustrated using
line segment intersection....................................................................... | algorithms and data structures.pdf |
This book is licensed under a Creative Commons Attribution 3.0 License
Updating the y-table and detecting an intersection.................................................................................... 289
Sweeping across intersections ................................................................................... | algorithms and data structures.pdf |
Plane-sweep applied to the closest pair problem.........................................................................................294
Implementation............................................................................................................................................ 295
Analysis................ | algorithms and data structures.pdf |
Part I: Programming
environments for motion,
graphics, and geometry
Part I of this text book will discuss:
• simple programming environments
• program design
• informal versus formal notations
• reducing a solution to primitive operations, and programming as an activity independent of language.
The purpose of an arti... | algorithms and data structures.pdf |
environments force programmers to express themselves in formal notations.
Programming is the realization of a solution to a problem, expressed in terms of those operations provided by a
given programming environment. Most programmers work in environments that provide very powerful operations
and tools.
The more pow... | algorithms and data structures.pdf |
is to write substantial, useful programs. In the early days of computing, before the proliferation of programming
languages during the 1960s, most programmers worked in environments that were exceedingly simple by modern
standards: Acquaintance with an assembler, a loader, and a small program library sufficed. The ... | algorithms and data structures.pdf |
This book is licensed under a Creative Commons Attribution 3.0 License
programming environment suitable for programming graphics and motion, and illustrates how it can gradually be
enriched to approach a simple but useful graphics environment.
Textbooks on computer graphics. The computer-driven graphics screen is a ... | algorithms and data structures.pdf |
This book is licensed under a Creative Commons Attribution 3.0 License
1. Reducing a task to given
primitives: programming
motion
Learning objectives:
• primitives for specifying motion
• expressing an algorithm in informal notations and in high- and low-level programming languages
• program verification
• program... | algorithms and data structures.pdf |
The environment. Consider a two-dimensional square grid, a portion of which is enclosed by a wall made up
of horizontal and vertical line segments that run halfway between the grid points ( Exhibit 1.1). A robot car enclosed
within the wall moves along this grid under computer control, one step at a time, from grid ... | algorithms and data structures.pdf |
1. Reducing a task to given primitives: programming motion
A program for the robot is a sequence of commands with distinct labels. The labels serve merely to identify the
commands and need not be arranged either consecutively or in increasing order. Execution begins with the first
command and proceeds to successive... | algorithms and data structures.pdf |
while not touch do forward;
and then translated it into the robot's language.
A program for this robot car to patrol the walls of a city consists of two parts: First, find a wall, the problem we
just solved. Second, move along the wall forever while maintaining two conditions:
1. Never lose touch with the wall; at ... | algorithms and data structures.pdf |
with its front bumper, then turn right to resume its position with the wall to its left.
Wall-following algorithm described informally
Idea of solution: Touch the wall with your left hand; move forward, turning left or right as required to keep
touching the wall.
Wall-following algorithm described in English: Cl... | algorithms and data structures.pdf |
This book is licensed under a Creative Commons Attribution 3.0 License
Exhibit 1.3: The robot turns around a spike.
Exhibit 1.4: Backing up in a blind alley.
Algorithm specified in a high-level language
The ideas presented informally in above section are made precise in the following elegant, concise program:
{ wall to... | algorithms and data structures.pdf |
three types of invariants to verify the wall-following program: "wall to left-rear", "wall to left-front", and "wall to
right-front". The relationships between the robot's position and the presence of a nearby wall that must hold for
each assertion to be true are illustrated in Exhibit 1.5 . Shaded circles indicat... | algorithms and data structures.pdf |
1. Reducing a task to given primitives: programming motion
Exhibit 1.6: Robot motions as predicate transformers.
Algorithm programmed in the robot's language
A straightforward translation from the high-level program into the robot's low-level language yields the
following seven-line wall-following program:... | algorithms and data structures.pdf |
and memory requirements. This process of program transformation can often be done syntactically, that is merely
by considering the definition of individual statements, not the algorithm as a whole. As an example, we derive a
five-line version of the wall-following program by transforming the seven-line program in t... | algorithms and data structures.pdf |
This book is licensed under a Creative Commons Attribution 3.0 License
5 goto 2 5 goto 2
6 forward 6 forward
7 goto 1 7 goto 1
An optimization technique called loop rotation allows us to shorten this program by yet another instruction. It
changes the structure of the program significantly, as we see from the way the ... | algorithms and data structures.pdf |
modify an instance of such a wall.
2. Program the wall-following algorithm and animate its execution when tracking a wall entered with the wall-
editor. Specifically, show the robot's position and orientation after each change of state.
Algorithms and Data Structures 13 A Global Text | algorithms and data structures.pdf |
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