The NURBS Book (Monographs in Visual Communication)

Book Description

The second, revised edition of this book covers all aspects of non-uniform rational B-splines necessary to design geometry in a computer-aided environment. Basic B-spline features, curve and surface algorithms, and state-of-the-art geometry tools are all discussed. Detailed code for design algorithms and computational tricks are covered, too, in a lucid, easy-to-understand style, with a minimum of mathematics and using numerous worked examples. The book is a must for students, researchers, and implementors whose work involves the use of splines.

Customer Reviews:

Good reference for implementers who are familiar with NURBS.......2003-07-24

This book is best for those who have at least become familiar with Bezier and NURBS curves and surfaces and want to start implementing some programs.

The illustrations are not as clear as they could be so it may make it a little difficult for first-timers to understand. If you're unfamiliar with Bezier and NURBS curves then "Curves and Surfaces for CAGD" by Farin is probably a better place to start. But if you get Farin's book make sure to get the 5th edition since earlier editions aren't as clear.

With that said there is a wealth of information about creating and manipulating NURBS geometry in this book. All explanations are followed by code implementation. The code is a little difficult to understand at first, but if you stick with it you'll understand their coding style.

4 stars since thier layout and illustrations could be a lot clearer.

An Essential Foundation.......2002-08-07

I own many books on the subject of NURBS. I always come back to this one while programming NURBS and reading research papers. It provides a fantastic foundation. It is an older book, so don't expect recent research to be included. For those that also want to know how to do ray tracing with NURBS surfaces look here:

...

Good luck!

This is a definitely a math book, not a programming book !.......2000-05-23

This book is complete, but there is too many math formula. The composition is appr. 80% formula explanation, 10% sample and 10% algorithm. So if you are a programmer you are wasting 3/4 pages of the book. But, since there's no other book about NURBS, as complete as this, you may want to buy this one or else you can take a look "Mathematical Element for Computer Graphics". It also contains 300 pages of NURBS.

Excellent introduction to splines for the non-mathematician.......2000-02-12

One of the greates assets of this book is that it is fairly comprehensive while still using a minimum amount of mathematics. The style is lucid, easy to follow; the numerous C-like algorithms can be adapted to one's own use, and deal with the most important aspect of NURBS. This is easily the best introductory NURBS text. The only problem I see is the lack of discussion for ray-surface intersection tests, which are necessary if NURBS are to be rendered by raytracing. I recommend "The Nurbs Book" to any engineers and graphics professionals interested in curved surfaces.

Start Point.......1999-12-29

Before owning this book i cassified NURBS as kind of mathematical definitions of curves and surfaces. I was wrong, now it opened my mind so i develop new NURBS surfaces based on well described primitives. Twisting, blending, extruding is good starting point to develop surface definitions you exactly need. How about lofting shapes along branch like path curves?

Manifolds, Tensor Analysis, and Applications (Applied Mathematical Sciences)

Average customer rating:

A complete book by very erudite authors
A Unique Reference
mixed bag: many virtues but many weaknesses
Poorly writen, filled with errors, very long, poorly indexed

Manifolds, Tensor Analysis, and Applications (Applied Mathematical Sciences)
Ralph Abraham , Jerrold E. Marsden , and Tudor Ratiu
Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover

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Fundamentals of Differential Geometry (Graduate Texts in Mathematics)
Calculus of Variations
Calculus on Manifolds: A Modern Approach to Classical Theorems of Advanced Calculus
An Introduction to Differentiable Manifolds and Riemannian Geometry, Revised (Pure and Applied Mathematics)
Differential Geometry, Lie Groups, and Symmetric Spaces (Graduate Studies in Mathematics)

ASIN: 0387967907

Book Description

The purpose of this book is to provide core material in nonlinear analysis for mathematicians, physicists, engineers, and mathematical biologists. The main goal is to provide a working knowledge of manifolds, dynamical systems, tensors, and differential forms. Some applications to Hamiltonian mechanics, fluid mechanics, electromagnetism, plasma dynamics and control theory are given using both invariant and index notation. The prerequisites required are solid undergraduate courses in linear algebra and advanced calculus.

Customer Reviews:

A complete book by very erudite authors.......2002-04-07

I actually read this entire book--it is quite long and dense. Actually I took the course from the author Jerry Marsden at Caltech and Tutor (Jerry's friend and co-author) gave a guest lecture while visiting. We flew through the entire thing and ch 9 on lie groups of his mechanics and symmetry text in a short 10 weeks! My background in math was relatively weak when taking the course so it was a little hard to keep up; i.e. I came from an engineering background. Anyway, it is probably the most complete/diverse text I've come across on the subject. Of course, it's actually more of a monograph than a text. Since I've read the whole thing, I have to admit there are "several" typos. But as it is that most people can't even write a damn email without a typo or two, the book really does a good job considering it is 800 pages of mostly dense mathematical rigor. I imagine that if I wrote 800 pages of mathematical symbols in latex, that I might forget a tilde or put something as subscript that should have been superscript here or there! None of these errors really matter too much-they should not hinder one's understanding. All and all I think that this book is a great ref, although I've never seen the index, if one exists. For the beginner, also check out Boothby's book, which covers a lot of the same material but tones it down a bit.

A Unique Reference.......2000-10-10

Students of mathematical physics in general, and general relativity in particular, face a formidable challenge in attempting to find coherent, readable references on manifold theory and tensor analysis. I think it fair to say that for every well-written work on the subject, there are ten that do more damage than good. Very few texts can claim to (1) be clear enough to assist the person who is studying alone, (2) offer valuable PHYSICAL insight into the subject, and (3) pass the standards of rigor that mathematicians would impose. Abraham, Marsden, and Ratiu manage to accomplish all three of these goals in this profoundly useful text. I studied from the first edition and I have taught from the second. The two chapters on differential forms, Hodge star duality, integration on manifolds, and the generalized Stokes' Theorem alone are worth the price of the entire book. I am unaware of any other reference which which treats differential forms with the same combination of clarity, physical motivation, and mathematical rigor. The concluding chapter on applications offers one of the clearest introductions to the relativistic form of Maxwell's equations to be found in any text. For students of physics who want to see the mathematics "done right," one would be hard pressed to do better than Abraham, Marsden, and Ratiu.

mixed bag: many virtues but many weaknesses.......2000-02-18

I took a course taught by the 3rd author (Tudor Ratiu) at UCSC using this book; I found both good and bad in it. Much of the bad for me was overcome by the inspiring and energetic presentation by one of the authors. One may view this book as basically a detailed elaboration of the "preliminary" chapters of the book "Foundations of Mechanics" by the 1st 2 authors. The strengths of this book are (a) the treatment which is general enough to include infinite-dimensional manifolds and not just the finite-dimensional case (most books just talk about the finite-dim'l case) and (b) the attempt to cover all theorems "full strength" (in the greatest generality obtaining the strongest conclusions from the weakest hypotheses). Neither of these (not counting the many typos) recommends this as a first or even second text for students, but it's hard to find any other books that treat the material at the same level of generality and precision, which is a must if attempting "hard" global analysis in areas such as fluid mechanics (from a geometric point of view). Correction of the many typos could make this an indispensable reference book for those requiring the techniques discussed. More discussion of finite-dimensional examples before jumping to infinite-dimensional ones (e.g. discussing finite-dimensional Grassmannians before jumping to the infinite-dimensional Banach manifold version) could make this into a tolerable text.

As it is, it's problematic, aggravating, and not for the faint of heart, but not without its virtues.

Possible alternatives for the infinite-dimensional point of view are Lang's manifolds book or some volume of the expensive multi-volume treatise on analysis by Dieudonne.

Poorly writen, filled with errors, very long, poorly indexed.......1999-09-21

We used this book in a graduate course at UCLA. The professor had to hand out a list of all the errors we encountered, and it was about ten pages typewritten. The professor, Geoff Mess, wrote at the top of this list that many of the students had complained about this book, and that it was a disappointment to him as well. I often found myself scanning hundreds of pages in search of what should have been contained in their sparse index. The book is unnecessarily long and wordy for the matter covered. In the introduction, the authors mention that they invite comments from the readers. It seems that they depend on their readers to correct their copious errors and their poor writing.

College Geometry: A Problem Solving Approach with Applications

Average customer rating:

A solid introduction to geometry that emphasizes learning through problem solving
not college level
An outstanding introduction to geometric thought

College Geometry: A Problem Solving Approach with Applications
Gary L. Musser , and Lynn E. Trimpe
Manufacturer: Prentice Hall
ProductGroup: Book
Binding: Paperback

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Similar Items:

Student Activity Manual for College Geometry
Teaching Secondary and Middle School Mathematics (2nd Edition)
Engaging Children in Science (3rd Edition)
Learning Math in Elementary and Middle School & IMAP Package (4th Edition)
Elementary Number Theory (5th Edition)

ASIN: 0023854502

Book Description

This book exposes readers to many practical applications of geometry, especially those involving measurement. A three- part organization divides topics into Problem Solving, Geometric Shapes, and Measurement; Formal Synthetic Euclidean Geometry; and Alternate Approaches to Plane Geometry.

Customer Reviews:

A solid introduction to geometry that emphasizes learning through problem solving.......2007-07-03

One of the problems a number of math students face is learning how to think about the problems they face. They simply never develop the necessary tool set that will allow them to understand what the problem is asking and what they should do to attack it. Once they have an answer, they are not sure if they have found the correct answer. This is a fine BASIC text for college and high school students who want to get a handle on dealing with geometry. If you have a deep mathematics background and are looking for an advanced college text on geometry, this is probably not for you.

However, if you want to learn the basics on how to think about geometry and a lot of help on how to solve a variety of geometric problems, this is a terrific text and will be a big help. I enjoy the way the text engages the student from the very beginning and asks him or her to THINK. It isn't a bunch of material to memorize. What the authors do is build the student's understanding through problem solving. If the student will take the time to work the problems and not give up on the problems he or she finds difficult, the understanding will come and will be more ingrained in his or her thought processes than would happen through memorization.

There are lots of geometric drawings, as one would hope, and there are a number of applications of geometry to real life and that should help the student, as well. Again, this is meant as a basic geometry text and can be suitable for a good high school student as well as non-majors in college that want to get an introduction to the basics of geometry.

not college level.......2005-04-11

This book is pitched at an extremely low level
quite beyond anything in the 'math for poets'
category - often dropping below even that of high
school. Indeed, the book compares unfavorably
with the canonical hs text by Jacobs. To give
just one example, it takes the authors 273 pages
to get to the idea of cross multiplication [a staple
in the repertoire of any decent middle school
student]. In particular, math majors as well
as anyone interested in the subject should
steer clear of this and consider instead books by
Pedoe, Court, Coxeter, etc. If you are looking
for a problem oriented approach to geometry, try
the relevant offering in the Schaum's series
[acknowledged masters of this approach].
In the meantime, let's not sacrifice any more trees
for products as weak as this.

An outstanding introduction to geometric thought.......2000-10-04

This is one of the few introductory level texts I have seen that gives some of the real flavor of mathematics, without being too challenging for beginning students. The initial section on problem solving is modelled on the famous book by Polya, "How to solve it," and has many simple but thought-stimulating problems. The following sections develop plane and solid geometry with many illustrated problems and interesting historical notes. The final chapters carefully introduce geometric proofs. There are also review sections on simple algebraic manipulations and basic logic, as well as a short section on the implications of alternate parallel postulates. Overall, the text has a well thought out development of basic skills and concepts, and enough interesting tidbits from more "advanced" topics to challenge the imagination of any student.

Local Cohomology: An Algebraic Introduction with Geometric Applications (Cambridge Studies in Advanced Mathematics)

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Local Cohomology: An Algebraic Introduction with Geometric Applications (Cambridge Studies in Advanced Mathematics)
M. P. Brodmann , and R. Y. Sharp
Manufacturer: Cambridge University Press
ProductGroup: Book
Binding: Hardcover

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ASIN: 0521372860

Book Description

This book provides a careful and detailed algebraic introduction to Grothendieck's local cohomology theory, and illustrates many applications for the theory in commutative algebra and in the geometry of quasi-affine and quasi-projective varieties. Topics covered include Castelnuovo-Mumford regularity, the Fulton-Hansen connectedness theorem for projective varieties, and connections between local cohomology and both reductions of ideals and sheaf cohomology. It is designed for graduate students who have some experience of basic commutative algebra and homological algebra, and also for experts in commutative algebra and algebraic geometry.

Fractal Geometry: Mathematical Foundations and Applications

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A rare find
What every student should know about fractals.
Theoretical as well as practical insight
Exposes fractal geometry as a real mathematical discipline.
One of the best books on fractals to be found anywhere!

Fractal Geometry: Mathematical Foundations and Applications
Kenneth Falconer
Manufacturer: Wiley
ProductGroup: Book
Binding: Paperback

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Chaos and Fractals: New Frontiers of Science
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ASIN: 0470848626

Book Description

Since its original publication in 1990, Kenneth Falconer's Fractal Geometry: Mathematical Foundations and Applications has become a seminal text on the mathematics of fractals. It introduces the general mathematical theory and applications of fractals in a way that is accessible to students from a wide range of disciplines. This new edition has been extensively revised and updated. It features much new material, many additional exercises, notes and references, and an extended bibliography that reflects the development of the subject since the first edition.
* Provides a comprehensive and accessible introduction to the mathematical theory and applications of fractals.
* Each topic is carefully explained and illustrated by examples and figures.
* Includes all necessary mathematical background material.
* Includes notes and references to enable the reader to pursue individual topics.
* Features a wide selection of exercises, enabling the reader to develop their understanding of the theory.
* Supported by a Web site featuring solutions to exercises, and additional material for students and lecturers.
Fractal Geometry: Mathematical Foundations and Applications is aimed at undergraduate and graduate students studying courses in fractal geometry. The book also provides an excellent source of reference for researchers who encounter fractals in mathematics, physics, engineering, and the applied sciences.
Also by Kenneth Falconer and available from Wiley:
Techniques in Fractal Geometry
ISBN 0-471-95724-0

Please click here to download solutions to exercises found within this title:

http://www.wileyeurope.com/fractal

Customer Reviews:

A rare find.......2006-10-07

I agree with all that was said by the other reviews here but add one important point. The physical layout, (typeface, drawings, whitespace etc.) of this book is brilliantly done. This is often overlooked by the producers of technical works who do it "on the cheap", but it is vital if one is to use the book day after day, as I have had to.

While the subject matter is not easy, this is an excellent book to motivate one to get stuck into the underlying mathematics. The reward is a little insight into the often beatiful theorems and practical results found in this stimulating field of study.

What every student should know about fractals........2003-02-10

Fractals make headlines from time to time[--are they everywhere?], and and they make lovely color pictures; but they are also part of a substantial mathematical theory, one with an
exciting mathematical history. This very important book presents
the subject in a way that it can be taught to students, and it starts with the basics, systematically, step by step, building up the material. Or it can be used for selfstudy! It has great exercises too! In view of the many applications to geometric analysis, to PDE, and to statistics, it is likely that fractal geometry will soon be a standard math course taught in many (more) math departments. By now it is widely recognized that the selfsimilarity aspects of the wavelet algorithms are key to their sucess. The book came out in 1990, and the author has an equally attractive book on the subject from 1985[The geometry of fractal sets] with a slightly more potential theoretic bent.

Theoretical as well as practical insight.......2001-08-13

The first part of the book is essentially of a theoretical nature, with a thorough treatment of fractal geometry at a mathematical point of view. The second part on the other hand provides a flavour of the problems of fractal geometry in practice...so mathematicians as well as people interested in applications only should both find this book interesting. The maths are not easy but quite "understandable" for science undergrads...some notions of calculus or topology would help... but the introduction is excellent and allows anyone to follow the course of the book (but for understanding the proofs a good math background is required).

Excellent for understanding the geometrical properties of fractals.

Exposes fractal geometry as a real mathematical discipline........2000-04-13

I appreciate Falconer's books on fractal geometry because they show the topic as it really is: a whole mathematical discipline on its own right and not just a nice temporary fashion.

It begins introducing basic topological concepts and then proceeds to develop the theory for several possible definitions of fractal dimension, showing the relations between them. Then it explores deeply the local geometry of different kinds of fractal objects, and studies some other geometrical situations, like the pojection of fractals (ever thought of a DIGITAL sundial? Here it is described!).

The book also includes a lot of applications to other areas of mathematics and physics, a great amount of graphics, and much more.

The text is suitable from third year undergraduate school and on. It is a larger but lighter version of "The Geometry of Fractal Sets".

One of the best books on fractals to be found anywhere!.......1998-03-20

The book opens the doors of mathematics: it isn't an easy door, but well worth the effort. It bridges the gap between beginner texts and advanced study and covers the basic material in a hard hitting manner. Those looking for "giltz" should look elsewhere. It is a book of great understanding and depth. Your unique Associates ID is: thefractaltransl.

Introduction to Vertex Operator Superalgebras and Their Modules (Mathematics and Its Applications)

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Introduction to Vertex Operator Superalgebras and Their Modules (Mathematics and Its Applications)
Xiaoping Xu
Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover

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ASIN: 0792352424

Book Description

This book presents a systematic study on the structures of vertex operator superalgebras and their modules. Related theories of self-dual codes and lattices are included, as well as recent achievements on classifications of certain simple vertex operator superalgebras and their irreducible twisted modules, constructions of simple vertex operator superalgebras from graded associative algebras and their anti-involutions, self-dual codes and lattices.
Audience: This book is of interest to researchers and graduate students in mathematics and mathematical physics.

Topology and Its Applications (Pure and Applied Mathematics: A Wiley-Interscience Series of Texts, Monographs and Tracts)

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Topology and Its Applications (Pure and Applied Mathematics: A Wiley-Interscience Series of Texts, Monographs and Tracts)
William F. Basener
Manufacturer: Wiley-Interscience
ProductGroup: Book
Binding: Hardcover

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A Geometric Approach to Differential Forms
Topology Now! (Classroom Resource Material)

ASIN: 0471687553

Book Description

This book provides a broad foundation for topology, including general, geometric, differential, combinatorial and algebraic topology. It is designed for use either for a first course in topology beginning in chapter one, a first course in geometric topology beginning in chapter three or a course in applied topology. The book is structured around the theoretical framework of topology, and abundant illustrations and applications provide intuition and put the subject in modern setting. Topics include open sets, compactness, homotopy, surface classification, index theory on surfaces, manifolds and complexes, topological groups, the fundamental group and homology. Modern applications of topology have played an important role solving a diverse spectrum of applied problems. In this text serious attention is given to recent applications of topology in computer graphics, economics, dynamical systems, condensed matter physics, biology, robotics, chemistry, cosmology, material science, computational topology, population modeling and other areas of science and engineering. Most applications are presented in optional sections, allowing an instructor to customize the presentation.

Harmonic Analysis on Symmetric Spaces and Applications II

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Harmonic Analysis on Symmetric Spaces and Applications II
Audrey Terras
Manufacturer: Springer-Verlag
ProductGroup: Book
Binding: Paperback

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A Study of Braids (Mathematics and Its Applications)

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A Study of Braids (Mathematics and Its Applications)
Kunio Murasugi , and B. Kurpita
Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover

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ASIN: 0792357671

Book Description

This book provides a comprehensive exposition of the theory of braids, beginning with the basic mathematical definitions and structures. Among the many topics explained in detail are: the braid group for various surfaces; the solution of the word problem for the braid group; braids in the context of knots and links (Alexander's theorem); Markov's theorem and its use in obtaining braid invariants; the connection between the Platonic solids (regular polyhedra) and braids; the use of braids in the solution of algebraic equations. Dirac's problem and special types of braids termed Mexican plaits are also discussed.
Audience: Since the book relies on concepts and techniques from algebra and topology, the authors also provide a couple of appendices that cover the necessary material from these two branches of mathematics. Hence, the book is accessible not only to mathematicians but also to anybody who might have an interest in the theory of braids. In particular, as more and more applications of braid theory are found outside the realm of mathematics, this book is ideal for any physicist, chemist or biologist who would like to understand the mathematics of braids.
With its use of numerous figures to explain clearly the mathematics, and exercises to solidify the understanding, this book may also be used as a textbook for a course on knots and braids, or as a supplementary textbook for a course on topology or algebra.

Wavelets through a Looking Glass (Applied and Numerical Harmonic Analysis)

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A masterpiece in wavelets
Distinguished link between math and computer science
A fresh look at wavelets
an intriguing new wavelet book
An Intriguiging New Book

Wavelets through a Looking Glass (Applied and Numerical Harmonic Analysis)
Ola Bratteli , and Palle Jorgensen
Manufacturer: Birkhäuser Boston
ProductGroup: Book
Binding: Hardcover

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ASIN: 0817642803

Book Description

This book combining wavelets and the world of the spectrum focuses on recent developments in wavelet theory, emphasizing fundamental and relatively timeless techniques that have a geometric and spectral-theoretic flavor. The exposition is clearly motivated and unfolds systematically, aided by numerous graphics. This self-contained book deals with important applications to signal processing, communications engineering, computer graphics algorithms, qubit algorithms and chaos theory, and is aimed at a broad readership of graduate students, practitioners, and researchers in applied mathematics and engineering. The book is also useful for other mathematicians with an interest in the interface between mathematics and communication theory.

Customer Reviews:

A masterpiece in wavelets.......2003-03-14

This is a very well written book on the theory of wavelets and its applications. The presentation is self-contained and may serve as an introduction for someone who wants to learn about this topic. It also is an excellent book for those who have an advanced graduate degree in applied mathematics since it demonstrates how to truly understand complex concepts. This book gives a general presentation of some recent developments in wavelet theory with an emphasis on techniques that have a geometric and spectral-theoretic flavor. It can be certainly used as a textbook for graduate students as well as as a reference book for the specialists and researchers. A very nice feature of the book are the tutorials at the beginning of each chapter and some sections, which serve as summaries of main ideas and guides through the background ideas and motivation. At the end of every chapter there are plenty of excercises of various level of difficulty. Overall, this is a great book and I recommend it highly to a motivated reader.

Distinguished link between math and computer science.......2003-03-11

This is an important mathematical reference written in excellent style. Wavelets have found applications in many areas of engineering and CS. The authors provide a detailed, rich and entertaining tour through this relatively young but important field for both math and CS/Eng. Connections are, e.g., made between advanced CS virtual-reality applications such as audio-systems processing, future applications such as quantum computing, and advanced math in functional analysis and operator theory.

A fresh look at wavelets.......2002-10-08

The Book by Bratteli and Jorgensen is a superb book on wavelet's theory. It is very well written and has new and a fresh point of view on the subject. Although there are several good books on wavelets, the book by Bratteli and Jorgensen covers an important niche that has not been covered before. In particular

1- The book covers the theory of wavelets from the point of view of operators and functional analysis and will appeal to a growing number of pure as well as applied mathematicians interested in the subject.

2- The writing of the book is very appealing: every chapter starts by a tutorial that gives motivation as well as intuition. It is then followed by a very clean mathematical development of the subject, together with many examples, figures, and applications from physics and engineering. A set of nice problems is provided at the end of each chapter. Thus this book can be used as a graduate textbook or for mathematical seminars in mathematics departments.

3- This book can even be used by experts in wavelet theory for learning about recent developments and new perspectives from operator theory and functional analysis.

I highly recommend this book.

an intriguing new wavelet book.......2002-09-09

This is a book about an important topic in applied mathematics by two authors with excellent credentials in both pure and applied areas. The reader will find many intriguing threads connecting wavelets to other parts of mathematics, including a wavelet index theorem, quantum computing, the ubiquitous C*-algebras O_n and, of course, spectral theory. The graphics are meticulously done.

I look forward to learning a lot from it.

An Intriguiging New Book.......2002-08-30

This is a book about an important topic in applied mathematics by two authors with excellent
credentials in both pure and applied areas.

The reader will find many intriguing threads connecting wavelets to other parts of mathematics, including a wavelet "index theorem", quantum computing, the ubiquitous Cuntz C*-algebras and, of course, spectral theory. The graphics are excellent. I look forward to learning a lot from it.

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