Download or read book On Covering Points with Conics and Strips in the Plane written by Praveen Tiwari and published by . This book was released on 2013 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Geometric covering problems have always been of focus in computer scientific research. The generic geometric covering problem asks to cover a set S of n objects with another set of objects whose cardinality is minimum, in a geometric setting. Many versions of geometric cover have been studied in detail, one of which is line cover: Given a set of points in the plane, find the minimum number of lines to cover them. In Euclidean space R^m, this problem is known as Hyperplane Cover, where lines are replaced by affine hyperplanes bounded by dimension d. Line cover is NP-hard, so is its hyperplane analogue. Our thesis focuses on few extensions of hyperplane cover and line cover. One of the techniques used to study NP-hard problems is Fixed Parameter Tractability (FPT), where, in addition to input size, a parameter k is provided for input instance. We ask to solve the problem with respect to k, such that the running time is a function in both n and k, strictly polynomial in n, while the exponential component is limited to k. In this thesis, we study FPT and parameterized complexity theory, the theory of classifying hard problems involving a parameter k. We focus on two new geometric covering problems: covering a set of points in the plane with conics (conic cover) and covering a set of points with strips or fat lines of given width in the plane (fat line cover). A conic is a non-degenerate curve of degree two in the plane. A fat line is defined as a strip of finite width w. In this dissertation, we focus on the parameterized versions of these two problems, where, we are asked to cover the set of points with k conics or k fat lines. We use the existing techniques of FPT algorithms, kernelization and approximation algorithms to study these problems. We do a comprehensive study of these problems, starting with NP-hardness results to studying their parameterized hardness in terms of parameter k. We show that conic cover is fixed parameter tractable, and give an algorithm of running time O8́7 ((k/1.38)^4k), where, O8́7 implies that the running time is some polynomial in input size. Utilizing special properties of a parabola, we are able to achieve a faster algorithm and show a running time of O8́7 ((k/1.15)^3k). For fat line cover, first we establish its NP-hardness, then we explore algorithmic possibilities with respect to parameterized complexity theory. We show W [1]-hardness of fat line cover with respect to the number of fat lines, by showing a parameterized reduction from the problem of stabbing axis-parallel squares in the plane. A parameterized reduction is an algorithm which transforms an instance of one parameterized problem into an instance of another parameterized problem using a FPT-algorithm. In addition, we show that some restricted versions of fat line cover are also W [1]-hard. Further, in this thesis, we explore a restricted version of fat line cover, where the set of points are integer coordinates and allow only axis-parallel lines to cover them. We show that the problem is still NP-hard. We also show that this version is fixed parameter tractable having a kernel size of O (k^2) and give a FPT-algorithm with a running time of O8́7 (3^k). Finally, we conclude our study on this problem by giving an approximation algorithm for this version having a constant approximation ratio 2. The electronic version of this dissertation is accessible from http://hdl.handle.net/1969.1/148314

Download or read book Multiple View Geometry in Computer Vision written by Richard Hartley and published by Cambridge University Press. This book was released on 2004-03-25 with total page 676 pages. Available in PDF, EPUB and Kindle. Book excerpt: A basic problem in computer vision is to understand the structure of a real world scene given several images of it. Techniques for solving this problem are taken from projective geometry and photogrammetry. Here, the authors cover the geometric principles and their algebraic representation in terms of camera projection matrices, the fundamental matrix and the trifocal tensor. The theory and methods of computation of these entities are discussed with real examples, as is their use in the reconstruction of scenes from multiple images. The new edition features an extended introduction covering the key ideas in the book (which itself has been updated with additional examples and appendices) and significant new results which have appeared since the first edition. Comprehensive background material is provided, so readers familiar with linear algebra and basic numerical methods can understand the projective geometry and estimation algorithms presented, and implement the algorithms directly from the book.

Download or read book Fundamentals of Mathematics written by Heinrich Behnke and published by MIT Press. This book was released on 1974 with total page 708 pages. Available in PDF, EPUB and Kindle. Book excerpt: Volume II of a unique survey of the whole field of pure mathematics.

Download or read book Index to Mathematical Problems 1975 1979 written by Stanley Rabinowitz and published by MathPro Press. This book was released on 1999 with total page 548 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Electromagnetic Fields Mapping of fields written by Ernst Weber and published by . This book was released on 1960 with total page 618 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Engineering written by and published by . This book was released on 1926 with total page 1028 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book State Plane Coordinate System of 1983 written by James E. Stem and published by . This book was released on 1989 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book History and Politics in French Language Comics and Graphic Novels written by Mark McKinney and published by Univ. Press of Mississippi. This book was released on 2011-02-03 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt: With essays by Baru, Bart Beaty, Cécile Vernier Danehy, Hugo Frey, Pascal Lefèvre, Fabrice Leroy, Amanda Macdonald, Mark McKinney, Ann Miller, and Clare Tufts In Belgium, France, Switzerland, and other French-speaking countries, many well-known comics artists have focused their attention on historical and political events. In works ranging from comic books and graphic novels to newspaper strips, cartoonists have addressed such controversial topics as French and Belgian collaboration and resistance during World War II, European colonialism and US imperialism, anti-Semitism in France, the integration of African immigrant groups in Europe, and the green and feminist movements. History and Politics in French-Language Comics and Graphic Novels collects new essays that address comics from a variety of viewpoints, including a piece from practicing artist Baru. The explorations range from discussion of such canonical works as Hergé's Tintin series to such contemporary expressions as Baru's Road to America (2002), about the Algerian War. Included are close readings of specific comics series and graphic novels, such as Cécile Vernier Danehy's examination of Cosey's Saigon Hanoi, about remembering the Vietnam War. Other writers use theoretical lenses as a means of critiquing a broad range of comics, such as Bart Beaty's Bourdieu-inspired reading of today's comics field, and Amanda Macdonald's analysis of bandes dessinées (French comic books) in New Caledonia during the 1990s. The anthology establishes the French-language comics tradition as one rich with representations of history and politics and is one of the first English-language collections to explore the subject.

Download or read book Functions of a Complex Variable with Applications written by Edgar Giraldus Phillips and published by . This book was released on 1947 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book How to Read Nancy written by Paul Karasik and published by Fantagraphics Books. This book was released on 2017-10-31 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: Everything that you need to know about reading, making, and understanding comics can be found in a single Nancy strip by Ernie Bushmiller from August 8, 1959. Paul Karasik and Mark Newgarden’s groundbreaking work How to Read Nancy ingeniously isolates the separate building blocks of the language of comics through the deconstruction of a single strip. No other book on comics has taken such a simple yet methodical approach to laying bare how the comics medium really works. No other book of any kind has taken a single work by any artist and minutely (and entertainingly) pulled it apart like this. How to Read Nancy is a completely new approach towards deep-reading art. In addition, How to Read Nancy is a thoroughly researched history of how comics are made, from their creation at the drawing board to their ultimate destination at the bookstore. Textbook, art book, monogram, dissection, How to Read Nancy is a game changer in understanding how the “simplest” drawings grab us and never leave. Perfect for students, academics, scholars, and casual fans.

Download or read book Manual NGB written by United States. National Guard Bureau and published by . This book was released on 1950 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book The Geometry of Schemes written by David Eisenbud and published by Springer Science & Business Media. This book was released on 2006-04-06 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: Grothendieck’s beautiful theory of schemes permeates modern algebraic geometry and underlies its applications to number theory, physics, and applied mathematics. This simple account of that theory emphasizes and explains the universal geometric concepts behind the definitions. In the book, concepts are illustrated with fundamental examples, and explicit calculations show how the constructions of scheme theory are carried out in practice.

Download or read book Electromagnetic Fields written by Ernst Weber and published by . This book was released on 1950 with total page 618 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Mathematical Reviews written by and published by . This book was released on 1998 with total page 684 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book The Builder written by and published by . This book was released on 1885 with total page 946 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Navigation Dictionary written by United States. Naval Oceanographic Office and published by . This book was released on 1969 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Geometrical Geodesy written by Maarten Hooijberg and published by Springer Science & Business Media. This book was released on 2007-12-18 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: Surveying a Century Ago As it was based on the principles of geometry and trigonometry, surveying may be may be looked upon as a branch of practical mathematics. Hence, it was necessary that land surveyors and hydrographers should have a fair general knowledge, not only of these subjects, but also of all the subjects comprised by the term mathemat ics. In addition, the knowledge of mathematics required in ordinary chain surveying and levelling was not very extensive but in geodetical work, the highest mathematical ability and great organising power were required for a proper conception and supervision of the operations (Threlfall, 1940). Only small area of a few hundred square kilometres can be accurately mapped and surveyed without a frame work, since no difficulty is encountered because of Earth-curvature. In the past, especially in hydrography due to the type of work, surveying was carried out on the principles of ordinary practice, but in a very rough man ner, rapidity of execution being of paramount importance, the permissible error was sometimes large. The relative positions of the main surface features were obtained by aid of portable instruments, such as sextants and lead lines, tide poles, and logships. Sketching, just like military surveying was often filling in the smaller detail. In contrary, survey works done by the national mapping agencies (NMAs) were of a higher-level, and comprised the delimitation of boundaries as well as topographical surveys.