Mathematical structures for computer graphics / / Steven J. Janke

• Record Nr.: UNINA9910460277003321
• Autore: Janke Steven J. <1947->
• Pubbl/distr/stampa: Hoboken, New Jersey : , : Wiley, , 2015; ©2015
• ISBN: 1-118-71198-X; 1-118-71212-9
• Edizione: [1st edition]
• Descrizione fisica: 1 online resource (889 p.)
• Classificazione: COM012040
• Disciplina: 006.601/51
• Soggetti: Computer graphics - Mathematics; Three-dimensional imaging - Mathematics; Electronic books.
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: Machine generated contents note: Preface iii 1 Basics 1 1.1 Graphics Pipeline 2 1.2 Mathematical Descriptions 5 1.3 Position 6 1.4 Distance 9 1.5 Complements and Details 13 1.6 Exercises 17 2 Vector Algebra 21 2.1 Basic Vector Characteristics 22 2.2 Two Important Products 31 2.3 Complements and Details 42 2.4 Exercises 46 3 Vector Geometry 49 3.1 Lines & Planes 49 3.2 Distances 55 3.3 Angles 63 3.4 Intersections 65 3.5 Additional Key Applications 73 3.6 Homogeneous Coordinates 86 3.7 Complements and Details 90 3.8 Exercises 94 4 Transformations 99 4.1 Types of Transformations 100 4.2 Linear Transformations 101 4.3 Three dimensions 113 4.4 Affine Transformations 123 4.5 Complements and Details 134 4.6 Exercises 145 5 Orientation 149 5.1 Cartesian Coordinate Systems 151 5.2 Cameras 159 5.3 Other Coordinate Systems 182 5.4 Complements and Details 190 5.5 Exercises 193 6 Polygons & Polyhedra 197 6.1 Triangles 197 6.2 Polygons 213 6.3 Polyhedra 230 6.4 Complements and Details 245 6.5 Exercises 250 7 Curves & Surfaces 255 7.1 Curve Descriptions 256 7.2 Bezier Curves 268 7.3 B-Splines 278 7.4 NURBS 295 7.5 Surfaces 300 7.6 Complements and Details 311 7.7 Exercises 316 8 Visibility 321 8.1 Viewing 321 8.2 Perspective Transformation 323 8.3 Hidden Surfaces 333 8.4 Ray Tracing 344 8.5 Complements ; and Details 351 8.6 Exercises 356 9 Lighting 359 9.1 Color Coordinates 359 9.2 Elementary Lighting Models 364 9.3 Global Illumination 384 9.4 Textures 391 9.5 Complements and Details 403 9.6 Exercises 408 10 Other Paradigms 411 10.1 Pixels 412 10.2 Noise 421 10.3 L-Systems 435 10.4 Exercises 443 A Geometry & Trigonometry 447 A.1 Triangles 447 A.2 Angles 449 A.3 Trigonometric Functions 450 B Linear Algebra 455 B.1 Systems of Linear Equations 455 B.2 Matrix Properties 458 B.3 Vector Spaces 460 .
• Sommario/riassunto: "This book is for readers who wish to understand the mathematical tools that are necessary to produce three-dimensional models and the resulting screen images. Written by an academic with over 20 years of teaching experience, the intent of the book is to show relevant and focused mathematical derivations that help students understand computer graphics. Intuitive, rather than just theorem/proof discussions set the tone for the presentation. Some algebra, high-school geometry, and trigonometry are presumed for adequate comprehension. Notions of why results are important give the reader a sense of ownership and application. Chapters are written in a two-tiered style so as to allow for flexibility in the level of mathematics desired. Two- and three-dimensional vector geometry is covered using transforms, curves, and surfaces. More focused graphics topics like perspective with the accompanying projective geometry, polyhedral as building blocks for objects, and ray retracing help pull the vector technique together. An assortment of other topics helps round-out the discussion. These include noise, randomness, and L-systems. Plentiful exercises are showcased throughout. An author-maintained web site includes further computer programming notes and solutions to selected exercises"--; "Explains the mathematical tools that are necessary to produce three-dimensional models and the resulting screen images. Demonstrates relevant and focused mathematical derivations that help students understand computer graphics"--

The theoretical foundation of dendritic function : selected papers of Wilfrid Rall with commentaries / / edited by Idan Segev, John Rinzel, and Gordon M. Shepherd

• Record Nr.: UNINA9910315236503321
• Autore: Rall Wilfried
• Pubbl/distr/stampa: Cambridge, : The MIT Press, 2003; Cambridge : , : MIT Press, , 1994
• ISBN: 9780262283373; 0262283379; 9780262515467; 0262515466; 9780585342573; 0585342571
• Descrizione fisica: 1 online resource (vii, 456 p. ) : ill.
• Collana: Computational neuroscience series
• Disciplina: 612.8/1046
• Soggetti: Dendrites - Mathematical models
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: "A Bradford book."
• Nota di bibliografia: Includes bibliographical references and index.
• Sommario/riassunto: This collection of fifteen previously published papers, some of them not widely available, have been carefully chosen and annotated by Rall's colleagues and other leading neuroscientists. Wilfrid Rall was a pioneer in establishing the integrative functions of neuronal dendrites that have provided a foundation for neurobiology in general and computational neuroscience in particular. This collection of fifteen previously published papers, some of them not widely available, have been carefully chosen and annotated by Rall's colleagues and other leading neuroscientists. It brings together Rall's work over more than forty years, including his first papers extending cable theory to complex dendritic trees, his ground-breaking paper introducing compartmental analysis to computational neuroscience, and his studies of synaptic integration in motoneurons, dendrodendritic interactions, plasticity of dendritic spines, and active dendritic properties. Today it is well known that the brain's synaptic information is processed mostly in the ; dendrites where many of the plastic changes underlying learning and memory take place. It is particularly timely to look again at the work of a major creator of the field, to appreciate where things started and where they have led, and to correct any misinterpretations of Rall's work. The editors' introduction highlights the major insights that were gained from Rall's studies as well as from those of his collaborators and followers. It asks the questions that Rall proposed during his scientific career and briefly summarizes the answers.