LEADER 05346nam 2200673 450 001 9910460277003321 005 20200520144314.0 010 $a1-118-71198-X 010 $a1-118-71212-9 035 $a(CKB)3710000000244412 035 $a(EBL)1789982 035 $a(SSID)ssj0001335643 035 $a(PQKBManifestationID)12543354 035 $a(PQKBTitleCode)TC0001335643 035 $a(PQKBWorkID)11286183 035 $a(PQKB)10021362 035 $a(PQKBManifestationID)16045145 035 $a(PQKB)21470231 035 $a(MiAaPQ)EBC1789982 035 $a(DLC) 2014023354 035 $a(CaSebORM)9781118712191 035 $a(Au-PeEL)EBL1789982 035 $a(CaPaEBR)ebr10933617 035 $a(CaONFJC)MIL646271 035 $a(OCoLC)881418267 035 $a(EXLCZ)993710000000244412 100 $a20140925h20152015 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aMathematical structures for computer graphics /$fSteven J. Janke 205 $a1st edition 210 1$aHoboken, New Jersey :$cWiley,$d2015. 210 4$dİ2015 215 $a1 online resource (889 p.) 300 $aDescription based upon print version of record. 311 $a1-322-15016-8 311 $a1-118-71219-6 320 $aIncludes bibliographical references and index. 327 $aMachine 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 . 330 $a"This book is for readers who wish to understand the mathematical tools that are necessary to produce three-dimensional models and the resulting screen images. Written by an academic with over 20 years of teaching experience, the intent of the book is to show relevant and focused mathematical derivations that help students understand computer graphics. Intuitive, rather than just theorem/proof discussions set the tone for the presentation. Some algebra, high-school geometry, and trigonometry are presumed for adequate comprehension. Notions of why results are important give the reader a sense of ownership and application. Chapters are written in a two-tiered style so as to allow for flexibility in the level of mathematics desired. Two- and three-dimensional vector geometry is covered using transforms, curves, and surfaces. More focused graphics topics like perspective with the accompanying projective geometry, polyhedral as building blocks for objects, and ray retracing help pull the vector technique together. An assortment of other topics helps round-out the discussion. These include noise, randomness, and L-systems. Plentiful exercises are showcased throughout. An author-maintained web site includes further computer programming notes and solutions to selected exercises"--$cProvided by publisher. 330 $a"Explains the mathematical tools that are necessary to produce three-dimensional models and the resulting screen images. Demonstrates relevant and focused mathematical derivations that help students understand computer graphics"--$cProvided by publisher. 606 $aComputer graphics$xMathematics 606 $aThree-dimensional imaging$xMathematics 608 $aElectronic books. 615 0$aComputer graphics$xMathematics. 615 0$aThree-dimensional imaging$xMathematics. 676 $a006.601/51 686 $aCOM012040$2bisacsh 700 $aJanke$b Steven J.$f1947-$0922086 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910460277003321 996 $aMathematical structures for computer graphics$92169822 997 $aUNINA