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Bibliografická citace

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BK
2nd ed.
Boca Raton : CRC Press, c2011
xxi, 824 s. : il. ; 25 cm

objednat
ISBN 978-1-56881-723-1 (váz.)
"An A K Peters book"--Tit. s.
Obsahuje bibliografii na s. 801-805 a rejstřík
000240537
Acknowledgments xiii // Introduction XV // 1 Cartesian Coordinate Systems 1 // 1.1 ID Mathematics 2 // 1.2 2D Cartesian Space 5 // 1.3 3D Cartesian Space 12 // 1.4 Odds and Ends 19 // 1.5 Exercises 27 // 2 Vectors 31 // 2.1 Mathematical Definition of Vector, and Other Boring Stuff 32 // 2.2 Geometric Definition of Vector 34 // 2.3 Specifying Vectors with Cartesian Coordinates 36 // 2.4 Vectors versus Points 39 // 2.5 Negating a Vector 43 // 2.6 Vector Multiplication by a Scalar 45 // 2.7 Vector Addition and Subtraction 47 // 2.8 Vector Magnitude (Length) 51 // 2.9 Unit Vectors 53 // 2.10 The Distance Formula 55 // 2.11 Vector Dot Product 56 // 2.12 Vector Cross Product 66 // 2.13 Linear Algebra Identities 70 // 2.14 Exercises 71 // 3 Multiple Coordinate Spaces 79 // 3.1 Why Bother with Multiple Coordinate Spaces? 80 // 3.2 Some Useful Coordinate Spaces 81 // 3.3 Basis Vectors and Coordinate Space Transformations . . 86 // 3.4 Nested Coordinate Spaces 106 // vii // vi Ń– Ń– Contents // 3.5 In Defense of Upright Space 108 // 3.6 Exercises 109 // 4 Introduction to Matrices 113 // 4.1 Mathematical Definition of Matrix 113 // 4.2 Geometric Interpretation of Matrix 124 // 4.3 The Bigger Picture of Linear Algebra 130 // 4.4 Exercises 132 // 5 Matrices and Linear Transformations 137 // 5.1 Rotation 138 // 5.2 Scale 144 // 5.3 Orthographic Projection 148 // 5.4 Reflection 151 // 5.5 Shearing 152 // 5.6 Combining Transformations 153 // 5.7 Classes of Transformations 154 // 5.8 Exercises 159 // 6 More on Matrices 161 // 6.1 Determinant of a Matrix 161 // 6.2 Inverse of a Matrix 168 // 6.3 Orthogonal Matrices 171 // 6.4 4x4 Homogeneous Matrices 176 // 6.5 4x4 Matrices and Perspective Projection 183 // 6.6 Exercises 189 // 7 Polar Coordinate Systems 191 // 7.1 2D Polar Space 191 // 7.2 Why Would Anybody Use Polar Coordinates? 201 // 7.3 3D Polar Space 203 //
7.4 Using Polar Coordinates to Specify Vectors 213 // 7.5 Exercises 214 // 8 Rotation in Three Dimensions 217 // 8.1 What Exactly is „Orientation“? 218 // 8.2 Matrix Form 220 // 8.3 Euler Angles 229 // 8.4 Axis-Angle and Exponential Map Representations 244 // 8.5 Quaternions 246 // 8.6 Comparison of Methods 273 // 8.7 Converting between Representations 275 // 8.8 Exercises 291 // Contents // ix // 9 Geometrie Primitives 295 // 9.1 Representation Techniques 295 // 9.2 Lines and Rays 297 // 9.3 Spheres and Circles 303 // 9.4 Bounding Boxes 304 // 9.5 Planes 311 // 9.6 Triangles 317 // 9.7 Polygons 332 // 9.8 Exercises 339 // 10 Mathematical Topics from 3D Graphics 343 // 10.1 How Graphics Works 345 // 10.2 Viewing in 3D 362 // 10.3 Coordinate Spaces 369 // 10.4 Polygon Meshes 381 // 10.5 Texture Mapping 393 // 10.6 The Standard Local Lighting Model 396 // 10.7 Light Sources 414 // 10.8 Skeletal Animation 424 // 10.9 Bump Mapping 431 // 10.10 The Real-Time Graphics Pipeline 438 // 10.11 Some HLSL Examples 457 // 10.12 Further Reading 475 // 10.13 Exercises 476 // 11 Mechanics 1: Linear Kinematics and Calculus 479 // 11.1 Overview and Other Expectation-Reducing Remarks 479 // 11.2 Basic Quantities and Units 483 // 11.3 Average Velocity 486 // 11.4 Instantaneous Velocity and the Derivative 490 // 11.5 Acceleration 513 // 11.6 Motion under Constant Acceleration 516 // 11.7 The Integral 530 // 11.8 Uniform Circular Motion 542 // 11.9 Exercises 549 // 12 Mechanics 2: Linear and Rotational Dynamics 553 // 12.1 Newton’s Three Laws 554 // 12.2 Some Simple Force Laws 562 // 12.3 Momentum 581 // 12.4 Impulsive Forces and Collisions 590 // 12.5 Rotational Dynamics 603 // 12.6 Real-Time Rigid Body Simulators 621 // 12.7 Suggested Reading 639 // 12.8 Exercises 640 // 13 Curves in 3D 645 // 13.1 Parametric Polynomial Curves 646 // 13.2 Polynomial Interpolation 653 //
13.3 Hermite Curves 665 // 13.4 Bézier Curves 670 // 13.5 Subdivision 685 // 13.6 Splines 690 // 13.7 Hermite and Bézier Splines 694 // 13.8 Continuity 697 // 13.9 Automatic Tangent Control 702 // 13.10 Exercises 711 // 14 Afterword 715 // 14.1 What Next? 715 // 14.2 Exercises 715 // A Geometric Tests 717 // A.l Closest Point on 2D Implicit Line 717 // A.2 Closest Point on a Parametric Ray 718 // A.3 Closest Point on a Plane 719 // A.4 Closest Point on a Circle or Sphere 719 // A.5 Closest Point in an A ABB 720 // A.6 Intersection Tests 720 // A.7 Intersection of Two Implicit Lines in 2D 721 // A.8 Intersection of Two Rays in 3D 722 // A.9 Intersection of a Ray and Plane 724 // A.10 Intersection of an AABB and Plane 725 // A.11 Intersection of Three Planes 726 // A.12 Intersection of Ray and a Circle or Sphere 727 // A.13 Intersection of Two Circles or Spheres 729 // A.14 Intersection of a Sphere and AABB 731 // A.15 Intersection of a Sphere and a Plane 732 // A.16 Intersection of a Ray and a Triangle 734 // A.17 Intersection of Two AABBs 737 // A.18 Intersection of a Ray and an AABB 740 // B Answers to the Exercises 745 // B.l Chapter 1 745 // B.2 Chapter 2 746 // B.3 Chapter 3 758 // B.4 Chapter 4 759 // B.5 Chapter 5 763 // B.6 Chapter 6 765 // B.7 Chapter 7 767 // B.8 Chapter 8 772 // B.9 Chapter 9 774 // B. 10 Chapter 10 779 // B.11 Chapter 11 781 // B. 12 Chapter 12 784 // B. 13 Chapter 13 792 // B. 14 Chapter 14 799 // Bibliography 801 // Index 807

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