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Mathematical Structures for Computer Graphics 无水印pdf.pdf

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    Cover
    Copyright
    Contents
    Preface
    1 Basics
    1.1 Graphics Pipeline
    1.2 Mathematical Descriptions
    1.3 Position
    1.4 Distance
    1.5 Complements and Details
    1.5.1 Pythagorean Theorem Continued
    1.5.2 Law of Cosines Continued
    1.5.3 Law of Sines
    1.5.4 Numerical Calculations
    1.6 Exercises
    1.6.1 Programming Exercises
    2 Vector Algebra
    2.1 Basic Vector Characteristics
    2.1.1 Points Versus Vectors
    2.1.2 Addition
    2.1.3 Scalar Multiplication
    2.1.4 Subtraction
    2.1.5 Vector Calculations
    2.1.6 Properties
    2.1.7 Higher Dimensions
    2.2 Two Important Products
    2.2.1 Dot Product
    2.2.2 Cross Product
    2.3 Complements and Details
    2.3.1 Vector History
    2.3.2 More about Points Versus Vectors
    2.3.3 Vector Spaces and Affine Spaces
    2.4 Exercises
    2.4.1 Programming Exercises
    3 Vector Geometry
    3.1 Lines and Planes
    3.1.1 Vector Description of Lines
    3.1.2 Vector Description of Planes
    3.2 Distances
    3.2.1 Point to a Line
    3.2.2 Point to a Plane
    3.2.3 Parallel Planes and Line to a Plane
    3.2.4 Line to a Line
    3.3 Angles
    3.4 Intersections
    3.4.1 Intersecting Lines
    3.4.2 Lines Intersecting Planes
    3.4.3 Intersecting Planes
    3.5 Additional Key Applications
    3.5.1 Intersection of Line Segments
    3.5.2 Intersection of Line and Sphere
    3.5.3 Areas and Volumes
    3.5.4 Triangle Geometry
    3.5.5 Tetrahedron
    3.6 Homogeneous Coordinates
    3.6.1 Two Dimensions
    3.6.2 Three Dimensions
    3.7 Complements and Details
    3.7.1 Intersection of Three Planes Continued
    3.7.2 Homogeneous Coordinates Continued
    3.8 Exercises
    3.8.1 Programming Exercises
    4 Transformations
    4.1 Types of Transformations
    4.2 Linear Transformations
    4.2.1 Rotation in Two Dimensions
    4.2.2 Reflection in Two dimensions
    4.2.3 Scaling in Two Dimensions
    4.2.4 Matrix Properties
    4.3 Three Dimensions
    4.3.1 Rotations in Three Dimensions
    4.3.2 Reflections in Three Dimensions
    4.3.3 Scaling and Shear in Three Dimensions
    4.4 Affine Transformations
    4.4.1 Transforming Homogeneous Coordinates
    4.4.2 Perspective Transformations
    4.4.3 Transforming Normals
    4.4.4 Summary
    4.5 Complements and Details
    4.5.1 Vector Approach to Reflection in an Arbitrary Plane
    4.5.2 Vector Approach to Arbitrary Rotations
    4.6 Exercises
    4.6.1 Programming Exercises
    5 Orientation
    5.1 Cartesian Coordinate Systems
    5.2 Cameras
    5.2.1 Moving the Camera or Objects
    5.2.2 Euler Angles
    5.2.3 Quaternions
    5.2.4 Quaternion Algebra
    5.2.5 Rotations
    5.2.6 Interpolation: Slerp
    5.2.7 From Euler Angles and Quaternions to Rotation Matrices
    5.3 Other Coordinate Systems
    5.3.1 Non-orthogonal Axes
    5.3.2 Polar, Cylindrical, and Spherical Coordinates
    5.3.3 Barycentric Coordinates
    5.4 Complements and Details
    5.4.1 Historical Note: Descartes
    5.4.2 Historical Note: Hamilton
    5.4.3 Proof of Quaternion Rotation
    5.5 Exercises
    5.5.1 Programming Exercises
    6 Polygons and Polyhedra
    6.1 Triangles
    6.1.1 Barycentric Coordinates
    6.1.2 Areas and Barycentric Coordinates
    6.1.3 Interpolation
    6.1.4 Key Points in a Triangle
    6.2 Polygons
    6.2.1 Convexity
    6.2.2 Angles and Area
    6.2.3 Inside and Outside
    6.2.4 Triangulation
    6.2.5 Delaunay Triangulation
    6.3 Polyhedra
    6.3.1 Regular Polyhedra
    6.3.2 Volume of Polyhedra
    6.3.3 Euler's Formula
    6.3.4 Rotational Symmetries
    6.4 Complements and Details
    6.4.1 Generalized Barycentric Coordinates
    6.4.2 Data Structures
    6.5 Exercises
    6.5.1 Programming Exercises
    7 Curves and Surfaces
    7.1 Curve Descriptions
    7.1.1 Lagrange Interpolation
    7.1.2 Matrix Form for Curves
    7.2 Bézier Curves
    7.2.1 Properties for Two-Dimensional B\'ezier Curves
    7.2.2 Joining Bézier Curve Segments
    7.2.3 Three-Dimensional Bézier Curves
    7.2.4 Rational Bézier Curves
    7.3 B-Splines
    7.3.1 Linear Uniform B-Splines
    7.3.2 Quadratic Uniform B-Splines
    7.3.3 Cubic Uniform B-Splines
    7.3.4 B-Spline Properties
    7.4 Nurbs
    7.5 Surfaces
    7.6 Complements and Details
    7.6.1 Adding Control Points to Bézier Curves
    7.6.2 Quadratic B-Spline Blending Functions
    7.7 Exercises
    7.7.1 Programming Exercises
    8 Visibility
    8.1 Viewing
    8.2 Perspective Transformation
    8.2.1 Clipping
    8.2.2 Interpolating the z Coordinate
    8.3 Hidden Surfaces
    8.3.1 Back Face Culling
    8.3.2 Painter's Algorithm
    8.3.3 Z-Buffer
    8.4 Ray Tracing
    8.4.1 Bounding Volumes
    8.4.2 Bounding Boxes
    8.4.3 Bounding Spheres
    8.5 Complements and Details
    8.5.1 Frustum Planes
    8.5.2 Axes for Bounding Volumes
    8.6 Exercises
    8.6.1 Programming Exercises
    9 Lighting
    9.1 Color Coordinates
    9.2 Elementary Lighting Models
    9.2.1 Gouraud and Phong Shading
    9.2.2 Shadows
    9.2.3 BRDFs in Lighting Models
    9.3 Global Illumination
    9.3.1 Ray Tracing
    9.3.2 Radiosity
    9.4 Textures
    9.4.1 Mapping
    9.4.2 Resolution
    9.4.3 Procedural Textures
    9.5 Complements and Details
    9.5.1 Conversion between RGB and HSV
    9.5.2 Shadows on Arbitrary Planes
    9.5.3 Derivation of the Radiosity Equation
    9.6 Exercises
    9.6.1 Programming Exercises
    10 Other Paradigms
    10.1 Pixels
    10.1.1 Bresenham Line Algorithm
    10.1.2 Anti-Aliasing
    10.1.3 Compositing
    10.2 Noise
    10.2.1 Random Number Generation
    10.2.2 Distributions
    10.2.3 Sequences of Random Numbers
    10.2.4 Uniform and Normal Distributions
    10.2.5 Terrain Generation
    10.2.6 Noise Generation
    10.3 L-Systems
    10.3.1 Grammars
    10.3.2 Turtle Interpretation
    10.3.3 Analysis of Grammars
    10.3.4 Extending L-Systems
    10.4 Exercises
    10.4.1 Programming Exercises
    Appendix A Geometry and Trigonometry
    A.1 Triangles
    A.2 Angles
    A.3 Trigonometric Functions
    Appendix B Linear Algebra
    B.1 Systems of Linear Equations
    B.1.1 Solving the System
    B.2 Matrix Properties
    B.3 Vector Spaces
    References
    Index
    End User License Agreement
    MATHEMATICAL STRUCTURES FOR COMPUTER GRAPHICS
    MATHEMATICAL STRUCTURES FOR COMPUTER GRAPHICS STEVEN J. JANKE
    Copyright © 2015 by John Wiley & Sons, Inc. All rights reserved Published by John Wiley & Sons, Inc., Hoboken, New Jersey Published simultaneously in Canada No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, (978) 750-8400, fax (978) 750-4470, or on the web at www.copyright.com. Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, (201) 748-6011, fax (201) 748-6008, or online at http://www.wiley.com/go/permission. Limit of Liability/Disclaimer of Warranty: While the publisher and author have used their best efforts in preparing this book, they make no representations or warranties with respect to the accuracy or completeness of the contents of this book and specifically disclaim any implied warranties of merchantability or fitness for a particular purpose. No warranty may be created or extended by sales representatives or written sales materials. The advice and strategies contained herein may not be suitable for your situation. You should consult with a professional where appropriate. Neither the publisher nor author shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages. For general information on our other products and services or for technical support, please contact our Customer Care Department within the United States at (800) 762-2974, outside the United States at (317) 572-3993 or fax (317) 572-4002. Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be available in electronic formats. For more information about Wiley products, visit our web site at www.wiley.com. Library of Congress Cataloging-in-Publication Data: Janke, Steven J., 1947- author. Mathematical structures for computer graphics / Steven J. Janke, Department of Mathematics, Colorado College, Colorado Spring, CO. pages cm Includes bibliographical references and index. ISBN 978-1-118-71219-1 (paperback) 1. Computer graphics–Mathematics. 2. Three-dimensional imaging–Mathematics. I. Title. T385.J355 2014 006.601′51–dc23 2014017641 Printed in the United States of America 10 9 8 7 6 5 4 3 2 1
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