3d computer graphics - a mathematical introduction with opengl

[...]... academic mathematician and by my participation in various applied computer projects, including projects in computer games and virtual reality This book was started while I was teaching a mathematics class at the University of California, San Diego (UCSD), on computer graphics and geometry That course was structured as an introduction to programming 3-D graphics in OpenGL and to the mathematical foundations... mathematics This is, however, the case Furthermore, the mathematics tends to be elegant and interdisciplinary The mathematics needed in computer graphics brings together constructions and methods from several areas, including geometry, calculus, linear algebra, numerical analysis, abstract algebra, data structures, and algorithms In fact, computer graphics is arguably the best example of a practical... images In pixel-based systems, the screen image will be stored as a bitmap, namely, as a table containing all the pixel colors A vector graphics system, on the other hand, will store the image as a list of commands – for instance as a list of pen up, pen down, and move commands Such a list of commands is called a display list Nowadays, pixel-based graphics hardware is very prevalent, and thus even graphics. .. even graphics systems that are logically vector based are typically displayed on hardware that is pixel based The disadvantage is that pixel-based hardware cannot directly draw arbitrary lines and must approximate lines with pixels On the other hand, the advantage is that more sophisticated figures, such as filled regions, can be drawn Modern vector graphics systems incorporate more than just lines and... graphics devices is vector graphics display terminals, which traditionally are monochrome monitors that can draw arbitrary lines On these vector graphics display terminals, the screen is a large expanse of phosphor and does not have pixels A traditional oscilloscope is also an example of a vector graphics display device Vector graphics displays and pixel-based displays use very different representations... iterative methods Chapter XII Animation and Kinematics Discusses key framing, ease in and ease out, representations of orientation, quaternions, interpolating quaternions, and forward and inverse kinematics for articulated rigid multibodies Appendix A Mathematics Background Reviews topics from vectors, matrices, linear algebra, and calculus Appendix B RayTrace Software Package Describes a ray tracing... Foley et al (1990) Another excellent recent book is M¨ ller and Haines (1999) The articles by Blinn (1996; 1998) and Glassner o (1999) are also interesting Finally, an enormous amount of information about computer graphics theory and practice is available on the Internet There you can find examples of OpenGL programs and information about graphics hardware as well as theoretical and mathematical developments... the mathematical concepts discussed in this book A ray tracer software package is also described; this software can also be downloaded from the Internet On the theoretical side, this book stresses the mathematical foundations of computer graphics, more so than any other text of which I am aware I strongly believe that knowing the mathematical foundations of computer graphics is important for being able... positioned at locations in either 2-space (R2 ) or 3-space (R3 ) and to have OpenGL automatically map the points into the proper location in the graphics image In the two-dimensional x y-plane, also called R2 , a position is set by specifying its x- and y-coordinates The usual convention (see Figure I.3) is that the x-axis is horizontal and pointing to the right and the y-axis is vertical and pointing upwards... customary expectations For example, in calculus, the x-, Team LRN I.2 Coordinates, Points, Lines, and Polygons 5 y a, b b a x Figure I.3 The x y-plane, R2 , and the point a, b y-, and z-axes usually point forward, rightwards, and upwards (respectively) The computer graphics convention was adopted presumably because it keeps the x- and y-axes in the same position as for the x y-plane, but it has the disadvantage . experience in programming and game development and has acted as consultant for SAIC and Angel Studios. Team LRN Team LRN 3-D Computer Graphics A Mathematical Introduction with OpenGL SAMUEL R. BUSS University. foundations of computer graphics along with a practical introduction to programming using OpenGL. I believe that understanding the mathematical basis is important for any advanced use of computer graphics. . matrices, linear al- gebra, and calculus. Appendix B. RayTrace Software Package. Describes a ray tracing software package. The software is freely downloadable. Team LRN xiv Preface Exercises are