Python Programming in OpenGL A Graphical Approach to Programming Stan Blank, Ph.D. Wayne City High School Wayne City, Illinois 62895 October 6, 2009 Copyright 2009 2 Table of Contents Chapter 1 Introduction......................................................................................6 Chapter 2 Needs, Expectations, and Justifications ..........................................8 Section 2.1 What preparation do you need? ...............................................8 Section 2.2 What hardware and software do you need?.............................8 Section 2.3 My Expectations.......................................................................9 Section 2.4 Your Expectations ....................................................................9 Section 2.5 Justifications...........................................................................10 Section 2.6 Python Installation..................................................................11 Exercises .....................................................................................................12 Chapter 3 Your First Python Program ............................................................13 Section 3.1 Super-3 Numbers...................................................................13 Section 3.2 Conclusion .............................................................................21 Exercises .....................................................................................................21 Chapter 4 Your First OpenGL Program..........................................................23 Section 4.1 The Interactive Python Interpreter..........................................23 Section 4.2 Introducing Python OpenGL...................................................24 Section 4.3 Odds, Ends, and Terminology................................................29 Section 4.4 Conclusion .............................................................................31 Exercises .....................................................................................................31 Chapter 5 2 Dimensional Graphics ................................................................33 Section 5.1 Plotting Points ........................................................................33 Exercises .....................................................................................................37 Section 5.2 Plotting 2D Functions .............................................................41 Exercises .....................................................................................................44 Sections 5.3 Parametric Equations .............................................................50 Exercises .....................................................................................................53 Section 5.4 An Example from Physics ......................................................65 Exercises .....................................................................................................74 Section 5.5 Polar Coordinates...................................................................80 Section 5.6 Conclusion .............................................................................89 Exercises .....................................................................................................90 Figures for Exercises 2-15...........................................................................95 Chapter 6 Patterns and Chaos in 2 Dimensions ............................................99 Section 6.1 PySkel ....................................................................................99 Section 6.2 Some Interesting Patterns....................................................101 Exercises ...................................................................................................106 Figures for exercises 7, 8, 9, and 10..........................................................111 Section 6.3 The Chaos Game.................................................................112 Exercises ...................................................................................................124 Section 6.4 The Barnsley Fern...............................................................129 Exercises ...................................................................................................133 Section 6.5 Chaos and the Logistic Map................................................136 Exercises ...................................................................................................143 Section 6.6 Predator-prey Relationships.................................................148 Exercises ...................................................................................................152 3 Chapter 7 Strange Attractors and Beautiful Fractals ....................................154 Section 7.1 Lorenz and the Weather.......................................................154 Exercises ...................................................................................................162 Section 7.2 Phase Portraits and Paint Swirls ..........................................167 Exercises ...................................................................................................170 Section 7.3 Mira (Look?) .........................................................................172 Exercises ...................................................................................................174 Section 7.4 The 3-Body Problem ............................................................175 Exercises ...................................................................................................178 Section 7.5 Newton’s Method and the Complex Plane ...........................183 Exercises ...................................................................................................193 Addendum: ................................................................................................203 Addendum II: .............................................................................................203 Section 7.6 The Julia Set .......................................................................205 Exercises ...................................................................................................211 Section 7.7 Explorations with the Mandelbrot Set ...................................222 Exercises ...................................................................................................240 Chapter 8 2D Animation...............................................................................246 Section 8.1 Follow the Bouncing Ball ......................................................246 Exercises ...................................................................................................255 Section 8.2 A Little Gravity!.....................................................................261 Exercises ...................................................................................................264 Section 8.3 A Little MORE Gravity... a 2-Body Simulation ......................265 Exercises ...................................................................................................279 Section 8.4 The REAL 3 Body Problem ..................................................281 Exercises ...................................................................................................291 Section 8.5 From 3Body to NBody Using Arrays.....................................294 Exercises ...................................................................................................307 Section 8.6 Navigating the Stars............................................................309 Exercises ...................................................................................................320 Chapter 9 3D and 3D Animation .................................................................322 Section 9.1 Rotating Objects in Space...................................................322 Exercises ...................................................................................................330 Section 9.2 Real Time Interactive Computer Animator (RTICA) ............336 The German Bell........................................................................................345 Exercises ...................................................................................................350 illiTorus ......................................................................................................353 Exercises ...................................................................................................359 Chapter 10 Animation and Display Lists .......................................................370 Electron Orbitals ........................................................................................370 The Quaternion Julia Set ...........................................................................375 Alternate Quaternion Julia Set and Mandelbrot Set...................................381 Chapter 11 Miscellaneous Programs ............................................................388 The Random Walk .....................................................................................388 The 3D Sierpinski Sponge .........................................................................391 Rendering Teapots ....................................................................................393 4 A Midpoint Conjecture ...............................................................................397