Moisés Cywiak and David Cywiak

Multi-Platform Graphics Programming with Kivy

Basic Analytical Programming for 2D, 3D, and Stereoscopic Design

1st ed.
Moisés Cywiak
Leon, Guanajuato, Mexico
David Cywiak
Queretaro, Mexico
ISBN 978-1-4842-7112-4e-ISBN 978-1-4842-7113-1
https://doi.org/10.1007/978-1-4842-7113-1
© Moisés Cywiak, David Cywiak 2021
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Acknowledgments

We would like to thank Natalie Pao, Jessica Vakili, Ahmed Gad, and James Markhan for providing valuable comments and suggestions during the review of this book.

Table of Contents
Chapter 1:​ Getting Started:​ Software installation 1
1.​1 Installing pip3 and IDLE 1
1.​2 Installing Kivy 2
1.​3 Installing Buildozer 3
1.​4 Summary 5
Chapter 2:​ Two-Dimensional Mapping and Rotation Equations of a Point 7
2.​1 Rotation Equations 7
2.​2 Mapping Spatial Two-Dimensional Points to the Screen 9
2.​3 Summary 12
Chapter 3:​ Two-Dimensional Polygon Programming 13
3.​1 Polygon Structure 15
3.​2 Drawing the Edges of the Polygon 18
3.​3 Filling the Polygon with Lines 19
3.​4 Rotating the Polygon 24
3.​5 Using the Kivy Platform 25
3.​6 Using Buildozer 35
3.​7 Summary 38
Chapter 4:​ Three-Dimensional Projections and Rotations 39
4.​1 Projecting a Three-Dimensional Point Onto a Plane 39
4.​2 Rotating a Point on a Plane 43
4.​3 Summary 46
Chapter 5:​ Programming Three-Dimensional Polygons 47
5.​1 Polygon Structure 49
5.​2 Basic Functions 50
5.​3 Summary 71
Chapter 6:​ Stereoscopic 3D Programming 73
6.​1 Basics of a Stereoscopic Scene 73
6.​2 Programming and ORing the Images 75
6.​3 Projections 76
6.​4 Polygon Structure 81
6.​5 DrawAxes Function 86
6.​6 Points of Projection 87
6.​7 Summary 106
Chapter 7:​ 3D Plots Programming 107
7.​1 Programming the Basic Operations 108
7.​2 Function Overview 109
7.​3 Generating the Axes, the Mesh, and the Function 109
7.​4 Plotting the Function on the Screen 111
7.​5 Rotating the Plot 114
7.​6 Summary 124
Chapter 8:​ Stereoscopic 3D Plots 125
8.​1 Creating the Function, Coordinates, and Mesh 126
8.​2 Creating Two Images for the Stereoscopic Effect 127
8.​3 Drawing the Plot 129
8.​4 Surfaces with Saddle Points 141
8.​5 Summary 143
Chapter 9:​ Parametric 3D Plotting 145
9.​1 Parametric Equations 146
9.​2 Plotting 147
9.​3 Summary 155
Chapter 10:​ Stereoscopic parametric 3D Plots 157
10.​1 Generating the Function 158
10.​2 Creating the PIL Images for the Stereoscopic Effect 159
10.​3 Plotting the Function 160
10.​4 Summary 172
Chapter 11:​ SymPy 173
11.​1 Analytical Expressions and Symbols 174
11.​2 Declaring Functions with Analytical Expressions 177
11.​3 Solving Equations 179
11.​4 Solving Simultaneous Equations 184
11.​5 Symbolic Differentiation 185
11.​6 Integration 187
11.​7 Incorporating SymPy Into Android Projects 189
11.​8 Summary 190
Chapter 12:​ Plotting Functions in Spherical Coordinates 191
12.​1 Overview of Spherical Coordinates 192
12.​2 Spherical Differential Equation Working Example 194
12.​3 The Associated Legendre Polynomials 196
12.​4 Plotting Functions in Spherical Coordinates 200
12.​5 Summary 212
Chapter 13:​ Stereoscopic Plots in Spherical Coordinates 213
13.​1 Creating the Stereoscopic Scenes 214
13.​2 Summary 229
Chapter 14:​ Stereoscopic Simple Numerical Method for Gravitational N-body 231
14.​1 The Gravitational N-body Problem 233
14.​2 Motion Equations 235
14.​3 Numerical Solution to the Dynamic Equations 236
14.​4 Capturing Numerical Data 238
14.​5 Five Planets Working Example 241
14.​6 Summary 256
Chapter 15:​ Stereoscopic Cylindrical Coordinates Plotting 257
15.​1 Ideal Lens Focusing:​ The Fresnel Diffraction Integral 259
15.​2 Departure from the Ideal Lens 262
15.​3 The Wave Aberration Function in Cylindrical Coordinates 263
15.​4 Stereoscopic Plot of Wave Aberration Terms in Cylindrical Coordinates 265
15.​5 Summary 278
Chapter 16:​ Stereoscopic Plotting of Three-Dimensional Conics 279
16.​1 Analytical Approach 280
16.​2 Stereoscopic Ellipsoid Plotting 283
16.​3 Hyperboloid 297
16.​4 Summary 311
Chapter 17:​ Two-Dimensional Fourier Transform 313
17.​1 One-Dimensional Fourier Transform 315
17.​2 The Rectangular and Sinc Functions 317
17.​3 Code for Calculating the Discrete One-Dimensional Fourier Transform 319
17.​4 Two-Dimensional Fourier Transform 323
17.​5 Discrete Two-Dimensional Fourier Transform 324
17.​6 The Fourier Transform of the Circular Function 341
17.​7 Fourier Transform of the Circular Function 342
17.​8 Summary 346
Chapter 18:​ Stereoscopic Two-Dimensional Fourier Transform 347
18.​1 Plotting the Functions 348
18.​2 Summary 363
Index 365
About the Authors
Moisés Cywiak

is a researcher in physical optical sciences. He has over 20 years of teaching experience in physics, mathematics, electronic engineering, and programming in C, C++, and Python at the Centro de Investigaciones en Óptica A.C.

 
David Cywiak

received his PhD in Physics in 2014 from the Universidad de Guanajuato. From 2012 to 2013, he collaborated as a guest researcher at the Dalton Cardiovascular Research Center, University of Missouri-Columbia, in the development of an optical-photoacoustic system intended for the detection of photoacoustic signals generated by cancerous cells. Since 2014, he has been working as a metrologist in the Thermometry Department at the Centro Nacional de Metrologia, México. His research includes photoacoustics, optical engineering, and radiation thermometry. He has over seven years of experience teaching physics, mathematics, and programming in C to undergraduate students. He also has over five years of experience teaching temperature measurement techniques and calibration of instruments in the thermometry area to industry professionals.

 
About the Technical Reviewer
Ahmed Gad

is a machine learning engineer pursuing his Phd in computer engineering at the University of Ottawa. He works with companies like Paperspace and NeptuneAI on machine learning projects and their documentation. Ahmed created PyGAD, a Python open-source library for building the genetic algorithm and has a history of four books in the field.

 
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