Geometry for Programmers

Master the math behind CAD, game engines, GIS, and more! This hands-on book teaches you the geometry used to create simulations, 3D prints, and other models of the physical world.

In Geometry for Programmers you will learn how to:

• Speak the language of applied geometry
• Compose geometric transformations economically
• Craft custom splines for efficient curves and surface generation
• Pick and implement the right geometric transformations
• Confidently use important algorithms that operate on triangle meshes, distance functions, and voxels

Geometry for Programmers guides you through the math behind graphics and modeling tools. It’s full of practical examples and clear explanations that make sense even if you don’t have a background in advanced math. You’ll learn how basic geometry can help you avoid code layering and repetition, and even how to drive down cloud hosting costs with more efficient runtimes. Cheerful language, charts, illustrations, equations, and Python code help make geometry instantly relevant to your daily work as a developer.

About the Technology

Geometry is at the heart of game engines, robotics, computer-aided design, GIS, and image processing. This book draws back what is for some a mathematical curtain, giving them insight and control over this central tool. You’ll quickly see how a little geometry can help you design realistic simulations, translate the physical world into code, and even reduce your cloud services bill by improving the efficiency of graphics-intensive applications.

About the Book

Geometry for Programmers is both practical and entertaining. Fun illustrations and engaging examples show you how to apply geometry to real programming problems, like changing a scan into a CAD model or developing 3D printing contours from a parametric function. And don’t worry if you aren’t a math expert. There’s no heavy theory, and you’ll learn how to offload most equations to the SymPy computer algebra system.

What’s Inside

• Speak the language of applied geometry
• Compose geometric transformations economically
• Craft custom splines for efficient curves and surface generation
• Confidently use geometry algorithms

About the Reader

Examples are in Python, and all you need is high school–level math.

About the Author

Oleksandr Kaleniuk is the creator of Words and Buttons Online, a collection of interactive tutorials on math and programming.

Table of Contents

1 Getting started

2 Terminology and jargon

3 The geometry of linear equations

4 Projective geometric transformations

5 The geometry of calculus

6 Polynomial approximation and interpolation

7 Splines

8 Nonlinear transformations and surfaces

9 The geometry of vector algebra

10 Modeling shapes with signed distance functions and surrogates

11 Modeling surfaces with boundary representations and triangle meshes

12 Modeling bodies with images and voxels

Review

“A one-of-a-kind book covering the practical applications of geometry in programming.”

—Maxim Volgin, KLM

“Have you ever wondered how game programmers, animators, and car manufacturers model visual reality? This book not only shows you how, it teaches you to understand and enhance the apps they use.”

—Ranjit Sahai, RAM Consulting

“An insightful tour of geometry using the powerful tool SymPy. You can get behind the scenes and apply these techniques to CAD and much more.”

—James J. Byleckie, BH Enterprises

“Approaches software development from a new angle!”

—Chris Kardell, DEBS

About the Author

Oleksandr Kaleniuk is the creator of Words and Buttons Online, a collection of interactive tutorials on math and programming. He works for Materialise as a senior software engineer specializing in geometric algorithms.