2 Terminology and jargon

This chapter covers

The similarities and the differences between numbers, vectors, and points
The informal terminology of triangles and functions
Generalizations of lines, planes, and curves
A list of function types you will often meet in practice
And the shortest possible introduction to matrix algebra

Every profession has its own language. A family of terms and concepts bound together by a web of non-trivial relations. Applied geometry has its own language too, it consists of rigid definitions coming from mathematics, and more flexible jargonisms coined up to simplify communications. For an outsider, however, both mathematician and a programmer, this combination of formal and intuitive naming creates a barrier.

This chapter gives an introduction to the basic language of applied geometry. It covers a lot of new words but don’t worry, at this point, you don’t need to develop a deep understanding of every one of them. This level of understanding comes from practice, and we will have plenty of that in the following chapters.

By the end of the chapter, you will become comfortable with terms like “near-degenerate triangle”, “non-manifold mesh”, or “continuous transformation of the standard cube”. This familiarity should not only help you go further through the book, but effectively seek more knowledge in libraries’ documentation, code comments, or online communities.

2.1 Numbers, points, and vectors

2.1.1 Numbers

2.1.2 Points

2.1.3 Vectors

2.1.4 Summary

2.2 Vertices and triangles

2.2.1 Being pedantic with triangles

2.2.2 Triangle quality

2.2.3 Summary

2.3 Lines, planes, and their equations

2.3.1 Lines and planes

2.3.2 The parametric equation for a 3D line

2.3.3 Summary

2.4 Functions and geometric transformations

2.4.1 What is a function?

2.4.2 Function types most commonly used in applied geometry

2.4.3 Summary

2.5 Curves, surfaces, and solid bodies

2.5.1 Standard cubes and manifolds

2.5.2 A parametric curve