2 Terminology and jargon

Every profession has its own language, a family of terms and concepts bound together by a web of relations. Applied geometry has its own language, too; it consists of rigid definitions from mathematics and more flexible jargon coined to simplify communications. For an outsider, however—even a mathematician or programmer—this combination of formal and intuitive naming creates a barrier.

This chapter gives you 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’ll have plenty of that in the following chapters.

By the end of the chapter, you’ll be comfortable with terms such as near-degenerate triangle, nonmanifold mesh, and continuous deformation field. This familiarity should help you not only go farther through this book, but also 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 Vectors

2.1.3 Section 2.1 summary

2.2 Vertices and triangles

2.2.1 Being pedantic about triangles

2.2.2 Triangle quality

2.2.3 Section 2.2 summary

2.3 Lines, planes, and their equations

2.3.1 Lines and planes

2.3.2 The parametric form for 3D lines

2.3.3 Section 2.3 summary

2.4 Functions and geometric transformations