Appendix A. Quick Reference Guide to 3D User Interface Mathematics

In this appendix, we provide a quick reference guide to working with scalars, vectors, points, matrices, and quaternions, which are important mathematical tools used in 3D UIs and 3D interaction techniques. It is not our intention to provide mathematical rigor in discussing these concepts but merely to provide practical descriptions and a common notation style to be used throughout the book. See the recommended reading list at the end of this appendix for more information.

We use the following notational conventions:

• Non-boldface letters (except for p and q) and lowercase Greek letters refer to scalars

• Example: the scalar λ, the distance D

• Lowercase boldface type refers ...

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