Affine space consists set points and vector space

66 Chapter 2 Vectors and Points

Figure 2.26 Alternate 3D Cartesian coordinate system.

into the y-axis. As with left-handed bases, we can have left-handed coordinate systems (and will be using them later in this book), but the majority of our work will be done in a right-handed coordinate system because of convention.

Q = P + v (2.7)

or, expanding our vector using n basis vectors that span V:

P = O + a0v0 + a1v1 + · · · + an−1vn−1 (2.8)

Q

v