Curves in 3D - 3D Math Primer for Graphics and Game Development - page 696

Figure 13.20
Creating Figure 13.19 with Adobe Photoshop .

at the “handle” used to control the shape of the curve, which is essentially
the same as the Bezier control point. (Photoshop calls the knots the “an-
chor points” and refers to the interior Bezier control points that are not
interpolated as “control points.”)
For example, Figure 13.20 is a screen capture taken while one author
was hard at work creating Figure 13.19. (The opacity of the actual figure
has been decreased to make it easier to see the Photoshop controls.)
While we're on the subject of Bezier curves, let's take this opportunity
to introduce the notation we use for Bezier splines. When we were dealing
with only a single Bezier segment, we referred to the ith control point on
that segment as b i . Here we use the notation f i to refer to the control point
“in front” of the ith knot, and a i for the control point “after” it. 18

This

notation is illustrated in Figure 13.21.
The important relationship between Hermite and Bezier forms was in-
troduced in Section 13.4.3. Let's restate it here in the newly-introduced

18 Note that by using knot-centric notation and assigning different letters to the control
points (based on handy mnemonic memory aids!), we are locking in the degree of the
segments to cubic. In other sources you'll find notation such as b i to refer to the ith
point on segment j, or just refer to all the points on the polygon as b i , where the knots
are b 0 , b 3 , b 7 . This notation has the advantage of being more general, but to read it
requires more mental effort—something we definitely want to minimize.