Bernstein Polynomial and B´ezier-Bernstein Spline - Bezier and Splines in Image Processing and Machine Vision - page 18

Fig. 1.5. Position of key pixel when K 1 = K 2 = C .

K j K K j

j j j

L

Q

(a) (b) (c)

K j+1 K j+1 K j+1

Fig. 1.6. Types of GE: (a) Arc with inflection point; (b) arc; (c) straight line.

(2) when K 1 = K 2 = C , the key pixels will have at least one corner
connection to its neighboring pixels. Similar arguments hold when the key
pixel lies on a vertical line.
Let ANB be the arc, with A and B being two successive key pixels as
shown in Figure 1.8. A pixel on the arc can go outside the line AC or BC if
and only if a sequence of collinear pixels exists such that its end pixels are
either corner connected or direct connected or a combination thereof, or a
pixel exists that has at least one corner connection with its neighboring pixel.