Curve subdivision splits a Bézier curve into smaller connected sections until each section is nearly flat enough to treat as a straight line. Computers can then draw those short lines instead of drawing the curve directly. section 2.2 section 2.5
De Casteljau’s paper-friendly procedure works like this:
- Mark halfway points on the lines joining the endpoints to the control points, and between the control points. section 2.2
- Find further halfway points between those new points; the final halfway point becomes the shared endpoint of two smaller curves. section 2.2
- Repeat the subdivision on the smaller curves until their sections are flat enough to replace with straight lines. section 2.2
The A–D curve
For a curve with endpoints A and D and control points B and C, midpoint construction produces points E, F, G, H, I, and J. The midpoint J divides the original curve into two connected curves, AEHJ and JIFD. section 2.2
Figure 2.8 De Casteljau curve subdivision
A figure makes the nested midpoint construction and the two resulting curves easier to follow. section 2.2
