Chaikin’s Algorithms for Curves (1974)
In 1974, George Chaikin introduced one of the first algorithms for
refinement (cut-corners). In contrast to his predecessors, Chaikin
developed an algorithm that worked directly on control polygons.
His new algorithm generated a new control polygon by cutting the
corner.
44
Chapter 3 – Polygon Subdivision
Figure 3-1: Two extraordinary vertices with valences of 6 and 3.
Figure 3-2: The initial, unrefined polygonal line with five P points: P
0
,P
1
,P
2
,
P
3
, and P
4
.
45
Chapter 3 – Polygon Subdivision
Figure 3-3: Refinement step 1. Chaikin’s method generates Q and R points,
while cutting the corners add refinement to the line.
Figure 3-4: Refinement step 2.
Figure 3-5: Refinement step 3. When increasing the refinements, the curve
gets smoother.
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