| Rendering a Bézier curve segment usually involves approximating the curve by a polyline. A well-known technique called recursive subdivision generates such an approximating polyline by subdividing the Bézier curve segment into two subsegments. Each subsegment is recursively subdivided until the maximum deviation of the subsegment from its chord is less than a predefined constant, the flatness. This ultimate subsegment can then be replaced by its chord. However, in this technique, subdividing curves slightly above the flatness threshold yields two subsegments whose maximum deviation may be much less than the flatness. The average deviation of all resultant subcurves will generally be less than the required flatness, implying that a greater number of approximating line segments than necessary will be generated. In the current research, the Bézier curve is subdivided in such a way that all ultimate subsegments are as long as possible, thus generating fewer polyline components. We have devised approximations and/or heuristics to ensure that the calculation overhead is acceptable. |
