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Given the graph of a function f(x) on an interval x = [a, b], what is the best fitting Bezier curve which matches the function? To answer this question, I provide six constraints:

• The coordinates at the end points must match (four constraints), and
• The derivatives at the end points must also match (another two constraints).

These, together with the minimization of the root mean squared error of the Bezier curve with the function itself provide excellent approximations of many functions.

The Maple worksheet which demonstrates this is BestFittingBezierCurves.mws and a power point presentation of the relevant information is provided here, too: BestFittingBezierCurves.ppt.

Figure 1 shows the implementation of these Bezier functions in the product CorelDRAW. The CorelDRAW cdr file may be downloaded here: BestFittingBezierCurves.cdr.

Figure 1. The application of the vectors found in the presentation for the best fitting Bezier curves.

For any questions, please contact me at dwharder@alumni.uwaterloo.ca.