Abstract: Implicit curves play an important role in medical image processing, geographic information
system, and numerical field visualization. On the basis of sampling point analysis and curve
approximation method, we introduce an algorithm for approximating planar implicit curves by means
of Hermite interpolation. The sampling points were firstly obtained by linearly interpolating each
edge of the grid cells distributed uniformly in the grid region. Then, we calculated the error between
curve segments before and after optimizing. Once the error meets the optimizing requirements, the
sampling points are consequently optimized. Finally, the algorithm approximated the implicit curves
by the Hermite interpolation method. Experiments have shown that even when the number of
sampling points is small, the curves drawn by the algorithm still have relatively higher smoothness
and accuracy.

Key words: graph plotting, implicit curve, Hermite interpolation, optimizing sampling point