The curve discretization is one of the fundamental issues in triangulation of planar region and the parameter domain of curved surface. In this paper

the conception of the curve's local feature point is presented. A fast algorithm for the acquisition of the curve's local feature point is proposed

according to the theory of parallel. Through optimizing the local feature point

the needless local feature point is omitted

and the feature point set requisite is obtained. Accordingly the curve discretization is realized

making use of the curve's local feature point. In the course of curve discretization

the quality influence of the succeeding triangulation

resulted by the tolerance of the discretization precision and the length of the approximation polygon edge

is fully considered in this method. If the approximation precision is high

the curve surface crack can be avoided. If the edge of the approximation polygon is too short

too dense triangle mesh will be created

which will result in long computation time and more memory space

or the long and narrow triangle mesh will be produced

which will make the quality of triangle mesh worse. Experiments indicate that the polygon consisting of the feature points can perfectly approximate the curve

and the algorithm is highly efficient.