Abstract: Demarcation points from a curve with least number of segments (lines and arcs) are extracted, and each of them can be fitted into a line or arc with least error. Chromosomes are encoded into binary strings. Mutation probabilities and crossover probabilities are calculated adaptively. The gaps between demarcation points are restricted. Points of a curve corresponding to genes of a chromosome which are 1s, are demarcation ones. The algorithm can deal with many cases including a line is intersecting or tangent to an arc, an arc is tangent to an arc, and some points are noisy ones, and can detect cusp and tangent points. The method can represent well a curve with lines and arcs, the algorithm is effective and robust.