Abstract: By using the specified method and constraint criteria for local interpolation, and the idea of transferring from part to whole in order to solve the problem efficiently, the general framework of the accumulated average arc length parameterization method was given, and three concrete accumulation average arc length parameterization methods and corresponding numerical algorithms were given under the framework. The objective of the accumulated average arc length parameterization method was to reduce the objective function value of the curve with respect to the smoothness obtained by the traditional method, and make the method have the flexibility to generate the curve satisfying the conditions according to designer’s requirements. Examples show that under the same constraint criterion, the objective function values of global interpolation curves obtained by the method can be less than that corresponding to chord length parameterization and centripetal parameterization.

Key words: parameterization method, local interpolation, constraint criterion, spline