By using reparameterization with a quadratic transformation on the parametric domain,an approximate arc-length parameterization method and the corresponding algorithm are presented for Bézier curves.

A new quantitative measure of "closeness" to arc-length parameterization is presented and according to this measure, the problem of identifying the optimum rational reparameterization of a degree n polynomial curve is shown.

When a nearly arc-length parameterization[1] for a Bézier curve has been obtained,the parameterization could only acquire C0-continuity.

Based on arc-length parametrical curves,we discussed the geometrical properties for planar regular local convex curves,proved that the planar local convex curves locates on the right semi-closed(left semi-closed)plane of tangent line at arbitrary point on the curve,and derived a few important properties at any point on the curve.

This paper involves arc length parameterization for parameer curves.

About the Calculation of Arc length of the Oriented Smoth Curve or Jordan;

The experimental results show that the optimum melting voltage is 35～36 V,the reasonable arc length is 25～29 mm.

A easy and feasible method to precisely measuring arc length on part's convexity is introduced in this paper.

Self-adaptation control technology of arc length for all-position TIG tube welding machine;