From the edge-parameter curve caused by the edge factor and the uniform linear motion parameter,the displacement parameter can be recognized accurately.

This article researches on how to make the curve edge translated into a straight line,introduces the measure formula between the pixel point and the space point,describes image processing ideas,and proved that this method can get better results by experiment.

The method acquires the axis of rotated object,and combines the two brim curves and characteristic points of the rotated object to realize the 3D reconstruction of rotated surface.

Note on geometric transformation of parameter curve;

A pixel-by-pixel generating algorithm for polynomial parameter curves of degree 4 is presented.

C~1 surface interpolation restricted to smooth parametric curve;

In response to new challenges and difficulties in multi-axis CNC machining, the angular interpolation for parametric curves is proposed and the general principle is outlined.

A new real time interpolation algorithm for complex parametric curve, including high order polynomial curve, Bezier curve, B spline curve, NURBS curve, etc, was developed, which is based on Gauss Legendre quadrature and polynomial interpolation.

A Sectional Step-length Algorithm for Rasterizing Parametric Curves;

The paper develops general interpolation principals for parametric curves with constant feedrate, and contour error's approximate evaluations are discussed also.

The expansion in U-series has advantageous properties for approximations in both quadratic norm and uniform,and it can be realized to exactly express a group of parametric curves and surfaces which are piecewise k-degree polynomials with limited number of terms of U-system.