Calculating methods for compound curve and oval curve;

Based on the property of easement curve, the authors proposed the calculation formulas of middle length of easement for oval curve and the formulas of any station coordinates.

The calculation of part easement curve is introduced after a detailed discussion on the calculation of geometric elements and station coordinates for oval curve in this paper; An attached flowchart is also supplied for reference.

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.

Numeric and curve parameters for freeform surface feature models