Method and system for spline interpolation, and their use in CNC

A method for controlling the movement of a cutting tool on a numerically-controlled device, running on a digital computer controlling said cutting tool, said method comprising:

• inputting to said digital computer:
• a plurality of codes defining a NURBS curve through which said cutter head will travel, said codes comprising:
• codes to specify an initial position of said cutting tool,
• codes to specify the order of said NURBS curve, codes to specify the number of control points in the control polygon of said NURBS curve,
• codes to specify the knot vector of said NURBS curve,
• and codes to define other positions defining said control polygon of said NURBS curve through which said cutting tool will travel;
• and a code specifying a desired feed rate;
• determining a curve length distance from said codes defining said NURBS curve through which said cutting tool will travel;
• determining an initial curve length step size from said desired feed rate and a value which represents the amount of time required to compute one step;
• determining a parametric step size with a node-based approximation of the derivative at said initial position on said NURBS curve through which said cutting tool will travel;
• determining distance traveled in step to be the euclidean distance traveled during said parametric step size;
• determining curve length difference to be the difference between said initial curve length step size and said distance traveled in step;
• modifying said parametric step sized based on an error measure of said curve length difference;
• computing a distance left for said cutting tool to travel for said cutting tool;
• determining an output position by evaluation of the parametric equations defined by said order, knot vector, and control points for said NURBS curve where a next parameter t is the sum of the current value of t and said parametric step size;
• and moving said cutting tool in accordance with said output positions.