Circle approximation for CADCAM using orthogonal C2 cubic B-splines

A method to approximate a circular arc of any subtended angle with orthogonal C2 cubic B-splines is presented. The approach is to specify end points and end tangent directions and to give extra points lying on the span to ensure the required level of accuracy. The critical elements are to use a parameterisation that is optimum for circular data and to determine the tangent magnitudes at the end points. The data can be sampled in any way, although evenly spaced data requires less points to achieve a given accuracy. The method is general and does not depend on any iterative schemes to determine the parameterisation, knot values or tangent magnitudes.