An Algebraic Method to Determine If a Point is on a Spline

This study is concerned with a parametrically defined spline and a point in space. If the point is on the spline, a determination is also made of the bay of the spline where the point lies and the parametric value in the bay that corresponds to the point. The splines are cubic and are represented in the normalized Hermite form. Splines in other forms can be converted into this form. Because the method of solution is algebraic in nature, it should be much faster than existing analytic-iterative-recursive techniques.