A reduced machining time and increased accuracy for the sculptured surface are very important when producing complicated parts. The step-size and tool-path interval are essential components in high speed and high resolution machining. If they are small, the machining time will increase, whereas if they are large, rough surfaces will be caused. In particular, the machining time, which is key in high speed machining, is affected by the tool-path interval more than the step-size. The conventional method for calculating the tool=path interval is to select a small parametric increment of a small increment based on the curvature of the surface. However, this approach also has limitations. The first is that the tool-path interval can not be calculated precisely. The second is that a separate tool-path interval needs to be calculated in each of the three cases. The third is that the conversion from Cartesian domain to parametric domain or vice versa must be necessary. Accordingly, the current study proposes a new tool-path interval algorithm that do not involve a curvature and that is not necessary for any conversion and a variable step-size algorithm for NURBS.