Curved Surface Design using Parametric B-Splines

The shape of a machine part will represent its functionality.  Lots of high precision mechanical parts, such as gears, cams, wings, blades, and car bodies, their performance are constrained by their geometrical shapes. With the fast progress of information, control, and computer science, the shape design and manufacturing problem had become how to transform a machine part’s surface data and design requirements into a computerized mathematical surface model. Which can be used in machining, testing, and product managing in a fast and precise way to reveal the part’s geometrical shape.  This research is aimed at a non-rectangular data points with the concept of coordinate mapping method.  We have proposed a rational B-Spline tensor product surface interpolation method on a non-rectangular data points successfully.  This method will overcome the problem involved in the traditional tensor product method that needed to constrain the surface interpolation data points into a rectangular grid.  Moreover, the rational B-Splines’ knot sequence can be changed freely, it represent this method have more flexibility and will not be effected by its surface interpolation method.

        The rational B-Spline tensor product interpolation method is a complete, uniform surface mathematical model to calculate the surface, which can precisely calculate it’s geometrical representation such as surface’s tangent, normal and curvature. Thus, we can use it to calculate the tool path and the tool size for machining and manufacturing data fast and precisely.