B-spline surface local updating with unorganized points

Abstract

This paper presents an approach to update a local area of a B-spline surface based on a set of locally distributed and unorganized points in three-dimensional space. The region of the original surface to be updated is first identified. The control points affecting these regions are further extracted or registered. The original B-spline surface is then updated by modifying part or all of the registered control points through a local fitting process. Surface local updating can be done either with or without affecting the neighboring patches of the region being updated. Depending on the number of patches involved in a region to be updated and whether the neighboring patches of a region are allowed for alteration, additional knots may need to be inserted in the corresponding patches before surface local updating. If the shape of a region is likely to become more complex after updating, additional knots may also need to be inserted in this region in order to obtain better fitting between the final updated surface and the locally distributed points. B-spline surface local updating is particularly useful for free-form surface design and shape modification based on physical mockups.