Meet The Constraints Of The Curve And Surface Modeling

Smooth connection between two adjacent surface patches is a basic and flexible problem. The construction method of increasing smooth degree through adjusting control points is a general handicap as well as an approach in surface design.Surface blending in terms of geometric continuous is more practical and welcome with view of geometric interpretation which is different to the traditional differential method based on algebra. First of all, the author gives a method for merging two Bezier surfaces with the construction of transition band, after discussing the G1,G2 continuous conditions of two Bezier tensor product surfaces and their geometric properties.Secondly,some reseaches on the parametric continuous conditions of two triangular B-B surfaces are involved in this paper,which suggest that blossoms and the multiaffine point of view helped to clarify and simplify the existing theory. Consequently, the author discusses a method for increasing the continuity between two functional triangular polynomial patches by adjusting their control points with the control points unchanged if the patches already meet with the disired level of continuity.Finally,the author presents a method to construct a smooth cubic B-spline curve which fairly fits 3D points while at the same time satisfies the length constraints. At the end by using the Lagrange multiplier's conditional extreme, resorting to Broyden method, finding the least square solution of the control points, we can obtain the fair quasi-fitting modeling B-spline curve.