Ball Bézier Curves And Its Application In Blending Of Pipe Surfaces

Basing on the theories of interval analysis,geometry tolerance, interval Bezier curves,disk Bézier curves,this thesis has discussed two aspects of problems:(1)the properties of ball Bezier curves;(2)its application in blending of pipe surfaces;First , we mainly discusse ball Bezier curves.We introduced the disk arithmetic and the plane disk Bezier curves.A disk in the plane R~2 is denned to be the setThe following operations are defined for disks < C_i,r_i >,i = 0, ...,n:Notice that the addition satisfies the associative and commutative laws;furthermore,themultiplicati< of a ball by a scalar can be distributed over addition. Basing on disk arithmetic,we have the definition of disk Bezier curves as follows:where are the Bernstein polynomials of degree n.Ball Bezier curves possess some interesting properties which Bezier has: (l)End interpolation. (2)Affine invariant. (3)Convex hull. (4)De Casteljau algorithm (5)Subdivision(6)Degree elevation and reduction.We introduced the ball arithmetic and the ball Bezier curves.Let...