The Study And Application Of NUAH B-Spline Curves And Surfaces

Non-uniform algebraic-hyperbolic B-spline curves and surfaces are studied inthis paper.The main research contents and achievements are as follows: 1.A set of k-order(k ≥ 3) NUAH B-spline bases are given,by which the NUAHB-spline curves are constructed.Their properties,especially,the limiting cases of k-ord-er UAH B-splines whenα → 0+ ,+∞ respectively and the subdivision formulae arestudied here.As an application,hyperbolic curves,hyperbolic sine curves and exponentcurves are explicitly expressed by the 3-order and 4-order UAH B-splines. 2.A set of n+1-order H Bézier-like bases are given form NUAH B-splines andthe according H Bézier-like curves are defined.It is shown that such bases and curvesshare the same properties as the Bernstein basis and the Bézier curves respectively.The sufficient and necessary conditions for position,tangency and curvature forcontinuity among 4-order H Bézier-like curves are given.The second equivalent formof the 4-order H Bézier-like curves is proposed to solve the unstable problems insubdivion calculation.A simple algorithm of constructing planar piecewise 4-order HBézier-like curves with all edges tangent to given control polygons is described.Thecurve can be used to express the hyperbolic sine curve for application for subdivisionalgorithm. 3.The tensor product surfaces are generated by the UAH B-splines and H Bézier-like bases and their limiting cases are considered UAH B-splines,C-B-splines andB-splines surfaces are used to approximated the according control grids constructedwith knots from an aerofoil,respectively,and so do H Bézier-like,C-Bézier and Béziersurfaces.Good results are got to prove the best approximation by UAH B-splines andH Bézier-like schemes among them.