Approximating tensor product Bézier surfaces with tangent plane continuity

AbstractWe present a simple method for degree reduction of tensor product Bézier surfaces with tangent plane continuity in L2-norm. Continuity constraints at the four corners of surfaces are considered, so that the boundary curves preserve endpoints continuity of any order α. We obtain matrix representations for the control points of the degree reduced surfaces by the least-squares method. A simple optimization scheme that minimizes the perturbations of some related control points is proposed, and the surface patches after adjustment are C∞ continuous in the interior and G1 continuous at the common boundaries. We show that this scheme is applicable to surface patches defined on chessboard-like domains

The geometry of optimal degree reduction of Bezier curves

Optimal degree reductions, i.e. best approximations of $n$-th degree Bezier curves by Bezier curves of degree $n$ - 1, with respect to different norms are studied. It is shown that for any $L_p$-norm the euclidean degree reduction where the norm is applied to the euclidean distance function of two curves is identical to componentwise degree reduction. The Bezier points of the degree reductions are found to lie on parallel lines through the Bezier points of any Taylor expansion of degree $n$ - 1 of the original curve. This geometric situation is shown to hold also in the case of constrained degree reduction. The Bezier points of the degree reduction are explicitly given in the unconstrained case for $p$ = 1 and $p$ = 2 and in the constrained case for $p$ = 2

Rational Cubic B-Spline Interpolation and Its Applications in Computer Aided Geometric Design

Because of the flexibility that the weights and the control points provide, NURBS have recently become very popular tools for the design of curves and surfaces. If the weights are positive then the NURB will lie in the convex hull of its control points and will not possess singularities. Thus it is desirable to have positive weights. In utilizing a NURB a designer may desire that it pass through a set of data points {xi} This interpolation problem is solved by the assigning of weights to each data point. Up to now little has been known regarding the relationship between these assigned weights and the weights of the corresponding interpolating NURB. In this thesis this relationship is explored. Sufficient conditions are developed to produce interpolating NURBS which have positive weights. Applications to the problems of degree reduction and curve fairing are presented. Both theoretical and computational results are presented

Aeronautical engineering: A continuing bibliography with indexes (supplement 204)

This bibliography lists 419 reports, articles, and other documents introduced into the NASA scientific and technical information system in August 1986

Eighteenth Space Simulation Conference: Space Mission Success Through Testing

The Institute of Environmental Sciences' Eighteenth Space Simulation Conference, 'Space Mission Success Through Testing' provided participants with a forum to acquire and exchange information on the state-of-the-art in space simulation, test technology, atomic oxygen, program/system testing, dynamics testing, contamination, and materials. The papers presented at this conference and the resulting discussions carried out the conference theme 'Space Mission Success Through Testing.