Algebraic B-Spline Curve Interpolation And Fitting

Curve and surface modeling is the fundamental of Computer-Aided Geometric Design (CAGD) and Computer Graphics (CG). The curve modeling is the basis of the surface modeling. Algebraic curve is a piecewise continuous algebraic curve which has advantages such as low degree, piecewise smoothness, local support, etc. In the thesis, the algebraic B-Spline curve interpolation and fitting for planar point set are investigated which can be extended to the algebraic surface modeling in the future. The thesis is organized as follows:· In Chapter I, the background and the state of art of researching on free form curve /surface modeling are briefly introduced. Especially, two types of the piecewise algebraic curve/surface, i.e., Bernstein-Bezier piecewise algebraic curve/surface and algebraic B-Spline curve/surface, are described in detail. Finally the main contributions of our research are given.· In Chapter II, an algebraic B-spline curve interpolating algorithm based on the signed distance field is proposed for the given planar point set of the low noise. A B-Spline function interpolates the given point set; meanwhile it fits the signed distance field of the given point set. The zero set of the B-Spline function is the constructed curve. Thus a high quality interpolating curve is obtained which can reveal the geometric features of the point set. Finally, the acceleration of the algebraic B-Spline interpolation and fitting is discussed where the large-scale linear equations are parallel solved by using Dual Core CPU.· In Chapter III, another algebraic curve interpolating method based on the signed distance field is proposed for the given planar point set of high noise. First the proposed method fits the signed distance field, and then it interpolates some points specified by users. This method can reconstruct the algebraic B-Spline curve fast. The curve rendering acceleration is also discussed by using the local support property of the B-Spline function.· Finally, the conclusion is drawn and future work is proposed.