Spherical splines for Hermite interpolation and surface design
MetadataShow full item record
The following dissertation consists of two parts. Throughout this dissertation, we assume that the spherical triangulation could be a part of a sphere with or without holes, or the whole sphere S2. In the first part, given a set of function values and derivatives at scattered data locations over a spherical surface, we first use the minimal energy method to find a Hermite interpolation on the spherical spline spaces over a spherical triangulation of the scattered data locations. We show that the minimal energy method produces a unique spherical Hermite interpolation spline of the given scattered data with derivatives. Also we show that the Hermite interpolatory surface converges to a given sufficiently smooth function f in L2 and L∞ norm if the values are obtained from this f. That is, the surface of the spherical Hermite interpolation spline resembles the given set of scattered data values and derivatives. Some numerical results are given to demonstrate our method. In the second part, for any integer r ≥ 0, we first give a method of Cr hole filling by the minimal energy quasi-Hermite interpolation method and delicate care of Cr related boundaries. Then we present a method to deal with point cloud with Cr continuity by using the minimal energy Hermite interpolation method or minimal energy quasi-Hermite interpolation method, and our surface can interpolate these points and their derivatives if they are given. Several numerical experiments are presented to show our methods.
Showing items related by title, author, creator and subject.
Robbins, Kelly Roy (uga, 2005-05)For the first study a multiple-trait model (MTM), a random regression model utilizing Legendre polynomials (RRML), and a random regression model construct with linear spline functions (RRMS) were applied for analysis of ...
Nam, Kyunglim (uga, 2005-08)As a generalized wavelet function, a wavelet frame gives more rooms for different construction methods. In this dissertation, first we study two constructive methods for the locally supported tight wavelet frame for any ...
Cho, Okkyung (uga, 2006-08)