Thesis (M.S.)--Rochester Institute of Technology, 2009. / Typescript. Includes bibliographical references (leaf 54).

Heidelberg, Univ., Diss., 2000.

Thesis (M.S.)--Brigham Young University. Dept. of Computer Science, 2008. / Includes bibliographical references (p. 65-66).

Thesis (Ph. D.)--University of Wisconsin--Madison, 1968. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliography.

Thesis (Ph. D.)--University of Alberta, 2010. / Title from pdf file main screen (viewed on July 30, 2010). A thesis submitted to the Faculty of Graduate Studies and Research in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Applied Mathematics, Department of Mathematical and Statistical Sciences, University of Alberta. Includes bibliographical references.

The creation of smooth interpolating curves and surfaces is an important aspect of computer graphics. Trigonometric interpolation in the form of the Fourier transform has been a popular technique. For computer graphics, simpler curves and surfaces like the B´ezier curve and B-spline curve have been more popular due to the computational efficiency. Fitting B-spline or B´ezier curves or surfaces to unorganised data points has been more challenging since these curves are not naturally interpolating. Normally a system of equations needs to be solved to obtain the curves or surfaces with the added problem of identifying data points to form piecewise continuous surfaces. We solve the problem of periodic interpolating curves and surfaces using harmonic interpolation [73]. We extend harmonic interpolation to handle an even number of data points. We then show how harmonic interpolation can be applied using geometry images [29] to create smooth interpolating surfaces. We introduce algorithms to manipulate the amount of interpolated points, and the location of the interpolated points. Finally, we show how a smooth interpolating surface created by harmonic interpolation can be converted to a series of B´ezier surfaces. The combination of techniques allows us to quickly create a smooth interpolating surface from a set of unorganised points that have a known spherical structure. Keywords: Interpolation, harmonic interpolation, trigonometric interpolation, B´ezier curves surface fitting, tensor product surfaces. / Prof. W.F. Steeb

This report analyzes and compares Barycentric Lagrange interpolation to Cardinal Trigonometric interpolation, with regards to computational cost and accuracy. It also covers some edge case scenarios which may interfere with the accuracy and stability. Later on, these two interpolation methods are applied on parameterized curves and surfaces, to compare and contrast differences with the standard one dimensional scenarios. The report also contains analysis of and comparison with regular Lagrange interpolation. The report concludes that Barycentric Lagrange interpolation is generally speaking more computationally efficient, and that the inherent need for periodicity makes Cardinal Trigonometric interpolation less reliable in comparison. On the other hand, Barycentric Lagrange interpolation is difficult to implement for higher dimensional problems, and also relies heavily on Chebyshev spaced nodes, something which can cause issues in a practical application of interpolation. Given ideal scenarios, Cardinal Trigonometric interpolation is more accurate, and for periodic functions generally speaking better than Barycentric Lagrange interpolation. Regular Lagrange interpolation is found to be unviable due to the comparatively big computational cost.

The two most common approaches used to formulate thermodynamic properties of pure substances are fundamental (or characteristic) equations of state (Helmholtz and Gibbs functions) and a piecemeal approach that is described in Adebiyi and Russell (1992). This thesis neither presents a different method to formulate thermodynamic properties of pure substances nor validates the aforementioned approaches. Rather its purpose is to present a method to generate property tables from existing property packages and a method to facilitate the accurate interpretation of fluid thermodynamic property data from those tables. There are two parts to this thesis. The first part of the thesis shows how efficient and usable property tables were generated, with the minimum number of data points, using an aerospace industry standard property package. The second part describes an innovative interpolation technique that has been developed to properly obtain thermodynamic properties near the saturated liquid and saturated vapor lines.

No description available.

A model reduction technique that is optimal in the H_∞-norm has long been pursued due to its theoretical and practical importance. We consider the optimal H_∞ model reduction problem broadly from an interpolation-based approach, and give a method for finding the approximation to a state-space symmetric dynamical system which is optimal over a family of interpolants to the full order system. This family of interpolants has a simple parameterization that simplifies a direct search for the optimal interpolant. Several numerical examples show that the interpolation points satisfying the Meier-Luenberger conditions for H₂-optimal approximations are a good starting point for minimizing the H_∞-norm of the approximation error. Interpolation points satisfying the Meier-Luenberger conditions can be computed iteratively using the IRKA algorithm [12]. We consider the special case of state-space symmetric systems and show that simple sufficient conditions can be derived for minimizing the approximation error when starting from the interpolation points found by the IRKA algorithm. We then explore the relationship between potential theory in the complex plane and the optimal H_∞-norm interpolation points through several numerical experiments. The results of these experiments suggest that the optimal H_∞ approximation of order r yields an error system for which significant pole-zero cancellation occurs, effectively reducing an order n+r error system to an order 2r+1 system. These observations lead to a heuristic method for choosing interpolation points that involves solving a rational Zolatarev problem over a discrete set of points in the complex plane. / Master of Science