This thesis introduces fractal interpolation functions, exposes advantages of fractal interpolation of real world objects and presents some newly developed procedures, associated with fractal interpolation process. The work briefly presents the context needed for introduction of fractal approach and relevant definitions. Also, the detailed description of fractal generating algorithms (deterministic, random iteration, “escape time”) as well as fractal classifications is presented. Since the research object is theoretical and practical aspects of fractal interpolation function analysis, special attention is paid to geometric fractals, obtained using systems of iterated functions (IFS). The notion of a fractal interpolation function is introduced in the work. The author shows that it is possible to generate fractal interpolation functions for various types of data. The generated functions are “close” (in the sense of Housdorf dimension) to the data under processing, i.e., it is possible to ensure that the fractal interpolation graph dimension were equal to the fractal dimension of experimental data (graph). The random iteration algorithm is used for the analysis of fractal interpolation functions, since it is relatively simple and fast enough. The author makes an attempt to analyze and solve the problem of choosing interpolation points (general case). A few approaches are proposed, namely the uniform distribution of interpolation points (for the interactive use) and collage. On... [to full text]

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An improvement in efficiency of direct digital frequency synthesis (DDFS) systems is demanded for low power frequency synthesis in wireless communications. Concurrently a reduction in cost is important for disposable, low resolution frequency synthesis in biomedical instrumentation systems. To meet both these needs a new ROM-less architecture is presented here that uses less than half the circuit area of previous state of the art systems and improves the efficiency by operating at up to a tenth of the power consumption. The main contribution presented in this thesis is a novel, efficient method of interpolation for DDFS that uses the nonlinear response of the CMOS differential switch already present in the high speed current steering DAC. The nonlinear response provides a smooth transition between the conventional, quantised DAC output. This interpolation may be performed with the conventionally discarded phase bits leading to highly compact and efficient DDFS architectures for application in instrumentation and communications systems. DDFS systems typically consist of a large overflowing accumulator to generate the phase, a ROM lookup table to convert the phase to amplitude and a DAC to perform the digital to analogue conversion. Approximations are often used to reduce the size of the ROM, however the most efficient DDFS systems remove the ROM completely and calculate the phase to amplitude conversion directly or store the conversion in a non-linear DAC. State of the art, high speed CMOS DACs consisting of thermometer decoded arrays of current steering cells are often used to reduce non-ideal effects that cause unwanted transients leading to a degradation in spectral purity (SFDR). A novel ROM-less technique is introduced here that uses the non-linear response of a current cell consisting of an ideal current source and differential current switch to interpolate between the output levels of a non-linear DAC. Using this technique two architectures are developed. A compact architecture using only four or six current cells suitable for instrumentation applications and a thermometer decoded architecture using 64 current cells for communications applications that require better spectral purity. The compact architecture is 100% efficient as all the bias current is used to form the output. The only additional component is a small linear phase DAC. One compact system with a nonlinear DAC of four current cells achieved an SFDR of -40dBc up to output frequencies of 1MHz for dielectrophoresis consumed only 5μW/MHz and a second compact system with a six cell nonlinear DAC for electrical impedance spectroscopy, achieved an SFDR of -48dBc for output frequencies up to 1MHz and consumed only 8μW/MHz. As an extension to improve the SFDR a segmented system with 64 current cells was developed. The larger number of current cells required the use of a modified thermometer decoder that had the added benefit of improving the spectral purity by linearising the response of each cell. The total active area was 0.6mm², less than half of state of the art ROM-less DDFS systems that include a DAC. Although measurement results of the 64 cell system were disappointing, simulations suggest that these problems may be solved in a future chip that should be able to achieve -70dBc SFDR at 100MHz. Despite the loss in performance from simulation to measurement, the measured 64 cell system still meets the spectral purity requirements of UMTS and Bluetooth, -60dBc SFDR.

Over the last decade, advances in fluid simulation and rendering have helped animators synthesize photorealistic shots for movies that would have been virtually impossible to create by manually animating the liquid. Despite the advent of these computational methods, fluid simulation in movie production still involves a large degree of trial and error. In this dissertation, we propose a set of techniques for creating animations of liquids that meet desired artistic criteria without the customary tuning of numerous physical parameters. The basis for our work is the mesh-based representation of the liquid surface which lends itself to efficient algorithms that can control the output of simulations. First, we show how an animator can create animated characters and shapes that behave as if they were made of water using our mesh-based control method. Our approach allows for multiple levels of control over the simulation, ranging from the overall tracking of the desired shapes to highly detailed secondary effects. Next, we present a novel technique for interpolating between fluid simulations with free surfaces. We construct 4D spacetime meshes from animations and register them using a non-rigid ICP algorithm. By incorporating user input to align visually important regions, we can produce plausible animations that look like a blend of the two input sequences, all without re-simulating the fluid. We demonstrate how this could have applications in pre-visualization and video games.

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Universiẗat, Diss., 2001--Duisburg.

Diss. Uppsala : Univ., 2002.

Thesis (Ph. D.)--Oregon State University, 1993. / Typescript (photocopy). Includes bibliographical references (leaves 68-70). Also available on the World Wide Web.

Zugl.: Erlangen, Nürnberg, Univ., Diss., 2008