Compact Parameterized Black-Box Modeling via Fourier-Rational Approximations

We present a novel black-box modeling approach for frequency responses that depend on additional parameters with periodic behavior. The methodology is appropriate for representing with compact low-order equivalent models the behavior of electromagnetic systems observed at well-defined ports and/or locations, including dependence on geometrical parameters with rotational symmetry. Examples can be polarization or incidence angles of a plane wave, or stirrer rotation in reverberation chambers. The proposed approach is based on fitting a Fourier-rational model to sampled frequency responses, where frequency dependence is represented through rational functions and parameter dependence through a Fourier series. Several examples from different applications are used to validate and demonstrate the approach

Moment-Based Order-Independent Transparency

Compositing transparent surfaces rendered in an arbitrary order requires techniques for order-independent transparency. Each surface color needs to be multiplied by the appropriate transmittance to the eye to incorporate occlusion. Building upon moment shadow mapping, we present a moment-based method for compact storage and fast reconstruction of this depth-dependent function per pixel. We work with the logarithm of the transmittance such that the function may be accumulated additively rather than multiplicatively. Then an additive rendering pass for all transparent surfaces yields moments. Moment-based reconstruction algorithms provide approximations to the original function, which are used for compositing in a second additive pass. We utilize existing algorithms with four or six power moments and develop new algorithms using eight power moments or up to four trigonometric moments. The resulting techniques are completely order-independent, work well for participating media as well as transparent surfaces and come in many variants providing different tradeoffs. We also utilize the same approach for the closely related problem of computing shadows for transparent surfaces

Doctor of Philosophy

dissertationWhile boundary representations, such as nonuniform rational B-spline (NURBS) surfaces, have traditionally well served the needs of the modeling community, they have not seen widespread adoption among the wider engineering discipline. There is a common perception that NURBS are slow to evaluate and complex to implement. Whereas computer-aided design commonly deals with surfaces, the engineering community must deal with materials that have thickness. Traditional visualization techniques have avoided NURBS, and there has been little cross-talk between the rich spline approximation community and the larger engineering field. Recently there has been a strong desire to marry the modeling and analysis phases of the iterative design cycle, be it in car design, turbulent flow simulation around an airfoil, or lighting design. Research has demonstrated that employing a single representation throughout the cycle has key advantages. Furthermore, novel manufacturing techniques employing heterogeneous materials require the introduction of volumetric modeling representations. There is little question that fields such as scientific visualization and mechanical engineering could benefit from the powerful approximation properties of splines. In this dissertation, we remove several hurdles to the application of NURBS to problems in engineering and demonstrate how their unique properties can be leveraged to solve problems of interest

New Models for High-Quality Surface Reconstruction and Rendering

The efficient reconstruction and artifact-free visualization of surfaces from measured real-world data is an important issue in various applications, such as medical and scientific visualization, quality control, and the media-related industry. The main contribution of this thesis is the development of the first efficient GPU-based reconstruction and visualization methods using trivariate splines, i.e., splines defined on tetrahedral partitions. Our methods show that these models are very well-suited for real-time reconstruction and high-quality visualizations of surfaces from volume data. We create a new quasi-interpolating operator which for the first time solves the problem of finding a globally C1-smooth quadratic spline approximating data and where no tetrahedra need to be further subdivided. In addition, we devise a new projection method for point sets arising from a sufficiently dense sampling of objects. Compared with existing approaches, high-quality surface triangulations can be generated with guaranteed numerical stability. Keywords. Piecewise polynomials; trivariate splines; quasi-interpolation; volume data; GPU ray casting; surface reconstruction; point set surface