Control of Curvature Extrema in Curve Modeling

We present a method for constructing almost-everywhere curvature-continuous curves that interpolate a list of control points and have local maxima of curvature only at the control points. Our premise is that salient features of the curve should occur only at control points to avoid the creation of features unintended by the artist. While many artists prefer to use interpolated control points, the creation of artifacts, such as loops and cusps, away from control points has limited the use of these types of curves. By enforcing the maximum curvature property, loops and cusps cannot be created unless the artist intends to create such features. To create these curves, we analyze the curvature monotonicity of quadratic, rational quadratic and cubic curves and develop a framework to connect such curve primitives with curvature continuity. We formulate an energy to encode the desired properties in a boxed constrained optimization and provide a fast method of estimating the solution through a numerical optimization. The optimized curve can serve as a real-time curve modeling tool in art design applications

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

Future Space-Transport-System Components under High Thermal and Mechanical Loads

This open access book presents the findings of Collaborative Research Center Transregio 40 (TRR40), initiated in July 2008 and funded by the German Research Foundation (DFG). Gathering innovative design concepts for thrust chambers and nozzles, as well as cutting-edge methods of aft-body flow control and propulsion-component cooling, it brings together fundamental research undertaken at universities, testing carried out at the German Aerospace Center (DLR) and industrial developments from the ArianeGroup. With a particular focus on heat transfer analyses and novel cooling concepts for thermally highly loaded structures, the book highlights the aft-body flow of the space transportation system and its interaction with the nozzle flow, which are especially critical during the early phase of atmospheric ascent. Moreover, it describes virtual demonstrators for combustion chambers and nozzles, and discusses their industrial applicability. As such, it is a timely resource for researchers, graduate students and practitioners

Mathematical Modeling of Biological Systems

Mathematical modeling is a powerful approach supporting the investigation of open problems in natural sciences, in particular physics, biology and medicine. Applied mathematics allows to translate the available information about real-world phenomena into mathematical objects and concepts. Mathematical models are useful descriptive tools that allow to gather the salient aspects of complex biological systems along with their fundamental governing laws, by elucidating the system behavior in time and space, also evidencing symmetry, or symmetry breaking, in geometry and morphology. Additionally, mathematical models are useful predictive tools able to reliably forecast the future system evolution or its response to specific inputs. More importantly, concerning biomedical systems, such models can even become prescriptive tools, allowing effective, sometimes optimal, intervention strategies for the treatment and control of pathological states to be planned. The application of mathematical physics, nonlinear analysis, systems and control theory to the study of biological and medical systems results in the formulation of new challenging problems for the scientific community. This Special Issue includes innovative contributions of experienced researchers in the field of mathematical modelling applied to biology and medicine

Surface Engineering of C/N/O Functionalized Materials

This book discusses the latest developments in the surface engineering of C/N/O functionalized materials, including both experimental and theoretical studies on heat treatment and surface engineering of metals, ceramics, and polymers