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"Hansford, Dianne"
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Practical linear algebra : a geometry toolbox
\"Practical Linear Algebra covers all the concepts in a traditional undergraduate-level linear algebra course, but with a focus on practical applications. The book develops these fundamental concepts in 2D and 3D with a strong emphasis on geometric understanding before presenting the general (n-dimensional) concept. The book does not employ a theorem/proof structure, and it spends very little time on tedious, by-hand calculations (e.g., reduction to row-echelon form), which in most job applications are performed by products such as Mathematica. Instead the book presents concepts through examples and applications. \"-- Provided by publisher.
Book
Using Digital Cloud Photogrammetry to Characterize the Onset and Transition from Shallow to Deep Convection over Orography
An automated method for segmenting digital images of orographic cumulus and a simple metric for characterizing the transition from shallow to deep convection are presented. The analysis is motivated by the hypothesis that shallow convection conditions the atmosphere for further deep convection by moistening it and preventing the evaporation of convective turrets through the entrainment of dry air. Time series of convective development are compared with sounding and surface data for 6 days during the summer of 2003. The observations suggest the existence of a threshold for the initiation of shallow convection based on the surface equivalent potential temperature and the saturated equivalent potential temperature above the cloud base. This criterion is similar to that controlling deep convection over the tropical oceans. The subsequent evolution of the convection depends on details of the environment. Surface fluxes of sensible and latent heat, along with the transport of boundary layer air by upslope flow, increase the surface equivalent potential temperature and once the threshold value is exceeded, shallow convection begins. The duration of the shallow convection period and growth rate of the deep convection are determined by the kinematic and thermodynamic structure of the mid- and upper troposphere.
Journal Article
Chapter 4 - Bézier Techniques
This chapter provides a thorough review of fundamental Bézier Techniques as a core tool of 3D modeling or computer aided geometric design (CAGD). Bezier techniques provide a geometric-based method for describing and manipulating polynomial curves and surfaces. Bézier techniques bring sophisticated mathematical concepts into a highly geometric and intuitive form. This form facilitates the creative design process. Bézier techniques are used in the context of numerical stability of floating point operations. The chapter describes curves, rectangular surfaces, and triangular surfaces. It introduces the foundations of Bézier techniques via the Bézier curve. It presents the properties and utility of Bézier curves, as well as an evaluation algorithm: the de Casteljau algorithm. The de Casteljau algorithm provides a means for evaluating Bézier curves. It also provides for greater understanding of Bézier methods as a whole. The chapter also discusses the building block of Bézier techniques: the Bernstein polynomials. It describes various properties of Bézier patches, such as endpoint interpolation, symmetry, affine invariance, bilinear precision, tensor product, and functional patches.
Book Chapter
Chapter 7 - Curve and Surface Constructions
This chapter introduces algorithms for the generation of Curves and Surfaces. It discusses some of the most fundamental interpolation and approximation methods in computer aided geometric design (CAGD). The developments emphasizes on Bézier and B-spline techniques because of their intuitive geometric definitions. The chapter focusses on polynomial curve methods, including Lagrange interpolation, point approximation, and Hermite interpolation. Next, a piecewise polynomial scheme, C2 cubic spline interpolation is presented. For C2 cubic spline interpolation, the choice of end conditions is important for the shape of the interpolant near the endpoints. The focus then moves to surface methods. The chapter describes interpolation to boundary curve data with Coons patches, interpolation to rectangular data with tensor product surfaces, approximation to large sets of data, and interpolation to point and derivative data. Mirroring the curve presentation, a piecewise polynomial surface scheme, C2 bicubic spline interpolation, is discussed. The chapter concludes with a discussion on volume deformations.
Book Chapter
Boundary curves with quadric precision for a tangent continuous scattered data interpolant
Conic sections and quadric surfaces have been studied and applied over time because of their beautiful underlying geometry, aesthetically pleasing forms, and engineering functionality. One of the primary interests of this thesis is to gain a better understanding of conics and quadrics in a parametric Bernstein Bezier formulation; this formulation is advantageous to fully integrate these forms into computer aided geometric modeling. Applying this understanding, a boundary curve scheme for triangular interpolants is developed which has quadric precision. If the given point and normal data comes from a quadric, then the resulting boundary curves will lie on this quadric. Each boundary curve is a conic section, represented in rational quadratic Bezier form. Special care is taken to handle data which imply an inflection point. This boundary curve scheme is then integrated into a tangent continuous interpolation scheme, represented in terms of rational quartic Bezier triangular patches. Reflection lines and Gouraud shaded images are used as surface interrogation tools.
Dissertation