With the swift advancement of geometric modeling industry and computer technology, traditional generalized Ball curves surfaces are challenging to achieve various complex surfaces. Constructing an interpolation curve for given discrete data points optimizing its shape have important research value in engineering applications. This article uses improved golden eagle optimizer design shape-adjust...

The active bending concept provides a new perspective for well-established structural type which has been used at various scales: the beam-string, consisting of beam with an attached lower tie in tension and bracing struts balancing forces between them. idea goes back to gutter beams Crystal Palace widely present large-scale structures. When slender is used, induces curvature increases depth sy...

Space filling curves are a class of fractals that are important mathematical descriptions of the appearance and shape of natural objects. There is growing interest in the modelling of such curves to measure pathology in medicine and biology. This work presents a method of modelling fractal curves, such as the boundary of brain white matter, and partitioning such curves in to segments having equ...

Pedal curves are the loci of the feet of perpendiculars to the tangents of a fixed curve to a fixed point called the pedal point. By varying the location of the pedal point, deformable pedal curves have an important feature of incorporating a global parameterized shape into the curve evolution framework. In this paper, a hybrid geometric active model based on deformable pedal curves for face co...

-Model cation-exchange curves are presented for an idealized kaolinite surface where the charge on the surface (1) has its origin in cation substitution in the structure, and hence, is pH independent; and (2) is produced by protonation/deprotonation reactions of oxide-like sites, and hence, depends on the acid and base strengths of the surface sites, as welt as the ionic strength. Two pH-indepe...

ACKNOWLEDGEMENTS I would like to thank my adviser Michael Zieve for teaching me to fish. I would like to thank Jeffrey Lagarias for helpful feedback in writing this thesis. I would like to thank my family (Peter, Susan, and Holly), my beautiful girlfriend Becky, and the community of Michigan graduate students for keeping me sane.

[1] The strong jet, with a speed between 500 and 600 m/s, is inferred in the equatorial region of Saturn by combining the nadir and limb observations of Composite Infrared Spectrometer (CIRS) aboard the Cassini spacecraft. A similar jet was discovered on Jupiter (F. M. Flasar et al., 2004a). These discoveries raise the possibility that intense jets are common in the equatorial stratospheres of ...