Fitting a triaxial ellipsoid to a geoid model

The aim of this work is the determination of the parameters of Earth’s triaxiality through a geometric fitting of a triaxial ellipsoid to a set of given points in space, as they are derived from a geoid model. Starting from a Cartesian equation of an ellipsoid in an arbitrary reference system, we develop a transformation of its coefficients into the coordinates of the ellipsoid center, of the three rotation angles and the three ellipsoid semi-axes. Furthermore, we present different mathematical models for some special and degenerate cases of the triaxial ellipsoid. We also present the required mathematical background of the theory of least-squares, under the condition of minimization of the sum of squares of geoid heights. Also, we describe a method for the determination of the foot points of the set of given space points. Then, we prepare suitable data sets and we derive results for various geoid models, which were proposed in the last fifty years. Among the results, we report the semi-axes of the triaxial ellipsoid of geometric fitting with four unknowns to be 6378171.92 m, 6378102.06 m and 6356752.17 m and the equatorial longitude of the major semi-axis –14.9367 degrees. Also, the parameters of Earth’s triaxiality are directly estimated from the spherical harmonic coefficients of degree and order two. Finally, the results indicate that the geoid heights with reference to the triaxial ellipsoid are smaller than those with reference to the oblate spheroid and the improvement in the corresponding rms value is about 20 per cent.

Fast custom apparel design and simulation for future demand-driven manufacturing

Purpose A common pipeline of apparel design and simulation is adjusting 2D apparel patterns, putting them onto a virtual human model and performing 3D physically based simulation. However, manually adjusting 2D apparel patterns and performing simulations require repetitive adjustments and trials in order to achieve satisfactory results. To support future made-to-fit apparel design and manufacturing, efficient tools for fast custom design purposes are desired. The purpose of this paper is to propose a method to automatically adjust 2D apparel patterns and rapidly generate acustom apparel style for a given human model. Design/methodology/approach The authors first pre-define a set of constraints using feature points, feature lines and ease allowance for existing apparels and human models. The authors formulate the apparel fitting to a human model, as a process of optimization using these predefined constraints. Then, the authors iteratively solve the problem by minimizing the total fitting metric. Findings The authors observed that through reusing existing apparel styles, the process of designing apparels can be greatly simplified. The authors used a new fitting function to measure the geometric fitting of corresponding feature points/lines between apparels and a human model. Then, the optimized 2D patterns are automatically obtained by minimizing the matching function. The authors’ experiments show that the authors’ approach can increase the reusability of existing apparel styles and improve apparel design efficiency. Research limitations/implications There are some limitations. First, in order to achieve interactive performance, the authors’ current 3D simulation does not detect collision within or between adjacent apparel surfaces. Second, the authors’ did not consider multiple layer apparels. It is non-trivial to define ease allowance between multiple layers. Originality/value The authors use a set of constraints such as ease allowance, feature points, feature lines, etc. for existing apparels and human models. The authors define a few new fitting functions using these pre-specified constraints. During physics-driven simulation, the authors iteratively minimize these fitting functions.

Robust Lane-Detection Method for Low-Speed Environments

Vision-based lane-detection methods provide low-cost density information about roads for autonomous vehicles. In this paper, we propose a robust and efficient method to expand the application of these methods to cover low-speed environments. First, the reliable region near the vehicle is initialized and a series of rectangular detection regions are dynamically constructed along the road. Then, an improved symmetrical local threshold edge extraction is introduced to extract the edge points of the lane markings based on accurate marking width limitations. In order to meet real-time requirements, a novel Bresenham line voting space is proposed to improve the process of line segment detection. Combined with straight lines, polylines, and curves, the proposed geometric fitting method has the ability to adapt to various road shapes. Finally, different status vectors and Kalman filter transfer matrices are used to track the key points of the linear and nonlinear parts of the lane. The proposed method was tested on a public database and our autonomous platform. The experimental results show that the method is robust and efficient and can meet the real-time requirements of autonomous vehicles.

Molar Interactions of Some Aromatic Hydrocarbons in n-Heptane by Viscometric Measurements at 298.15K

The viscosities, η , of pure n-heptane, toluene, o-xylene, mesitylene, and some of their binary mixtures covering the whole composition range have been measured at 298.15K. Deviations in viscosity, ∆η , was calculated using experimental results. The concentration dependencies of η were correlated to polynomial expressions, whereas, ∆η were fitted to the Redlich–Kister equation. Moreover, the values of the excess Gibbs free energy of activation, ∆G#E, of these mixtures were determined. Viscosity measurements of the binary systems were correlated with Grunberg and Nissan the three-body and four-body McAllister expressions. In all systems, ∆η were found to be negative in the whole range of composition with a single lobe having minimum at 0.6 mple fraction of aromatic hydrocarbon. While dispersive forces are suggested to dominate in n-heptane + toluene, for the other two systems ‘favourable geometric fitting’ overpowers them due to the increasing number of – CH3 groups in the relevant aromatic hydrocarbons. The Chittagong Univ. J. Sci. 40 : 97-110, 2018