Normal Vector Calculation Research Articles

Analysis of thick, non-planar boundaries using the discontinuity analyser

Abstract. The advent of missions comprised of phased arrays of spacecraft, with separation distances ranging down to at least mesoscales, provides the scientific community with an opportunity to accurately analyse the spatial and temporal dependencies of structures in space plasmas. Exploitation of the multi-point data sets, giving vastly more information than in previous missions, thereby allows unique study of their small-scale physics. It remains an outstanding problem, however, to understand in what way comparative information across spacecraft is best built into any analysis of the combined data. Different investigations appear to demand different methods of data co-ordination. Of the various multi-spacecraft data analysis techniques developed to affect this exploitation, the discontinuity analyser has been designed to investigate the macroscopic properties (topology and motion) of boundaries, revealed by multi-spacecraft magnetometer data, where the possibility of at least mesoscale structure is considered. It has been found that the analysis of planar structures is more straightforward than the analysis of non-planar boundaries, where the effects of topology and motion become interwoven in the data, and we argue here that it becomes necessary to customise the analysis for non-planar events to the type of structure at hand. One issue central to the discontinuity analyser, for instance, is the calculation of normal vectors to the structure. In the case of planar and `thin' non-planar structures, the method of normal determination is well-defined, although subject to uncertainties arising from unwanted signatures. In the case of `thick', non-planar structures, however, the method of determination becomes particularly sensitive to the type of physical sampling that is present. It is the purpose of this article to firstly review the discontinuity analyser technique and secondly, to discuss the analysis of the normals to thick non-planar structures detected in magnetometer data. Key words. Space plasma physics (discontinuities; instruments and techniques)

Analysis of thick, non-planar boundaries using the discontinuity analyser

The advent of missions comprised of phased arrays of spacecraft, with separation distances ranging down to at least mesoscales, provides the scientific community with an opportunity to accurately analyse the spatial and temporal dependencies of structures in space plasmas. Exploitation of the multi-point data sets, giving vastly more information than in previous missions, thereby allows unique study of their small-scale physics. It remains an outstanding problem, however, to understand in what way comparative information across spacecraft is best built into any analysis of the combined data. Different investigations appear to demand different methods of data co-ordination. Of the various multi-spacecraft data analysis techniques developed to affect this exploitation, the discontinuity analyser has been designed to investigate the macroscopic properties (topology and motion) of boundaries, revealed by multi-spacecraft magnetometer data, where the possibility of at least mesoscale structure is considered. It has been found that the analysis of planar structures is more straightforward than the analysis of non-planar boundaries, where the effects of topology and motion become interwoven in the data, and we argue here that it becomes necessary to customise the analysis for non-planar events to the type of structure at hand. One issue central to the discontinuity analyser, for instance, is the calculation of normal vectors to the structure. In the case of planar and `thin' non-planar structures, the method of normal determination is well-defined, although subject to uncertainties arising from unwanted signatures. In the case of `thick', non-planar structures, however, the method of determination becomes particularly sensitive to the type of physical sampling that is present. It is the purpose of this article to firstly review the discontinuity analyser technique and secondly, to discuss the analysis of the normals to thick non-planar structures detected in magnetometer data. Key words. Space plasma physics (discontinuities; instruments and techniques)

レタリングCAD (その3) *

Many kinds of letters and Japanese characters, such as“Gothic”, “Mincho”, and special decorative letters, can be seen on posters and signs in daily life. These letters, however, are mainly drawn by expert lettering designers, with taking a lot of time, effort and cost.This paper introduces some special decorative letters drawn with a micro-computer, and main theme is focused on how to draw decorative parts. Letters without decorative parts are drawn by the method of contours. Decorative parts can be created effectively from a few sample points data by means of mathematical methods, such as interpolation, calculation of normal vector and so on.Designers can decorate letters easily and quickly using a mouse as a man-machine interfase on this system, furthermore these letters can be magnified to any size keeping their high quality.

Global and local deformations of solid primitives

New hierarchical solid modeling operations are developed, which simulate twisting, bending, tapering, or similar transformations of geometric objects. The chief result is that the normal vector of an arbitrarily deformed smooth surface can be calculated directly from the surface normal vector of the undeformed surface and a transformation matrix. Deformations are easily combined in a hierarchical structure, creating complex objects from simpler ones. The position vectors and normal vectors in the simpler objects are used to calculate the position and normal vectors in the more complex forms; each level in the deformation hierarchy requires an additional matrix multiply for the normal vector calculation. Deformations are important and highly intuitive operations which ease the control and rendering of large families of three-dimensional geometric shapes.