The mid-facet of a simplex in n-dimensional Euclidean space which was introduced quite recently is an important geometric element. An analytic expression for the mid-facet area of a simplex is firstly given. In order ...The mid-facet of a simplex in n-dimensional Euclidean space which was introduced quite recently is an important geometric element. An analytic expression for the mid-facet area of a simplex is firstly given. In order to obtain the expression,the exterior differential method was presented. Furthermore, the properties of the mid-facets of a simplex analogous to median lines of a triangle (such as for all mid-facets of a simplex,there exists another simplex such that its edge-lengths equal to these mid-facets area respectively, and all of the mid-facets of a simplex have a common point) were proved. Finally, by applying the analytic expression, a number of inequalities which combine edge-lengths, circumradius, median line, bisection area and facet area with the mid-facet area for a simplex were established.展开更多
The multi-scale expression of enormously complicated laneway data requires differentiation of both contents and the way the contents are expressed. To accomplish multi-scale expression laneway data must support multi-...The multi-scale expression of enormously complicated laneway data requires differentiation of both contents and the way the contents are expressed. To accomplish multi-scale expression laneway data must support multi-scale transformation and have consistent topological relationships. Although the laneway data generated by traverse survey-ing is non-scale data it is still impossible to construct a multi-scale spatial database directly from it. In this paper an al-gorithm is presented to first calculate the laneway mid-line to support multi-scale transformation; then to express topo-logical relationships arising from the data structure; and,finally,a laneway spatial database is built and multi-scale ex-pression is achieved using components GIS-SuperMap Objects. The research result is of great significance for improv-ing the efficiency of laneway data storage and updating,for ensuring consistency of laneway data expression and for extending the potential value of a mine spatial database.展开更多
文摘The mid-facet of a simplex in n-dimensional Euclidean space which was introduced quite recently is an important geometric element. An analytic expression for the mid-facet area of a simplex is firstly given. In order to obtain the expression,the exterior differential method was presented. Furthermore, the properties of the mid-facets of a simplex analogous to median lines of a triangle (such as for all mid-facets of a simplex,there exists another simplex such that its edge-lengths equal to these mid-facets area respectively, and all of the mid-facets of a simplex have a common point) were proved. Finally, by applying the analytic expression, a number of inequalities which combine edge-lengths, circumradius, median line, bisection area and facet area with the mid-facet area for a simplex were established.
基金Project 2005B018 supported by the Science Foundation of China University of Mining and Technology
文摘The multi-scale expression of enormously complicated laneway data requires differentiation of both contents and the way the contents are expressed. To accomplish multi-scale expression laneway data must support multi-scale transformation and have consistent topological relationships. Although the laneway data generated by traverse survey-ing is non-scale data it is still impossible to construct a multi-scale spatial database directly from it. In this paper an al-gorithm is presented to first calculate the laneway mid-line to support multi-scale transformation; then to express topo-logical relationships arising from the data structure; and,finally,a laneway spatial database is built and multi-scale ex-pression is achieved using components GIS-SuperMap Objects. The research result is of great significance for improv-ing the efficiency of laneway data storage and updating,for ensuring consistency of laneway data expression and for extending the potential value of a mine spatial database.
