Papers by Keyword: Circle

Abstract: Three theorems are proposed in this paper. The first theorem is that a connected undirected graph G is an Euler graph if and only if G can be expressed as the union of two circles without overlapped sides. Namely, equation satisfies. The second theorem is that a connected simple undirected graph is a Hamilton graph if and only if G contains a sub-graph generated by union of circles of sub-graphs derived from two endpoints of common side. Namely, the equation satisfies (meaning of symbols in the equations see main body of this paper). The third theorem is that a connected simple undirected graph is a Hamilton graph if and only if the loop sum of two circles, and, of sub-graphs derived from two endpoints of common side in graph G is a sub-graphs of loop graph C_n.

Abstract: This paper extracted green space distribution information from multi-temporal LANDSAT multi-spectral remote sensing images to analyze the evolution of Nanjing’s green space between 1988 and 2007. The findings suggest that the current distribution of green space is not balanced and that the total area of green space has decreased over time. The trend towards fragmentation is obvious in the disproportionately large decline in medium-sized green spaces. Mountain forest and other large green spaces, however, have been better protected. Before 1998, the fragmentation was most apparent in the green spaces of the city’s inner circle. After 1998, the green space in the city’s middle circle began to suffer from the effects of severe human interference. After 2003, the outer circle of green space began to fragment and diminish as a result of urbanization, and the original ecological corridor surrounding the city collapsed.

Abstract: There is no fixed form for circles not parallel to drawing, with the lens ellipse, and perspective ellipse changes with the size of circle, distance from the screen angle and the relative location of sites location. It is a hardful thing both for manual and for computer graphics. A mathematical model procedure is developed according to the perspective transformation, as long as inputting size of circle, distance from the drawing (coordinates) to the relative angle, as well as site location (coordinates), other parameters to determine the size, and the direction and position of perspective ellipse is determined.