悬链曲面

Show model combines growth model, math model and VR technologies to design the proper object structure of each organ of virtual plant. First of all,research background, research content of virtual plant area and Virtual Reality technology are introduced. The concept of VR and research content of virtual plant are defined. Secondly, we analyze math model of virtual plant, including Bezier curve, NURBS curved surface, fractal system, L-system and Catenary curve. Thirdly, we give show model of virtual plant in detail. Finally, the design of the platform and growth model on XML script is introduced , and how to show the virtual plant in the platfrom is discussed too.

本文首先介绍了虚拟植物领域的研究背景、研究内容和虚拟现实技术，明确了虚拟现实的概念和虚拟植物的研究范畴，然后介绍了虚拟植物器官的数学模型，对各个器官展开了拓扑结构分析，建立有针对性的数学模型，先后介绍了Bezier曲线，NURBS曲面，分形系统，L-系统和悬链线曲线，接着详细分类介绍了虚拟植物器官的显示模型，最后介绍了虚拟作物平台的设计，平台中基于XML脚本的生长模型，以及虚拟作物在作物平台中的显示。

This paper begin with a review of curves and surfces modeling, then we discuss the parametric polynomial minimal surface. This is followed by a discussion of the representations of catenoids and helicoids. Next, we discuss the numeric approximations to the minimal surfaces with piecewise polygons and B-Spline surfaces.

全文安排如下首先，我们简要回顾曲面造型历史和发展现状在第二和第三章，讨论参数多项式极小曲面；在第四章讨论悬链面和螺旋面的表示；在第五章讨论极小曲面的分片线性逼近；在第六章讨论极小曲面的B-样条逼近；最后，我们对全文做简单的总结。

The catenoids are the only nonplanar minimal surface of roation, the right helicoids are the only skew ruled minimal surface of roation, but they can not be represented in form of NURBS.

悬链面是唯一的旋转极小曲面，正螺面是唯一的直纹极小曲面表示，它们在建筑和机械制造行业有广泛应用，但是它们都不能用NURBS精确表示，这个工程应用带来很多不便。

On the other hand, the more important thing is because the urban housing is a kind of heterogeneity products.

另一方面，更重要的是由于城市住房是一种异质性产品。

Climate histogram is the fall that collects place measure calm value, cent serves as cross axle for a few equal interval, the area that the frequency that the value appears according to place is accumulated and becomes will be determined inside each interval, discharge the graph that rise with post, also be called histogram.

气候直方图是将所收集的降水量测定值，分为几个相等的区间作为横轴，并将各区间内所测定值依所出现的次数累积而成的面积，用柱子排起来的图形，也叫做柱状图。