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。

Plunder melds and run with this jewel!

掠夺melds和运行与此宝石！

My dream is to be a crazy growing tree and extend at the edge between the city and the forest.

此刻，也许正是在通往天国的路上，我体验着这白色的晕旋。