曲面

The main content reads as follows: Chapter 1 gives a survey on the three methods by which regular geometric modeling can be rended, including parametric curves/surfaces modeling method, algebraic curves/surfaces modeling method and subdivision. Moreover we introduce in greater detail about two means for subdivision which fit into two class: geometric subdivision and algebraic subdivision.

全文主要内容如下：第一章首先对CAGD中构造&规则几何形体&的三类造型方法：参数曲线、曲面造型方法，代数曲线、曲面造型方法及细分法——曲线、曲面的离散化造型方法，作了较系统的综述，并对两类主要的细分法——几何方法与代数方法，作了较详细的介绍。

This paper applies the concept of "contact" in Differential Geometry into the machining of sculptured surfaces, presentes the contact principle of the machining of complicated surfaces, using the circumference circle of the cylindrical cutter to sweep curved surfaces instead of ball-end mill .

把微分几何中曲线与曲面之间的&切触&概念应用于复杂曲面的数控加工，提出用圆柱铣刀和圆锥盘铣刀的外圆在五坐标联动中加工三维自由曲面的最佳切触条件。

The AL-alloy deformation rule and the cutting force are studied in high-speed ball-end milling of curved surface; in this case, the cutting forces model is established by means of microelements. Through the theory analysis and experiment studies, the relationship of the curvature of machined surface and cutting forces is developed, and these establish the basis for choosing the tool path of high-speed cutting.

对高速铣削时铝合金材料的变形规律以及采用球头铣刀加工曲面时的切削力进行了研究；采用微元法建立了基于曲面加工的球头铣刀切削力模型；通过理论分析和实验研究建立了加工曲面曲率和切削力的关系，为高速切削刀具路径优选奠定了基础。

This algorithm works as following: blending faces between each two of surfaces is constructed firstly, then constructing the corner blend with Coons surface.

该算法的思路是首先对多张曲面中的两两曲面之间进行过渡，之后，对于在交点处的部分采用多张孔斯曲面片构建过渡面。

The constructed surface not only has the same structure to the bicubic Coons pacth, but also it can help us to obtain different surfaces by changing the values of the parameters. Furthermore, it can accurately represent torus、ellipsoid and so on.

所构造的曲面不仅具有双三次Coons曲面片的相似的结构，可以通过改变参数，得到不同的曲面片，而且还能精确地表示圆环面、球面、椭球面等二次曲面。

This text mainly introduced the UG basic entity to set up the basic operation of mold and curved face shape;The software of UG CAM weaves the operation process of distance automatically;The UG CAM medium-sized chamber milling、curved face outline milling ...etc.

本文主要介绍了UG 基本实体建模和曲面造型的基本操作；UG CAM 软件自动编程的操作流程；UG CAM 中型腔铣、曲面轮廓铣等加工类型的自动编程方法；UG CAM 后置处理方法；曲面零件在加工中心上的加工工艺规程等。

Based on the garment design with the meshes, we assort spline curve into two types, that is to raisene idea that the ring and characteristic line are the basic geometry elements of three-dimensional garment model.

从人体服装设计所用曲面出发，通过对样条曲线进行分类，提出将环和特征线作为人体服装三维建模最基本的几何元素，并详细介绍了利用双线性插值法对人体服装中的两类子曲面进行三维建模的方法，从而在将参数化方法运用到高层次图素如样条曲线、曲面等方面作了尝试和推广

Additionally, the approximate flattening of surface strip using lines linking midpoints on perpendicular lines between geodesic curves and the unconditional extreme value method are discussed.

提出了用测地线方程、曲面上两点间短程线来计算膜结构曲面测地线的方法，同时，采用测地线间垂线的中点连线和用无约束极值法进行空间条状曲面近似展开的分析。

The torsion of the intersection curve of two surfaces in R3 can be expressed by geodesic torsions,normal curvatures and the angle between surfaces.

即两曲面交线的挠率可以用两曲面的测地挠率、法曲率及两曲面的夹角表示。

In this study, a commercial CAD/CAM Software is used to plan and generate the multi-axis tool path, and a table rotating/tilting type five-axis machining center is used to perform the experimental machining operation. The material of the die studied is NAK 80 die tool steel, and the geometries are modeled as concave and convex spherical surfaces. Milling parameters considered are spindle speed, feed rate, and different types of cutting tool path. The experimental results show that the surface roughness for concave spherical surface is about 0.247 μm and roundness is about 0.0283 mm and the surface roughness for convex spherical surface is about 0.250 μm and spherical roundness is about 0.0551 mm under the cutting conditions mentioned in this study.

本研究的实验方法与步骤包括利用商用CAD/CAM系统针对实验对象规划三轴/五轴同动加工路径，并经后处理程式转换，在本实验室之平台倾斜/旋转型之五轴加工机上进行实验，实验对象为NAK80模具钢材料之凹与凸球形曲面之加工，此外考虑的切削条件有主轴转速、进给速度、加工路径等，在本研究所设定之最佳切削条件下，凹球形曲面之真圆度约为0.0283 mm，粗糙度为0.247 μm，而在相同切削条件下，凸球形曲面之真圆度为0.0551 mm，粗糙度为0.250 μm。

Breath, muscle contraction of the buttocks; arch body, as far as possible to hold his head, right leg straight towards the ceiling (peg-leg knee in order to avoid muscle tension).

呼气，收缩臀部肌肉；拱起身体，尽量抬起头来，右腿伸直朝向天花板（膝微屈，以避免肌肉紧张）。

The cost of moving grain food products was unchanged from May, but year over year are up 8%.

粮食产品的运输费用与5月份相比没有变化，但却比去年同期高8％。