1、外文资料翻译资料来源：International Journal of machinery文章名：Machinery manufacturing complex surface书刊名：International Journal of machinery作 者：Pohl出版社：MacmillanPublishersLtd.章 节：第三章页 码：P21-28文 章 译 名：曲面建模理论姓 名：学 号：指导教师(职称)：专 业：班 级：所 在 学 院：英文原文 In practical engineering applications, some curves and surfaces can be
2、 generated by mathematical functions, and some curves and surfaces are described by a set of data points given by the user. Therefore, according to the description method, the curve and surface can be divided into two categories：（1）Regular curves and surfaces, such as circular, parabolic, spiral cur
3、ve and sphere, cylinder, cone and so on, can be expressed by mathematical equations.（2）Free curves and surfaces: in the design of aircraft, cars, ships and other products, it is difficult to use a mathematical equation to describe the shape of these products, generally referred to as the free curve
4、and free surface. Surface modeling is a kind of modeling method to describe the surface of the object by means of the description of the surface or the surface of the object. If the wire frame model is a wire to construct object, surface modeling is to take faces of the epidermis of these wire skins
5、. When modeling, the complex external surface is decomposed into a number of basic surface elements. Through the splicing of these basic surface elements, the surface is formed. Figure 1-1 shows the blending process of surfaces. Surface modeling, also known as NURBS modeling, Non-Uniform is the abbr
6、eviation of Rational B-Splines NURBS, is the non uniform rational B spline. The specific explanation is:.Non-Uniform (non uniform) - refers to the scope of the influence of a control vertex can change. This is very useful when creating an irregular curved surface. Similarly, unity of the curves and
7、surfaces in perspective projection is not without change, for interactive 3D modeling this is a serious defect; rational (rational) - is that each NURBS objects can be defined by mathematical expressions; B-spline (B-spline) - refers to construct a curve with a line, at one or more points to be inte
8、rpolated. In a simple way, NURBS is a kind of modeling method to make curved surface objects. NURBS shape is always defined by the curve and surface, so it is difficult to generate an edge in the NURBS surface is very difficult. It is because of this feature, we can use it to make a variety of compl
9、ex surface modeling and performance of special effects, such as human skin, appearance or streamlined sports car, etc. The curved surface modeling not only NURBS modeling, it is composed of curves and surfaces, and then there is a three-dimensional model of the curve. The curve can control the curva
10、ture, direction and length of the curve. Is one of the two most popular modeling methods, and the other is polygon modeling. Curve and surface design can be traced back to the distant era. During the second world war under the pressure of aviation product design and production, the drawing method of
11、 descriptive geometry in the design of the products by practical application. After the Second World War, with the invention and application of the computer, people use the computer to replace a large number of manual drawing. For surface design people originally used is a practice known as loft, na
12、mely by constructing many longitudinal curve to contact a set of predefined good cross-sectional method to carry out. In modern CAD/CAM systems, the surface is generally considered as a combination of a number of surface patches, each of which can be represented in mathematical form. The earliest a
13、surface into system is put forward by the American Boeing company of Ferguson (Ferguson) in 1963, the difference between it and traditional method is defined curves and surfaces with parametric method, rather than the Cartesian coordinate method. Because parameter method can use simple mathematical
14、form expression of space curve, and no longer need with space curves in two mutually perpendicular coordinate plane projection to determine, and the parameters can be conveniently of coordinate transformation and the curve and surface expression of simple. So it is a very natural form to use paramet
15、ric curves and surfaces, and it has become a standard method. Significant progress has been made since the advent of the first curved surface. In 1963, Ferguson (Ferguson) of the United States of America (Boeing) first proposed the method that the curve surface expressed as the parameter vector func
16、tion, and introduced the parameter three time curve. The parametric form of the curve and surface is the standard form of the mathematical description of the shape. In 1964, MIT Coons proposed a very general surface theory, capable of deployment of a smooth surface with four free boundary curves, and explains how to make the surface patch be
