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【速搜问答】几何造型是什么

问答 admin 1个月前 (04-11) 32次浏览 已收录 0个评论

汉英对照:
Chinese-English Translation:

几何造型系统是指能够定义、描述、生成几何模型,并能够进行交互编辑处理的系统称为几何造型系统。采用几何造型技术,可以将物体的形状及其各种属性存储在计算机内,形成该物体的几何模型。这样的几何模型是对原物体确切的数学表达,或对其某种状态的真实模拟。

Geometric modeling system refers to the system that can define, describe, generate geometric model, and edit interactively, which is called geometric modeling system. Using geometric modeling technology, the shape and various attributes of the object can be stored in the computer to form the geometric model of the object. Such a geometric model is the exact mathematical expression of the original object, or the real simulation of its state.

几何造型系统是指能够定义、描述、生成几何模型,并能够进行交互编辑处理的系统称为几何造型系统。采用几何造型技术,可以将物体的形状及其各种属性存储在计算机内,形成该物体的几何模型。这样的几何模型是对原物体确切的数学表达,或对其某种状态的真实模拟。

Geometric modeling system refers to the system that can define, describe, generate geometric model, and edit interactively, which is called geometric modeling system. Using geometric modeling technology, the shape and various attributes of the object can be stored in the computer to form the geometric model of the object. Such a geometric model is the exact mathematical expression of the original object, or the real simulation of its state.

简述

sketch

几何造型系统就是利用计算机产生、处理、存取和输出形体各种表示的系统。在几何造型系统中各种形体表示的产生和修改是通过输入语言实现的。输入语言既可以是简单的图形交互处理命令语言,也可以是模块结构的类似于程序设计的语言,对输入语言的基本要求是能提供体素调用,并能产生一种或几种表示模式的结构。当然具有多种表示模式的系统比只具有一种表示模式的系统更为有效和通用。但我们现有的知识和几何造型之间还存在着较大的差距,其中最突出的问题是应用。应用具有广泛的含义,而对于应用问题的抽象处理我们还知道得不多。象如何根据几何模型把应用定义成函数?如何把这些函数和适应各种表示的算法结合起来等,这些问题还难以作出明确的回答。另外在算法上还有许多问题值得我们去研究,如各种表示模式间的转换算法,某些表示模式下有关性质的分析算法,以及有关算法的评价等。

Geometric modeling system is a system that uses computer to produce, process, access and output various representations of shapes. In geometric modeling system, the generation and modification of various shape representations are realized by input language. Input language can be either a simple command language for graphic interactive processing or a programming language with modular structure. The basic requirement of input language is that it can provide voxel call and produce one or more representation patterns. Of course, the system with multiple representation patterns is more effective and universal than the system with only one representation pattern. But there is still a big gap between our existing knowledge and geometric modeling, and the most prominent problem is the application. Application has a wide range of meanings, but we don’t know much about the abstract processing of application problems. For example, how to define applications as functions according to geometric models? How to combine these functions with algorithms adapted to various representations? It is difficult to give a clear answer to these questions. In addition, there are many problems worthy of our study in the algorithm, such as the transformation algorithm between various representation patterns, the analysis algorithm of some properties under some representation patterns, and the evaluation of relevant algorithms.

功能

function

一个完整的几何造型系统,一般应具有以下功能:

A complete geometric modeling system should generally have the following functions:

1)输入形体(形体定义) 即通过计算机的输入设备,将形体的几何信息输入计算机。常用的输入方式有交互方式和文本方式两种。

1) Input shape (shape definition) is to input the geometric information of the shape into the computer through the input device of the computer. There are two common input methods: interactive mode and text mode.

2)形体的计算机内部表示数据的存储、处理与管理输入的信息在计算机内进行处理后,将以适当的数据结构表示,对这些信息应有相应的处理与管理。

2) The data storage, processing and management are represented in the computer of the shape. After the input information is processed in the computer, it will be represented by the appropriate data structure, and these information should be processed and managed accordingly.

3)形体的变换处理由于形体的空间位置和空间形状可能存在变化,因此应提供变换功能,可使系统对形体的处理更加方便。

3) Because the spatial position and shape of the shape may change, the transformation function should be provided to make the system more convenient.

4)形体的显示和输出设计的好坏和正确与否通常需要经过视觉来判断,在交互定义形体时,输入的信息是否正确,应能实时反馈给用户。显示处理包括增加视觉效果的消隐显示,浓淡图显示和透视等功能。造型系统还应能将造型结果以一定的格式输出,以供其他应用程序使用。

4) Whether the display and output design of the shape is good or bad and correct or not usually needs to be judged by vision. When defining the shape interactively, whether the input information is correct or not should be able to feed back to the user in real time. Display processing includes adding visual effects of hidden display, shading display and perspective and other functions. The modeling system should also be able to output the modeling results in a certain format for other applications.

5)形体的编辑处理主要用于对已定义的形体进行局部或整体修改。

5) Shape editing is mainly used to modify the defined shape locally or as a whole.

6)查询功能使用户在设计时,能方便地查看已设计形体的有关信息,如形状参数等。用户在几何造型时,就是利用上述功能表达自己的设计意图,定义相应的形体。并为后续应用(如模具设计、数控加工和有限元分析等)准备数据。

6) The query function makes it easy for users to view the information about the designed shape, such as shape parameters, etc. In geometric modeling, users use the above functions to express their design intention and define the corresponding shape. And prepare data for subsequent applications (such as mold design, NC machining and finite element analysis).

模型

Model

1、线框造型系统

1. Wireframe modeling system

1959~1970 年 CAD 技术以线框造型(Wireframe Modeling)为主,它是最早采用的几何造型方式。线框造型是利用形体的顶点和棱边表示物体几何形状,通过对点和边的修改来改变构造形体的形状,即构造模型是一个简单的线框图,与该模型相关的数学表达是直线或曲线方程、点的坐标以及边和点的连接信息,该连接信息决定哪些点分别是哪条边的端点以及哪条边在哪个点上与其他边相邻。线框造型可以生成、修改、处理二维和三维线框几何体,可以生成点、直线、圆、二次曲线、样条曲线等,也可以对这些基本线框元素进行修剪、延伸、分段、连接等处理,生成更复杂的曲线。线框造型的另一种方法是通过三维曲面的处理来进行,即利用曲面与曲面的求交、曲面的等参数线、曲面边界线、曲线在曲面上的投影、曲面在某一方向的分模线等方法来生成复杂曲线。实际上,线框功能是进一步构造曲面和实体模型的基础工具。在复杂的产品设计中,往往是先用线条勾画出基本轮廓,即所谓“控制线”,然后逐步细化,在此基础上构造出曲面和实体模型。

From 1959 to 1970, the main CAD technology was wireframe modeling, which was the earliest geometric modeling method. Wireframe modeling is to use the vertex and edge of the body to represent the geometric shape of the object, and change the shape of the construction body by modifying the points and edges. That is to say, the construction model is a simple wireframe. The mathematical expression related to the model is the linear or curve equation, the coordinates of the points and the connection information of the edges and points. The connection information determines which points are the endpoint of which edge and which point The point at which the edge is adjacent to the other edges. Wireframe modeling can generate, modify and process 2D and 3D wireframe geometry, generate points, lines, circles, conics, splines, etc., and also trim, extend, segment and connect these basic wireframe elements to generate more complex curves. Another method of wireframe modeling is through the processing of three-dimensional surface, that is, using the intersection of surface and surface, isoparametric line of surface, boundary line of surface, projection of curve on surface, parting line of surface in a certain direction to generate complex curve. In fact, the wireframe function is the basic tool for further constructing surface and solid models. In the complex product design, it is often the first to use lines to outline the basic outline, that is, the so-called “control line”, and then gradually refine, on this basis to construct the surface and solid model.

由线框造型所产生的数字模型称为线框模型。线框模型的优点主要包括,数据结构简单、模型所需数据量小、处理时间短、建模方便、操作容易;线框模型包含了形体的三维数据可以产生任意视图。同时,线框模型的缺点是明显的,它用顶点和棱边来表示物体,只能表达基本的几何信息,不能有效表达几体数据间的拓扑关系,由于没有面的信息,不能表示表面含有曲面的物体;另外,它不能明确地定义给定点与物体之间的关系(点在物体内部、外部或表面上),存在“多义性”问题,所以线框模型不能处理许多重要问题,如不能生成剖切图、消隐图、明暗色彩图,不能用于数控加工,CAE 及 CAM 均无法实现,使其应用范围受到了很大的限制。正是由于这些问题的存在,线框造型正在逐渐被曲面造型和实体造型所取代。

The digital model produced by wireframe modeling is called wireframe model. The advantages of wireframe model mainly include simple data structure, small amount of data required, short processing time, convenient modeling and easy operation; wireframe model contains 3D data of the body, and can generate any view. At the same time, the disadvantage of wireframe model is obvious. It uses vertex and edge to represent the object, which can only express the basic geometric information, and can not effectively express the topological relationship between several volume data. Because there is no surface information, it can not represent the object with surface; in addition, it can not clearly define the relationship between a given point and the object (the point is inside, outside or on the surface of the object) The wire frame model can’t deal with many important problems, such as it can’t generate section drawing, hidden drawing, light and dark color drawing, it can’t be used in NC machining, and it can’t realize CAE and cam, which limits its application. Because of these problems, wireframe modeling is gradually replaced by surface modeling and solid modeling.

2、曲面造型系统

2. Surface modeling system

1970~1980 年是第一次 CAD 技术革命阶段。CAD 技术以曲面造型(SurfaceModeling)为主,曲面造型是在线框造型的基础上增加面的信息,利用平面和曲面来表示形体的一种造型方法。曲面造型起源于飞机、船舶的外形放样工艺,由 Coons、 Bezier 等大师于 60 年代奠定其理论基础。经过 30 多年的发展,曲面造型,已经形成了以有理 B 样条曲面(Rational B-Spline Surface)参数化特征设计和隐式代数曲面(mplicit Algebraic Surface)表示两类方法为主体,以插值(Interpolation)、拟合(Fitting)、逼近(Approximation)三种手段为骨架的几何理论体系。

1970-1980 is the first revolution of CAD technology. CAD technology is mainly based on surface modeling. Surface modeling is a modeling method that adds surface information on the basis of wireframe modeling, and uses plane and surface to represent shape. Curved surface modeling originated from the lofting process of aircraft and ships, and its theoretical foundation was established by Coons, Bezier and other masters in the 1960s. After more than 30 years of development, surface modeling has formed a geometric theory system based on rational B-spline surface parametric feature design and implicit algebraic surface representation, with interpolation, fitting and approximation as the skeleton.

由曲面造型所构造的模型称为曲面模型。曲面模型增加了有关面的信息,使得曲面造型方法丰富,扩大了线框模型的应用范围,能够满足面面求交线面消隐、明暗色彩图、数控加工等需要。但在该模型中,依然存在“多义性”问题,只有一张张面的信息,物体究竟存在于表面的哪一侧,并没有给出明确的定义,无法计算和分析物体的整体性质,如物体的表面积、体积、重心等;也不能将这个物体作为一个整体去考察它与其他物体相互关联的性质,如是否相交等曲面造型系统通常用于构造复杂曲面,如汽车、飞机、船舶等对外形要求较高的产品的造型设计。Catia、 Alias studio tools 是典型的曲面造型系统。

The model constructed by surface modeling is called surface model. The surface model increases the information about the surface, enriches the surface modeling methods, expands the application scope of the wire frame model, and can meet the needs of surface intersection, surface blanking, light and dark color map, NC machining and so on. However, in this model, there is still the problem of “polysemy”. There is only one piece of surface information, and there is no clear definition of which side of the surface the object exists, so it is impossible to calculate and analyze the overall properties of the object, such as the surface area, volume, center of gravity, etc; We can’t take this object as a whole to investigate the properties of its correlation with other objects, such as whether it intersects or not. Surface modeling system is usually used to construct complex surfaces, such as automobile, aircraft, ship and other products with high shape requirements. CATIA and alias studio tools are typical surface modeling systems.

3、实体造型系统

3. Solid modeling system

1980~1985 年是第二次 CAD 技术革命阶段,此时 CAD 技术以实体造型(SolidModeling)为主。早在 1970 年,就在线框模型和曲面造型研究的基础上,出现了实体造型的理论。实体造型理论为实现产品由设计到生产的环节采用同一数据信息提供了技术上的可行性,大大地促进了 CAD 产业的发展。实体造型用于构造具有封闭空间、称为实体的几何形体。它在曲面造型的基础上,增加了实体存在于表面哪一侧的定义,增加了给定点与形体之间的关系信息(点在形体内部、外部或在形体表面),克服了线框造型和曲面造型的局限性。

1980-1985 is the second CAD technology revolution stage, at this time CAD technology is mainly solid modeling. As early as 1970, based on the research of wireframe model and surface modeling, solid modeling theory appeared. Solid modeling theory provides technical feasibility for the realization of using the same data information in the process of product design and production, and greatly promotes the development of CAD industry. Solid modeling is used to construct geometry with closed space called solid. On the basis of surface modeling, it adds the definition of which side the entity exists on the surface, and adds the relationship information between the given point and the shape (the point is inside, outside or on the surface of the shape), which overcomes the limitations of wire frame modeling and surface modeling.

由实体造型所构造的模型称为实体模型。与线框模型、曲面模型不同,实体模不允许有单一的面或线。实体模型是最高级的三维物体模型,它能完整地表示物体的所有形状信息可以无歧义地确定一个点是在物体外部、内部或表面上,这种模型能够进一步满足物性计算、有限元分析等应用的要求。

The model constructed by solid modeling is called solid model. Different from wireframe model and surface model, solid model does not allow single face or line. Solid model is the most advanced three-dimensional object model, which can completely represent all the shape information of the object, and can unambiguously determine whether a point is on the outside, inside or surface of the object. This model can further meet the requirements of physical property calculation, finite element analysis and other applications.

实体造型技术是计算机视觉、计算机动画、计算机虚拟现实等领域中建立 3D 实体模型的关键技术,所以实体造型技术也称为 3D 几何造型技术。早期的实体造型系统一般是用多面体结构,实体的表面用小平面近似地表示。随着实体造型理论和研究的发展,先后提出了实体造型正则集理论和非正则集理论,用以描述非流形实体,一些流形、复形等拓扑学概念被引入几何造型。SDRC 公司于 1979 年发布了世界上第一个完全基于实体造型技术的大型 CAD/CAE 软件—1-DEAS。由于实体造型技术能够精确表达零件的全部属性,在理论上有助于统一 CAD、CAE、CAM 的模型表达,给设计带来了惊人的方便性,代表着未来 CAD 技术的发展方向。

Solid modeling technology is the key technology of building 3D solid model in the fields of computer vision, computer animation, computer virtual reality, so solid modeling technology is also known as 3D geometric modeling technology. The early solid modeling system generally used polyhedron structure, and the surface of solid was approximately represented by facet. With the development of solid modeling theory and research, regular set theory and irregular set theory of solid modeling are proposed to describe non manifold solid. Some topological concepts such as manifold and complex are introduced into geometric modeling. SDRC company released the world’s first large-scale CAD / CAE software 1-deas based on solid modeling technology in 1979. Because solid modeling technology can accurately express all the attributes of parts, it is helpful to unify the model expression of CAD, CAE and cam in theory, and brings amazing convenience to design, which represents the development direction of CAD technology in the future.


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