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# 【速搜问答】几何造型是什么

1年前 (2021-04-11) 212次浏览

Chinese-English Translation:

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.

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.

sketch

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.

function

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).

Model

1、线框造型系统

1. Wireframe modeling system

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.

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.

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 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.

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.

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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