Параметрическая модель геометрических объектов

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Аннотация

Предметом исследования являются методы создания параметрических моделей геометрических объектов, используемых в современных САПР, которые обеспечивают эффективную модификацию описаний объектов проектирования. Выделены три подхода при создании параметрических моделей - предварительная, параллельная и последующая параметризация. Описаны области применения моделей каждого типа, их характеристики и средства, с помощью которых они формируются. Отмечено, что предварительные или программные модели используются для формирования простых конструкторских объектов и элементов оформления чертежей. Параллельные методы формирования являются наиболее распространенными при создании графических изображений плоских и объемных тел произвольной конфигурации. Последующая параметризация применяется для формирования параметрических моделей ранее созданных конструкторских чертежей. Для создания моделей последнего типа используется автоматическое генерирование базовых сеток основных элементов изображения, которые адаптивно изменяются в зависимости от присвоенных новых значений размерных обозначений, используемых в исходном описании чертежа. В качестве метода исследования используется сравнительный анализ различных систем параметризации, позволяющий выявить основные подходы, используемые в них при формировании различного вида параметрических моделей графических объектов Новизна предлагаемого авторами подхода классификации современных параметрических систем заключается в упорядочивании различных направлений параметризации, а также методов и средств используемых при создании различных параметрических моделей в зависимости от соотношения времени их создания и построения соответствующих им изображений. В рамках такого подхода легко рассматривать и сравнивать всевозможные САПР вне зависимости от конкретных подходов и средств создания геометрических моделей, используемых в этих системах. Ключевые слова: параметризация, модель, чертеж, сетка, формирование параметрических моделей, программные макросы, параллельная параметризация, последующая параметризация, базовая сетка чертежа, адаптивная сеточная модель

параметрическая модель геометрический объект

Abstract

The research is focused on methods for creating parametric models of geometric objects used in modern CAD, which provide an effective modification of the descriptions of the objects of design. The authors select three approaches to creating parametric models: preliminary, parallel and subsequent parameterization. The paper describes the application of models of each type, its characteristics ad means by which they are formed. The authors note that preliminary or software models are used for the formation of the simple design of objects and drawings of design elements. Parallel methods of formation are the most common when creating graphic images of flat and three-dimensional objects of arbitrary configuration. Subsequent parameterization is used to generate parametric models of previously created design drawings. To create the latter type of models an automatic generation of basic key elements of the image grid is used. The elements adaptively change depending on the size designations assigned new values used in the original description of the drawing. As a method of study the authors use comparative analysis of different parameterization systems, allowing to identify the main approaches used in them in the formation of various types of parametric models of graphic objects. The novelty of the approach proposed by the authors of modern parametric classification systems is in the ordering of the various areas of parameterization as well as methods and means used to create a variety of parametric models depending on the time of its creation and the relation of building the corresponding image. Under this approach, it is easily to view and compare all kinds of CAD, regardless of the specific approaches and tools for creating geometric models used in these systems.

Keywords:

parameterization, model, drawing, grid, building parametric models, software macros, parallel parameterization, subsequent parameterization, basic drawing grid, adaptive model mesh

Already in the 80s, when were enough developed and introduced geometric model representation of the CAD design objects, became necessary in the mechanism, allows automatic modification of the forms created the model after construction simply by changing the values by setting new values. From the point of view of the designer this is a completely natural process more efficient editing of the prototype and quickly achieves the desired results as for three-dimensional and flat objects.

The solution of this problem has been accomplished based on the methods of automatic creation parametric models of the geometric objects. Wherein the process of creating a parametric model (parametric modeling [1]) of geometric object or figure provides by the formation of a quantitative relationships for each of all the constituent elements (graphics primitives). The parameters of each graphics primitive are determined on the basis their relative positions and relationships as a function of the independent parameters, which define the form of the object or figure. Usually this process incorrectly identify with the process of parameterization. After all, according to the parameterization theory under parameterization process is understood as the process of determining a set of independent parameters and the required quantity for a complete form determination of the object or form in general. At the same time, the parametric model of a geometrical object is defined through these general parameters of each specific graphics primitive, from which the object is formed.

In this way, in parametric modeling graphics primitives systems, constituents of total design objects, saves information about own parameters in a function from the basic parameters of the object in general. Therefore, primitives can be modified at any time by changing the values of the basic parameters. In this regard, the emergence of parametric modeling systems (designing), that often called parameterization system, should be considered essential, one might even say revolutionary, qualitative leap in the development systems of designing. They have opened absolutely new horizons of the acceleration of design processes and manufacture of new, modified products and ensure their life cycle.

In the practice of creating a CAD design, developed two basic directions for forming parametric models of geometric objects [2, 3] - one based on a programmatic approach, and the second - in the creation of these models at the same time when designer draws thumbnail of image, drawing or 3D object (parallel formation of the parametric model in the process of creating an image of the object).

Programmatic Approach creating parametric CAD models in 80 s historically had a powerful basis, since its application involved to obtain description of the model in high level language terms in the form of the program procedures, which can be embedded directly in the CAD. To obtain a parametric model unnecessary to make changes in the internal structure of the system design. When using the programmatic approach the process of creating the details is written as a sequence of commands with a number of keys parameters-values, defining the final form of the object being created. In fact, carried out the creation software of product (macro), forming of the corresponding graphical model. Subsequent application of a macro creation allows obtaining family of the same type of graphic objects according to the values of dimensional control variables, which were set by the designer. The programmatic approach has several directions -- procedural, structural, object-oriented programming and the predicate, which has different ways and methods of creating and organizing the corresponding programs.

The use of the programmatic approach of parametrization implies some interactive work, but this interactivity is very limited and reduced only to the input values of defining parameters within a pre-determined range of values. Increase the functionality of this type of models seems possible by the introduction of the requested parameters of the model is not only numeric values, but also can be a simple conditional expressions.

The main disadvantages of the programmatic approach - defining a limited number of parameters in the model because of the increasing complexity of the writing of the macro, predetermination of the range, and insufficient controls the correctness of the result, which can be semantically incorrect due to violation of the value range of a parameter. Finally, and most importantly, model obtained in this way programmatically is focused on building options only one specific project design and operational object is not editable. After finishing the procedure of constructing, the only way to change the built-in graphic representation comes down to an erase operation, recall the program, set new values of all its parameters and reconstructing image again. Nomenclature of software models, presented in many CAD, determined by system developers and generally allows the user limited capabilities in of automation design terms. If the system is open for expansion, the constructor needs to have programming skills and software debugging to create new program models. This presents to users constructors, additional requirements knowledge of high level programming languages.

In this regard, a programmatic approach is used only for solving a limited range of tasks. Usually it reduced to create simple program, but commonly used of macros, forming graphical objects, which do not require subsequently any in-line editing. However, a more expedient and macros generate a parametric program, allowing not only to form a corresponding image, but also effectively (quickly) adjust (edit) earlier formed submission by simply changing the values of its parameters. To do this, the user should not be given the opportunity to select, erase and redraw he appropriate macro. It needs to select it and override only its changing values. To do this, along with the choice of the macro designer must provide detailed information about its external and internal parameters, for example, in the form of a table with easily editable data.

In the CAD design, this approach is currently used only for the formation the elements of design drawings. In particular, it is used for applying dimensional and technological notation on drawings, forming areas of hatching, creating images of standard design of object (nuts, bolts, screws, washers, springs, bearings and etc.). It is used to create images of simple flat and volumetric graphical objects (for example, parallelograms, polyhedral, diamonds, parallelepipeds, cylinders, spheres, hemispheres, cones, tori, wedges, and etc.). On the basis of the models of these objects in further constructing is more complex geometric model. The programmatic approach is used to create and support graphical elements of drawings, which include a variety of arrows, balloons, shelves, additional signs, braces, refer to the sections and cross-sections, frames, axes, refer to databases, etc. elementary objects. In the architectural CAD program models are used to build walls, windows, doors, stairs, etc. building components, and various building structures.

In the schematic systems of the programming models may be applied to form electronic components, electrical circuits and printed circuit boards. Macros can be used to form any other type of circuits. As a language, which lets you create procedural software models, the designer can use any high-level language, as well as Auto LISP, Diesel, DCL and ActiveX technology in the composition of the environment AutoCAD, which initially focused on building software models.

Interactive approach provides the ability to create parametric models of objects, amenable to further modification, in the process of building their images. Unlike the programmatic approach, implementation of parameterization interactive methods required revision of the internal structure and model representation of a geometric object, compared with the already established organizing data principles in a previously existing CAD. The implementation of the new organization of the internal data structure leads to necessity a large conventional image processing systems or to develop entirely new systems. Possibilities of high automation processing of creation models, Possibilities of high automation processing for creation models, flexible editing and modifying objects, provides interactive models, became the reason that models are used in the most advanced systems of design automation.

The interactive approach suggests not only the use parameterization formed graphics primitives and images, but also to a built-in mechanism for the conversion of CAD graphic description of the object in the parametric model. As a part of this mechanism is provided, the modification of image according to the given new dimensional values. The development costs of such systems is relatively high, but justified by the versatility of the process of building a parametric model for any image and does not require programming knowledge from the constructors. This provides simplicity and quickness of obtaining modified objects, also supported by automatic bond of all stages of the design, engineering calculations, technological preparation, manufacturing and providing the product life cycle at the expense of using to describe a single graphical database. Where in parametric model at the interactive approach is created directly during image formation (parallel parametrization). To create such model is simpler, so it is easy to ensure the preservation of the internal structure of the system all necessary data formed on the primitives. CAD-system, in which the model is built at the same time with a portrayal of the image, called systems with internal parameterization, which underlines feature of the internal organization of data in such systems and fact, for that the constructor to create it does not require any further actions. Systems, which based on mechanism internal parameterization, allow user to construct some of the basic version of the object, and then change its parameters - dimensional designations, set conditions of constructions, relationships, etc. All these data are processed by the system core and the correctness of the final result are controlled at the input stage. In addition to the powerful processing core, it uses special data structures, which required for parallel conservation of parameterized models.

Can distinguish a few basic methods of organizing systems with parallel parameterization, (rigid parameterization or chronological (history-based) parameterization, predicate (Rule-based) approach and object-oriented design), which are based on certain geometric kernels (graphics library) - ASIS, Parasolid, Granite One, Compass, LGS and others.

The advantage of parallel methods of parameterization is a high degree of automation of formation processes and modification of the model.

The main disadvantages - it is often not possible to import such parametric models to other systems and build parametric models of previously created image design objects that appear in standard electronic formats exchange of graphic information (ASIS, Parasolid, DWG, DXF, STEP, IGES, etc.). This is related to the fact that these formats do not suggest to save all the data about the relationship between graphic primitives of images.

Therefore, importing parametric descriptions to other systems with parallel parameterization, built on other graphical and geometrical cores, often pointless, since as a result of this model turn out to non-parametric. In such cases it is necessary to carry out a full rendering of imported image in the system, which provides a process of internal parameterization.

Along with the newly created parametric models of design objects in the modern enterprises and in the design bureaus there are a huge amount of non-parametric descriptions of the parts and structures. They are represented in the form of descriptions of design drawings, created earlier, and their total number in the world is estimated at several billion copies. To translate descriptions of such objects in the modern parametric form submission must either re-create their models in parametric systems. However, this process takes a long of time and greater labor expenditures qualified designers. More expedient at presence of previously created electronic nonparametric graphical description of the image (drawing or sketch) to use methods so called subsequent parameterization of these images.

Subsequent parameterization corresponds to the case when the processes of graphic descriptions and the construction of the corresponding parametric models are separated in time. Thus in the source image file the description of the sketch or drawing details explicitly lists only information about the graphic primitives that constitute the image. Here is no explicit information about the methods and the sequence of their formation (algorithm of their formation) and the mutual relationships between the primitives. File, although it contains a description of the parameterized sketch or drawing, in which there is necessary sufficiency number of size designations to describe the form of the object in general, but the dimension designations not directly related to each graphics primitives within the graphic description of an object. The amount of these dimensional symbols (parameters) is significantly smaller compared with which is necessary for the direct implementation of automatic modification and redrawing each graphical primitive drawing by means of a computer.

For these options it is proposed to use a new type of parametric model, adaptive base mesh of original drawing to the dimensional notations, which may automatically formed based on analysis of the basic components of the graphic primitives drawing based on analysis of basic components of the graphical primitives drawing [4]. The construction of such an adaptive parametric grid model based on the fact that well-formed description of the details represented in the form of design drawings. However, this description is not parametric for the computer, since there is no explicit connection between the parameters each inbounds in his graphical primitive with values of sizes, installed in the drawing, also with the other parameters of graphical primitives. Therefore, for obtaining a parametric model of the object, represented in the description of the drawing, is required those or otherwise to determine its electronic model of parametric data for each graphical primitives.

Automatic creation of parametric adaptive grid model includes:

- the formation of the starting grid of the main base of the drawing, elements of which are defined by all the characteristic points of basic graphical primitives, constituting a graphical image details are provided on it. Elements of these grids (are orthogonal axes X and Y and angular, taking into account the slope of the points and segments which are relative to the axis X) correspond to the initial values of the coordinates and the inclinations of the primitives of the original image;

- establishing for those elements grid of new coordinate values and the slopes of primitives in accordance with new values sizes entered by the user sizes, which should correspond to the new, modified, image of drawing.

If the communications (the old coordinate value - the new value of the coordinates) between all elements of base orthogonal grids are installed then all the basic graphic primitives of the drawing, they can easily be redrawn by replacing their old values description of the coordinates to the new values. After that, using information of grid model, may relatively easy to redraw and all the rest, subsidiary or elements of registration, drawing (axial line, dimensional and technological notations hatch area, additional species, etc.).

As a result, based on the description of the original drawing will automatically get rebuilt. As a result, based on the description of the original drawing will automatically get rebuilt an image of the drawing Details according to the new set of dimensional parameters entered by the designer.

For the automatic creation of an adaptive parametric grid model of the drawing according to with a set of new values of dimensional notation should:

- to analyze the initial description of the drawing and to identify in it all the graphical primitives and arrange them into groups (the basic primitives constituting the image from the image details, dimensional notations, axes, technological designations, etc.) and within each group (e. g., lines, arcs, circles, etc.) ;

- on the basis of calculating the coordinates X, Y and the characteristic of the points of all graphical primitives (Fig. 1, a), defining image of the detail create basic orthogonal coordinate grid on axes X (X1, X2, …, X10) и Y (Y1, Y2, …, Y8) (Fig. 1, b) and the angular grid (Alf) ;

Fig. 1, a Fig. 1, b

- detect and identify all kinds of details, presented in the description of the drawing, and establish communication between the elements of the orthogonal grid in coordinates X and Y, relating to different views;

- define coordinates of the base point (BP) in the drawing (see Fig. 1), the position which shouldn't change during its modification according to the new dimensional values. For the base point it is accepted that, which is connected to the base view is a central point of symmetry of the species or lying on its axis of symmetry, or connected with this point of highest amount of size;

- establish the dimensional relationships between all the elements of each constituent in the base grid of drawing (by Xi, Yjand Ak) by processing at the beginning a simple linear (symmetrical and asymmetrical horizontal and vertical), and radial, diametrical and angular dimensional notations, then all parallel sizes available on the drawing. For each grid connection is formed as a set of individual entries for each pair. For example, for a grid X each entry is represented in the form of a set of (Xi, Xk VVik). Thus, in these elections, linking elements of grids, setting quantitative relationship between the coordinates of the base points of the initial primitive definition of the drawing (e. g., Xi, Xk) through the numerical (or functional) value of the linking parameter, the value of which is determined the new value of the size or aggregate size of the drawing according to the requirements of its modifications.

For the sketch shown in Fig. 1, and, after the processing of all size notations will be installed between the following elements of the basic grid:

- for the X coordinate: ((X3 X6 L1) (X1 X3 R) (X5 X8 L1) (X8 X10 R) (X6 X8 (P1 * Cos A)) (X7 X9 (P1 * Cos A)) (X3 X5 (P1 * Cos A)) (X2 X4 (P1 * Cos A))),

and

- coordinate Y: ((R Y3 Y1) (Y6 Y8 R) (Y3 Y6 (P1 * Sin A)) (Y2 Y5 (P1 * Sin A)) (Y4 Y7 (P1 * Sin A))).

Analyzing formed dimensional grid can reveal that this network is not properly covered by the base points P5 (X2, Y4), P9 (X4, Y7), P6 (X7, Y2) and P13 (X9, Y5) of the basic graphical primitives. And these points and their corresponding graphical elements obviously are not connected with one dimensional notation, and without including them in the grid dimension is impossible to form a complete parametric model of the object. In such cases, the second step of the algorithm for the raw elements of a basic grid (X2, X4, X7 and X9) in the cycle consistently reveals:

- the point at which the associated element of the base grid, for example, a point P5, with elements X2 and Y4;

- basic graphics primitives, which belongs to the detected by point P5. In this case, segment P5-P9, Obliquely to the axis at an angle A, obliquely to the abscissa axis at an angle A, and the arc which is determined by reference points P5, P1 and the center point P4 and the value of the radius R.

- type of the relationship between the identified segment and an arc on the basis of the direction (vector) of the segment and a vector, determine the coordinates of the center point of the arc P4, and points P5. As a result, such analysis revealed that the point P5 is interface point (tangency), of the arc and the segment, coming at an angle A;

- the condition of tangency, radius of arc and angle of a line of tangency (angle of a line connecting point of tangency with the center of the arc) determined by the values of the offset point of tangency P5 relative to the coordinates of the arc's center P4 along the x-axis (DX54) and Y (DY54). These values (DX54 = R * Cos A and DY54 = R * Sin A) have quantitative relationship between the basic elements of the basic grid and thereby allow for refill communications to the XY coordinates corresponding records (X2 X3 (R * Cos A)) and (Y3 Y4 (R * Sin A)).

Similarly, the communication corresponding coordinates supplemented by identifying the offset of the second point P6 from the center of the bottom right of the arc, Similarly, the communication corresponding coordinates supplemented by identifying the offset of the second point P6 from the center of the bottom right of the arc, in which it is accompanied with the second parallel line. Then adding entries (X7 X6 (R * Cos A)) and (Y2 Y3 (R * Sin A)).

It should be noted that the DX76 = DX54, and DY54 = DY76, as segments interface are equal and parallel to each other. These conditions allow us to identify immediately the Communications elements grids X4 with X5, Y7, with Y6, X9 and X8 with and Y5, to Y6,

As a result of all the elements of the source base grid are connected to each other via the new values of dimensional notations. This allows you to calculate the new coordinates for all elements of a basic grid of the drawing, given the fact that the coordinates of the base point will not change.

Thus, it may be fully formed parametric adaptive grid model of the drawing, which is represented as a set of records the coordinates X and Y, wherein each old value of the coordinates of the characteristic points of the graphic primitives (Xi _old и Yj _old) match of its new value (Xi _new и Yj _new), which corresponds to the new set of input values of sizes:

((X 1_ old X 1_ new) (X 2_ old X 2_ new) …… (Xi _ old Xi _ new) …… (X (n -1) _ old X (n -1) _ new) (Xn _ old X n_ new)),

((Y 1_ old Y 1_ new) (Y 2_ old Y 2_ new) …… (Yj _ old Yj _ new) …… (Y (k -1) _ old Y (k -1) _ new) (Yk _ old Yk _ new)).

Forming such a parametric model adaptive grid, can automatically rebuild source image detail drawing, you can automatically rebuild the source image of the drawing details and get modified image sequentially by redrawing each base entity, substituting in his original description of the new coordinates instead of the previously used old.

After redrawing the basic elements of an image in the drawing also can automatically add all of the necessary support elements and the forming elements, using conditions of their connection with the initial basic primitives.

As follows from the above material, the proposed parametric adaptive grid model and the corresponding drawing of modified details are generated automatically.

Conclusion

At present, the widely used parametric model for the formation of macro elements of design and construction drawings and components of various kinds of technical documentation. However, such models are not promptly modified, what is their disadvantage.

Very efficient and widespread system of creating 3D-models of engineering objects. They also include in their structure means for forming drawings, but design elements of this type of documents they are not yet developed. There is in them no means for automatic generation of parametric models nonparametric previously created design documents. In this regard, it is necessary to pay special attention to the development of systems subsequent parameterization.

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