KR20000032763A - Geometric constraint solution for parametric design - Google Patents

Abstract

PURPOSE: A geometric solution for parametric design is disclosed is to minimize the numerical instability in designing CAD models by concentrating on the constructive approach and the numerical approach. CONSTITUTION: A parametric design's geometric solution method is composed of graph generation(100), construction plan generation(200), plan evaluation(300), and model modification(400). The CAD model input(11), based on geometric entities and constraints is processed by supervised input(c1)(100). A new graph is generated and processed through (11), (c1), second supervised input(c2), graph reduction and classification(M2), rule reasoning method(M1) and results in the creation and classification of design history(200). Design history is then processed by (11), (c1), (M1), and cluster analysis algorithm (M3), and the evaluation of system and output of variable model design is made(300). Based on the (300)'s variable model design, a new measurement and constraints is created by API calls system and evaluated by (300), and a new variable model design is created.

Description

Geometric Constraints Solution for Parametric Design

The present invention relates to a method for effectively solving geometrical constraints for parametric design, and more particularly to a new method for parametric design that can solve various geometrical constraint problems in an effective and short time.

Parametric design is a methodology for solving geometrical constraints between geometric elements. In other words, parametric design is a method of CAD that defines a shape by expressing a constant relationship between geometric elements such as points, lines, curves, and faces, which are the basic units for defining the shape, as a function of dimensions.

Therefore, the shape defined in this way can be transformed into various similar shapes according to the value of the dimension giving the positional relationship of the shape elements, unlike the existing shape definitions. Conventional CAD systems were used for drawing or shape modeling after design variables were determined during the design process.However, in parametric design, the model is modeled only with the conceptual shape of the designer, and the design variables are determined as constraints are gradually specified. It was recognized as a way to reflect the process as it is.

FIG. 6 shows a shape designed by a parametric design technique and a modified shape according to a dimension value change. As shown in FIG. 6, this approach can be usefully used in the initial design stage, which requires a lot of modifications because the design modification process is performed by a simple dimension value change. In the future, this research will be actively conducted and applied to various products such as product design, simulation and building structure design.

There are two conventional parametric solutions.

1) Numerical approach and

2) There is a constructive approach.

The numerical approach is to define the shape by constraining the shape constraints in the form of an equation and solving the system of equations. The main advantage is that, in theory, it can solve various types of constraint problems that can be expressed as equations. However, there are big disadvantages as follows.

First, most constraints are expressed as high-dimensional equations, causing numerical instability in finding solutions, and there is no solution consistency. Second, numerical methods are inefficient due to the complexity of high-dimensional equations. Third, since the numerical method cannot obtain a plurality of solutions, it is impossible to obtain a solution suitable for the user's intention.

Because of this problem, most parametric design systems follow an analytical approach to solving geometric problems.

The analytic approach expresses a set of constraints as knowledge, such as graphs or predicate symbols, and processes the expressed knowledge to produce a series of design histories. Then, the generated history is sequentially solved to gradually restrict the degrees of freedom of the geometric elements. This approach symbolically handles constraints, which minimizes the numerical instability of the numerical approach.

However, constraint problems that can be handled are limited and inefficient in generating design history.

It is an object of the present invention to provide a geometric constraint solving method for parametric design that can efficiently handle various geometric problems while minimizing numerical instability.

The present invention is based, in part, on a constructive approach and partly based on a numerical approach. The analytical approach solves the Ruler-and-compass Constructible shapes, and the numerical approach solves the Ruler-and-compass Non-constructible shapes.

Thus, the efficiency of the geometric solver can be maximized by combining the efficiency of the analytical approach with the universality of the numerical approach.

1 is a functional diagram of a geometric constraint solution proposed in the present invention.

2 is a constraint graph generation of the CAD model based on FIG.

3 is a graph cluster classification diagram based on degrees of freedom in order to efficiently solve geometrical constraints according to the present invention.

4 is a plan generation process for the model of FIG.

5 is a classification diagram illustrating a solution of a graph cluster classified in FIG. 3.

Figure 6 is a simple illustration that can be solved by the present invention.

<Description of the code | symbol about the principal part of drawing>

10: CAD model input part 20: reference constraint part

30: processing algorithm unit 40: user input unit

50: output unit 100: constraint graph generation unit

200: pharmaceutical plan generation unit 300: plan evaluation unit

400: Shape Correction

Geometric constraints problems are expressed in terms of geometric elements and constraints. The geometric elements used in the present invention are composed of points, lines, circles with radius, line segments, and arcs. Constraints include Distance, Angle, Parallelism, Concentricity, Tangency, Perpendicularity, and Incidence. Geometric elements have degrees of freedom that indicate their shape, size, position, posture, and so on. Lines and points have two degrees of freedom and circles have three degrees of freedom. Rigid bodies also have three degrees of freedom.

Geometric constraints, on the other hand, serve to remove this degree of freedom. Most constraints remove 1-degree of freedom, with some exceptions. The distance between the two straight lines eliminates two degrees of freedom because they must satisfy the parallelism and distance at the same time. And, the central coincidence relationship also eliminates two degrees of freedom. Therefore, in order to solve the geometric constraint problem, constraints must remove all degrees of freedom of a given geometric element.

Configuration and operation of the geometric constraint solving process in the present invention is largely two steps, as shown in FIG. A plan generation process of generating and classifying design histories (clusters) from geometric elements and constraints; This course is designed to evaluate the generated design history and output the variable design model. In order to perform the plan generation process 200 and the plan evaluation process 300, the constraint graph generation process 100 is performed as a preprocessing process. The shape modification process 400 is used to modify the CAD model in which the constraints are completely solved through the first to third processes.

Accordingly, the present invention, as shown in Figure 1, receives the CAD model (I1) consisting of the geometric entities (Geometric entities) and constraints (Constrains), the geometric constraints, shapes given to the first control input (C1) And a first step (100) of generating a constraint graph based on the geometric elements;

The constraint graph generated in the constraint graph generation process 100 receives the CAD model input (I1), the first control input (C1), the second control input (C2) for the cluster formation classification law, and graph reduction and A construction plan generation (200) for generating and classifying a design history based on the classification (M2) and rule inference (M1) method;

Evaluation of the constraint system by receiving the design history generated in the plan generation process 200 by the CAD model input (I1), the first control input (C1), rule inference (M1), cluster analysis algorithm (M3) A plan evaluation process 300 for outputting a variable design model;

Based on the variable design model generated by the plan evaluation process 300, new dimensions and constraints are received by API calls and fed back to the plan evaluation process 300 to create a new variable design model. Modification process 400 is made.

In the input I1 of the CAD model input unit 10, geometric elements and constraints for the basic CAD model are input, and the first control input C1 and the second control input () of the reference constraint unit 20 are input. C2) is a reference constraint condition part that controls the input values input from the CAD model input part 10 to receive only the values that can be processed by comparing whether the input values can be processed by the system, which are preset by the main program. have. The rule inference (M1), graph reduction and classification (M2), and cluster analysis algorithm (M3) are processing algorithms 30 that provide each algorithm to be processed in the present invention, and are processing algorithms of the main program. In addition, the API call is a user input unit 40 for the user to enter a modification condition when performing the shape modification process, the evaluation and the variable design model of the constraint system generated in the plan evaluation process through the output unit 50 Output

First, the CAD model input unit 10 receives a basic CAD model, which is composed of geometric elements and constraints. The constraint graph generation process 100 first checks whether the input CAD model is valid according to the criterion of the first control input C1 and then generates a constraint graph if it is valid. When a CAD model as shown in FIG. 2A is input, a constraint graph as shown in FIG. 2B is generated.

When the constraint graph is completed, the plan generation process 200 generates a series of design histories (clusters) that gradually satisfy the constraints. This classifies each cluster type as shown in FIGS. 3A to 3D, and generates a design history of the process as in steps 1 to 5 of FIG. 4 according to the classified form. The methodology used at this time is rule inferencing method and graph reduction.

The plan evaluation process 300 newly calculates coordinate values (positions and postures) of each shape element based on the generated design history. That is, the evaluation process removes the constraints according to the design history by applying different solutions according to the cluster types classified as shown in the table shown in FIG. 5.

The modification process 400 of the CAD model is performed by assigning new values to the dimensions & constraints in user inputs (API Calls) and then recalculating the design history generated in the plan generation process 300. Details of each process are described below.

Constraint graph generation process 100 represents the CAD model as a constraint graph, as shown in Figure 2 (a) and (b). In the constraint graph, each node represents a geometric element and each arc represents a constraint.

2 (a) shows a CAD model. P0 to P3 represent points, and L0 to L3 represent geometric elements such as lines. D1 and D2 are constraints that constrain geometric elements. Each node (circle) represents a geometric element and each edge (straight line) represents a constraint. For example, the node P0 represents a point with two degrees of freedom (x, y coordinates) and is connected to two straight lines L0 and L3. The L3 node is a straight line having 2-degrees of freedom, passes through P0 and P3, has a right angle (P) relationship with L0, and has a distance of D2 from L1.

In the plan generation process 200, the subgraphs satisfying the constraints are classified from the constraint graph to form a series of rigid bodies having three degrees of freedom (FIG. 3 (a)). Rigid bodies with three degrees of freedom are referred to as clusters. A cluster is a set of geometric elements and constraints, and the relative position and attitude relationships between the elements are fixed. The process of creating a constraint graph into a rigid body by repeatedly performing a cluster process of finding a rigid body having three degrees of freedom and making it into one cluster and R _i is a plan generation process.

3 (a) to (d) are classification diagrams classifying rigid bodies. For example, FIG. 3A is composed of three geometric elements G _{1 to} G ₃ and three constraints. Thus, the shape elements have six degrees of freedom. However, three constraints give a total of three degrees of freedom. In other words, if a set of shapes have three degrees of freedom in two dimensions, they become rigid bodies (two degrees of freedom due to movement and one degree of freedom due to rotation). Similarly, FIGS. 3B to 3D each refer to rigid bodies. The reason for classifying the rigid bodies according to the graph form is to apply the correct solution according to the classification form of the graph during the plan evaluation process. Where G _i is a geometric element (or cluster) having two degrees of freedom, R _i is a cluster (or geometric element) having three degrees of freedom, and R _ij is a geometric element in the cluster R _i .

Therefore, (b) of FIG. 3 shows a form in which an element G ₁ having two degrees of freedom and an element R ₁ having three degrees of freedom are connected by two constraints, and FIG. The elements R ₁ and R ₂ are connected by three constraints, and FIG. 3C can be further classified into three cases. That is, (c ₁ ) of FIG. 3 is a structure in which one element R ₁₁ and three elements R ₂₁ , R ₂₂ , and R ₂₃ are each connected with one constraint, and two elements and three elements. , 3 elements and 3 elements are respectively connected.

FIG. 4 illustrates the overall process of finding and solving rigid bodies on the constraint graph according to the cluster classification of FIG. 3.

For example, step 1 (STEP 1) finds a cluster consisting of constraints that remove 2-degrees of freedom. For example, elements L3 and L1 are connected to edge D2, with two degrees of freedom G2, Change the form of L0 connected to D1 to G1. That is, if the condition of step 1 is given to Fig. 2B, it can be displayed by the constraint graph shown on the right side of step 1 of Fig. 4. If this is changed again by clustering in Step 2, R1, P0, P1, and P2 shown on the right are connected to each other by two constraints. Proceeding to the stem 5 in the same process, it becomes one element R4, and the design history of steps 1 to 5 is found and stored.

As such, in the plan generation process 200, each constraint graph is classified into rigid structures, and each classified rigid structure is classified into classifications until only one rigid body is finally obtained while changing the graph by the stepwise clustering as shown in FIG. It performs the clustering accordingly and saves the history of the design.

The plan evaluation process 300 satisfies the constraint by sequentially calculating the position and attitude of the geometric elements within each cluster.

In the evaluation process, the method adapted to the characteristics of each cluster is applied, thereby achieving both efficiency and universality. A cluster in the form of a ruler-and-compass constructible (RCC) can be solved by a rule-based method (Resolution A). This method calculates the position and attitude of geometric elements by selection and inference of rules.

Extended ruler-and-compass constructible (ERCC) clusters are solved by analytical techniques (Resolution B). It is calculated by a function consisting of a series of rotations and translations written to satisfy geometric constraints.

The cluster in the form of a roller-and-compass non-constructible (RCNC) is solved by a numerical technique (Resolution C) (Newton-Raphson Method). We solve the constraint problem by numerically obtaining a transformation matrix representing the positional relationship between two internal clusters.

The roll reasoning method of the solution A, the analytical method of the solution B, and the numerical method of the solution C are well known methodologies, and detailed descriptions thereof will be omitted.

For example, if the cluster type as shown in (a) of FIG. 3 has one edge connection and an RCC cluster type having three G nodes, the constraint is removed by solution A, which is a roll inference method.

In addition, in the case of (C) of FIG. 3, the cluster type is three edge connections, the type of (c1) of FIG. 3 in which three constraints are connected to one geometrical element R11, and two to one element. In the case of an ERCC type cluster of type (c2) of FIG. 3 connected with constraints, the constraint is solved using analytical solution B, and each geometric element of FIG. c3) In the case of cluster of type RCNC, solution constraint is solved by numerical method, solution C.

As described above, the constraints are solved by applying the above-described solutions A, B, or C according to the cluster type and the type of the figure. The process is performed in turn according to the design history as shown in FIG. You will create a design model.

In addition, the shape modification process 400 modifies the shape of the variable design model generated through the plan evaluation process 300 according to the input condition of the user input unit 40 and feeds it back to the plan evaluation process 300. Create the design model you want.

Figure 6 is a simple illustration that can be solved by the present invention, as shown in the form of Figures 6 (a) and (c) of Figure 6 through the above four processes as shown in Figure 6 (b) and (d) In addition to changing the shape to), you can also change the dimensions to obtain the desired design model.

As described in detail above, the present invention can efficiently handle various geometric problems while minimizing numerical instability.

According to the present invention, the development of a husk that can solve various geometrical constraints imposed during the design process can greatly shorten the time required for design speed and design modification. In addition, the methodology designed as an open structure can be used as a component technology of CAD can be applied to various fields. In particular, it is possible to easily develop an intelligent CAD system based on the present invention.

In addition, most three-dimensional modelers in Korea depend on imported goods, and in the domestic case, they are limited to 2D design or curved modeling. As such, the open architecture of the product will not only improve CAD technology but also serve as the basis for developing complex software technology.

Claims (3)

A constraint graph generation process of receiving a CAD model consisting of geometric elements and constraints and creating a constraint graph representing geometric elements as nodes and constraints as edges (straight lines); A plan generation process of generating and classifying a series of design histories that gradually satisfy the constraints when the constraint graph is completed; A plan evaluating process of generating a variable design model by newly calculating coordinate values (positions and attitudes) of each shape element by applying different solutions according to the classified cluster types; A shape correction process for feeding back the variable design model generated in the plan evaluation process to give a new value to the dimensions and constraints as a user input to recalculate the design history generated in the plan evaluation process; Geometric constraint solving method for a parametric design, characterized in that The method of claim 1, wherein the plan generation process, Classifying a subgraph satisfying the constraint from the constraint graph; A second step of creating a series of rigid bodies having three degrees of freedom in which the relative position and attitude relations between the elements are determined as a set of geometric elements and constraints by the subgraph classification; The third step is to find a rigid body having 3-degrees of freedom and repeat the first and second steps to make it into a cluster R _i to generate a design history that makes the constraint graph into one rigid body. Geometric constraint solution for metric design. According to claim 1, wherein the plan evaluation process, The constraints are satisfied by sequentially calculating the position and attitude of the geometric elements within each cluster, According to the characteristics of each cluster, a cluster of RCC (Ruler-and-compass constructible) type is based on a rule inference method (Rule-based method) which calculates the position and attitude of geometric elements by rule selection and inference. Extended ruler-and-compass constructible (ERCC) clusters are analytical techniques that are calculated by a function consisting of a series of rotations and translations created to satisfy geometric constraints. In the case of a cluster-and-compass non-constructible (RCNC) cluster, the Newton-Raphson method numerically obtains a transformation matrix representing a positional relationship between two internal clusters. A method for solving geometric constraints for parametric designs, characterized by solving constraints.