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Study on Model Simulation Design Based on Open CASCADE Platform

CAD-based geometric design has been widely used in various industries in the society. With the continuous improvement of design complexity, higher requirements are placed on the model simulation design of high-precision and high-confidence. The paper analyzes the simulation process of 3D model and improves the feature extraction method in the process based on the research of OpenCASCADE platform. Firstly, the CAD platform geometry model is used to develop the model concept map, and then the model's three-view projection map is used to extract feature information; meanwhile, the complex surface adjustment and description are used to represent the model feature information. Finally, the graph feature vector obtained by the complex facet and transformation is calculated by using the maximum and minimum approximations as the distance between the feature references, so as to evaluate the similarity between the models. the experiment have shown that the projection mapping of complex surface adjustment can accurately identify the fluctuations of complex surfaces in the model, and facilitate the more precise acquisition of feature parameters. The related functions studied in the paper will help to further improve the development capability of 3D models based on OpenCASCADE, which can make the faster implementation of high-precision simulation design requirements. Keywords-OpenCASCADE; CAD; Model Simulation


I. INTRODUCTION
Model processing and expression in the mechanical design drawing is inseparable from CAD model. The effect display of CAD model can be used to perform three-dimensional rotation and perspective special effects inspection to represent the completeness of model establishment. However, it is much more complicated to copy the prototype only in the case of a prototype. First, since the precise parameters of the original object are not grasped that require a series of measurement and conceptualization processes, but the details of the measurement and expression of the original object are not accurate enough, the deviation of the retrieval precision is easily generated, which requires and calculates the physical object to be prototyped and a more adequate description, so as to obtain accurate model parameters [1][2][3].

A. Model simulation process
The model simulation design in the paper is taken as the research object, and a representation method for complex surface adjustment and reconciliation is proposed. The box screening of the surface adjustment of the original physical model is carried out, and the model projections of different complexity levels are applied to different packaging boxes for feature vector extraction [4]. Firstly, the user applies the CAD model projected in the model library to extract the feature information according to the conceptual design requirements and extracts the feature information, and uses the complex facet and descriptor to represent the feature information. Finally, the target model is returned from the database according to the feature information similarity measure result, and pushed to the users; the implementation process is shown in Figure 1.

B. Model geometry metric
In order to accurately identify and screen small, narrow and irregular objects in large-scale complex CAD models, a method in the paper is proposed to measure the size and space occupancy of the model.

1) Model size metric based on approximate minimum bounding box
Due to the advantages of simple calculations and small storage space, AABB bounding boxes and bounding spheres in computer graphics are widely used for approximating expressions of primitive geometric models for such things as collision/intersection calculations, occlusion queries, etc.
However, the encircled ball contains too much redundant volume; while the faces of the AABB bounding box are axially parallel, it is easy to be affected by the direction of the model that have with uneven distribution in three axial directions, which is as shown in Figure 2. Therefore, the accuracy of the approximate calculation of the model size of using the volume of the OBB bounding box is more accurate .

C. Algorithm principle
In mathematical statistics, for two-dimensional random variables (X, Y), in addition to the mean, standard deviation, and variance, the covariance is described as a linear correlation between X and Y. The equation of calculating the covariance cov(X,Y) is as follows.
Where, E represents the expected value of the variable.
The smaller the covariance, the more independent the two variables are, namely, the linear correlation is small.
A three-dimensional random variable (x, y, z) is constructed by inputting the vertex coordinates ,, of the model. The above covariance calculation formula is used to establish a covariance matrix, which is as follows.
Where, the leading diagonal element is actually the variance of the variable, and the non-diagonal element represents the covariance between the variables. The elements of the covariance matrix are real and symmetric.
The covariance matrix defines the propagation (variance) and direction (covariance) of the vertex data. The similar transformation of the covariance matrix is as follows.
The last three matrices in the equation are that the last one is the inverse matrix of the first one, and the middle one is the diagonal matrix; then the three eigenvectors of A are The model A is located on the equatorial plane surrounding the ball S, which is located on the coordinate plane xy of the coordinate system xyz.
Step2. A series of rays are generated from the center of the surrounding sphere, and the intersection of these rays Step1. The Chebyshev point position of the sampling Then model A can be represented by the Chebyshev point position (i, j), which is Step2. Normalization.
In general, different graphics have different sizes. If two shapes are the same and the sizes are different that the {d i } is different. Therefore, the graphics need to be normalized.
Unification of model A is generally normalized to the long or short side of the minimum bounding box of its model A.
The normalization factor of the paper is the radius r of the bounding sphere, and its normalization is as shown in equation7.
Where, v is a predefined constant.
Step4. Fasting and complex surface adjustment and transformation.
The rotation invariant descriptor of model A is obtained by using the method proposed in [16] to perform fast complex surface adjustment and transformation. A corresponding rotation invariant will be obtained for each frequency. The method can avoid the one-to-many correspondence and the instability caused by the shape disturbance, so as to obtain the rotation invariant descriptor of the model A.
Bandwidth B determines the density of the sampling points. When B is small, many details will be lost. When B is large, the model A is more accurate, but the time is relatively large. Therefore, we need to make trade-offs.
When the bandwidth B gotten by the experiments is 64, the accuracy is -3 5 10  , which can meet the graphics retrieval requirements. As a result, the bandwidth in the paper is set to 64.

C. Feature Vector Similarity Extraction
The similarity comparison problem between the graphics is converted into the distance metric between the feature vectors by using complex surface adjustment and transformation to obtain the feature vectors of the graphics.
The Euclidean distance is selected to calculate the distance between the feature vectors. Assuming that the eigenvectors of the two models f and g are 1 , , ,  OpenCASCADE, which is bound to have great significance and broad market prospects.