Elsevier

Computers & Graphics

Volume 38, February 2014, Pages 97-107
Computers & Graphics

Special section on CAD/Graphics 2013
Feature-based simplification of boundary representation models using sequential iterative volume decomposition

https://doi.org/10.1016/j.cag.2013.10.031Get rights and content

Highlights

  • Simplifying the CAD models is needed for various engineering activities.

  • A new feature-based simplification method of B-rep models is proposed.

  • This method first generates a feature-based model from a B-rep model.

  • Sequential iterative volume decomposition is applied for feature-based model generation.

  • Feature-based simplification is then applied to the generated feature-based model.

Abstract

When computer-aided design (CAD) models generated in the design phase are used for engineering activities such as engineering analysis, distributed collaborative design, and virtual prototyping, a process for simplifying the CAD models is needed. In this study, a feature-based simplification method of boundary representation (B-rep) models using sequential iterative volume decomposition is proposed. This method generates a feature-based model from a B-rep model by sequentially and iteratively applying the four volume decomposition methods (fillet, round, and chamfer decomposition; wrap-around decomposition; volume split decomposition; and cell-based decomposition). Then, feature-based simplification is applied to the generated feature-based model. To demonstrate the proposed method, a prototype system is implemented, and experiments with test cases are performed. Based on the experimental results, we verified that the proposed method successfully simplified B-rep models.

Introduction

Physics-based simulations play an important role during the product realization process. These simulations help in reducing the need for expensive physical prototyping and hence shorten the product development time and reduce the product development cost. In order to get accurate results in a timely manner from these simulations, one must utilize simplified CAD models that retain the important details and eliminate the irrelevant ones [1].

Three-dimensional (3-D) CAD models are simplified by suppressing constituents that have low importance, which is quantitatively evaluated. Based on the representation of the CAD model, simplification methods are classified into mesh simplification, boundary representation (B-rep) model simplification, and feature-based simplification. Feature-based simplification is superior to the other approaches for engineering activities such as engineering analysis, distributed collaborative design, and virtual prototyping [2].

Feature-based simplification uses a feature-based model as an input. In feature-based modeling, a feature, which is a shape with engineering meaning, is a basic modeling unit, and the final shape is completed by incrementally applying features. A feature is additive or subtractive. An additive feature is applied by a regularized Boolean union operation (denoted by ∪), and a subtractive feature is applied to by a regularized Boolean subtraction operation (denoted by –). Since Boolean operations are a binary operation, a feature-based model can be represented by a binary tree, which is called a feature tree in feature-based modeling. In a feature tree, the leaf nodes are the volumes of the features, the internal nodes are Boolean operations, and the root node is the shape to be modeled.

In feature-based simplification, a simplification unit is a feature, and features with low importance are suppressed. The importance of the feature is evaluated by a pre-defined metrics. The type and volume of features are generally used as the metric. Feature-based simplification uses a feature-based model as an input. However, it is difficult to access a feature-based model; that is, although commercial CAD systems support feature-based models, the application programming interface (API) of a CAD system should be used to process a feature-based model. Using the API is very restrictive. Therefore, it is very difficult or almost impossible for third parties to implement feature-based simplification using the API. Instead of using the API, it might be possible to export information contained in CAD models in standard file formats such as IGES and STEP. Unfortunately, there is no commercial CAD system currently available that can export information from a feature-based model using standard file formats. Furthermore, considering the protection of intellectual property, sharing feature-based models may be dangerous because they contain design intent. For these reasons, it is currently not easy to use feature-based models.

To resolve this problem, we propose a feature-based simplification method of B-rep models using sequential iterative volume decomposition. The proposed method consists of a feature recognition stage and a feature-based simplification stage. In the feature recognition stage, a feature tree is generated by the volume decomposition of a B-rep model. In the feature-based simplification stage, the importance of features is evaluated, and a simplified model with a given level of detail (LOD) is generated by suppressing features that have low importance.

To apply the proposed feature-based simplification to a B-rep model, a feature-based model should be generated from the B-rep model. Volume decomposition methods are used to generate a feature-based model. The volume decomposition methods are used to decompose a complex shape into simple volumes. By mapping the simple volumes to features, a feature-based model is generated. In this study, however, the type of feature (except a round, a fillet, or a chamfer) is not recognized. The only recognized property is whether a feature is additive or subtractive. For this reason, in this study, a feature tree is called a “volume decomposition tree.”

Because feature-based simplification suppresses features of low importance, the configuration of a volume decomposition tree has a significant effect on the results of the simplification. Therefore, the process needs to improve the quality of the volume decomposition tree generated from a B-rep model. To improve the quality, we propose a sequential iterative volume decomposition method. This method decomposes a B-rep model by sequentially and iteratively applying the four volume decomposition methods (fillet, round, and chamfer decomposition; wrap-around decomposition; volume split decomposition; and cell-based decomposition). For the cell-based decomposition method, and the fillet, round, and chamfer decomposition method, the existing approaches were used. For wrap-around decomposition, a method proposed by Koo and Lee [8] was enhanced to be suitable to our volume decomposition approach. A volume split decomposition method was developed to process concave inner loops of a B-rep model.

The sequential iterative volume decomposition method has the following characteristics. First, a volume decomposition tree with both a Boolean union and a subtraction can be generated from a B-rep model with quadric surfaces. Previous volume decomposition methods cannot be applied to a B-rep model with quadric surfaces [3], [4], or a volume decomposition tree could have either a Boolean union or a subtraction [5], [6], [7]. Second, the proposed wrap-around decomposition approach was developed by improving the wrap-around operation proposed by Koo and Lee [8]. In addition, we developed a volume split decomposition method that complements cell-based decomposition and results in a good volume decomposition tree.

The remainder of this paper is organized as follows. A discussion of related works is given in Section 2. The basic operations for the sequential iterative volume decomposition, and the method for generating a volume decomposition tree from a B-rep model, are explained in 3 Basic volume decomposition operations, 4 Sequential iterative volume decomposition method, respectively. In Section 5, the method for simplifying a CAD model using the generated volume decomposition tree is described. The implementation and the experimental results are demonstrated and discussed in Section 6, and our closing remarks and summary are given in Section 7.

Section snippets

CAD model simplification methods

Based on the representation of a CAD model, simplification methods of CAD models are classified into mesh simplification, B-rep model simplification, and feature-based simplification.

Mesh simplification methods are mainly used in computer graphics. They simplify models by reducing the number of triangles in a mesh. Mesh simplification methods are classified into two methods based on how they reduce the triangles. In the incremental decimation methods [9], [10], [11], [12], [13], vertices or

Basic volume decomposition operations

The basic operations used in the sequential iterative volume decomposition method are fillet, round, and chamfer decomposition; wrap-around decomposition; volume split decomposition; and cell-based decomposition.

Sequential iterative volume decomposition method

The sequential iterative volume decomposition method is used to decompose a shape into volumes by sequentially and iteratively applying the four volume decompositions. In the proposed method the four volume decomposition methods are sequentially applied in the order of the fillet, round, and chamfer decomposition; the wrap-around decomposition and the volume split decomposition; and the cell-based decomposition. The proposed method is iterative because the wrap-around decomposition and the

Feature-based simplification using a volume decomposition tree

To simplify a CAD model using a volume decomposition tree generated by sequential iterative volume decomposition, four steps are needed. In the first step, the volume decomposition tree represented by a binary tree is first transformed to an infix expression using in-order traversal, wherein the operations of the infix expression are regularized Boolean union or subtraction, and the operands are the decomposed volumes (features). In the second step, the importance of the features is evaluated

Implementation and experiments

A prototype system that can simplify B-rep models using feature-based simplification was implemented using the proposed method. In our implementation, the C++ language, ACIS geometric modeling kernel, Hoops3D visualization library, and Microsoft foundation classes (MFCs) were used.

Fig. 15(a) shows the results of the feature-based simplification of the ANC101 part using sequential iterative volume decomposition. Fig. 16, Fig. 17 show the results of simplification of the part used by Lee [2] and

Conclusion

In this study, feature-based simplification of B-rep models using sequential iterative volume decomposition is proposed. The proposed method consists of two stages: (1) a feature recognition stage, wherein a volume decomposition tree is generated by the volume decomposition of a B-rep model, and (2) a feature-based simplification stage, wherein the importance of features is measured, and a simplified model with a given level of detail (LOD) is generated by suppressing features of low importance.

Acknowledgment

This work was supported by the Dong-A University research fund. The authors gratefully acknowledge this support.

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