Recognition And Suppression Of Blends In A Tessellated Solid Model

Abstract

Blend recognition and suppression from a tessellated model is important in applications such as model simplification in analysis and collaborative design where tessellated models are being used. This could also be used to pre-process the model before attempting to recognize form features in it.

A procedure is described for recognizing and subsequently suppressing blends (fillets/rounds) in a tessellated model of a part. Earlier efforts on recognizing secondary features such as blends have used the boundary representation (B-Rep) of the part as input. Blend recognition and suppression from a tessellated model has not been addressed to the best of our knowledge. There has been work reported on the related problem of segmentation of tessellated surfaces. Segmentation refers to the decomposition of the object into regions where the underlying surfaces having similar characteristics. The segmented surface may be of any of surface like plane surface. There are two broad approaches to segmentation - vertex-based and edge-based. The vertex-based method clusters triangles consisting of connected vertices having the same attribute. One drawback of this method is that the boundaries of the clustered regions are not clearly defined due to difference in the labels of contiguous vertices. The edge-based method is based upon the dihedral angle at each edge in the tessellated model. The main drawback of this method is that edges in the boundary of the segmented patches are disconnected. This will result in an incomplete bounding loop when used for recognizing features. Smooth transitions at the boundary of features cannot be trapped with this approach. These techniques cannot be therefore used for recognizing blends. There have been efforts to recognize and suppress blends in a B-Rep model. Suppressing blend features in a B-Rep model is easier (compared to suppression from tessellated model) because smooth edges provide a clue to presence of blends. In the case of a tessellated model, the bounding loop of blends will not consist of smooth edges and no explicit signature is available for blends. In B-Rep model, information about the radius of blend is also available while this is not directly available in a tessellated model. Constant radius blends meet the requirements of most blending features encountered in mechanical part design. The surfaces forming a constant radius blend may be classified as cylindrical, spherical and toroidal surfaces. Spherical blend is formed by a blending operation at a vertex at which either three concave linear edges or three convex linear edges are incident. Blending operation on a linear edge forms cylindrical blend. Toroidal blend is formed by a blending operation on a circular edge. This circular edge may be closed (end vertices are identical) or open. Toroidal blend is also formed at a vertex at which at least one convex and one concave edge is incident. So toroidal blend can be classified into closed toroidal blend, open toroidal blend and vertex toroidal blend. In recognition process, for every triangle, cylindrical, spherical and toroidal surface parameters are calculated. In the second step, triangles having same surface parameters are clustered. The cluster of triangles are then classified as a blend or a form feature. Finally, toroidal blends are classified as one of the three types of toroidal blend.

Procedures for the suppression of edge cylindrical blend and edge toroidal blend are described. At the present time, vertex blends are not suppressed individually. Rather in the process of suppressing edge blends, vertex blends are also suppressed. The parent surfaces that were blended are identified using the bounding loops of the blends. Triangles in the blend are then deleted and the parent surfaces are extended to suppress the feature. The key issues in suppression are - identification of all the surfaces at the blend, identification of the entities that were blended (edges and vertices) and updating the tessellated model.

Results of constant radius blend recognition and suppression, on benchmark parts from NIST design repository are presented. This is followed by a discussion on the correctness of the recognition procedures. The thesis concludes by summarizing the contributions and identifies the following are as recognition of variable radius blends, blends on non-linear surfaces, suppression of all small volumetric feature as areas for further research.