Geometry based triangulation of multiple trimmed NURBS surfaces

Abstract NURBS surfaces, conforming to the geometrical contours of the part to be realised, play an important role in the design and simulation of the manufacturing process of many engineering applications, particularly in the area of composite laminates. A laminate can have an arbitrary topology, and its constituent layers invariably have different surface and contour characteristics. Consequently, the geometrical complexity to be dealt with, in the realm of computer aided design of composite laminates, is considerably enhanced. The individual layers constituting the laminate are represented in the form of B-Rep with constituent NURBS surfaces and curves. For the design and manufacturing simulation of a laminate, various operations like trimming, sewing and offsetting have to be carried out. To perform these operations directly on the B-Rep is complex and very tedious; a better approach is to break it down into precise piecewise planar representation. This paper presents a methodology for generating such a representation (triangulation). Though the method is based on known techniques in literature, the analytical approach and the treatment of the subject presented is unique and has not been reported before. A few important features of the proposed approach are: (1) simultaneous triangulation of multiple surfaces yielding a crack-free representation, (ii) tight control over the quality of triangulation leading to better results for both singly curved and multiply connected surfaces, and (iii) automatic elimination of spurious triangles. Also, the merging techniques of polygonised trimmed NURBS surfaces proposed in the paper is independent of B-Rep tolerance and has been carried out in the Euclidean space, unlike the existing works. The model assumes the surface to be no more than C0 continuous. The methodology has been adopted to generate triangulation of various real life aircraft component surfaces (B-Reps). The methodology proposed is applicable for the triangulation of general NURBS B-Rep.

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