Geometry based triangulation of multiple trimmed NURBS surfaces

NURBS surfaces, conforming to the geometrical contours of the part to be re alised, play an important role in the design and simulation of the manufact uring process of many engineering applications, particularly in the area of composite laminates, ii laminate can have an arbitrary topology, and its c onstituent layers invariably have different surface and contour characteris tics. Consequently, the geometrical complexity to be dealt with, in the rea lm of computer aided design of composite laminates, is considerably enhance d. The individual layers constituting the laminate are represented in the f orm 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 d irectry on the B-Rep is complex and very tedious; a better approach is to b reak it down into precise piecewise planar representation. This paper prese nts a methodology for generating such a representation (triangulation). Tho ugh the method is based on known techniques in literature, the analytical a pproach and the treatment of the subject presented is unique and has not be en reported before. A few important features of the proposed approach are: (I) simultaneous triangulation of multiple surfaces yielding a crack-free r epresentation, (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 te chniques of polygonised trimmed NURBS surfaces proposed in the paper is ind ependent 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 th an C-0 continuous. The methodology has been adopted to generate triangulati on of various real life aircraft component surfaces (B-Reps). The methodolo gy proposed is applicable for the triangulation of general NURBS B-Rep. (C) 2001 Elsevier Science Ltd. All rights reserved.