Design of plane developments of doubly curved surfaces

• Published in: Computer aided design 1997-10, Vol.29 (10), p.675-685
• Main Authors: Azariadis, Phillip, Aspragathos, Nikos
• Format: Article
• Language: English
• Subjects: Applied sciences; Computer aided design; Computer science; control theory; systems; doubly curved surfaces; Exact sciences and technology; isomorphic patterns; planer developments; Software
• ISSN: 0010-4485; 1879-2685
• DOI: 10.1016/S0010-4485(97)00013-4

This paper deals with the approximate design of planar developments of doubly curved surfaces and their refinements in order to derive a final plane pattern with limited gaps and overlaps. The hole problem is divided in three stages; the stage of defining the staring guide-strip, the stage of designing the initial pattern and the stage of its refinement. The introduced method dealing with the first stage of the problem is based on elements of the geodesic and Gaussian curvature. In addition, an alternative technique for generating an initial planar development of a doubly curved surface is presented. Two methods for the refinement of the initial pattern are proposed, supported by a set of indices for measuring the accuracy of the flattened component. The first one is based on the surface geometry and the second one on the concept of generalized inverses. By way of illustration, all the proposed methods are presented in parallel with the generation and the refinement of plane patterns of a torus quadrant. In addition, an application of these methods in the 3D surface of a shoe last is demonstrated.