Approximate continuity in geomeric modeling

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Scientific and engineering applications often require an existing object be reproduced as a patchwise surface of designated continuity. Current solutions fail to meet the smoothness criteria of many industrial and scientific applications. The goal of my research is to find acceptable surface reproduction techniques. Previous researchers used G1 continuity as the definition of smooth. Unfortunately, surfaces produced by the G1 schemes can fail to appear visually smooth. In earlier work, I defined eG1 continuity between two patches to mean that adjacent patches share a common boundary, but the angle between the normals of the two patches at a point on the boundary is bounded by a user defined epsilon. By relaxing the G1 continuity conditions to eG1, I have been able to improve patch shape and create visually smoother patch networks. For industrial applications, such small discontinuities are acceptable since the manufacturing process has limited precision.