Approximate continuity in geomeric modeling

科学和工程应用通常要求现有对象被复制为具有指定连续性的面片状表面。目前的解决方案不能满足许多工业和科学应用的平滑标准。我的研究目标是找到可接受的表面复制技术。以前的研究人员使用G1连续性作为平滑的定义。不幸的是，由G1方案产生的表面可能在视觉上看起来不光滑。在以前的工作中，我定义了两个面片之间的eG1连续性，意味着相邻的面片共享一个公共边界，但边界上一点上两个面片的法线之间的角度由用户定义的epsilon界定。通过将G1连续性条件放宽为eG1，我已经能够改善面片形状并创建视觉上更平滑的面片网络。对于工业应用，这种小的不连续是可以接受的，因为制造过程的精度有限。

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.