Approximate continuity in geomeric modeling

几何建模中的近似连续性

• 批准号: RGPIN-2016-03879
• 负责人: Mann, Stephen
• 金额: $ 1.6万
• 依托单位: University of Waterloo
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2017
• 资助国家: 加拿大
• 起止时间: 2017-01-01 至 2018-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=634647
• 关键词: Approximate; continuity; geomeric; modeling

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.

科学和工程应用通常需要将现有物体复制为具有指定连续性的补丁状表面。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。以前的研究者使用G1连续性作为光滑的定义。不幸的是，G1方案产生的表面在视觉上可能不光滑。在早期的工作中，我定义了两个补丁之间的eG1连续性，这意味着相邻的补丁共享一个共同的边界，但是两个补丁在边界上一点的法线之间的夹角由用户定义的epsilon限定。通过将G1连续性条件放宽到eG1，我已经能够改善斑块形状并创建视觉上更平滑的斑块网络。对于工业应用，这种小的不连续性是可以接受的，因为制造过程的精度有限。