I would like to ask you question to confirm if I understand “fairness of surface” correctly.
Are my following three perceptions correct?
- When evaluating the “smoothness” of a surface, there are 2 indicators: continuity and fairness.
- When the curvature changes gradually, the surface is fair. When the curvature changes suddenly, it is unfair.
- In Rhino, fairness is checked with the _ CurvatureAnalysis command. A gradual change in color means fair. A sudden change in color means unfair.
The images below are examples of when fairness is better than continuity for evaluating smoothness.
The 3dm file is continuity vs fairness.3dm (1.5 MB) .
The surface on the right of the image is relatively unfair because of the rapid color change.
I think it will be useful for people who have the same questions as me, so I will attach a link to the information source that I looked up when I created the question.
- official help of _CurvatureAnalysis command
- how to use _CurvatureAnalysis command, see rhino official guide level2 p134
- “Fairness is an elastic concept and different applications may have different requirements. Still, researchers three that regularly distributed curvature is favorable”
- “A rough consensus is that a surface is’ fair 'if it has optimal monotonicity and distribution of curvature”
- forum: local continuity vs. Fairness
- forum: Being curvature continuous is not in itself a measure of quality