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+--- Thread: Path: Smooth Transition Between Sections (/Thread-Path-Smooth-Transition-Between-Sections)
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RE: Path: Smooth Transition Between Sections - Espermaschine - 01-15-2018
@ofnuts: can you explain the inflection point thing some more, please
RE: Path: Smooth Transition Between Sections - Ofnuts - 01-15-2018
(01-15-2018, 04:38 PM)Espermaschine Wrote: @ofnuts: can you explain the inflection point thing some more, please
https://en.wikipedia.org/wiki/Inflection_point
In other words, a point where the tangent to the curve intersects the curve, typically, the anchor I put on the left of "B" in the XCF I posted.
The rationale is that even if you can have an elementary Bezier curve with an inflection point, it puts a lot of constraints on the tangents to get it right. If you put an anchor on it, then the Bezier curves on each side have no such points and are simpler to do. Also, on the inflection point non-symmetrical tangents (but still co-linear of course) still make a smooth-looking curve, so you have a bit more margin on the handles.
RE: Path: Smooth Transition Between Sections - Espermaschine - 01-15-2018
Yeah, but how do you decide where to put the nodes ?
EDIT: i guess you can see it in the animation of the wikipedia article: its when the handle changes direction
https://en.wikipedia.org/wiki/File:Animated_illustration_of_inflection_point.gif
RE: Path: Smooth Transition Between Sections - Ofnuts - 01-15-2018
(01-15-2018, 08:49 PM)Espermaschine Wrote: Yeah, but how do you decide where to put the nodes ?
I eyeball the inflection points (when there are such points). Otherwise I try to see where the curvature radius changes fast. Sometimes I have to add an anchor in the middle of a long curve. I also move the anchor along the line. But the fewer nodes, the better.
Example below from an image you find here: https://en.wikipedia.org/wiki/Airfoil (the original image is an SVG but I didn't even look at it, I imported the 1000px PNG version). On that one there is a hardly visible inflexion point towards the end of the extrados. My initial anchoring didn't work welll until I put an anchor on (or near) it.
RE: Path: Smooth Transition Between Sections - Espermaschine - 01-15-2018
All clear now. I didnt fully understand what inflection point means.
The word meaning is more obvious in german
RE: Path: Smooth Transition Between Sections - Ofnuts - 01-15-2018
Also "point d'inflection" in French, rather obvious to me, but then maybe I did too much math in my youth.