Here’s my proposal; If I want to connect two positions on the surface, then the shortest path would be the best centerline of the tape. I compared between geodesic curve and “curve on surface”. And mostly the geodesic curve has the shorter length.
I made a pipe, and got the intersection curves. With them, I made a ruled surface for my tape.
Do you think if it’s in a good way? Or Is there a better solution?
The shortest path on a surface is indeed a geodesic line. I don´t however think that it is the best option if you want to avoid wrinkles, due to the fact that the geodesic in 3d space is curved. So I think that if you want to do this physically, the better option will be section cuts perpendicular to the surface. Or maybe not. Have to be tested. Then a hot air gun to get rid of eventual wrinkles. After all the tape is usually a film with not much dimensional stability and would allow for a good deal of heat treatment.
I would try dividing the surface with both evenly spaced geodesics and section cuts (with the width of the tape) and compare the results. You can also use paneling tools to project the strips onto 2d.
What I want to say was that I cannot apply your method to connect two positions on the surface.
You drew the curve on 2d plane. And projected(or pulled) to the target surface.
If the target surface looks planar on the specific view, the projection will be good solution.
But, if you see my attached GH file, the surface is double-curvatured.
If you pull the curves, the start & end of the tape is not same as that I planned originally.
If you project the curves, the width of the tape is not uniform on the surface.
they don’t have to be planar. You can also use an “offset on surface” or your pipe approach for getting the offset curves. Its just a bit more difficult to do the blends then. As an alternative you could also stay planar, but defining the plane in a way that it averages the initial surface. However, I still believe you should simplify the base surface, otherwise your curves will be horrible and error is very likely to occur. Intersections and projections always increase cpcount (at least in Rhino), which makes it much more difficult to actually dealing with wrinkles. You should also notice that surfaces with strong curvature and strong change in curvature always look bad in one perspective where in others it looks okay. This is actually one of the most common problems I have to deal on work. That’s why I’m used to value simplification much higher than accuracy in terms of numbers. You might also noticed that I used a viewpoint with parallel projection in order to evaluate it better
Imagine a doubly curved surface. Imagine 4 individual points. If you connect them 2 by 2 with geodesic lines, then the geodesics follow the shortest path on the surface… which is not a straight line. This is why the width between them is non-uniform. This is why I suggested to test it out with section cuts, because then you can have some control over the uniformity.
As you can see in my image, you can have geodesics which are curved in 3d but relatevely straight in 2d or section cuts which are straight in 3d but curved in 2d. I know of no method in which you can have both.
My question is do you plan to do this in the real world or it is just a model? If you do plan to do it, then I suggest the following approach. Pannel the surface using geodesics. Make sure your pannels are a bit smaller than the width of your tape. Flattem then in 2d. Then print the resulting strips in 1:1 scale. Cut out the patterns out of your tape and you are good to go. No wrinkles what so ever
What do you mean by “follow”? Do you mean the central curve, going down the middle of the strip, lies on a target surface? Or do you mean the strip itself is a subset of the surface? In either case, I think this is very doable.