Could someone help me with the first problem I’m trying to solve in GH?

I’ve been stuck on this task for a week now and would really appreciate a helping hand. This is the first project I’m tackling in Grasshopper, so I’m a total beginner.

Here’s the problem:

I’ve a 2D cycloid curve that imitates the movement of a bicycle. I can adjust the radius, density, and number of cycles of the cycloid, and I’d like to keep these factors adjustable in the future as well.

The task is to place this 2D curve onto a waving 3D surface so that the cycloid follows the surface’s perimeter curve while also remaining inside/on top of the surface.

Right now, the 2D cycloid runs straight along the X-axis, but when I move it to follow the 3D perimeter curve, I also need to find a way to close the shape.

Any advice or examples on how to approach this would be greatly appreciated!

Here’s also a picture that tries to illustrate the problem:

Dear @krowgj
welcome to the forum.
are you following some tutorials to learn grasshopper ? which ?

did you manage step 1. the cycloid and can you provide data for 2. the Target Curve and Surface. ?

(you can drag & drop rhino files, images and .gh files to the post-edit window to upload and share)

A deformation from 2d (x,y) to Surface (u,v) can be done by flowAlongSurface in vanilla Rhino and with the
Sporph component in Grasshopper.

maybe follow some tutorials that gives you some knowledge about _flowAlongSrf first, then on Sporph … google will find many, and also there are many topics in this forum…

Mapping from 2d (x,y) to Surface (u,v) has some flaws. If you want to understand them you need to work through Essential Mathematics for Computational Design.

Which constraints do you want to follow, wenn the cycloid-Curve gets deformed on the surface ? what s the overall target of this excercise / challenge ? just some fancy graphics ?
…or do you want to visualise the exact physical pedal position/ movement of a bicycle when its ridden on a curved surface ? - which will be much more challenging.

Take care that x,y,z follow the right hand rule. general x is drawn left to right, y down to up. (not like your graph at 1.)

kind regards - tom

the main task is to build a suitable Base Surface to get Sporph to work correctly
u-v directions have to map.
this is why my i rotate the plane for the base Surface
(Plane Surface)

if you want to understand it more bake the geometry and look at it with rhinos _dir command to see u green and v red direction.
task_Sporph_tomp_00.gh (20.3 KB)

hope this helps, happy spaghetti - tom

Thanks so much for all your help @Tom_P ! I truly appreciate your time and effort. This helps me forward a lot.