A-Frame 3D rope, or string that is bend curve - aframe

How to create A-Frame 3D rope, or string that is bend curve?
I can't find this in the manual.

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Projecting triangle onto a sphere

I'm looking to build a spherical mesh out of equilateral triangles. I've calculated the points of the triangle and managed to create a flat mesh out of them.
I'm now stuck on how to translate these points from a flat surface onto a sphere
My goal is to achieve something similar to the result from this video. Where the creator does something close to what I'm trying to do by projecting points from a plane onto a sphere.
I've tried looking for "projecting triangle onto a sphere" results online but I've not managed to find anything that would bring me closer to a solution.

I have a mesh, how to find its deepest point that could fit a sphere?

So I have a 3D polygon based mesh surface (2.5D). I want to find its deepest point (minimum) that could fit a sphere of radius r. How to do such thing not utilizing physics engine?

Rotating a 2D graph to a 3D view

Any advice please as to how would I go about plotting 'by hand' a stock standard 2D sine graph 'rotated' into a 3D view like in the diagram?

how can i get 2d angle from a 3d quaternion rotation?

I would like to know how can i get 2d angle from a 3d quaternion rotation?
for example I have a 3d skeletal bones and I wanna my 2d sprite follow the rotation from for example Head bone in 2d orthogonal camera.
thanks for answers.
is there any ways?

Depth interpolation for surface removal with perspective projection

This seems like a question for which an answer should readily available on the web or books but my quest for an answer has led me so far only to blind alleys that turned out to be dead ends.
I'm trying to draw 3D lines in real-time with hidden surface removal (the lines are edges of solid objects).
So I have two 3D points that were projected to 2D points using perspective projection. For each point I have computed the depth of the point. Now I want to draw the line segment that joins the 2 points, and for hidden surface removal to work I have to compute, for each intermediary 2D point on the 2D line (that results from the projection) the depth of the corresponding 3D point (the 3D point that is projected on that intermediary 2D point).
My problem is that, since the depth function isn't linear when you do perspective projection, I can't interpolate the depth of the 2 original 3D points to compute the depth of the intermediary point.
So how do I compute the depth of each point on the line with a method that's compatible with the constraints of real-time rendering?
Thanks in advance for any help.
Use homogeneous coordinates, which can be linearly interpolated in screen space: http://www.cs.unc.edu/~olano/papers/2dh-tri/

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