Algorithm for bending a series of vertices at an arbitrary angle?

Question

I am looking for some information on how to "bend" an arbitrary list of points/vertices similar to the bend modifier you can find in typical 3D modelling programs.

I want to provide a list of points, a rotation focal point, and a "final angle." For my purposes, I will always be saying "points at minimum y of the set will not change, points at maximum y will be rotated at the maximum angle, everything in between is interpolated."

Example Image of starting configuration and desired result, given a 90 degree rotation:

Can anyone suggest a resource that would explain how to go about this? I'm prepared to code it (C++) but I'm wracking my brain on a concept that would make this work. It would be easy to generate the vertices, but the application I'm writing this for takes in user-created content and needs to bend it.

(Edited to add: I don't need a miracle matrix or deep equation solution... if you say something like "for each vertex, do this" that's good enough to get the green checkmark)

Thanks!

If an image is crucial to the question, please post the image in the question, not a link to it. — Beta, Apr 11 '21 at 06:49
this looks like very similar problem to this [How to bend a cylinder in three.js?](https://stackoverflow.com/a/54050883/2521214) — Spektre, Apr 11 '21 at 08:04
@WillNess: Really? I don't see it on [the list](https://stackoverflow.com/help/privileges)... — Beta, Apr 11 '21 at 16:10
@Beta I think I saw such complaints in the comments though I'm not sure.... — Will Ness, Apr 11 '21 at 16:22
@Beta yes that is right low rep users can not post images .. .which is weird as images and code are usually crucial to questions ... — Spektre, Apr 11 '21 at 18:34

score 1 · Accepted Answer · answered Apr 11 '21 at 06:48

You seem to be transforming a straight line to a circular arc, preserving distances between adjacent points.

So, if the point A is the one you want to hold constant, pick another point B to be the center of that circle. (The nearer B is to A, the more severe the bending.) Now for any point C you want to transform, break the vector C-B into the component parallel to A-B (call that component R) and the component perpendicular to it (call that k). The magnitude of R will be the radius of the circle you map C to, and you can transform the magnitude of 'k' into distance along that circle:

theta = |k|/|R|
C` = B + R cos(theta) + k|R|/|k| sin(theta)

Algorithm for bending a series of vertices at an arbitrary angle?

1 Answers1