I am trying to implement linear bending of a mesh by following what Alan H. Barr explained in his Global and local deformations of solid primitives paper (ACM link, Direct Link hosted on a faculty page, pag.5). The issue I have is that I don't quite understand the formulas involved:

y formula

z formula

Assuming we bend the mesh by an angle theta angle, where y hat is the clamped value of y between some specified ymin and ymax. k is the bending rate expressed in [rad/m] (and thus the radius of curvature is 1/k). The axis of bending is [s, y_0, 1/k]', where s is a free parameter and y0 is the bending center.

Can somebody explain, possibly with an image, the terms in the formulas above? I guess that I should look for an angle alpha = pi/2 + theta, since cos(alpha) = -sin(theta), sin(alpha) = cos(theta), but I am not able to figure it out. Thanks!


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