I’m diving headfirst into simulating a page curl effect for my custom OpenGL rendering engine, and honestly, it’s been quite the journey. Initially, I tried following the approach from the paper “Turning pages of 3D electronic books,” using a cone to create the curl. It worked to a certain extent, but the parameters were super finicky—just a slight tweak, and the whole thing would behave unexpectedly.

So, I made the switch to a cylinder-based method, which seemed like a good idea at the time. I mapped the points of the page surface onto a cylinder, and I started to see some pretty nice curl effects. However, that’s where things got tricky. While the curl looks fantastic, I’ve run into a major issue: preserving the spine of the book during the simulation. Every time I adjust the axis and radius parameters for the cylinder, the deformation seems to ruin the illusion, making the spine look awkward and unrealistic.

To give you an idea of what I’m working with, I’m using a Right-Handed coordinate system where the axis of the cylinder and the page lie on the XZ plane. The algorithm I’ve implemented is pretty straightforward in pseudocode, but even though it runs fine on both CPU and GPU, making the curl look physically limited is the real struggle.

Here’s a snippet of the algorithm I’m using:

“`plaintext
let radius be the radius of the cylinder.
let axis be the axis of the cylinder.

for each vertex V of the mesh:
let P be the projection of V on the axis,
let D be the distance from V to P,
let theta be D / radius

let dir be the direction of the PV vector
let delta be dir * cos(theta) * radius

update V to (V.x + delta.x, sin(theta * radius))

Render the mesh.
“`

I’m hoping someone has dealt with a similar challenge or has insights into limiting the curl effect without compromising the actual look of the spine. Any suggestions on parameter adjustments or additional constraints would be immensely helpful!