Mathematical modeling of cylindrical mirror reflection art

Questions
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Hello everyone,
I’m working on a mathematical modeling problem: The Art of Reflection.
The problem is about designing a chaotic pattern on a flat paper such that, when viewed in a vertical ideal cylindrical mirror, it reflects a clear portrait/text/pattern.

Core Problem (Simplified)

• Paper: flat A4 plane

• Mirror: ideal vertical cylindrical surface

• Given a target reflected image (in the mirror), find the original paper pattern

• Also determine: cylinder radius, position, orientation

My Questions :

  1. How to build the coordinate transformation model between the paper plane and the cylindrical mirror reflection?

  2. How to implement image unwarping/warping from the mirror image to the paper pattern in Mathematica?

  3. Given a binary/logo image (like a face or text), how to compute and export the distorted paper pattern automatically?

Thank you very much for your help!

2

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