I am looking for some help creating a simple formula to help etch Wedding Rings.
The Setup
I have a Laser firing from a central point 280mm above the surface. The beam is directed in X,Y axis to plot the design.
I have a wedding ring, in this example 20mm diameter and 8mm wide, a flattened torus shape. Siting on the base at a 45deg angle.
The Area to be etched
From the lasers view looking at the ring, the ring will look like an ellipse 20mm x 14mm, and I would like to etch the inside area.
Problem
I need to Calculate this surface as a 2d area, My only requirement is the sides of the shape. I need to know the Curve, and Trapezoidal correction. This example shows a ring with a flat surface though this can be closer to a torus, some rings are flat some torus.
In Software
I will draw my intended shape, I am looking how to create 2 formulas, one to find the amount I squish the circle by, so in this case 14mm.
The second formula is adjusting the sides, the trapezoid sides. This coorects the blur from the ring being on an angle as well as the amount from being flat on the inside to being a complete torus. If this example was a torus it would have curves on the sides, not straight.
Final Requirements
Input:
- Inner Ring Diameter
- Ring Width
Output
- Ring Width X Ring Height
- Amount to adjust Trapezoid
Let me know if you need anymore information to clarify objective.
Thank you for your help.
I had created ths question earlier which may have more context to help fully understand the question. I apologise for the multiple questions.
Finished Item
This is a finished item and how it ends up looking on the ring. For reference.
