I am trying to create a custom neck band label for my bottle of brew, and I am having difficulty determining the exact shape that will make it wrap around the neck so that the top and bottom edges are straight.
I imagine there is some sort of formula to do this, but I haven't been able to figure it out. The neck is roughly a cone, and I have determined that the arc length of the top of the label needs to be equal to the circumference of the skinny part of the neck, and the arc length of the bottom of the label ought to be equal to the circumference of the fat part of the neck. This will make the label appear to be straight when it is applied to the bottle (this is what I'm aiming for). My problem however is determining what shape to make the curve, because although I know what to make the arc lengths, the diameter of the circle which they come from can be different, and it is this shape need to know.
Sorry if this post is confusing. If there is anyone who prides themself in math or geometry, please see if you can figure something out.
Thanks,
JohnBen
I imagine there is some sort of formula to do this, but I haven't been able to figure it out. The neck is roughly a cone, and I have determined that the arc length of the top of the label needs to be equal to the circumference of the skinny part of the neck, and the arc length of the bottom of the label ought to be equal to the circumference of the fat part of the neck. This will make the label appear to be straight when it is applied to the bottle (this is what I'm aiming for). My problem however is determining what shape to make the curve, because although I know what to make the arc lengths, the diameter of the circle which they come from can be different, and it is this shape need to know.
Sorry if this post is confusing. If there is anyone who prides themself in math or geometry, please see if you can figure something out.
Thanks,
JohnBen