Normal Cup - Angus Dutta

Description

Normal Cup(p-normal to be exact)The horizontal cross sections of the cup are the unit (radius = 1) circles of a family of distance norms called p-norms.- Read more about p-norms here: https://en.wikipedia.org/wiki/Lp_space- At the base of the cup p = 2/3and at the top p = π + 2/3. (mostly I because these are fun numbers, it’s not so deep.)- The value of p varies linearly through the height of the cup, which in units of the "radius" of the cup is e by the way.- I’ve added notches at two interesting values of p: 1 (grid space) and 2 (euclidean space).- That means the height of the cup is π times the gap between those notches. (Because 2 - 1 = 1 and π+ 2/3 - 2/3 = π)The inside of the cup is a bit funky, basically it is the same as the outside but with two main changes:1. The "radius" of the "circles" reduces to zero instead of being constant. The relation is something like r = ((z - b)/h)^(1/(π+e)).2. The minimal value of p on the inner surface is 2 (so we end in a circle).I hope this nerdy thing brings you joy and not too strong of a headache.-----V2 changes:1. Thickened the walls of the cup (it was too thin at the top)2. Increased the minimum value of pfrom 1/πto 1/e(it was too thin at the bottom)3. Made the final value of pbe π + min_pso that the height would actually be πin units of the gap between the notches4. Increased power of radius decay for inner wall radius (so the cup would have a flatter internal base and use less material)5. Changed height of cup (in units of…