Help with identifying a shape

as part of a project i will attempt to create the shape of a corrugated/ridged cupcake base. I would like to create it from a pure geometry if possible so as a starting point i would like to know how to refer to the shape which i am hoping will help me search better to start me off in he right direction.

Anyone have any ideas what the mathematical name for a shape like this would be?

My eventual goal will be to have the parameters editable via a gui (depth, angle, ridge density etc…) so any pointers on where to start with the maths would be much appreciated.

just to add some clarification, the photo i have posted is just an example. I am not necessarily worried about the shape having a “thickness” or the pleats being rounded in anyway. More a mathematically “pure” version of the shape in the photo, with ridged sides and a flat base

I’ve never seen a mathematical formal definition of cupcake cases^^.

However, playing around with a plane geometry and some trigonometric functions could do the trick:


You absolute beauty!

I can’t believe how minimal the code is. That’s the nature of eloquence I suppose… I will grab it and have a play around. Thanks very much for such a flying start.

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With the addons you can create many different shapes. You just have to find out the right functions. :slightly_smiling_face:

see GitHub - hofk/THREEf.js: three.js addon, to produce almost infinite many time-varying geometries / buffer geometries with functions (cylindrical coordinates) and

In the forms library:
quite similar

 //0020 curved shell  @author hofk 
 radius:		80,
 radiusSegments:	80,
 rCircHeight:	function ( u, v, t ) { return Math.sqrt( v ) },
 topHeight:	function ( u, t ) { return 0.8 + 0.2 * Math.sin( 16 * Math.PI * u ) }