# Defining flat pattern angles from 3D shapes

Question asked by Luke Harris on Dec 17, 2017

I'm working on a series of origami models, and i'm trying to figure out a formula that will enable me to calculate my crease pattern angles, given a pre-determined 3D angle. This is to save me time keep modelling up in SolidWorks every time I want to make a soft model. I have attached an image as an example:

If A is 45 degrees, what other parameters must I know in order for me to calculate the fold angles on my flat crease pattern? (see question mark on image). My initial assumption is that if my shape is a cylinder, then I first have to know how many V pleats (instances) I have (360 degrees / X number of instances). So if for example my cylinder is divided into 30 V pleats (12 degrees each), the angle of the V pleats on my crease pattern will naturally differ to those of a model with, say, 60 instances, to achieve the same 45 degree angle in 3D.

Is there a quick formula that will help me figure out my angles before modelling them up in SW? And what are my dimension drivers?

Note: Width (W) and Height (H) have been marked on my sketch, though I don't believe these factors contribute in anyway to the equation...