¶ Making a Von Karman nosecone from a formula
The procedure to generate geometry from a mathematical formula is based itself on two features: A "Formula" and a "Parallel Curve". Both of these items should be made from the "Generative Shape Design" or "Generative Wireframe and Surface" apps. This tutorial assumes that you know how to use parameters.
- Create 2 parameters of type Length, R and L; and create one parameter of type Real, C
- Create two lines from the origin on the direction of both the X and the Y axes. Make the Y length equal to L and the X length equal to R
- In GSD/GWS,go to "Tools" and create a Law.
- In the "Formal Parameters" tab, create a Real parameter called "x" and a Length parameter called "y"
- The code that you need to put should look something like this:
let theta(angle)
theta = acos(1-2*x)
y = ( R * sqrt(theta - ((sin(2*theta))/2)*1rad + 1rad*C*(sin(theta)**3)))/sqrt(PI)
Source: Federal University of Paraná
You can see that this formula differs from what you might get from another notebook. The reason why is that in the formula editor, an x parameter is normalized from 0 to 1, which is the same thing that the (2x/L) term in the theta expression is accomplishing. So the actual term to be used for the formula itself is just 2x (this mistake stole 5h of my life). The length of the curve is accounted for in a later part. The R parameter is, however, relevant in the law.
- To translate the law into geometry, you will use a Parallel Curve. This command is located in the "Wireframe" section. Select the Y axis curve. Then, select the "Law" option under "Offset". Select the law, and everything is done!