How Can You Parametrize a Skewed Helical Surface?

[Mbert]

Dear colleagues,

I am trying to parametrize a surface that follows an helix. The basic equations for this surface are:

x = R1*cos(theta)
y = R1*sin(theta)
z = B1*theta + h

where "theta" and "h" are the parameters and R1 and B1 are constants. I am looking for the parametrization of this surface, but skewed, so that the left and right edges (at theta_min and theta_max) are normal to the helix, instead of being parallel to Z (and the other 2 edges remain parallel to the helix).

At the moment, I use a FOR loop to modify the vertices to skew my surface, but I was wondering if there was a more straightforward way, through a new parametrization.


M.

 

[jvicens]

Dear M.,

Thank you for your question. To parametrize a surface that follows a helix, you can use the following equations:

x = R1*cos(theta)
y = R1*sin(theta)
z = B1*theta + h

To skew the surface, you can modify the equations as follows:

x = R1*cos(theta) + (theta - theta_min)*(R1*cos(theta_max) - R1*cos(theta_min))/(theta_max - theta_min)
y = R1*sin(theta) + (theta - theta_min)*(R1*sin(theta_max) - R1*sin(theta_min))/(theta_max - theta_min)
z = B1*theta + h + (theta - theta_min)*(B1*(theta_max - theta_min) + h - B1*theta_min)/(theta_max - theta_min)

This will create a surface with the left and right edges normal to the helix, while the other two edges remain parallel to the helix. You can adjust the values of theta_min and theta_max to control the degree of skewness in your surface.

I hope this helps. Let me know if you have any further questions.