How to find parametric equation of cylinder around an arbitrary normal vector?

[mikeitexpert]

I need to learn, how I can intersect a half-cylinder and a plane in 3D and get the equation of the curve created in 3D using Matlab.

I started by making a parametric equation for the cylinder around Z-axis as cylinder's normal vector and then rotated to an arbitrary normal axis N and radius R.

To make it a half-cylinder I added constraint z > 0; however, I don't know how to transform/rotate this constraint so that I only have half of the cylinder.

Please let me know your ideas and thought.

Regards

 

[Deleted member 4993]

I need to learn, how I can intersect a half-cylinder and a plane in 3D and get the equation of the curve created in 3D using Matlab.

I started by making a parametric equation for the cylinder around Z-axis as cylinder's normal vector and then rotated to an arbitrary normal axis N and radius R.

To make it a half-cylinder I added constraint z > 0; however, I don't know how to transform/rotate this constraint so that I only have half of the cylinder.

Please let me know your ideas and thought.

Regards

Can you get the curve (equation) created by "full cylinder" and the plane?