Finding the intersection of geometric objects

I need to find a curve that is the intersection of two planes in three dimensions and a helical coil.

For the helical coil, I need to specify,

r1=radius of the helix

r2=radius of the coil

Currently, I am able to model the helix as a curve.

I need to make a surface on it.

Answer 1

[Doug Hull]

I think we are not getting the whole problem here.

The intersection of two planes is either:

• a plane (identical to both planes)
• a line
• the null set (if they are parallel)

The line is the only really interesting case here.

A helical coil is going to need more information than that to specify it, like the rate of the rise. I am thinking of your helical coil as a spring.

The intersection of a 'spring' and a line is going to be

• zero points
• one point
• two points
• infinite points

I think you are going to need to specify more about this problem before we can really help beyond this.

Answer 2

[ashwin devotta]

Hi Doug,

Thank you for the reply and sorry for getting back a bit late.

I am trying to model a twist drill.

In this case, I came across two challenges.

I use the Left hand cartesian coordinate system.

Challenge 1:

I actually draw four planes (P1,P2,P3 and P4).

Both planes P1 and P2 are obtained by certain rotation and translation in a coordinate system.

P3 and P4 are obtained by rotating the Planes P1 and P2 around Z axis.

The intersection of four planes leads to the creation of four lines. I project these four lines onto XY plane. I need to control the angle between the lines at this point. My variables are the angles and distances that I use in the rotation and translation matrixes that I use in the creation of P1 and P2.

Challenge 2: A 3 dimensional helical spring is created, with the only difference being the cross section of the helical spring. The axis the helical spring is the same axis used to create planes P3 and P4. The cross section is determined by the resulting curve of the intersection of the 3d helical spring and the planes P1,P2,P3 and P4.

I have tried to my level best to describe the problem.

I can provide with some presentations that I have done to explain my problem.

Thank you once again Doug for your reply.

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