How Can I Create 3D Vectors Based on Magnitude and Polar Coordinates?

[kevdoig]

I'm tring to visualise some data i have a need a little help.
The format of the data is a magnitude and 2d polar co-ordinates of recorded stress values.
These readings must be visualised in a 3D manner representing a pipe. I can generate the start coordinates for each vector, but as each is on a 2D plane, i don't know how to create 3D vectors for these from only the magnitude and a set of polar co-ordinates, given there the only known 3D information is the start point of each vector.
Any help would be much appreciated!

Kev

 

[0rthodontist]

I assume the 2-d coordinates are meant to wrap the outside of the pipe? If the "start point" is in the center of one part of the pipe, then probably the 3-d coordinates, with the pipe axis running along the z axis, are something like $$(R \cdot cos(\theta), R \cdot sin(\theta), r)$$
where r and $$\theta$$ are from your 2-d coordinates and R is the radius of the pipe.

If you did this then the stress magnitudes would have to be indicated by a color. Maybe you should just visualize in rectangular coordinates as a graph over the plane, where the vertical coordinate is the stress magnitude and you treat $$\theta$$ as your y-coordinate and r as your x-coordinate.

 

[kevdoig]

The 3D co-ordinates are the dimensions of the pipe, the 2d information is a magnitude and a 0-180degree reading for stress values. This must be altered to allow a 3d visualisation as part of my project.

 

[kevdoig]

to clarify here is an example of the data i will have available:

3d-co-ordinates(location) magnitude of force direction

(1,1,1) 500 70degrees
(-1,-1,-1) 740 34degrees

the numbers are obviously just examples, but this will be the information i have for each point. I really just need to know how to transform the direction/magnitude vector into 3 to plot. Sorry if my last posts were unclear

 

[kevdoig]

am now working on the assumption that i can calculate a vector which is on the same plane as the 2d point (as for the plane will cross the centre of the pipe, and point in question, both of which i will have 3D points for), calculate the equation of the plane, and then put the point that i need in 3d into this equation to get the cartesian co-ordinates. Does this sound correct (or at least feasible).
If so can somebody suggest how i can get the plane normal from a vector and a point on the plane, as i cannot quit understand that much yet... or tell me I'm way off the mark with this idea!