Can Camera Distance Affect Angle of Foreshortening in Video Measurements?

[sarah Jane]

Hi.

I was wondering if anyone could help me with the following problem.
I am doing a independent lab at the moment. I am using video footage to measure displacement of a ball. I have cameras set up on the x and y-axis where a ball is in line with the centre of both cameras. I have 1cm grids on the wall behind the ball in both directions. I apply a spin and a wind across the ball and use the video footage to measure the maximum displacement of the ball.
So it goes... →camera → Ball → cm grid.

The ball is in line with the edge of the grid in the y direction. The grid not in line with the camera - I have been informed - suffers from a angle of fore-shortening when looking at this part when measuring displacement on the video footage.
I was wondering if there is a theory for this angle of fore-shortening or the best way to calculate how this will affect my results.

Thanks.

 

[phinds]

I think you need to supply a diagram, but it sounds like it should be a simple trig problem

 

[sarah Jane]

I have this diagram that I've quickly drawn up. It's rather simple because I don't have a better program other than paint on my current computer.

Focusing on camera 2. When looking at the recording video footage from this camera. The squares (on the cm grid in line with camera 2) on furthest right, appear smaller/shortened due to the camera.

 

[phinds]

As I said, it seems to be just a simple trig problem

 

[sarah Jane]

That is what I thought initially but when I used trig it didn't seem to apply correctly.
I want to know how much the cm squares furthest from the camera have reduced due to the cameras effect.
Using trig I didn't find this answer - unless I have calculated it incorrectly.

 

[phinds]

That is what I thought initially but when I used trig it didn't seem to apply correctly.
I want to know how much the cm squares furthest from the camera have reduced due to the cameras effect.
Using trig I didn't find this answer - unless I have calculated it incorrectly.

Well, I suppose I could sit here all night and just guess at the various ways you might have tried to calculate it but in the interests of brevity, why don't you lay it out. You'll likely need a better diagram.

And now that I look at it, I doubt it's a SIMPLE trig problem, but I think it's solvable.

 

[David Lewis]

Can you move the cameras farther away from the grid backgrounds and the ball closer the to the grids?