Can Camera Distance Affect Angle of Foreshortening in Video Measurements?

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Discussion Overview

The discussion revolves around the impact of camera distance on the angle of foreshortening in video measurements, particularly in the context of measuring the displacement of a ball using video footage and a grid background. Participants explore the theoretical implications and practical calculations related to this phenomenon.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant describes a setup involving cameras and a grid to measure the displacement of a ball, noting that the grid suffers from an angle of foreshortening when viewed from the camera.
  • Another participant suggests that the issue may be a simple trigonometric problem, implying that basic trigonometry could provide a solution.
  • A later reply indicates that the initial assumption of it being a simple trig problem may not hold, as the participant struggled to apply trigonometry correctly to find the reduction in size of the grid squares due to the camera's effect.
  • One participant requests a better diagram to clarify the situation and suggests that the problem might be solvable despite initial doubts about its simplicity.
  • Another participant proposes moving the cameras farther away from the grid and bringing the ball closer to the grids as a potential adjustment to the setup.

Areas of Agreement / Disagreement

Participants do not reach a consensus on whether the problem is a simple trigonometric issue or more complex. There are differing opinions on the effectiveness of trigonometry in solving the problem, and suggestions for adjustments to the experimental setup are made without agreement on the best approach.

Contextual Notes

Participants express uncertainty regarding the application of trigonometry and the effects of camera positioning on measurements. There is a lack of clarity on the assumptions made in the calculations and the specific definitions of foreshortening in this context.

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

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.
 
As I said, it seems to be just a simple trig problem
 
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.
 
sarah Jane said:
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.
 
Can you move the cameras farther away from the grid backgrounds and the ball closer the to the grids?
 

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