Calculating coordinates of intercepts from field of view to target

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SUMMARY

This discussion focuses on calculating the coordinates of intercepts between a camera's field of view (FOV) and the flight path of a ball in a 2D plane. The user has the X/Y coordinates of both the camera and the ball at various times and seeks to determine where the FOV intersects the ball's trajectory. Key considerations include the possibility of the camera rotating, which affects the intercept calculations. The discussion emphasizes the need for complete information about the camera's orientation to accurately solve the problem.

PREREQUISITES
  • Understanding of 2D coordinate systems
  • Knowledge of basic geometry and intercept calculations
  • Familiarity with camera orientation and field of view concepts
  • Experience with mathematical modeling of motion
NEXT STEPS
  • Research methods for calculating intercepts in 2D geometry
  • Learn about camera transformations and rotations in computer graphics
  • Explore algorithms for determining intersections between lines and shapes
  • Study the mathematics of projectile motion and its representation in 2D space
USEFUL FOR

Mathematicians, computer graphics developers, and anyone involved in motion tracking or simulation in 2D environments will benefit from this discussion.

jisbon
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Homework Statement
Find the coordinates of the intersection between field of view and ball in motion
Relevant Equations
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Say we are working in a 2D plane, with a camera and a ball flying past as shown.
Camera at bottom, ball flying from left to right
Given that I have the X/Y coordinates of the camera, as well as the coordinates of the ball at any given time during the 'flight', how am I supposed to calculate the coordinate where the field of view intercepts the flight path? In this case, I am trying to find the coordinate in red color.
Finding coordinate where FOV intercepts path
It is also possible for the camera to rotate around its position too, and this also changes the interception of the coordinates as shown.
Only 1 interception in this case
Any kind souls here able to give me a jumpstart on how to solve this problem? Not sure where I can start. To recap, I have the coordinates of the camera, coordinates of ball at any time, and would like to find if FOV:
  1. Both sides intercepts (if so, find both of the coordinates)
  2. One side intercept (if so, find coordinate)
  3. No intercept
2,1, and no intercepts
 
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jisbon said:
It is also possible for the camera to rotate around its position too, and this also changes the interception of the coordinates as shown.
That makes the question impossible to answer without more information. The intercept coordinates depend on the orientation of the camera.
You need to post the entire problem, including all information given, verbatim as in the question. If in doubt, photograph the entire question and post the image.
 

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