Day 4

Today, my partner and I began to use some of the equations that Carl gave us yesterday. He showed us two different equations that would map a coordinate from the broadcast footage onto a location in the hockey rink. My partner and I would choose four reference points from a screenshot of the broadcast footage (shown above) and then plug it into a matrix equation to find three scale factors. We would then repeat the process using the set values on the hockey rink diagram. From there, we would create two more matrices using the scale factors. We would take the inverse of one matrix and multiply it with the other matrix, and then multiply that value with the matrix including coordinates from another given point that were were trying to map onto the hockey rink. From there we could extract the location in the hockey arena. After several attempts, our answers were very far away from the expected result, so we changed the scale on of the hockey rink from centimeters to feet. The other equation includes listing many of the coordinates from the broadcast footage in a pattern, and then taking the transposed inverse, multiplying it by its inverse, then taking the inverse of that entire matrix. From there, we multiplied it by its transposed inverse again, and then multiplied it by a matrix containing the known points on the hockey arena. This approach took a a lot of time with very little accuracy and I had a lot of difficulties completing it. However, it is allows for more than four points to be used, which should be more accurate once we work through them more. Both equations will be tried again tomorrow with different units, hopefully with more accuracy. Using feet should be easier hopefully because the measurements are considerably smaller than the centimeter measurements. Hopefully tomorrow with more work and different units my partner and I will be able to produce more accurate results.