One of our recent award winning videos required some math during production. It was a spot for the Red Cross. The goal was to get a birds eye view of 125 people forming a giant red cross with red cards. The problem was, there wasn't any way to get 125 people onto a giant white cyc with the camera high enough in the air. No one say, "wide angle lens." That's not the look we wanted.
The only way to accomplish the effect was to shoot 5 groups of 25 on a giant green screen. We found a 60 foot by 30 foot green screen cloth, and we set it up in the Carolina First Center. Our original plan to achieve the proper perspective for the outside wings was to move the camera, but during setup we realized that wasn't possible for lighting and other logistical reasons. We had to shoot all five groups in the same area with a static camera.
My challenge was to capture the side angles with the right perspective. Someone standing on the right side of the cross should have more of the right side of their body exposed, and conversely on the left. Also, the center group is going to naturally keystone between the top row and bottom row of people. When the wings are added it all must have the same keystone.
I'm going to spare you from the numbers (mainly because I lost the paper). I do remember that the camera was about 30 feet in the air. With green tape and a tape measure in hand I marked off where the center group should stand. I diagrammed the stage and mapped out where everyone would stand if we had enough room. I calculated the angle that the side groups were at in relation to the camera. Keeping the angle, I then taped off standing locations on the screen.
It felt weird shooting people standing sideways and it made the director really nervous, but the end result was seamless. I knew that trigonometry class would pay off someday.