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# (Solved): Show all work An American football field is of a size 100 yards (91.44m ) long between the goal l ...

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An American football field is of a size 100 yards ) long between the goal lines and 160 feet ( wide. Furthermore, assume that the football field is perfectly aligned north-south along its length and east-west along its width and is entirely flat with zero elevation everywhere. Mathematically, we will impose a 3D coordinate system with the origin at the center of the field, running along the width (positive sense is eastward), running along the length (positive sense is northward), and pointing up from the grass field. One camera platform is located at the west side of the field, 5 yards outside the 30 yard line on the south side. A camera is positioned on top of the elevated platform at a height of 10 feet (platform tripod). The camera is aimed right at the center of the field (or the origin of the field coordinate system) with no left-right head tilt. The in the camera uses the popular format ( ) with a 1080p HD pixel resolution (1920x 1080 ). The camera is equipped with a lens of a variable focal length that can change from to . The focal point is right in the middle of the CCD and we will assume that the lens is perfectly ground with no discernible spherical, tangential or other nonlinear distortion. Based on this simplified configuration, answer the following questions: 1. From the given data above, Derive a mapping equation that will take a coordinate measured in the football field (in meter) to a coordinate measured in the camera system (in meter). You should be specific about the components in this transform, such as and , in one of the standard forms: , or . You do not need to multiply out the equations.

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