Anamorphic Football Pitch Sponsors
Football pitch sponsor logos appear flat and perfectly proportioned on TV, but walk onto the pitch and they're massively stretched and distorted. How is this illusion created mathematically?
Where this idea comes from
Start here — this is the source that inspired this exploration.
Introduction
Next time you watch a football match, look at the sponsor logos painted on the pitch. On screen they look perfectly normal — flat rectangles with clean text. But in reality, those logos are wildly stretched and skewed on the grass. This is anamorphic projection: the logo is pre-distorted so that when viewed from the main camera angle, perspective compression makes it appear flat. This exploration investigates how transformation matrices can model the relationship between the 'true' logo shape and the distorted version painted on the pitch. Students will explore how camera position, viewing angle, and pitch geometry determine the transformation needed. This exploration relies on matrix transformations, which are HL-only content in both AI and AA; SL students could instead approach the distortion informally, by measuring stretch ratios directly rather than building a matrix model.
Guiding Questions
- What does the logo actually look like when you stand on the pitch, compared with how it looks on TV?
- Model the transformation from the flat logo to the stretched pitch version using a 2D transformation matrix (combining stretches, shears and rotations). This is only an approximation: a real camera view is a projective transformation, not a single matrix of this kind, so check where your model's predictions start to disagree with the real image.
- What role do the camera's height and viewing angle play in determining the distortion, and how does your matrix model change with them?
- Could you design your own anamorphic image for a specific viewing angle, and test it?