Mathematical Perseus vs. Medusa Picture

The old greek myth about the hero Perseus is one of the most famous myths. Perseus set off to kill the monster Medusa, a woman with snakes for hair and a petrifying gaze. With the help of Athen and Hermes, he managed to kill Medusa by using is shiny shield as a mirror to reflect the petrifying gaze on the monster.

Now here's the maths:
All points are set in the R³. The point P (-1/-1/2) describes Perseus' head. The point M (3/3/0) describes Medusa's head. The point S (0/0/1.5) is in the middle of the shield. Medusa is looking straight at Perseus' head.

Calculate the Matrix for the Linear Transformation, which reflects the image of Medusa on the plane of the Shield.

Stone texture: hippo2.deviantart.com/art/Tila…
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