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UV mapping - parallelogram tiling on a plane

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Hello, I've been searching a way to calculate the uv coordinates on a plane. It was a succes as I used the following formula to get an image onto my plane. (There are no tiles of my image, just 1 image strechted in my plane) This is how I calculated the UV coordinates: is my intersection point from a ray from the camera that hits the plane. (here we fill the intersection point into the equation to get our u) (here we fill in the intersection point into the equation to get our v) The plane is defined by it's normal vector and an offset. Now I want to put textures onto my plane, however I want to be able to not only make rectangle tiles, but I also want to make parallelogram tiles. This will be done by defining two directional vectors I call one xVec and the other yVec. How can I change my u function and v function to be able to map parallelogram tiles? The size of the tile is specified by the length of those vectors. Thanks for your help!

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