A [[Planes|Planar]] [[Function|Map]] is a type of [[Bitmap Image|Texture]] map for a plane / is typically used for a planar reflected with [[Environment Mapping]]. This is useful for things like calm water or a [[Mirror]]. ![[Pasted image 20251126165854.png]] >[!info] >*Pros*: >- Easy to generate >- Only need one map >- Reasonably good approximation > >*Cons*: >- Specific use >- View dependent, this needs to be regenerated for different viewer positions or orientations. To generate the map: - Mirror the camera position and orientation along the reflector [[Planes|Plane]] (see [[Mirroring across a Plane]]) - For the side vector use the 'up x-direction' - Render the scene from the new camera position to generate the [[Environment Map]]. Projecting into [[Texture Coordinates|Texture Space]] can be done by using a [[Perspective Projection]] with aspect ratio $\alpha = 1$ and FOV $\theta=45 \degree$. $\huge \begin{align} u &= \frac{1}{2} - \frac{\cot(\theta _{x})}{2} \frac{v_{x}}{v_{y}} \\ v &= \frac{1}{2} - \frac{\cot(\theta _{y})}{2} \frac{v_{y}}{v_{x}} \\ \end{align}$