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Actually I just had to solve the following equation to find a solution, consistent with the presence of the "2" in the numerator: $\frac{1}{1+\Lambda (m)}=\frac{2}{1+\sqrt{1+\alpha ^{2}tan_{2}\theta_{m} }}$ $1+\Lambda (m)=\frac{1+\sqrt{1+\alpha ^{2}tan_{2}\theta_{m} }}{2}$ $\Lambda (m)=\frac{-1+\sqrt{1+\alpha ^{2}tan_{2}\theta_{m} }}{2}$


Quick idea: render platforms color to screen quad render mesh and platforms to screen quad, but as a mask. For example mesh is white, rest is black. in another pass sample these textures and if mask is white, color it with sample from first texture. Render to screen.

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