= Projected area
{title2=$A_\perp=A\cos\theta$}
The <projected area> of a planar patch viewed from a direction is the <area> of its perpendicular shadow onto a plane normal to that direction. If $\mathbf n$ and $\mathbf s$ are its <unit normal> and viewing <unit vector>, then $A_\perp=A|\mathbf n\cdot\mathbf s|$ by the <dot product>. On the outward side, this is $A\cos\theta$. For a <rectangle> tilted around one edge, the width perpendicular to that edge contracts by $\cos\theta$ and the edge length stays fixed, proving the formula. At grazing view $A_\perp=0$; interpret the <radiance> definition by a limit rather than dividing by zero.
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