Isophote

In geometry, an isophote is a curve on an illuminated surface that connects points of equal brightness. One supposes that the illumination is done by parallel light and the brightness b is measured by the following scalar product:

${\displaystyle b(P)={\vec {n}}(P)\cdot {\vec {v}}=\cos \varphi }$

where ⁠${\displaystyle {\vec {n}}(P)}$⁠ is the unit normal vector of the surface at point P and ⁠${\displaystyle {\vec {v}}}$⁠ the unit vector of the light's direction. If b(P) = 0, i.e. the light is perpendicular to the surface normal, then point P is a point of the surface silhouette observed in direction ⁠${\displaystyle {\vec {v}}.}$⁠ Brightness 1 means that the light vector is perpendicular to the surface. A plane has no isophotes, because every point has the same brightness.

In astronomy, an isophote is a curve on a photo connecting points of equal brightness. ^[1]