# light geometry and art

I'm a professional artist.

I have a question regarding light logic. I have simplified the problem a bit.

Imagine a segment in 3D space, AB of known length and a point light illuminating the segment. Say the light is at (0,5,8) and the mid point of the segment at (2,3,1).

I want to get a deeper understanding of how much light reaches the segment. I can think of the segment as the diameter of a sphere, rotating around its midpoint. How can I compare the distance of A and B from the point light source to determine which is closer, hence lighter?

I know that if the segment lies on a plane parallel to the xy plane, then the point closer to the vertical axis off the light source will be lighter. If the mid point of the segments is at 90 degrees with the light direction, then A and B will be equally illuminated.

I'm trying to figure out what happens when one point is higher then the other. Normally a point being higher will translate to lighter. Is this always the case?

Thanks

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How are you characterizing "lighter" (brighter)? Are you simply regarding points closer to the light source as being lighter? – EuYu Jul 29 '13 at 1:45
Well, I would need to look at distance from the light and the angle with the direction of the light. – raff Jul 29 '13 at 2:07
A better sample problem would be a plane, like the flat side of A book. How does the value change on the plane by rotating it off its centre? – raff Jul 29 '13 at 2:14