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• Mathematical highlighting

Funky mathematical thinking…. By Cenotaphe, the upside down mini-student… (http://www.cenotaphe.net) Here’s the very comprehensible exemple of the stop signe. If you take a zenithal lighting, the side stays the same color, the top is the the most highlighted, and the bottom side is the darkest possible, and I’ll let you figure out what goes on the inclined sides  The following picture shows what it should look like. During a mini stage, where I was explained the zenithal way of painting, my warped brain tried finding a mathematical way to define the luminosity that should be applied to the different areas of a mini…. And we managed to find something!! The idea is to use the slope of the tangent to the surface. The luminosity coefficient that should be given to the surface is equal to the opposite of the inverse of the tangent to the surface. In the first column of the grid in the illustration you have the coefficient of the tangent, in the second column the opposite of the inverse of the tangent. The third column then shows the color as it comes out with the correct luminosity (the base color being on the side of the cylinder). Here you can see in perspective the result, as it would be applied to the half cylinder. Of course this small equation only takes into account a unique source of zenithal lighting. The algorithm would need to be much more advanced to take into account more complex lighting with multiples sources of different intensity, which as most probably already been done in the field of 3D rendering. Translation done by FrenchKid, Article by Jeremie Bonamant and Cenotaphe 1 Comment
1. Ishamael -
To author and OP: Nice article. In an ideal world, all battles take place at high noon so this is a perfect reference tool already done up for us.

To Frank Battalglia: You are confusing two uses of the word tangent. The author is speaking about an angle formed between the horizon line and the tangent line (the line touching the curved surface exactly once). You then mistakenly interpret him to mean the trigonometric function, tangent, the ratio of two lengths of a right triangle, e.g. tan(x). Then you give a solution from physics which is correct but describes a situation other than this one. The textbook situation you are referring to is one where the source is behind an observer who is looking at a plane. The effect discussed in this article is for the observer seeing the sum effect of reflection for many different "planes" (to wit: one for each normal angle on the curved surface) from a light source above the object.

To samwisethegreat: You are totally correct that this is logical. The logic you are describing has a name. It is mathematics applied to the principles of (scarier word coming here) physics.
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