# Mathematical highlighting

by

Published on 07-08-2006 01:29 PM
Number of Views: 55192

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

## vBulletin Message