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Eric | all galleries >> In Box >> Forum Pictures > My Cosine Equation
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My Cosine Equation

cos(a) * cos(b) = cos(c ),
where a is an angle drawn from the z-axis toward the y-axis,
b is an angle drawn from the z-axis toward the x-axis, and
c is the angle spanning the two lines on a diagonal.

I discovered this formula by hacking together a bunch of complex trig formulas, digging to get to this one value. At the time I was writing my own raytracer, which involves a lot of 3D trig math. Once I finally got to c, I simplified the equation down (it was 2 page widths in length handwritten) and I was totally surprised when all I had left was cos(c ) = cos(a) * cos(b)!

It is extremely elegant. I have been unable to find this forumula anywhere else, so I am wondering if I have stumbled upon some sort of new mathematical Identity. Should I be famous?


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