# Maths pain, trying to plot a certain point inside a triangle

Hello all,

I’m Phil, been a PHP web guy for about a decade and this year I’ve been digging into some objective C app dev and playing with openframeworks for a couple of weeks. Now the code side of things isn’t a problem, but it’s been 15ish years since I left school and did much more than basic arithmetic and I’m stuck on something I’m trying.

What I’d like to do is draw and equilateral triangle composed of a red, green, and blue triangle proportioned to represent an RGB colour. Working out the relative percentage area’s of the equilateral isn’t a problem, but plotting the point where they meet is.

I knocked up a diagram http://philrennie.co.uk/openframeworks/fourmasssets/pointp.jpg

For equilateral triangle ABC, I’d like to work out the coordinates of point P if for example
Tri APC = 30% the area of ABC
Tri ABP = 20% the area of ABC
Tri CPB = 50% the area of ABC

I’ve found I can get the lengths for lines x, y and z using height = (2 * area) / base, but now I’m a bit stumped find P to satisfy the constraints.

I’m also assuming that given there will be a bunch of fractional numbers involved that may never add up to exactly 100% of the overall area, if I can find P given just two of the areas I can let the third one eat up the rounding errors.

I’ve googled around and did find some info on ternary plots that looked like it might be helpful but I can’t make any sense of the equations listed as the notation is all greek to me now.
http:// en.wikipedia.org/wiki/Ternary_plot
(excuse me breaking the link, the forum software complained about the number of links I can make as a new user)

I’m running right up against the old saying ‘use it or lose it’ when it comes to my maths at the moment
The end goal I’m looking for is to fill the screen with a load of these equilaterals tessellated, then I’m going to treat them as huge ‘pixels’ pulling their colours from the webcam to achieve a very low-res version of the image. Speaking to the camera, pulling out pixel info, drawing the poly’s I’m fine with, it’s just the pesky maths.

here’s the unbroken wikipedia link