# Triangle's contributory moment of inertia

## Main Question or Discussion Point

Triangle's contributory moment of inertia :D

Howdy.

I'm designing a 2-dimensional physics engine for use in games and simulations and have hit a roadblock.
The rotation system requires a value corresponding to the proportion between an object's regular inertia and its rotational inertia. EG, for a ring the proportion is 1, for a disc it's .5 evidently. Basically, <THIS> is what I'm after.

Anyway, what I need is an algorithm to find the average distance [not scaled] from a given point (x,y) to all points in the AREA of a triangle [(x1,y1), (x2,y2), (x3,y3)]. To say it differently, I need to find the average distance from all points within a given triangle to (x,y). Being in basic calculus [CURSE YOU PUBLIC EDUCATIONNNN] I'm not so familiar with integrals, so a solved algorithm is what I need.

Just to provide extra perspective, solid shapes will consist of multiple triangles [as it pertains to area, anyway.] and a weighted mean based on area will be used when computing their overall center of rotation and their average distribution. [what we're finding.] I plan to use the three-point formula for area and a trig algorithm to find the mass midpoint of each triangle. [If there's a way to do this without trig, tell me. Those tend to run faster.] There will be no variation in density in a triangle.

So, who among you is man enough to crack this nut?