Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Triangle's contributory moment of inertia

  1. Oct 5, 2007 #1
    Triangle's contributory moment of inertia :D


    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?
  2. jcsd
  3. Oct 8, 2007 #2

    Pretty please? I'll be your friend. You'll get in the credits!
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook