4/30  can someone tell me how to get the coordinates for the center
      of gravity of a triangle, given the coordinates of the three
      vertices.  thanks a lot.
        \_ google.  (sorry, couldn't help myself)
        \_ http://www.google.com/search?q=triangle+center+gravity+coordinates
        \_ I think it's x = (x1 + x2 + x3) / 3, similar for y and z -- yuen
           \- it depends on how the mass is distributed. again, it is a
           fairly strightforward [high school calculus] integration problem.
           \_ I think it's safe to assume that the mass is evenly distributed
              (if not, the fact that it's a triangle is irrelevant), in which
              case the integration stuff decomposes into more straightforward,
              simpler equations...
        \_ Just find the midpoints of each side and then caculate the
           point at which the lines from the opposite verticies to the
           midpoint intersect. I tried to derive the formula but my
           brain hurts a little too much from reading squid code this
           afternoon.
              \- for a right triangle defined by the origin and (x,y) the CM
              is at 2/3x, 1/3y [pf left as an exercise to the reader. for an
              arb triangle it isnt as simple. if you are looking at a physical
              object, then there are empircal ways to find it for arb objs--psb
              \_ Does it make a different if the plane is flat or curved?
                 \_ Yes.  It won't work if the plane is curved w.r.t. the
                    co-ordinate system.
                    co-ordinate system.  -- yuen
                    \_ So how do you find the cg of a triangle if the
                       plane is curved?
                       \- once again: if the plane is curved, then it isnt
                       a triangle. notice the angles dont sum to 180deg either
                       in that case. by integration you can find the center of
                       mass of "any" 3-d shape with any "reasonable" desity
                       function. in practice, for weird shapes you find the
                       a plumb line. Computing something like a moment of
                       center of mass with empirical techniqies, such as with
                       a plumb line. Determining something like a moment of
                       inertia is harder. --psb
                       \_ Yes the angles don't sum to 180, but I though that
                          the only requirement was 3 sides and only in the
                          special case of non-curved planes (eculidiean?)
                          did the sum of the angles = 180 degrees apply.
                          I forget how to find the cg via integration,
                          url please. thnx.
                          \- the web isnt the answer to everything. go dig up
                          your high school calculus book. it will do for a
                          plane triangle.
                          \_ Don't have my high school calc book. I haven't
                             had a calc book since the last day of school
                             junior year. url please. thnx.
                             \_ get up from your goddamn terminal and go
                                to a fucking library, you lazy fuck.
        \_ for a triangle in a euclidian plane, think about this.
           the ratio of areas goes as the sqaure of the ratio of lengths
           pick a side of the triangle and divide the triangle with a line
           parallel to that side such that the area of the whole triangle
           to the new triangle created by the line is 2:1.  repeat with
           different side and determine where the two lines intersect.
           such a process could be adapted for a spherical surface.