From: Todd Benson <caduceass@...>
Date: 2008-04-22T10:20:15+09:00
Subject: Re: [QUIZ] Triangle Area (#160)

On Mon, Apr 21, 2008 at 6:50 PM, Adam Shelly <adam.shelly@gmail.com> wrote:
> On 4/21/08, Todd Benson <caduceass@gmail.com> wrote:
>
>  > I suppose another way to approach it could be to use a matrix
>  > transformation to get your 'base' (turn the triangle, or the
>  > coordinate system; however you prefer to see it) and use a simple
>  > 1/2(b*h).
>
>  1/2(b*h) wa the first thing I thought of when I read the quiz title.
>  Here's my implementation:
>
>  class Triangle
>   def area
>     pts = [@a, @b, @c]
>     #filter out degenerate triangles
>     return 0 if pts.uniq!
>
>     #move one point to the origin
>     offset = pts[0]*-1.0
>     pts.map!{|v|v+=offset}
>
>     #find the angle of one leg
>     angle=Math::atan(pts[1][1]/pts[1][0])
>
>     #rotate that leg so it lies along X axis
>     rotmat = Matrix.rows( [[Math::cos(angle),Math::sin(angle)],
>                            [-Math::sin(angle),Math::cos(angle)]])
>     pts.map!{|v|rotmat*v}
>
>     #use basic geometry
>     base = pts[1][0].abs
>     height = pts[2][1].abs
>     area=base*height/ 2.0
>   end
>  end
>
>
>  -Adam

That is awesome!  It's almost exactly what I had in mind.  The cool
thing about it is you can expand it, if need be, to three dimensions
with only a couple changes.

Only a couple of small things.  You want to return 0 if Vector objects
happen to be uniq!?  Or, are you using my nested array model?  For
example...

[Vector[1, 1], Vector[1, 1], Vector[1, 1]].uniq!
=> nil

That's using 1.8.6 on Windoze.

Also, "bad" triangles can have legs that are almost collinear, which,
depending on your use case, you might have to check for.  I didn't.
Sigh :/  But, it turns out I didn't have to.  It correctly returns an
area of 0.0.

For performance reasons -- which I don't really often care about when
I use Ruby -- you could set up Math::sin and Math::cos before the
creation of the Matrix, since that Matrix creation is calling both
twice.

Good stuff!

Todd