Check if a given point is inside a triangle

triangle_check.rb

# encoding: utf-8
require 'pp'

class Point
  attr_accessor :x, :y

  def initialize(x=0.0, y=0.0)
    @x = x
    @y = y
  end
end

class Triangle
  attr_accessor :points

  def initialize(points=[])
    @points = points
  end

  def area
    compute_area(@points)
  end

  def inside?(point)
    pab = compute_area([point, @points[0], @points[1]])
    pbc = compute_area([point, @points[1], @points[2]])
    pac = compute_area([point, @points[0], @points[2]])

    (pab + pbc + pac) == area
  end

  private

  # Finds the area of a polygon
  # From: http://en.wikipedia.org/wiki/Polygon#Area_and_centroid
  def compute_area(points)
    c     = points.last
    area  = 0

    points.each do |point|
      area  += c.x * point.y - point.x * c.y
      c     = point
    end

    area.abs / 2.0
  end
end

t = Triangle.new([Point.new(0,0), Point.new(10,10), Point.new(10, 0)])
pp t
pp t.inside?(Point.new(5,5)) # => true
pp t.inside?(Point.new(3,8)) # => false

t = Triangle.new([Point.new(0,0), Point.new(10, 0), Point.new(0, 0)])
pp t
pp t.inside?(Point.new(5,5)) # => false
pp t.inside?(Point.new(3,8)) # => false
pp t.inside?(Point.new(2,0)) # => true