find a point within a triangle

point_inside_a_triangle.rb

#Stephen Nguyen - July 10

# drew a point within a triangle and realized that the point within the 
# triangle makes 3 smaller triangles whose area is equal to the area of the triangle
# if outside the triangle the area will always be greater than the the area of the triangle
# method will calculate the area of three points by inputting the length of the 3 triangle sides into heron's formula
# heron's formula was looked up to complete this http://matrixpp.blogspot.com/2012/11/herons-formula.html 

def area(point_1, point_2, point_3)
  side_1 = Math.hypot(point_2[0]-point_1[0], point_2[1]-point_1[1])
  side_2 = Math.hypot(point_3[0]-point_1[0], point_3[1]-point_1[1])
  side_3 = Math.hypot(point_3[0]-point_2[0], point_3[1]-point_2[1])
  s = ((side_1 + side_2 + side_3)/2)
  area = Math.sqrt(s*(s-side_1)*(s-side_2)*(s-side_3))
end

def inside_triangle?(point_1, point_2, point_3, point_x)
  area_1 = area(point_x, point_1, point_2)
  area_2 = area(point_x, point_2, point_3)
  area_3 = area(point_x, point_1, point_3)
  #if true then point is inside the triangle
  (area_1 + area_2 + area_3) == area(point_1, point_2, point_3)
end

#inside
inside_triangle?([0,0],[0,5],[5,0],[1,1]) == true
#on vertex
inside_triangle?([0,0],[0,5],[5,0],[0,0]) == true
#way outside positive
inside_triangle?([0,0],[0,5],[5,0],[99,99]) == false
#way outside negative
inside_triangle?([0,0],[0,5],[5,0],[-99,-99]) == false

# improvements 3-4 arguments per method is too many
# could be more readable & object oriented if triangle and points were their own classes

triangle.rb

#this was a terrible path to go down. I have corrected my solution below.



#if output of three checks is equal for checks then point 4 is within the triangle
#if output is different for three checks then point 4 is outside of the triangle
def inside_triangle?(point1, point2, point3, point4)
  if check(point1, point2, point4) == check(point1, point3, point4) &&
    check(point2, point3, point4) == check(point1, point3, point4) &&
    check(point1, point2, point4) == check(point2, point3, point4)
    return true
  else
    false
  end
end

def check(pointa, pointb, point4)
((point4[0] - pointa[0]) * (pointb[1] - pointa[1])) - ((pointb[0] - pointa[0]) * (point4[1]- pointa[1]))
end

point1 = [1,1]
point2 = [1,5]
point3 = [5,1]

point4 = [99,99]
inside_triangle?(point1, point2, point3, point4) == false
point4 = [1,1]
inside_triangle?(point1, point2, point3, point4) == true
#broken
point4 = [1,2]
inside_triangle?(point1, point2, point3, point4) == true