Line Intersection with Matrices

intersect.rb

require 'matrix'

####
##  Random program that uses matrices to find intersection between 2 lines
##  the linear algebra way.
##  I am not sure why I made this, but it's probably because I like matrices


class Line 
  attr_reader :slope, :offset

  def initialize(slope, offset)
    @slope = slope
    @offset = offset
  end

  def to_s
    "y = #{slope}x + #{offset}"
  end
  alias :inspect :to_s
end


####
##  Parse equation for a line looking like 'y = 3/4x + 12'
def parse_line(str)
  match_data = str.match(/^y\s+?=\s+?(\d+\/\d+)\s?x\s+?\+\s+?(\d+)/)
  fail("Could not parse #{str}") if match_data.nil?

  offset = match_data[2].to_i
  numerator, denominator = match_data[1].split(/\//).map(&:to_i)
  Line.new(Rational(numerator, denominator), offset)
end


####
##  Turn a system of linear equations into a matrix equation
def to_matrices(lines)
  fail("Need two lines") unless lines.size == 2

  rows = lines.map{|line| [-line.slope, 1] }
  matrix_a = Matrix.rows(rows)

  rows = lines.map{|line| [line.offset] }
  matrix_b = Matrix.rows(rows)

  [matrix_a, matrix_b]
end


#  So since A * [x] = B
#               [y]
#  then [x] = A^-1 * B
#       [y]
def intersection(lines)
  fail("Need two lines") unless lines.size == 2
  a, b = to_matrices(lines)
  x = a.inverse * b
  x.column(0).map do |element|
    element.denominator == 1 ? element.to_i : element
  end
end

##  Make some lines.
lines = [
  parse_line('y = 2/4x + 2'),
  parse_line('y = 5/2x + 10')
]

puts "Finding the intersection between these lines:\n\n"
lines.each do |line|
  puts line
end

puts "\nThe point of intersection is:\n\n"

puts intersection(lines)


##  Output #######################################
#  Finding the intersection between these lines:
#
#  y = 1/2x + 2
#  y = 5/2x + 10

#  The point of intersection is:

#  Vector[-4, 0]