Find the intersection of two lines: Difference between revisions

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=={{header|APL}}==

<lang apl>

⍝ APL has a powerful operator the « dyadic domino » to solve a system of N linear equations with N unknowns

⍝ We use it first to solve the a and b, defining the 2 lines as y = ax + b, with the x and y of the given points

⍝ System for line 1 will be:

⍝ 0 = 4a + b

⍝ 10 = 6a + b

⍝ The two arguments to be passed to the dyadic domino are:

⍝ The (0, 10) vector as the left argument

⍝ The ( 4 1 ) matrix as the right argument.

⍝ ( 6 1 )

⍝ The following solver will take ⍵ the matrix of coordinates, one point per row, then massage the argument to extract x,y

⍝ and inject 1, where needed

⍝ Applied twice, we now have a, b and a', b' defining the two lines, we need to resolve it in x and y

⍝ y = ax + b

⍝ y = a'x + b'

⍝ In order to reuse the same solver, we need to format it a little bit, and change the sign of a and a', and multiply (a,b) by (-1, 1):

⍝ b = -ax + y

⍝ b' = -a'x + y

A ← 4 0

B ← 6 10

C ← 0 3

D ← 10 7

solver ← {(,2 ¯1↑⍵)⌹(2 1↑⍵),1}

I ← solver 2 2⍴((¯1 1)×solver 2 2⍴A,B),(¯1 1)×solver 2 2⍴C,D

</lang>

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