Find the intersection of a line with a plane: Difference between revisions

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=={{header|APL}}==

<lang APL>⍝ Find Intersection of a line with a plane

⍝ The intersection I belongs to a line defined by point D and vector V, means that t exists, so that I = D + tV

⍝ I belongs to the plan defined by point P and normal vector N. This means that the IP vector is normal to vector N

⍝ This translates to their scalar product is zero.

⍝ (P - I).N = 0 <=> (P - D - tV).N = 0

⍝ Using distributivity, then associativity, the following equations are established:

⍝ (P - D - tV).N = (P - D).N - (tV).N = (P - D).N - t(V.N) = 0

⍝ so that : t = ((P - D).N) ÷ (V.N)

⍝ In APL, A.B is coded +/A x B

V ← 0 ¯1 ¯1

D ← 0 0 10

N ← 0 0 1

P ← 0 0 5

t ← (+/(P - D) × N) ÷ +/V × N

I ← D + t × V

</lang>

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I

0 ¯5 5