Find the intersection of two lines: Difference between revisions
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⍝ The following solver will take ⍵ the matrix of coordinates, one point per row, then massage the argument to extract x,y |
⍝ The following solver will take ⍵ the matrix of coordinates, one point per row, then massage the argument to extract x,y |
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⍝ and inject 1, where needed |
⍝ and inject 1, where needed |
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⍝ Applied twice, we now have a, b and a', b' defining the two lines, we need to resolve it in x and y |
⍝ Applied twice, we now have a, b and a', b' defining the two lines, we need to resolve it in x and y, in order to determine |
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⍝ their intersection |
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⍝ y = ax + b |
⍝ y = ax + b |
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⍝ y = a'x + b' |
⍝ y = a'x + b' |
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⍝ In order to reuse the same solver, we need to format |
⍝ In order to reuse the same solver, we need to format a little bit the arguments, and change the sign of a and a', therefore |
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⍝ multiply (a,b) by (-1, 1): |
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⍝ b = -ax + y |
⍝ b = -ax + y |
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⍝ b' = -a'x + y |
⍝ b' = -a'x + y |