Find the intersection of two lines: Difference between revisions
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Intersection point: Lines are parallel |
Intersection point: Lines are parallel |
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</pre> |
</pre> |
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===Using a geometric algebra library=== |
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See task [[geometric algebra]]. |
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<syntaxhighlight lang=raku>use Clifford; |
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# We pick a projective basis, |
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# and we compute its pseudo-scalar and its square. |
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my ($i, $j, $k) = @e; |
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my $I = $i∧$j∧$k; |
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my $I2 = ($I**2).narrow; |
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# Homogeneous coordinates of point (X,Y) are (X,Y,1) |
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my $A = 4*$i + 0*$j + $k; |
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my $B = 6*$i + 10*$j + $k; |
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my $C = 0*$i + 3*$j + $k; |
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my $D = 10*$i + 7*$j + $k; |
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# We form lines by joining points |
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my $AB = $A∧$B; |
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my $CD = $C∧$D; |
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# The intersection is their meet, which we |
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# compute by using the De Morgan law |
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my $ab = $AB*$I/$I2; |
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my $cd = $CD*$I/$I2; |
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my $M = ($ab ∧ $cd)*$I/$I2; |
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# Affine coordinates are (X/Z, Y/Z) |
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say ($M / ($M·$k).narrow) X· $i, $j;</syntaxhighlight> |
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{{out}} |
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<pre>(5 5)</pre> |
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=={{header|REXX}}== |
=={{header|REXX}}== |
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