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

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(→‎With a geometric algebra library: simplify and add module version import requirement)
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See task [[geometric algebra]]
See task [[geometric algebra]]


<syntaxhighlight lang=raku>use Clifford;
<syntaxhighlight lang=raku>use Clifford:ver<6.2.1>;


# We pick a projective basis and we compute
# We pick a (non-degenerate) projective basis and
# we define the dual and meet operators.
# the pseudo-scalar along with its square
my $I = [∧] my ($i, $j, $k, $l) = @e;
my $I = [∧] my ($i, $j, $k, $l) = @e;
sub prefix:<∗>($M) { $M/$I }
my $I2 = ($I**2).narrow;
sub infix:<∨>($A, $B) { ∗((∗$B)∧(∗$A)) }


my $direction = -$j - $k;
my $direction = -$j - $k;
$direction /= sqrt($direction**2);


# Homogeneous coordinates of (X, Y, Z) are (X, Y, Z, 1)
# Homogeneous coordinates of (X, Y, Z) are (X, Y, Z, 1)
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# A plane is a trivector
# A plane is a trivector
my $plane = (5*$k + $l) ∧ ($k*-($i∧$j∧$k));
my $plane = (5*$k + $l) ∧ ($k*-$i∧$j∧$k);


# The intersection is the meet, and
# The intersection is the meet
⚫
my $m = $line ∨ $plane;
# according to the De Morgan Law,
# the meet is the dual of the join of the duals.
⚫
my $LINE = $line*$I/$I2;
my $PLANE = $plane*$I/$I2;
my $M = $LINE∧$PLANE;
my $m = $M*$I/$I2;


# Affine coordinates of (X, Y, Z, W) are (X/W, Y/W, Z/W)
# Affine coordinates of (X, Y, Z, W) are (X/W, Y/W, Z/W)
say $m/($m·$l).narrow X· ($i, $j, $k);</syntaxhighlight>
say $m/($m·$l) X· ($i, $j, $k);</syntaxhighlight>
{{out}}
{{out}}
<pre>(0 -5 5)</pre>
<pre>(0 -5 5)</pre>
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