Curve that touches three points: Difference between revisions

Content added Content deleted
(adding lambdatalk contribution)
m (→‎{{header|Raku}}: sync up 'rref', factor out points)
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=={{header|Raku}}==
=={{header|Raku}}==
(formerly Perl 6)
(formerly Perl 6)

{{works with|Rakudo|2018.10}}
Kind of bogus. There are an infinite number of curves that pass through those three points. I'll assume a quadratic curve. Lots of bits and pieces borrowed from other tasks to avoid relying on library functions.
Kind of bogus. There are an infinite number of curves that pass through those three points. I'll assume a quadratic curve. Lots of bits and pieces borrowed from other tasks to avoid relying on library functions.


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<lang perl6>use Image::PNG::Portable;
<lang perl6>use Image::PNG::Portable;

# the points of interest
my @points = (10,10), (100,200), (200,10);


# Solve for a quadratic line that passes through those points
# Solve for a quadratic line that passes through those points
my (\a, \b, \c) =
my (\a, \b, \c) = (rref (.[0]², .[0], 1, .[1] for @points) )[*;*-1];
rref([[10², 10, 1, 10],[100², 100, 1, 200],[200², 200, 1, 10]])[*;*-1];


# General case quadratic line equation
# Evaluate quadratic equation
sub f (\x) { a*x² + b*x + c }
sub f (\x) { a×x² + b×x + c }


⚫
my ($w, $h) = 500, 500; # image size
# Scale it up a bit for display
my $scale = 2;
my $scale = 2; # scaling factor


⚫
my ($w, $h) = (500, 500);
my $png = Image::PNG::Portable.new: :width($w), :height($h);
my $png = Image::PNG::Portable.new: :width($w), :height($h);


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}
}


# Highlight the 3 defining points
# Highlight the defining points
dot(|$_, $png, 2) for (10,10,[255,0,0]), (100,200,[255,0,0]), (200,10,[255,0,0]);
dot( | $_, $(255,0,0), $png, 2) for @points;


$png.write: 'Curve-3-points-perl6.png';
$png.write: 'Curve-3-points-perl6.png';
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sub rref (@m) {
sub rref (@m) {
return unless @m;
return unless @m;
my ($lead, $rows, $cols) = 0, +@m, +@m[0];
my ($lead, $rows, $cols) = 0, @m, @m[0];
for ^$rows -> $r {
for ^$rows -> $r {
$lead < $cols or return @m;
$lead < $cols or return @m;
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}
}
@m[$i, $r] = @m[$r, $i] if $r != $i;
@m[$i, $r] = @m[$r, $i] if $r != $i;
my $lv = @m[$r;$lead];
@m[$r] »/=» $ = @m[$r;$lead];
@m[$r] »/=» $lv;
for ^$rows -> $n {
for ^$rows -> $n {
next if $n == $r;
next if $n == $r;
@m[$n] »-=» @m[$r] »*» (@m[$n;$lead] // 0);
@m[$n] »-=» @m[$r] »×» (@m[$n;$lead] // 0);
}
}
++$lead;
++$lead;
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sub line($x0 is copy, $y0 is copy, $x1 is copy, $y1 is copy, $png, @rgb) {
sub line($x0 is copy, $y0 is copy, $x1 is copy, $y1 is copy, $png, @rgb) {
my $steep = abs($y1 - $y0) > abs($x1 - $x0);
my $steep = abs($y1 - $y0) > abs($x1 - $x0);
($x0,$y0,$x1,$y1) »*=» $scale;
($x0,$y0,$x1,$y1) »×=» $scale;
if $steep {
if $steep {
($x0, $y0) = ($y0, $x0);
($x0, $y0) = ($y0, $x0);
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}
}
$error += $Δerror;
$error += $Δerror;
if $error >= 0.5 {
if $error ≥ 0.5 {
$y += $y-step;
$y += $y-step;
$error -= 1.0;
$error -= 1.0;
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sub dot ($X is copy, $Y is copy, @rgb, $png, $radius = 3) {
sub dot ($X is copy, $Y is copy, @rgb, $png, $radius = 3) {
($X, $Y) »*=» $scale;
($X, $Y) »×=» $scale;
for ($X X+ -$radius .. $radius) X ($Y X+ -$radius .. $radius) -> ($x, $y) {
for ($X X+ -$radius .. $radius) X ($Y X+ -$radius .. $radius) -> ($x, $y) {
$png.set($x, $y, |@rgb) if ( $X - $x + ($Y - $y) * i ).abs <= $radius;
$png.set($x, $y, |@rgb) if ( $X - $x + ($Y - $y) × i ).abs <= $radius;
}
}
}</lang>
}</lang>
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