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Implement several options for the GraphTool in hardcopy that should have been implemented before. #1333

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Implement several options for the GraphTool in hardcopy that should have been implemented before. #1333

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120 changes: 102 additions & 18 deletions macros/graph/parserGraphTool.pl
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Original file line number Diff line number Diff line change
Expand Up @@ -331,8 +331,12 @@ =head1 OPTIONS

=item scaleX, scaleY (Default: C<< scaleX => 1, scaleY => 1 >>)

These are the scale of the ticks on the x and y axes. That is the distance between two
successive ticks on the axis (including both major and minor ticks).
These are the scale of the tick distances on the x and y axes. That is the distance between two
successive major ticks on the axis will be the product of the ticks distance and the scale.
This is usually used in conjunction with the C<scaleSymbolX> and C<scaleSymbolY> options. For
example, if C<ticksDistanceX> is 2, C<scaleX> is 3, and C<scaleSymbolX> is 'a', then the first
positive major x axis tick will occur 6 units to the right and be labeled '2a', and the next
major x axis tick will occur 12 units to the right and be labeled '4a'.

=item scaleSymbolX, scaleSymbolY (Default: C<< scaleSymbolX => '', scaleSymbolY => '' >>)

Expand Down Expand Up @@ -1195,6 +1199,47 @@ sub generateHTMLAnswerGraph {
END_SCRIPT
}

# This is essentially copied from contextFraction.pl.
sub continuedFraction {
my ($x) = @_;

my $step = $x;
my $n = int($step);
my ($h0, $h1, $k0, $k1) = (1, $n, 0, 1);

while ($step != $n) {
$step = 1 / ($step - $n);
$n = int($step);
my ($newh, $newk) = ($n * $h1 + $h0, $n * $k1 + $k0);
last if $newk > 10**8; # Bail if the denominator is skyrocketing out of control.
($h0, $h1, $k0, $k1) = ($h1, $newh, $k1, $newk);
}

return ($h1, $k1);
}

sub formatTickLabelText {
my ($self, $value, $axis) = @_;
my $coordinateHintsType = $self->{"coordinateHintsType$axis"} // $self->{coordinateHintsType};
if ($coordinateHintsType eq 'fraction' || $coordinateHintsType eq 'mixed') {
my ($num, $den) = continuedFraction(abs($value));
if ($num && $den != 1 && !($num == 1 && $den == 1)) {
if ($coordinateHintsType eq 'fraction' || $num < $den) {
$value = ($value < 0 ? '-' : '') . "\\frac{$num}{$den}";
} else {
my $int = int($num / $den);
my $properNum = $num % $den;
$value = ($value < 0 ? '-' : '') . "$int\\frac{$properNum}{$den}";
}
}
}
my $scaleSymbol = $self->{"scaleSymbol$axis"} // '';
return
$value eq '0' ? '0'
: $scaleSymbol ? ($value eq '1' ? $scaleSymbol : $value eq '-1' ? "-$scaleSymbol" : "$value$scaleSymbol")
: $value;
}

sub generateTeXGraph {
my ($self, %options) = @_;

Expand All @@ -1203,7 +1248,7 @@ sub generateTeXGraph {

return &{ $self->{printGraph} } if ref($self->{printGraph}) eq 'CODE';

my @size = $self->{numberLine} ? (500, 100) : (500, 500);
my @size = $self->{numberLine} ? (500, 110) : (500, 500);

my $graph = main::createTikZImage();
$graph->tikzLibraries('arrows.meta');
Expand Down Expand Up @@ -1264,32 +1309,71 @@ sub generateTeXGraph {
}

# Horizontal axis ticks and labels
my @xTicks = grep { $_ < $self->{bBox}[2] }
map { $_ * $self->{ticksDistanceX} } (1 .. $self->{bBox}[2] / $self->{ticksDistanceX});
push(@xTicks,
my @xTicks =
grep { $_ > $self->{bBox}[0] }
map { -$_ * $self->{ticksDistanceX} } (1 .. -$self->{bBox}[0] / $self->{ticksDistanceX}));
map { -$_ * $self->{ticksDistanceX} * $self->{scaleX} }
reverse(1 .. -$self->{bBox}[0] / ($self->{ticksDistanceX} * $self->{scaleX}));
my $numNegative = @xTicks;
# Add zero if this is a number line and 0 is in the given range.
push(@xTicks, 0) if ($self->{numberLine} && $self->{bBox}[2] > 0 && $self->{bBox}[0] < 0);
push(@xTicks, 0) if $self->{numberLine} && $self->{bBox}[2] > 0 && $self->{bBox}[0] < 0;
push(@xTicks,
grep { $_ < $self->{bBox}[2] }
map { $_ * $self->{ticksDistanceX} * $self->{scaleX} }
(1 .. $self->{bBox}[2] / ($self->{ticksDistanceX} * $self->{scaleX})));
my $tickSize = $self->{numberLine} ? '9' : '5';
$tikz .=
"\\foreach \\x in {"
. join(',', @xTicks)
. "}{\\draw[thin] (\\x,${tickSize}pt) -- (\\x,-${tickSize}pt) node[below]{\\(\\x\\)};}\n"
"\\foreach \\x/\\label in {"
. join(',', map { "$_/" . $self->formatTickLabelText($_ / $self->{scaleX}, 'X') } @xTicks)
. "}{\\draw[thin, opacity = 0.5] (\\x,${tickSize}pt) -- (\\x,-${tickSize}pt) "
. "node[baseline, yshift = -15pt, opacity = 1]{\\(\\label\\)};}\n"
if (@xTicks);

# Add horizontal axis minor ticks.
splice(@xTicks, $numNegative, 0, 0) if !$self->{numberLine} || ($self->{bBox}[0] <= 0 && $self->{bBox}[2] >= 0);
unshift(@xTicks, $xTicks[0] - $self->{ticksDistanceX} * $self->{scaleX}) if $self->{bBox}[0] < 0;
push(@xTicks, $xTicks[-1] + $self->{ticksDistanceX} * $self->{scaleX}) if $self->{bBox}[2] > 0;
my @xMinorTicks;
my $xMinorTickDelta = $self->{ticksDistanceX} * $self->{scaleX} / ($self->{minorTicksX} + 1);
for my $tickIndex (0 .. $#xTicks - 1) {
push(@xMinorTicks, map { $xTicks[$tickIndex] + $_ * $xMinorTickDelta } 1 .. $self->{minorTicksX});
}
$tikz .=
"\\foreach \\x in {"
. join(',', @xMinorTicks)
. "}{\\draw[thin, opacity = 0.5] (\\x,0) -- (\\x,-${tickSize}pt);}\n"
if (@xMinorTicks);

# Vertical axis ticks and labels
unless ($self->{numberLine}) {
my @yTicks = grep { $_ < $self->{bBox}[1] }
map { $_ * $self->{ticksDistanceY} } (1 .. $self->{bBox}[1] / $self->{ticksDistanceY});
push(@yTicks,
my @yTicks =
grep { $_ > $self->{bBox}[3] }
map { -$_ * $self->{ticksDistanceY} } (1 .. -$self->{bBox}[3] / $self->{ticksDistanceY}));
map { -$_ * $self->{ticksDistanceY} * $self->{scaleY} }
reverse(1 .. -$self->{bBox}[3] / ($self->{ticksDistanceY} * $self->{scaleY}));
my $numNegative = @yTicks;
push(@yTicks,
grep { $_ < $self->{bBox}[1] }
map { $_ * $self->{ticksDistanceY} * $self->{scaleY} }
(1 .. $self->{bBox}[1] / ($self->{ticksDistanceY} * $self->{scaleY})));
$tikz .=
"\\foreach \\y in {"
. join(',', @yTicks)
. "}{\\draw[thin] (5pt,\\y) -- (-5pt,\\y) node[left]{\$\\y\$};}\n"
"\\foreach \\y/\\label in {"
. join(',', map { "$_/" . $self->formatTickLabelText($_ / $self->{scaleY}, 'Y') } @yTicks)
. "}{\\draw[thin, opacity = 0.5] (5pt,\\y) -- (-5pt,\\y) node[left, opacity = 1]{\$\\label\$};}\n"
if (@yTicks);

# Add vertical axis minor ticks.
splice(@yTicks, $numNegative, 0, 0);
unshift(@yTicks, $yTicks[0] - $self->{ticksDistanceY} * $self->{scaleY}) if $self->{bBox}[3] < 0;
push(@yTicks, $yTicks[-1] + $self->{ticksDistanceY} * $self->{scaleY}) if $self->{bBox}[1] > 0;
my @yMinorTicks;
my $yMinorTickDelta = $self->{ticksDistanceY} * $self->{scaleY} / ($self->{minorTicksY} + 1);
for my $tickIndex (0 .. $#yTicks - 1) {
push(@yMinorTicks, map { $yTicks[$tickIndex] + $_ * $yMinorTickDelta } 1 .. $self->{minorTicksY});
}
$tikz .=
"\\foreach \\y in {"
. join(',', @yMinorTicks)
. "}{\\draw[thin, opacity = 0.5] (0, \\y) -- (-5pt, \\y);}\n"
if @yMinorTicks;
}

# Border box
Expand Down