Make multipath allow points.

Hmm... It seems a dataset should just be made to allow curve parts, and
the multipath should be eliminated.

Author: drgrice1

lib/Plots/JSXGraph.pm

@@ -417,6 +417,11 @@ sub add_multipath {
 	for (0 .. $#paths) {
 		my $path = $paths[$_];
 
+		if (ref $path eq 'ARRAY') {
+			$self->{JS} .= "board.create('curve', [[$path->[0]], [$path->[1]]], { visible: false }),\n";
+			next;
+		}
+
 		($start_x, $start_y) =
 			(', ' . $path->{Fx}->eval($var => $path->{tmin}), ', ' . $path->{Fy}->eval($var => $path->{tmin}))
 			if $cycle && $_ == 0;

lib/Plots/Plot.pm

@@ -297,13 +297,17 @@ sub add_multipath {
 	my $steps = (delete $options{steps}) || 30;
 	$data->{context} = $self->context;
 	$data->{paths}   = [
-		map { {
-			Fx   => $data->get_math_object($_->[0], $var),
-			Fy   => $data->get_math_object($_->[1], $var),
-			tmin => $data->str_to_real($_->[2]),
-			tmax => $data->str_to_real($_->[3]),
-			@$_[ 4 .. $#$_ ]
-		} } @$paths
+		map {
+			@$_ == 2
+				? [@$_]
+				: {
+					Fx   => $data->get_math_object($_->[0], $var),
+					Fy   => $data->get_math_object($_->[1], $var),
+					tmin => $data->str_to_real($_->[2]),
+					tmax => $data->str_to_real($_->[3]),
+					@$_[ 4 .. $#$_ ]
+				}
+		} @$paths
 	];
 	$data->{function} = { var => $var, steps => $steps };
 	$data->style(color => 'default_color', width => 2, mark_size => 2, %options);

lib/Plots/Tikz.pm

@@ -620,21 +620,27 @@ sub draw {
 			for (0 .. $#paths) {
 				my $path = $paths[$_];
 
-				my $xfunction = $data->function_string($path->{Fx}, 'PGF', $var);
-				my $yfunction = $data->function_string($path->{Fy}, 'PGF', $var);
-
 				++$count while $self->{names}{"${curve_name}_$count"};
+				push(@pathData, ["${curve_name}_$count"]);
+				$self->{names}{ $pathData[-1][0] } = 1;
+
+				if (ref $path eq 'ARRAY') {
+					$tikzCode .=
+						"\\addplot[name path=$pathData[-1][0], draw=none] coordinates {($path->[0], $path->[1])};\n";
+					push(@{ $pathData[-1] }, @$path, @$path);
+					next;
+				}
+
 				push(
-					@pathData,
-					[
-						"${curve_name}_$count",
-						$path->{Fx}->eval($var => $path->{tmin}),
-						$path->{Fy}->eval($var => $path->{tmin}),
-						$path->{Fx}->eval($var => $path->{tmax}),
-						$path->{Fy}->eval($var => $path->{tmax})
-					]
+					@{ $pathData[-1] },
+					$path->{Fx}->eval($var => $path->{tmin}),
+					$path->{Fy}->eval($var => $path->{tmin}),
+					$path->{Fx}->eval($var => $path->{tmax}),
+					$path->{Fy}->eval($var => $path->{tmax})
 				);
-				$self->{names}{ $pathData[-1][0] } = 1;
+
+				my $xfunction = $data->function_string($path->{Fx}, 'PGF', $var);
+				my $yfunction = $data->function_string($path->{Fy}, 'PGF', $var);
 
 				my $steps = $path->{steps} // $data->{function}{steps};
 

macros/graph/plots.pl

@@ -197,15 +197,22 @@ =head2 PLOT FUNCTIONS
 
 =head2 PLOT MULTIPATH FUNCTIONS
 
-A multipath function is defined using multiple parametric paths pieced together
-into into a single curve, whose primary use is to create a closed region to be
-filled using multiple boundaries.  This is done by providing a list of
-parametric functions, the name of the parameter, and a list of options.
+A multipath function is defined using multiple parametric paths and points
+pieced together into into a single curve. This is done by providing a list of
+parametric functions and points, the name of the parameter, and a list of
+options. A parametric function is specified by a reference to an array
+containing an x function, a y function, the minimum value for the parameter, and
+the maximum value for the parameter, followed by options.  A point is specified
+by a reference to an array containing the coordinates of the point.  One reason
+for creating a multipath is to create a closed region to be filled using
+multiple boundaries.
 
     $plot->add_multipath(
         [
-            [ $function_x1, $function_y1, $min1, $max1, %path_options ],
-            [ $function_x2, $function_y2, $min2, $max2, %path_options ],
+            [ $function_x1, $function_y1, $min1, $max1, %path_options1 ],
+            [ $function_x2, $function_y2, $min2, $max2, %path_options2 ],
+			[ $point_x1, $point_x2 ]
+			[ $function_x3, $function_y3, $min3, $max3, %path_options3 ],
             ...
         ],
         $variable,
@@ -222,19 +229,19 @@ =head2 PLOT MULTIPATH FUNCTIONS
 The paths have to be listed in the order they are followed, but the
 minimum/maximum values of the parameter can match the parametrization. The
 following example creates a sector of radius 5 between pi/4 and 3pi/4, by first
-drawing the line from (0,0) to (5sqrt(2),5/sqrt(2)), then the arc of the circle
-of radius 5 from pi/4 to 3pi/4, followed by the final line from (-5sqrt(2),
-5sqrt(2)) back to the origin.
+drawing the arc of the circle of radius 5 from pi/4 to 3pi/4, followed by the
+line from (-5 sqrt(2), 5 sqrt(2)) to the origin, and then drawing the line from
+the origin to (5 sqrt(2), 5 sqrt(2)).
 
     $plot->add_multipath(
         [
-            [ 't',       't',       0,           '5/sqrt(2)' ],
             [ '5cos(t)', '5sin(t)', 'pi/4',      '3pi/4' ],
-            [ '-t',      't',       '5/sqrt(2)', 0 ],
+            [ 0, 0 ],
         ],
         't',
         color => 'green',
         fill  => 'self',
+		cycle => 1
     );
 
 Note that the ending point of one path does not need to be the same as the