The triangle plot markers
It is natural to expect that the triangle marker is placed in such a way that its center of mass (center of circumcircle) coincides with the point it marks. That's how it is implemented in all major scientific plotting software, for example Origin:
Some time ago I published my own implementation of triangle-based plot markers. Let us check how the new markers are implemented:
ListLinePlot[{{Missing[]}, {{0, 0}}}, PlotTheme -> "Monochrome",
ImageSize -> 10, Ticks -> False, AxesOrigin -> {0, 0},
BaseStyle -> {Magnification -> 10, Thickness -> Tiny}]
%[[1, 2, 2, 2, -1]] // InputForm
GeometricTransformation[Inset[Graphics[{<...>
Line[{Offset[{0., 2.7625}],
Offset[{-2.7625, -2.022290355909023}],
Offset[{2.7625, -2.022290355909023}],
Offset[{0., 2.7625}]}]}], {0., 0.}],
{{{0., 0.}}, {{0., 0.}}}]
Apart of the fact that the curve is not closed, the triangle is positioned in a strange way: the "center" is placed on the
2.022290355909023/(2.7625 + 2.022290355909023)
0.4226497308103742
part of the height of the triangle instead of expected 1/3 (the center of circumcircle). So current implementation is clearly wrong and leads to producing incorrect plots. Here is an example of correct implementation:
Graphics[{AbsoluteThickness[1], JoinedCurve[
Line[{Offset[{0, 2}], Offset[{Sqrt[3], -1}],
Offset[{-Sqrt[3], -1}]}], CurveClosed -> True]},
ImageSize -> 10, Axes -> True, Ticks -> False, AxesOrigin -> {0, 0},
BaseStyle -> {Magnification -> 10, Thickness -> Tiny}]
The following is correct implementation of both empty and filled triangle plot markers of strictly identical sizes with consistent explicit control over their sizes and thickness:
emptyUpTriangle =
Graphics[{AbsoluteThickness[absoluteThickness],
JoinedCurve[Line[{Offset[size {0, 2}], Offset[size {Sqrt[3], -1}],
Offset[size {-Sqrt[3], -1}]}], CurveClosed -> True]},
AlignmentPoint -> {0, 0}];
filledUpTriangle =
Graphics[{Triangle[{Offset[size {0, 2} + absoluteThickness {0, 1}],
Offset[size {Sqrt[3], -1} + absoluteThickness {Sqrt[3/4], -1/2}],
Offset[size {-Sqrt[3], -1} + absoluteThickness {-Sqrt[3/4], -1/2}]}]},
AlignmentPoint -> {0, 0}];
{emptyLeftTriangle, filledLeftTriangle, emptyDownTriangle,
filledDownTriangle, emptyRightTriangle, filledRightTriangle} =
Flatten[{emptyUpTriangle, filledUpTriangle} /. {x_?NumericQ, y_?NumericQ} :>
RotationTransform[#][{x, y}] & /@ {Pi/2, Pi/3, -Pi/2}];
SeedRandom[12]
ListLinePlot[Accumulate /@ RandomReal[3, {8, 10}] Range[8],
PlotMarkers -> {emptyUpTriangle, filledUpTriangle, emptyLeftTriangle,
filledLeftTriangle, emptyDownTriangle, filledDownTriangle,
emptyRightTriangle, filledRightTriangle}, AspectRatio -> 1]
And here is an extended version which includes open triangles with white filling:
size = 4; absoluteThickness = 2;
triangle[Up, Empty] =
Graphics[{AbsoluteThickness[absoluteThickness],
JoinedCurve[Line[{Offset[size {0, 2}], Offset[size {Sqrt[3], -1}],
Offset[size {-Sqrt[3], -1}]}], CurveClosed -> True]},
AlignmentPoint -> {0, 0}];
triangle[Up, Filled] =
Graphics[{Triangle[{Offset[size {0, 2} + absoluteThickness {0, 1}],
Offset[size {Sqrt[3], -1} + absoluteThickness {Sqrt[3/4], -1/2}],
Offset[size {-Sqrt[3], -1} + absoluteThickness {-Sqrt[3/4], -1/2}]}]},
AlignmentPoint -> {0, 0}];
triangle[Up, Open] =
Graphics[{{White, Triangle[{Offset[size {0, 2}], Offset[size {Sqrt[3], -1}],
Offset[size {-Sqrt[3], -1}]}]}, {AbsoluteThickness[absoluteThickness],
JoinedCurve[Line[{Offset[size {0, 2}], Offset[size {Sqrt[3], -1}],
Offset[size {-Sqrt[3], -1}]}], CurveClosed -> True]}},
AlignmentPoint -> {0, 0}];
triangle[dir_: {Up, Right, Down, Left}, fill_: {Empty, Filled, Open}] :=
triangle[Up, fill] /. {x_?NumericQ, y_?NumericQ} :>
RotationTransform[dir /. {Right -> -Pi/2, Down -> Pi/3, Left -> Pi/2}][{x, y}]
pl = ListPlot[Flatten[Table[{{n, y}}, {y, Range[2]}, {n, 6}], 1],
PlotMarkers ->
Flatten@Table[triangle[dir, fill],
{dir, {Up, Right, Down, Left}}, {fill, {Empty, Filled, Open}}],
GridLines -> {Range[6], Range[2]},
PlotRange -> {{0, 7}, {0, 3}}, Axes -> False, Frame -> True]
Other plot markers
Not only triangle plot markers have problems:
ListLinePlot[{{#, 0}} & /@ Range[5], PlotTheme -> "Monochrome",
ImageSize -> 70, Ticks -> False, Axes -> False, Frame -> True,
BaseStyle -> {Magnification -> 15, Thickness -> Tiny},
PlotRange -> {{0.5, 5.5}, All}, AspectRatio -> 1/10,
FrameTicks -> None, BaselinePosition -> Center,
GridLines -> {Range[5], {0}},
GridLinesStyle -> Directive[{Dashing[None], Gray}],
Method -> {"GridLinesInFront" -> True}]
Cases[%, g_Graphics :>
Show[g, ImageSize -> 8, BaseStyle -> {Magnification -> 16},
BaselinePosition -> Center], Infinity]
Cases[%[[4]], _Line, Infinity]
{Line[{Offset[{-2.5, -2.5}], Offset[{2.125, -2.125}],
Offset[{2.125, 2.125}], Offset[{-2.125, 2.125}],
Offset[{-2.125, -2.125}]}]}
As one can see, the square starts from the point {-2.5, -2.5} and ends in {-2.125, -2.125}!
