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Ternary and Piper Diagrams

Ternary and Piper diagrams are two specialized graph types with applications primarily in the geosciences and civil engineering. Origin supports both graph types, including color-mapped contour and 3D variations of the ternary diagram.

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2D ternary diagrams

Two-dimensional ternary diagrams depict relative quantities of components in a three-part system. Because quantities are normalized to 1 or 100%, knowing only two of the three components allows you to describe the system. The standard 2D ternary diagram typically displays a scatter or line plot. Ternary diagrams such as this have a number of applications in the geosciences. Go to the Graph Gallery to view more ternary diagrams.

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This 2D ternary graph was created to determine what combinations of the three particle types would yield the highest packing fraction. Each line in the graph represents a constant value for the packing fraction as a function of the fractional contribution of the three particles (course, fine, and medium) in the mixture.

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The three axes of a ternary plot usually display a range from 0 to 1, or 0 to 100%. In this graph, the data points were concentrated in one corner of the ternary diagram, so the Scale-In tool (Tools toolbar) was used to focus on that region of the plot. When you do this, the axis scale values are adjusted.

Some customizations commonly made to 2D ternary diagrams:

  • Display percentages instead of fractions, on the axis scales.
  • Change the axis scale range graphically using the Scaling tool or manually using the Axis Dialog box.
  • Reverse axis scale direction.

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Ternary contour diagrams

In addition to the standard 2D ternary scatter plot, Origin also supports ternary contour plots. These plots can be used, for example, to chart the response of an independent variable to changes in a mixture of three components.

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This ternary contour plot displays a couple of customizations worth noting. The XYZ data are plotted in the layer twice, once as a color-mapped contour plot (XYZZh), and the second time as a scatter diagram (XYZ only). Further, the XYZ point at row index #2 has special significance and, thus, special formatting and labeling have bee applied to this data point (the point labelled as "1170").

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This ternary contour plot has been customized by applying a built-in color palette ("Pumpkin Patch"). Other customizations include smoothing and labeling of contour lines, and the reversing of the order of levels in the color scale.

Some customizations commonly made to ternary contour diagrams:

  • Customize the color map.
  • Add contour lines and label them.
  • Overlay a dataset as a scatter plot.

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3D ternary colormap surface and 3D ternary scatter diagrams

A 3D ternary diagram adds a third dimension to the standard ternary diagram. As with the 2D ternary diagram, you can plot data as a color contour plot or as a scatter plot. Plots can be projected onto the bottom face of the prism as color contour lines or using drop lines.

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This is a 3D color mapped ternary diagram. Note that the plot has also been projected onto the bottom plane by hiding the plot fill and leaving only the contour lines.

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This is a 3D ternary scatter diagram. This diagram was constructed by first creating a 3D color mapped surface, then using the Plot Details dialog box to change the plot type to scatter. Once the plot was converted to a scatter diagram, droplines were added to the bottom plane.

Some customizations commonly made to 3D ternary diagrams:

  • Customize the color map.
  • Show a uniform color on the bottom of the ternary surface.
  • Project a contour plot onto a plane.
  • Resize, move, rotate or stretch a 3D ternary diagram.
  • Create a 3D ternary scatter diagram with droplines.

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Piper diagrams

Piper diagrams are used to plot water sample chemistry. The diagram has three parts: Two triangular diagrams similar to the 2D ternary diagram, form the base of the diagram. One triangular diagram, is used to plot sample cations Ca, Mg, and Na; the other is used to plot sample anions SO4, HCO3 and Cl. Cations and anions are then projected onto a diamond-shaped (four-sided) summary diagram with the sample plotting at the intersection of anionic and cationic constituents. Go to the Graph Gallery to view more Piper diagrams.

Origin gives you the option to incorporate total dissolved solids into the summary diagram by adding a bubble component to the sample scatter point symbol. Bubble size correlates with the concentration of total dissolved solids (TDS) in the sample; the larger the bubble, the higher the TDS.

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Two customizations worth noting in this Piper diagram: (1) the diagram displays a point-by-legend that lists each sample by location and (2) the diamond-shaped summary portion of the diagram plots both cations+anions and the total dissolved solids (TDS) of each sample. Bubble size is proportional to the level of TDS.

Some customizations commonly made to Piper diagrams:

  • Plot total dissolved solids with cations+anions.
  • Customize plot symbols and colors.
  • Add a point-by-point legend.

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