Ternary Plots, 3D

A ternary plot can be used to examine relations between four or more dimensions where three of those dimensions represent components of a mixture (i.e., the relations between them is constrained such that the values of the three variables add up to the same constant). One typical application of this graph is when the measured response(s) from an experiment depends on the relative proportions of three components (e.g., three different chemicals) which are varied in order to determine an optimal combination of those components (e.g., in mixture designs).

The responses associated with the proportions of the component variables (X, Y, and Z) in a ternary graph are plotted in a 3-dimensional display for each level of the grouping variable (or user-defined subset of data). One component graph is produced for each level of the grouping variable (or user-defined subset of data) and all the component graphs are arranged in one display to allow for comparisons between the subsets of data (categories).
See also, Data Reduction.

In this type of ternary graph, 3D scatterplot data are represented through the use of an X-Y- Z plane (defined via a triangular coordinate system) positioned at a user-selectable level of the vertical V-axis (which "sticks up" through the middle of the plane) and categorized by each level of the grouping variable (or user-defined subset of data). One component graph is produced for each level of the grouping variable (or user-defined subset of data) and all the component graphs are arranged in one display to allow for comparisons between the subsets of data (categories).
The level of the X-Y-Z plane can be adjusted in order to divide the X-Y-Z-V space into meaningful parts (e.g., featuring different patterns of the relation between the three variables).

A surface is fit to a four-coordinate data set in this 3-dimensional ternary graph categorized by each level of the grouping variable (or user-defined subset of data). One component graph is produced for each level of the grouping variable (or user-defined subset of data) and all the component graphs are arranged in one display to allow for comparisons between the subsets of data (categories).

In this type of ternary graph, you can examine the relations between four or more dimensions (X, Y, Z, and V1, V2, etc.) as a 3D trace plot categorized by each level of the grouping variable (or user-defined subset of data). One component graph is produced for each level of the grouping variable (or user-defined subset of data) and all the component graphs are arranged in one display to allow for comparisons between the subsets of data (categories).

In this type of ternary graph, the 3-dimensional surface (fitted to a four-coordinate data set) is projected onto a 2-dimensional plane as an area contour.

In this type of ternary graph, the 3-dimensional surface (fitted to a four-coordinate data set) is projected onto a 2-dimensional plane as a line contour (see graph below).

This type of ternary graph allows you to examine the relations between four or more dimensions (X, Y, Z, and V1, V2, etc.) as "deviations" from a specified base-level of the V- axis where three of those dimensions (X, Y, and Z) represent components of a mixture (i.e., the relations between them is constrained such that the values of the three variables add up to the same constant for each case).

This type of ternary graph offers a distinctive method of representing 3D scatterplot data through the use of an X-Y-Z plane (defined via a triangular coordinate system) positioned at a user-selectable level of the vertical V-axis (which "sticks up" through the middle of the plane). The level of the X-Y-Z plane can be adjusted in order to divide the X-Y-Z- space into meaningful parts (e.g., featuring different patterns of the relation between the three variables).