1. A graphing computer system comprising: a processor; and a non-transitory computer-readable storage medium that includes instructions that are configured to be executed by the processor such that, when executed, the instructions cause the graphing computer system to perform operations including: receiving a request at the graphing computer system to display a geometric plot having at least two axes, wherein an axis of the at least two axes has one or more non-ordinal categorical index values, and wherein the request specifies a dataset including at least three vertices that define a shape to be displayed in the geometric plot, the shape being rotatable at any angle within the geometric plot; using the dataset to generate first display data corresponding to a first location of a first vertex, wherein the first vertex is generated at a first non-ordinal categorical index value of the axis plus or minus a first fractional distance relative to the first non-ordinal categorical index value along the axis; using the dataset to generate second display data corresponding to a second location of a second vertex, wherein the second vertex is generated at a second non-ordinal categorical index value of the axis plus or minus a second fractional distance relative to the second non-ordinal categorical index value along the axis; and transmitting the first and second display data to a graphing engine to facilitate display of the shape on the geometric plot.