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578 appendix cFigure C.8 Geometric and file representations of 1-D, 2-D, and 3-D data sets. The letters a, b,c, d, ...represent numerical values that may be scalars or vectors.The corresponding data are called regular data. The coordinates of a single datumwithin a regular set can be generated from three parameters:1. The origin of the data, for instance, the first datum at (x =0,y=0).2. The size of the steps in each dimension for the independent variables, forexample, (∆x, ∆y).3. The total number of data in the set, for example, N.The data structures used by spreadsheets store dependent variables with theirassociated independent variables, for instance, {x, y, z(x, y)}. However, as alreadydiscussed for the Gnuplot surface plot (Figure 3.8 right), if the data are regular,then storing the actual values of x and y is superfluous for visualization since onlythe fact that they are evenly spaced matters. That being the case, regular data needonly contain the values of the dependent variable f(x, y) and the three parametersdiscussed previously. In addition, in order to ensure the general usefulness of a dataset, a description of the data and its structure should be placed at the beginning ofthe set or in a separate file.Figure C.8 gives a geometric representation of 1-D, 2-D, and 3-D data structures.Here each row of data is a group of lines, where each line ends with a return character.The columns correspond to the different positions in the row. The differentrows are separated by blank lines. For the 3-D structure, we separate values for thethird dimension by blank spaces from other elements in the same row.−101COPYRIGHT 2008, PRINCET O N UNIVE R S I T Y P R E S SEVALUATION COPY ONLY. NOT FOR USE IN COURSES.ALLpup_06.04 — 2008/2/15 — Page 578