Page 379 - Excel for Scientists and Engineers: Numerical Methods

356 EXCEL: NUMERICAL METHODS

(6) When all Nedges have been evaluated, if the number of crossings is odd,
the point lies inside the figure.

This "inside or outside" calculation can be done either with worksheet
formulas or with a VBA custom function. The following portion of a spreadsheet
(Figure 15-1 6) illustrates the calculation using worksheet formulas.

Figure 15-16. Inside/outside determined by using worksheet formulas.
(folder 'Chapter 15 Examples', workbook 'Inside or Outside Figure', sheet 'Single Point Diagram')

Note that, in the table of coordinates of the line segments that describe the
figure (A6:B14 in Figure 15-16), the coordinates of the initial point are repeated
in line 15 so as to complete the figure. (This of course is also necessary to create
a chart of the figure.) Thus the nine rows of points shown in Figure 15-16
describe eight line segments. That's why there are formulas in rows 7 through
14, but not in row 6. (It would be equally suitable to have formulas in rows 6
through 13 and not in row 14.)
The formulas in row 7 are:
in cell C7: =AND($A$19>A6,$A$19>A7)
in cell D7: =IF(C7=TRUE,"",AND($A$I 9<A6,$A$19<A7))
in cell E7: =IF(OR(D7=TRUE,D7=""),"",AND($B$19>B6,$B$19>87))