![]() ![]() ![]() ![]() The parser is robust enough that the above example can be pasted into the computer's data entry area and it will work (try it).The commas in the above example are only meant to group the data pairs for the reader - they have no significance to the area computer's data parser.For example, older land surveys (before the era of cheap computer power) regularly fail this test. For applications using field data consisting of length vectors that are subsequently converted to Cartesian form, it's a good idea to compare the beginning and ending Cartesian coordinates - they should be equal. Again, for an accurate area calculation, the described polygon should be a closed figure - the last coordinate should equal the first.The conversion from polar to Cartesian coordinates is trivial, but it's important to keep this requirement in mind. Many applications of this method use original data sources consisting of polar vectors (an example is land survey legal descriptions), but this method requires Cartesian coordinates.It's this property of the method that subtracts the area of inflections from a complex figure as in Figure 1 - the "inflections" represent a counterclockwise traversal within the polygon. "Clockwise Rule": the order of the vectors is significant - if the perimeter is traversed clockwise, the area result is positive, if counterclockwise, it's negative (Figure 1).the last coordinate should equal the first. The origin vertex chosen within the polygon is irrelevant to either area or perimeter calculation, only that the figure be closed, i.e.Here are some important properties of this method: This article (PDF) shows one of the least complex (but by no means simple) expressions: References include the Wikipedia Shoelace Formula article, a similarly complex method in the Polygon article, and a number of articles that seem calculated more to demonstrate the author's erudition than to provide the least complex embodiment of the method. ![]() But most online articles describe the method in unnecessarily complex ways. Versions have existed since the time of Gauss or before. I certainly don't claim originality for this method. The problem is to compute the area and perimeter length of a two-dimensional, closed figure like a room's floor plan, or a plot of land, or any other two-dimensional bounded figure (an "irregular polygon"), regardless of how complex. This article describes a simple solution to a geometric problem, one that I find described in overly complex ways online. ![]()
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