[Boost-bugs] [Boost C++ Libraries] #11928: surveyor area method is inaccurate

Subject: [Boost-bugs] [Boost C++ Libraries] #11928: surveyor area method is inaccurate
From: Boost C++ Libraries (noreply_at_[hidden])
Date: 2016-01-21 19:00:40

#11928: surveyor area method is inaccurate
 Reporter: Charles Karney <charles@…> | Owner: barendgehrels
     Type: Bugs | Status: new
Milestone: To Be Determined | Component: geometry
  Version: Boost 1.58.0 | Severity: Problem
 Keywords: area |
 The following code illustrates a problem with the "surveyor" strategy
 for computing planar areas. It computes the area of a square of area
 2 and the same square translated by 10^8^ in x and y. bg::area
 incorrectly computes the area in the second case as 0.

 #include <iostream>
 #include <boost/geometry.hpp>

 namespace bg = boost::geometry;
 typedef bg::model::point<double, 2, bg::cs::cartesian> pt;

 int main() {
   bg::model::polygon<pt, false, false> poly;
   // A simple square of area 2
   bg::read_wkt("POLYGON((1 0,0 1,-1 0,0 -1))", poly);
   // Computes the correct area (= 2)
   std::cout << "area " << bg::area(poly) << "\n";
   // The same square shifted by (10^8 10^8)
   bg::read_wkt("POLYGON((100000001 100000000, \
                          100000000 100000001, \
                           99999999 100000000, \
                          100000000 99999999))", poly);
   // Should give 2 but instead gives 0
   std::cout << "area " << bg::area(poly) << "\n";

 Running this code gives
 area 2
 area 0

 * Surely it's a bad idea to embed the algorithm name "surveyor" into
   the API. Computing 2d areas is really straightforward. Users
   shouldn't need to worry about the underlying method. Maybe
   "planar_area" is a better name.
 * In any case "surveyor" is a rather silly name of the type beloved of
   Wikipedia editors. There's no evidence that surveyors actually used
   this method.
 * It's more expensive (at 2*n multiplies and 2*n additions) than
   applying the trapezium rule (otherwise known as "doing the
   integral"), i.e., summing (x[i+1] - x[i]) * (y[i+1] + y[i]) / 2,
   which clocks in at n multiplies and 3*n additions.
 * Finally, as this example illustrates, it's subject to catastrophic
   loss of accuracy, while the trapezium rule will give the exact
   result. (Kahan contrasts evaluating x*x - y*y compared with (x - y) *
   (x + y) with x = 1e15+1, y = 1e15-1. The former result is wrong
   by 1.5% while the latter is exact.)

Ticket URL: <https://svn.boost.org/trac/boost/ticket/11928>
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