Negative buffer on MultiPolygon loses precision in area calculation

[sghofrany]

Using Boost: 1.84 C++ 17

I am attempting to go from a Point to a Polygon using a positive buffer value and then using the resulting Polygon to generate a smaller Polygon with a negative buffer. However, the resulting smaller polygon has a noticeable area difference than what I'd expect when calculating the area by hand. Here is the example I am running:

Steps:

1. Point -> Buffer with a value of 10 -> produces Polygon A
2. Polygon A -> Buffer with a value of -3 -> Produces Polygon B

Very accurate:

Expected Area for Step 1: 312.56671980047457
Actual Area for Step 1:  312.566719800474857038

Not so accurate:

Expected Area for Step 2: 153.93022477684056
Actual Area for Step 2:  153.897440054815035637

Although the area difference doesn't seem that different in Step 2, you have to realize that is mainly the result of the high pointsPerCircle value. If I lower that to say 36 instead, we start seeing a difference in a meter or more in the output.

Buffer Code:

int pointsPerCircle = 360;
boost::geometry::strategy::buffer::distance_symmetric<double> distanceStrategy(buffer);
boost::geometry::strategy::buffer::side_straight sideStrategy;
boost::geometry::strategy::buffer::join_round joinStrategy(pointsPerCircle);
boost::geometry::strategy::buffer::end_round endStrategyRound(pointsPerCircle);
boost::geometry::strategy::buffer::point_circle circleStrategy(pointsPerCircle);

MultiPolygonType geometry;
MultiPolygonType result;
boost::geometry::buffer(geometry, result, distanceStrategy, sideStrategy, joinStrategy, endStrategyRound, circleStrategy);

Area code:

long double area = boost::geometry::area(result);

Is the expected behavior for negative buffers, or am I doing something wrong?

[vissarion]

Thanks for opening this issue. Could you please provide a complete working example?

[sghofrany]

Thanks for opening this issue. Could you please provide a complete working example?

I'll try, does it need to be in repo or can I just share the code here?

[vissarion]

Just paste the code here please. See for example, https://github.com/boostorg/geometry/issues/1238

[sghofrany]

Here is a basic example:

// Calculate the expected area of the buffered geometry using Area of Triangle formula.
// https://www.cuemath.com/measurement/area-of-triangle-with-2-sides-and-included-angle-sas/
inline double expectedArea(double bufferAmount, double pointsPerCircle) {
  double degreesBetweenPoints = 360.0 / pointsPerCircle;
  double rad = (boost::math::constants::pi<double>()/180) * degreesBetweenPoints;
  double expectedArea = bufferAmount * bufferAmount * sin(rad) * 0.5 * pointsPerCircle;

  return expectedArea;
}

int main() {
  using PointType = boost::geometry::model::d2::point_xy<double>;
  using PolygonType = boost::geometry::model::polygon<PointType>;
  using MultiPolygonType = boost::geometry::model::multi_polygon<PolygonType>;

  double bufferAmount = 10;
  int pointsPerCircle = 36;

  boost::geometry::strategy::buffer::side_straight sideStrategy;
  boost::geometry::strategy::buffer::join_round joinStrategy(pointsPerCircle);
  boost::geometry::strategy::buffer::end_round endStrategyRound(pointsPerCircle);
  boost::geometry::strategy::buffer::point_circle circleStrategy(pointsPerCircle);

  boost::geometry::strategy::buffer::distance_symmetric<double> distanceStrategy(bufferAmount);

  string wkt = "POINT (0 0)";

  MultiPolygonType result;
  auto point = boost::geometry::from_wkt<PointType>(wkt);

  // Buffer a point to a MultiPolygon
  boost::geometry::buffer(point,
                          result,
                          distanceStrategy,
                          sideStrategy,
                          joinStrategy,
                          endStrategyRound,
                          circleStrategy);

  std::cout << boost::geometry::area(result) << "\n";
  std::cout << expectedArea(bufferAmount, static_cast<double>(pointsPerCircle)) << "\n";

  double negativeBuffer = -3;
  MultiPolygonType negativeResult;

  boost::geometry::strategy::buffer::distance_symmetric<double> distanceStrategyNegative(negativeBuffer);

  // Buffer the result of the previous step by -3
  boost::geometry::buffer(result,
                          negativeResult,
                          distanceStrategyNegative,
                          sideStrategy,
                          joinStrategy,
                          endStrategyRound,
                          circleStrategy);

  std::cout << "Negative Buffer:" << boost::geometry::area(negativeResult) << "\n";
  // we use (bufferAmount + negativeBuffer) because we need the updated radius (10 + -3 = 7)
  std::cout << "Negative Buffer:" << expectedArea((bufferAmount + negativeBuffer), static_cast<double>(pointsPerCircle)) << "\n";

return 0;
}

[sghofrany]

@vissarion I was wondering if you had a chance to take a look at this, thanks

[barendgehrels]

I get, with an adapted variant (where I increase the number of points per circle):

314.159
314.159
Detected:153.913
Expected:153.938

Which looks good to me. In positive buffers, automatically more points are used. Therefore the difference in precision. If you use negative buffers, points are closer together so might get a difference, depending on the number of points you use. Closing as "not a bug"

My code, now including the necessary includes and avoiding using namespace std:

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


// Calculate the expected area of the buffered geometry using Area of Triangle formula.
// https://www.cuemath.com/measurement/area-of-triangle-with-2-sides-and-included-angle-sas/
inline double expectedArea(double bufferAmount, double pointsPerCircle) {
  double degreesBetweenPoints = 360.0 / pointsPerCircle;
  double rad = (boost::math::constants::pi<double>()/180) * degreesBetweenPoints;
  double expectedArea = bufferAmount * bufferAmount * sin(rad) * 0.5 * pointsPerCircle;

  return expectedArea;
}

int main() {
  using PointType = boost::geometry::model::d2::point_xy<double>;
  using PolygonType = boost::geometry::model::polygon<PointType>;
  using MultiPolygonType = boost::geometry::model::multi_polygon<PolygonType>;

  double bufferAmount = 10.0;
  int pointsPerCircle = 36000;

  boost::geometry::strategy::buffer::side_straight sideStrategy;
  boost::geometry::strategy::buffer::join_round joinStrategy(pointsPerCircle);
  boost::geometry::strategy::buffer::end_round endStrategyRound(pointsPerCircle);
  boost::geometry::strategy::buffer::point_circle circleStrategy(pointsPerCircle);

  boost::geometry::strategy::buffer::distance_symmetric<double> distanceStrategy(bufferAmount);

  PointType point{0.0, 0.0};
  MultiPolygonType result;

  // Buffer a point to a MultiPolygon
  boost::geometry::buffer(point,
                          result,
                          distanceStrategy,
                          sideStrategy,
                          joinStrategy,
                          endStrategyRound,
                          circleStrategy);

  std::cout << boost::geometry::area(result) << "\n";
  std::cout << expectedArea(bufferAmount, static_cast<double>(pointsPerCircle)) << "\n";

  double negativeBuffer = -3;
  MultiPolygonType negativeResult;

  boost::geometry::strategy::buffer::distance_symmetric<double> distanceStrategyNegative(negativeBuffer);

  // Buffer the result of the previous step by -3
  boost::geometry::buffer(result,
                          negativeResult,
                          distanceStrategyNegative,
                          sideStrategy,
                          joinStrategy,
                          endStrategyRound,
                          circleStrategy);

  std::cout << "Detected:" << boost::geometry::area(negativeResult) << "\n";
  // we use (bufferAmount + negativeBuffer) because we need the updated radius (10 + -3 = 7)
  std::cout << "Expected:" << expectedArea((bufferAmount + negativeBuffer), static_cast<double>(pointsPerCircle)) << "\n";

return 0;
}

[barendgehrels]

36000 is a bit absurd, but with 360 you get:

314.143
314.143
Detected:153.897
Expected:153.93