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