У меня квадрат и форма. Пересечение возвращает действительный результат почти всегда. Исключение составляют только те случаи, когда точка фигуры находится близко к границе прямоугольника.
Пример ниже:
Синий - квадрат. Серый это форма; Красные точки - это оригинальные точки на фигуре. Пересечение (зеленый) маршрутизация до ближайшего пона вместо создания нового 
Достаточно переместить немного битов, и все будет сделано в ожидаемый путь.
#include <boost/geometry.hpp>
#include <boost/geometry/geometries/polygon.hpp>
#include <boost/multiprecision/cpp_bin_float.hpp>
using namespace boost::geometry::model;
using namespace boost::multiprecision;
typedef polygon<d2::point_xy<double> > my_polygon_t;
typedef std::vector<my_polygon_t> my_polygons_t;
int main () {
my_polygon_t in1, in2;
boost::geometry::read_wkt (
"POLYGON((3600.000000000000000 16320.000000000000000, 3839.000000000000000 16320.000000000000000, "
"3839.000000000000000 16639.000000000000000, 3600.000000000000000 16639.000000000000000 ))", in1);
boost::geometry::read_wkt (
"POLYGON(("
"4406.149999999999636 15806.600000000000364, 4409.229999999999563 15821.899999999999636, 4419.989999999999782 15853.500000000000000, 4436.909999999999854 15880.200000000000728,"
"4444.079999999999927 15900.200000000000728, 4447.670000000000073 15925.299999999999272, 4445.109999999999673 15939.399999999999636, 4433.829999999999927 15962.899999999999636,"
"4404.609999999999673 16012.700000000000728, 4393.340000000000146 16020.600000000000364, 4344.899999999999636 16045.500000000000000, 4306.710000000000036 16057.799999999999272,"
"4272.619999999999891 16072.399999999999636, 4260.060000000000400 16085.899999999999636, 4250.829999999999927 16100.500000000000000, 4230.590000000000146 16195.899999999999636,"
"4204.189999999999600 16340.799999999999272, 4179.579999999999927 16365.799999999999272, 4160.100000000000364 16381.500000000000000, 4131.909999999999854 16398.700000000000728,"
"4095.519999999999982 16425.299999999999272, 3849.469999999999800 16495.500000000000000, 3821.789999999999964 16500.099999999998545, 3787.440000000000055 16506.299999999999272,"
"3775.650000000000091 16513.500000000000000, 3685.949999999999818 16645.200000000000728, 3672.110000000000127 16652.900000000001455, 3577.789999999999964 16810.900000000001455,"
"3526.530000000000200 16882.599999999998545, 3526.019999999999982 16888.000000000000000, 3618.030000000000200 16932.200000000000728, 3799.750000000000000 16833.900000000001455,"
"3920.210000000000036 16785.500000000000000, 3999.150000000000091 16778.500000000000000, 4004.530000000000200 16760.799999999999272, 4010.420000000000073 16756.500000000000000,"
"4014.010000000000218 16758.500000000000000, 4020.159999999999854 16773.400000000001455, 4024.780000000000200 16777.500000000000000, 4041.179999999999836 16780.400000000001455,"
"4052.199999999999818 16778.799999999999272, 4083.469999999999800 16769.799999999999272, 4148.060000000000400 16748.799999999999272, 4211.880000000000109 16739.400000000001455,"
"4246.729999999999563 16728.900000000001455, 4348.229999999999563 16667.599999999998545, 4359.760000000000218 16656.000000000000000, 4411.020000000000437 16564.299999999999272,"
"4426.399999999999636 16553.700000000000728, 4436.140000000000327 16549.599999999998545, 4532.250000000000000 16538.700000000000728, 4650.920000000000073 16515.299999999999272,"
"5053.050000000000182 16422.200000000000728, 5047.930000000000291 16401.000000000000000, 5034.090000000000146 16402.299999999999272, 5032.800000000000182 16394.900000000001455,"
"5066.380000000000109 16387.700000000000728, 5075.350000000000364 16418.599999999998545, 5183.770000000000437 16396.400000000001455, 5290.390000000000327 16372.799999999999272,"
"5319.090000000000146 16357.100000000000364, 5329.340000000000146 16350.899999999999636, 5411.869999999999891 16144.700000000000728, 5444.680000000000291 16052.899999999999636,"
"5486.710000000000036 15809.200000000000728, 5502.090000000000146 15717.399999999999636, 5485.689999999999600 15712.000000000000000, 5486.199999999999818 15695.799999999999272,"
"5339.079999999999927 15664.399999999999636, 5327.289999999999964 15679.000000000000000, 5218.369999999999891 15647.399999999999636, 5215.420000000000073 15629.700000000000728,"
"5158.899999999999636 15616.700000000000728, 5138.529999999999745 15636.600000000000364, 5120.199999999999818 15734.299999999999272, 5117.260000000000218 15750.700000000000728,"
"5071.510000000000218 15741.000000000000000, 5046.390000000000327 15731.500000000000000, 5029.220000000000255 15728.399999999999636, 5029.220000000000255 15928.799999999999272,"
"5011.789999999999964 15937.299999999999272, 5011.020000000000437 15766.600000000000364, 5010.510000000000218 15697.700000000000728, 5002.050000000000182 15597.299999999999272,"
"4998.970000000000255 15583.399999999999636, 4995.130000000000109 15581.399999999999636, 4950.529999999999745 15587.200000000000728, 4906.960000000000036 15607.200000000000728,"
"4904.399999999999636 15612.899999999999636, 4909.520000000000437 15725.100000000000364, 4835.449999999999818 15729.000000000000000, 4831.100000000000364 15737.700000000000728,"
"4838.529999999999745 15869.899999999999636, 4848.529999999999745 15972.700000000000728, 4855.960000000000036 16045.700000000000728, 4852.109999999999673 16035.200000000000728,"
"4833.920000000000073 15848.399999999999636, 4824.949999999999818 15733.799999999999272, 4799.960000000000036 15724.700000000000728, 4749.079999999999927 15683.600000000000364,"
"4733.189999999999600 15667.500000000000000, 4479.449999999999818 15805.899999999999636, 4416.659999999999854 15796.600000000000364 ))", in2);
boost::geometry::correct (in1);
boost::geometry::correct (in2);
my_polygons_t output;
boost::geometry::intersection (in1, in2, output);
for (size_t id = 0; id < output.size (); id++) {
const my_polygon_t& ref = output[id];
std::cout << "Intersection: " << boost::geometry::wkt (ref) << "\n";
}
return 0;
}