Merge pull request #23690 from chacha21:rotatedRectangleIntersection_precision

better accuracy for _rotatedRectangleIntersection() (proposal for #23546) #23690

_rotatedRectangleIntersection() can be (statically) customized to use double instead of float for better accuracy
this is a proposal for experimentation around #23546

for better accuracy, _rotatedRectangleIntersection() could use double. It will still return cv::Point2f list for backward compatibility, but the inner computations are controlled by a typedef

- [X] I agree to contribute to the project under Apache 2 License.
- [X] To the best of my knowledge, the proposed patch is not based on a code under GPL or another license that is incompatible with OpenCV
- [X] The PR is proposed to the proper branch
- [X] There is a reference to the original bug report and related work
- [x] There is accuracy test, performance test and test data in opencv_extra repository, if applicable
      Patch to opencv_extra has the same branch name.
- [x] The feature is well documented and sample code can be built with the project CMake

modules/imgproc/test/test_intersection.cpp

@@ -486,4 +486,23 @@ TEST(Imgproc_RotatedRectangleIntersection, regression_19824)
     EXPECT_LE(intersections.size(), (size_t)7);
 }
 
+TEST(Imgproc_RotatedRectangleIntersection, accuracy_23546)
+{
+    RotatedRect r1(
+        Point2f(824.6421183672817f, 280.28737007069833f),
+        Size2f(565.0f, 140.0f),
+        -177.80506896972656f);
+    RotatedRect r2(
+        Point2f(567.3310438828003f, 270.42527355719545f),
+        Size2f(275.0f, 50.0f),
+        92.19493103027344f);
+
+    std::vector<Point2f> intersection;
+    double intersectionArea = 0;
+    int interType = cv::rotatedRectangleIntersection(r1, r2, intersection);
+    intersectionArea = (intersection.size() <= 2) ? 0. : cv::contourArea(intersection);
+    EXPECT_EQ(INTERSECT_PARTIAL, interType);
+    EXPECT_EQ(intersection.size(), (size_t)4);
+    ASSERT_LE(std::abs(intersectionArea-7000), 1e-1);
+}
 }} // namespace