Merge pull request #27149 from liane-lin:4.x

Fix #25696: Solved the problem in Subdiv2D, empty delaunay triangulation #27149

Detailed description

Expected behaviour:
Given 4 points, where no three points are collinear, the Delaunay Triangulation Algorithm should return 2 triangles.

Actual:
The algorithm returns zero triangles in this particular case.

Fix:
The radius of the circumcircle tends to infinity when the points are closer to form collinear points, so the problem occurs because the super-triangles are not large enough,
which then results in certain edges are not swapped. The proposed solution just increases the super triangle, duplicating the value of constant for example.

### Pull Request Readiness Checklist

See details at https://github.com/opencv/opencv/wiki/How_to_contribute#making-a-good-pull-request

- [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
- [ ] There is accuracy test, performance test and test data in opencv_extra repository, if applicable
      Patch to opencv_extra has the same branch name.
- [ ] The feature is well documented and sample code can be built with the project CMake

modules/imgproc/src/subdivision2d.cpp

@@ -493,7 +493,7 @@ void Subdiv2D::initDelaunay( Rect rect )
 {
     CV_INSTRUMENT_REGION();
 
-    float big_coord = 3.f * MAX( rect.width, rect.height );
+    float big_coord = 6.f * MAX( rect.width, rect.height );
     float rx = (float)rect.x;
     float ry = (float)rect.y;
 

modules/imgproc/test/test_subdivision2d.cpp

@@ -50,4 +50,18 @@ TEST(Imgproc_Subdiv2D_getTriangleList, regression_5788)
     EXPECT_EQ(trig_cnt, 105);
 }
 
+TEST(Imgproc_Subdiv2D, issue_25696) {
+    std::vector<cv::Point2f> points{
+        {0, 0}, {40, 40}, {84, 104}, {86, 108}
+    };
+
+    cv::Rect subdivRect{cv::Point{-10, -10}, cv::Point{96, 118}};
+    cv::Subdiv2D subdiv{subdivRect};
+    subdiv.insert(points);
+
+    std::vector<cv::Vec6f> triangles;
+    subdiv.getTriangleList(triangles);
+
+    ASSERT_EQ(static_cast<size_t>(2), triangles.size());
+}
 }}