From fc7e70ef4a5cec91a4029cc749d5ee390f5e5f22 Mon Sep 17 00:00:00 2001
From: Galina Bykova <g.bykova@g.nsu.ru>
Date: Mon, 1 Dec 2025 21:22:11 +0330
Subject: [PATCH] fix bug in approxPolyDP: calculate distance to a segment, not
 to a line

---
 modules/imgproc/src/approx.cpp           | 24 +++++++++++++++++++-----
 modules/imgproc/test/test_approxpoly.cpp | 13 +++++++++++++
 2 files changed, 32 insertions(+), 5 deletions(-)

diff --git a/modules/imgproc/src/approx.cpp b/modules/imgproc/src/approx.cpp
index 6c89f1d879..433ca669d5 100644
--- a/modules/imgproc/src/approx.cpp
+++ b/modules/imgproc/src/approx.cpp
@@ -586,26 +586,40 @@ approxPolyDP_( const Point_<T>* src_contour, int count0, Point_<T>* dst_contour,
 
         if( pos != slice.end )
         {
-            double dx, dy, dist, max_dist = 0;
+            double dx, dy, max_dist_2_mul_segment_len_2 = 0;
 
             dx = end_pt.x - start_pt.x;
             dy = end_pt.y - start_pt.y;
+            double segment_len_2 = dx * dx + dy * dy;
 
             CV_Assert( dx != 0 || dy != 0 );
 
             while( pos != slice.end )
             {
                 READ_PT(pt, pos);
-                dist = fabs((pt.y - start_pt.y) * dx - (pt.x - start_pt.x) * dy);
+                double projection = ((pt.x - start_pt.x) * dx + (pt.y - start_pt.y) * dy);
 
-                if( dist > max_dist )
+                double dist_2_mul_segment_len_2;
+                if ( projection < 0 )
                 {
-                    max_dist = dist;
+                    dist_2_mul_segment_len_2 = ((pt.x - start_pt.x) * (pt.x - start_pt.x) + (pt.y - start_pt.y) * (pt.y - start_pt.y)) * segment_len_2;
+                } else if ( projection > segment_len_2 )
+                {
+                    dist_2_mul_segment_len_2 = ((pt.x - end_pt.x) * (pt.x - end_pt.x) + (pt.y - end_pt.y) * (pt.y - end_pt.y)) * segment_len_2;
+                } else
+                {
+                    double dist = ((pt.y - start_pt.y) * dx - (pt.x - start_pt.x) * dy);
+                    dist_2_mul_segment_len_2 = dist * dist;
+                }
+
+                if( dist_2_mul_segment_len_2 > max_dist_2_mul_segment_len_2 )
+                {
+                    max_dist_2_mul_segment_len_2 = dist_2_mul_segment_len_2;
                     right_slice.start = (pos+count-1)%count;
                 }
             }
 
-            le_eps = max_dist * max_dist <= eps * (dx * dx + dy * dy);
+            le_eps = max_dist_2_mul_segment_len_2 <= eps * segment_len_2;
         }
         else
         {
diff --git a/modules/imgproc/test/test_approxpoly.cpp b/modules/imgproc/test/test_approxpoly.cpp
index 2b07c1a7b5..347b03ae8a 100644
--- a/modules/imgproc/test/test_approxpoly.cpp
+++ b/modules/imgproc/test/test_approxpoly.cpp
@@ -377,6 +377,19 @@ TEST(Imgproc_ApproxPoly, bad_epsilon)
     ASSERT_ANY_THROW(approxPolyDP(inputPoints, outputPoints, eps, false));
 }
 
+TEST(Imgproc_ApproxPoly, distace_between_point_and_segment)
+{
+    vector<Point2f> inputPoints = {
+        { {0.f, 0.f}, {4.f, 2.f}, {11.f, 1.f}, {8.f, 0.f} }
+    };
+    std::vector<Point2f> result;
+    approxPolyDP(inputPoints, result, 1.9, false);
+    vector<Point2f> expectedResult = {
+        { {0.f, 0.f}, {11.f, 1.f}, {8.f, 0.f} }
+    };
+    ASSERT_EQ(result, expectedResult);
+}
+
 struct ApproxPolyN: public testing::Test
 {
     void SetUp()