diff --git a/src/geom/Geometry.cpp b/src/geom/Geometry.cpp
index 7d5f17c6f8..4339335870 100644
--- a/src/geom/Geometry.cpp
+++ b/src/geom/Geometry.cpp
@@ -39,6 +39,7 @@
 #include <geos/algorithm/InteriorPointLine.h>
 #include <geos/algorithm/InteriorPointArea.h>
 #include <geos/algorithm/ConvexHull.h>
+#include <geos/algorithm/locate/SimplePointInAreaLocator.h>
 #include <geos/geom/prep/PreparedGeometryFactory.h>
 #include <geos/operation/intersection/Rectangle.h>
 #include <geos/operation/intersection/RectangleIntersection.h>
@@ -322,10 +323,19 @@ Geometry::intersects(const Geometry* g) const
         return predicate::RectangleIntersects::intersects(*p, *this);
     }
 
+    auto typ = getGeometryTypeId();
+    if (typ == GEOS_CURVEPOLYGON && g->getGeometryTypeId() == GEOS_POINT) {
+        auto loc = locate::SimplePointInAreaLocator::locatePointInSurface(*g->getCoordinate(), *detail::down_cast<const Surface*>(this));
+        return loc != Location::EXTERIOR;
+    } else if (typ == GEOS_POINT && g->getGeometryTypeId() == GEOS_CURVEPOLYGON) {
+        auto loc = locate::SimplePointInAreaLocator::locatePointInSurface(*getCoordinate(), *detail::down_cast<const Surface*>(g));
+        return loc != Location::EXTERIOR;
+    }
+
 #if USE_RELATENG
     return operation::relateng::RelateNG::intersects(this, g);
 #else
-    if (getGeometryTypeId() == GEOS_GEOMETRYCOLLECTION) {
+    if (typ == GEOS_GEOMETRYCOLLECTION) {
         auto im = relate(g);
         bool res = im->isIntersects();
         return res;
diff --git a/tests/unit/capi/GEOSIntersectsTest.cpp b/tests/unit/capi/GEOSIntersectsTest.cpp
index 395d2698ca..b86d8c282c 100644
--- a/tests/unit/capi/GEOSIntersectsTest.cpp
+++ b/tests/unit/capi/GEOSIntersectsTest.cpp
@@ -234,5 +234,30 @@ void object::test<11>()
     ensure_equals("curved geometry not supported", GEOSIntersects(geom2_, geom1_), 2);
 }
 
+// test PIP special case for CurvePolygon
+template<>
+template<>
+void object::test<12>()
+{
+    geom1_ = fromWKT("CURVEPOLYGON (COMPOUNDCURVE(CIRCULARSTRING(0 0, 1 1, 2 0), (2 0, 0 0)))");
+    geom2_ = fromWKT("POINT (0.1556955 0.5355459)");
+
+    // PostGIS would return false here because geom2 is inside geom1
+    // but outside the linearized form of geom1
+    ensure_equals(GEOSIntersects(geom1_, geom2_), 1);
+    ensure_equals(GEOSIntersects(geom2_, geom1_), 1);
+}
+
+template<>
+template<>
+void object::test<13>()
+{
+    geom1_ = fromWKT("CURVEPOLYGON (COMPOUNDCURVE(CIRCULARSTRING(0 0, 1 1, 2 0), (2 0, 0 0)))");
+    geom2_ = fromWKT("POINT EMPTY");
+
+    ensure_equals(GEOSIntersects(geom1_, geom2_), 0);
+    ensure_equals(GEOSIntersects(geom2_, geom1_), 0);
+}
+
 } // namespace tut