diff --git a/lib/Slic3r/Polygon.pm b/lib/Slic3r/Polygon.pm
index 124d9ae99..5b13e13ff 100644
--- a/lib/Slic3r/Polygon.pm
+++ b/lib/Slic3r/Polygon.pm
@@ -45,34 +45,52 @@ sub subdivide {
     return Slic3r::Polygon->new(@new_points);
 }
 
-# angle is checked on the internal side of the polygon
 sub concave_points {
     my ($self, $angle) = @_;
     
     $angle //= PI;
     
+    # input angle threshold is checked on the internal side of the polygon
+    # but angle3points measures CCW angle, so we calculate the complementary angle
+    my $ccw_angle = 2*PI-$angle;
+    
     my @points = @$self;
     my @points_pp = @{$self->pp};
-    return [
-        map $points[$_],
-        grep Slic3r::Geometry::angle3points(@points_pp[$_, $_-1, $_+1]) < $angle,
-        -1 .. ($#points-1)
-    ];
+    
+    my @concave = ();
+    for my $i (-1 .. ($#points-1)) {
+        next if $points[$i-1]->coincides_with($points[$i]);
+        # angle is measured in ccw orientation
+        my $vertex_angle = Slic3r::Geometry::angle3points(@points_pp[$i, $i-1, $i+1]);
+        if ($vertex_angle <= $ccw_angle) {
+            push @concave, $points[$i];
+        }
+    }
+    return [@concave];
 }
 
-# angle is checked on the internal side of the polygon
 sub convex_points {
     my ($self, $angle) = @_;
     
     $angle //= PI;
     
+    # input angle threshold is checked on the internal side of the polygon
+    # but angle3points measures CCW angle, so we calculate the complementary angle
+    my $ccw_angle = 2*PI-$angle;
+    
     my @points = @$self;
     my @points_pp = @{$self->pp};
-    return [
-        map $points[$_],
-        grep Slic3r::Geometry::angle3points(@points_pp[$_, $_-1, $_+1]) > $angle,
-        -1 .. ($#points-1)
-    ];
+    
+    my @convex = ();
+    for my $i (-1 .. ($#points-1)) {
+        next if $points[$i-1]->coincides_with($points[$i]);
+        # angle is measured in ccw orientation
+        my $vertex_angle = Slic3r::Geometry::angle3points(@points_pp[$i, $i-1, $i+1]);
+        if ($vertex_angle >= $ccw_angle) {
+            push @convex, $points[$i];
+        }
+    }
+    return [@convex];
 }
 
 1;
\ No newline at end of file
diff --git a/t/geometry.t b/t/geometry.t
index 7ff2a2aac..a9326782b 100644
--- a/t/geometry.t
+++ b/t/geometry.t
@@ -2,7 +2,7 @@ use Test::More;
 use strict;
 use warnings;
 
-plan tests => 29;
+plan tests => 33;
 
 BEGIN {
     use FindBin;
@@ -189,3 +189,27 @@ my $polygons = [
 }
 
 #==========================================================
+
+{
+    my $square = Slic3r::Polygon->new(
+        [150,100],
+        [200,100],
+        [200,200],
+        [100,200],
+        [100,100],
+    );
+    is scalar(@{$square->concave_points(PI*4/3)}), 0, 'no concave vertices detected in convex polygon';
+    is scalar(@{$square->convex_points(PI*2/3)}), 4, 'four convex vertices detected in square';
+}
+
+{
+    my $square = Slic3r::Polygon->new(
+        [200,200],
+        [100,200],
+        [100,100],
+        [150,100],
+        [200,100],
+    );
+    is scalar(@{$square->concave_points(PI*4/3)}), 0, 'no concave vertices detected in convex polygon';
+    is scalar(@{$square->convex_points(PI*2/3)}), 4, 'four convex vertices detected in square';
+}