diff --git a/t/geometry.t b/t/geometry.t
index 24fbf52d9..d85c8bbcf 100644
--- a/t/geometry.t
+++ b/t/geometry.t
@@ -2,7 +2,7 @@ use Test::More;
 use strict;
 use warnings;
 
-plan tests => 33;
+plan tests => 38;
 
 BEGIN {
     use FindBin;
@@ -213,3 +213,29 @@ my $polygons = [
     is scalar(@{$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 $triangle = Slic3r::Polygon->new(
+        [16000170,26257364], [714223,461012], [31286371,461008],
+    );
+    is scalar(@{$triangle->concave_points(PI*4/3)}), 0, 'no concave vertices detected in triangle';
+    is scalar(@{$triangle->convex_points(PI*2/3)}), 3, 'three convex vertices detected in triangle';
+}
+
+{
+    my $triangle = Slic3r::Polygon->new(
+        [16000170,26257364], [714223,461012], [20000000,461012], [31286371,461012],
+    );
+    is scalar(@{$triangle->concave_points(PI*4/3)}), 0, 'no concave vertices detected in triangle having collinear point';
+    is scalar(@{$triangle->convex_points(PI*2/3)}), 3, 'three convex vertices detected in triangle having collinear point';
+}
+
+{
+    my $triangle = Slic3r::Polygon->new(
+        [16000170,26257364], [714223,461012], [31286371,461008],
+    );
+    my $simplified = $triangle->simplify(250000)->[0];
+    is scalar(@$simplified), 3, 'triangle is never simplified to less than 3 points';
+}
+
+__END__
diff --git a/t/perimeters.t b/t/perimeters.t
index 17e1b31c7..49217fd82 100644
--- a/t/perimeters.t
+++ b/t/perimeters.t
@@ -266,7 +266,7 @@ use Slic3r::Test;
         my $was_extruding = 0;
         my @seam_points = ();
         my $print = Slic3r::Test::init_print($model_name, config => $config);
-        Slic3r::GCode::Reader->new->parse(Slic3r::Test::gcode($print), sub {
+        Slic3r::GCode::Reader->new->parse(my $gcode = Slic3r::Test::gcode($print), sub {
             my ($self, $cmd, $args, $info) = @_;
     
             if ($info->{extruding}) {
diff --git a/xs/src/libslic3r/MultiPoint.hpp b/xs/src/libslic3r/MultiPoint.hpp
index ba3c72e50..eaca9b8eb 100644
--- a/xs/src/libslic3r/MultiPoint.hpp
+++ b/xs/src/libslic3r/MultiPoint.hpp
@@ -17,6 +17,8 @@ class MultiPoint
     Points points;
     
     operator Points() const;
+    MultiPoint() {};
+    explicit MultiPoint(const Points &_points): points(_points) {};
     void scale(double factor);
     void translate(double x, double y);
     void translate(const Point &vector);
diff --git a/xs/src/libslic3r/Point.cpp b/xs/src/libslic3r/Point.cpp
index 9debe9e8e..76da85334 100644
--- a/xs/src/libslic3r/Point.cpp
+++ b/xs/src/libslic3r/Point.cpp
@@ -160,6 +160,13 @@ Point::ccw(const Line &line) const
     return this->ccw(line.a, line.b);
 }
 
+// returns the CCW angle between this-p1 and this-p2
+double
+Point::ccw_angle(const Point &p1, const Point &p2) const
+{
+    return Line(*this, p1).orientation() - Line(*this, p2).orientation();
+}
+
 Point
 Point::projection_onto(const MultiPoint &poly) const
 {
diff --git a/xs/src/libslic3r/Point.hpp b/xs/src/libslic3r/Point.hpp
index 514eb51cd..60127b1b7 100644
--- a/xs/src/libslic3r/Point.hpp
+++ b/xs/src/libslic3r/Point.hpp
@@ -48,6 +48,7 @@ class Point
     double distance_to(const Line &line) const;
     double ccw(const Point &p1, const Point &p2) const;
     double ccw(const Line &line) const;
+    double ccw_angle(const Point &p1, const Point &p2) const;
     Point projection_onto(const MultiPoint &poly) const;
     Point projection_onto(const Line &line) const;
     Point negative() const;
diff --git a/xs/src/libslic3r/Polygon.cpp b/xs/src/libslic3r/Polygon.cpp
index 14206b189..36c644243 100644
--- a/xs/src/libslic3r/Polygon.cpp
+++ b/xs/src/libslic3r/Polygon.cpp
@@ -158,8 +158,12 @@ Polygon::contains(const Point &point) const
 Polygons
 Polygon::simplify(double tolerance) const
 {
-    Polygon p = *this;
-    p.points = MultiPoint::_douglas_peucker(p.points, tolerance);
+    // repeat first point at the end in order to apply Douglas-Peucker
+    // on the whole polygon
+    Points points = this->points;
+    points.push_back(points.front());
+    Polygon p(MultiPoint::_douglas_peucker(points, tolerance));
+    p.points.pop_back();
     
     Polygons pp;
     pp.push_back(p);
@@ -225,21 +229,17 @@ Polygon::wkt() const
 void
 Polygon::concave_points(double angle, Points* points) const
 {
-    /*  input angle threshold is checked on the internal side of the polygon
-        but ccw() returns 0 for collinear, >0 for ccw and <0 for cw */
-    double ccw_angle = angle - PI;
-    
     // check whether first point forms a concave angle
-    if (this->points.front().ccw(this->points.back(), *(this->points.begin()+1)) >= ccw_angle)
+    if (this->points.front().ccw_angle(this->points.back(), *(this->points.begin()+1)) >= angle)
         points->push_back(this->points.front());
     
     // check whether points 1..(n-1) form concave angles
     for (Points::const_iterator p = this->points.begin()+1; p != this->points.end()-1; ++p) {
-        if (p->ccw(*(p-1), *(p+1)) >= ccw_angle) points->push_back(*p);
+        if (p->ccw_angle(*(p-1), *(p+1)) >= angle) points->push_back(*p);
     }
     
     // check whether last point forms a concave angle
-    if (this->points.back().ccw(*(this->points.end()-2), this->points.front()) >= ccw_angle)
+    if (this->points.back().ccw_angle(*(this->points.end()-2), this->points.front()) >= angle)
         points->push_back(this->points.back());
 }
 
@@ -252,21 +252,17 @@ Polygon::concave_points(Points* points) const
 void
 Polygon::convex_points(double angle, Points* points) const
 {
-    /*  input angle threshold is checked on the internal side of the polygon
-        but ccw() returns 0 for collinear, >0 for ccw and <0 for cw */
-    double ccw_angle = angle - PI;
-    
     // check whether first point forms a convex angle
-    if (this->points.front().ccw(this->points.back(), *(this->points.begin()+1)) <= ccw_angle)
+    if (this->points.front().ccw_angle(this->points.back(), *(this->points.begin()+1)) <= angle)
         points->push_back(this->points.front());
     
     // check whether points 1..(n-1) form convex angles
     for (Points::const_iterator p = this->points.begin()+1; p != this->points.end()-1; ++p) {
-        if (p->ccw(*(p-1), *(p+1)) <= ccw_angle) points->push_back(*p);
+        if (p->ccw_angle(*(p-1), *(p+1)) <= angle) points->push_back(*p);
     }
     
     // check whether last point forms a convex angle
-    if (this->points.back().ccw(*(this->points.end()-2), this->points.front()) <= ccw_angle)
+    if (this->points.back().ccw_angle(*(this->points.end()-2), this->points.front()) <= angle)
         points->push_back(this->points.back());
 }
 
diff --git a/xs/src/libslic3r/Polygon.hpp b/xs/src/libslic3r/Polygon.hpp
index 76e668024..778825f3e 100644
--- a/xs/src/libslic3r/Polygon.hpp
+++ b/xs/src/libslic3r/Polygon.hpp
@@ -19,6 +19,9 @@ class Polygon : public MultiPoint {
     operator Polyline() const;
     Point& operator[](Points::size_type idx);
     const Point& operator[](Points::size_type idx) const;
+    
+    Polygon() {};
+    explicit Polygon(const Points &points): MultiPoint(points) {};
     Point last_point() const;
     Lines lines() const;
     void lines(Lines* lines) const;