diff --git a/main.cc b/main.cc
index 08d04bc..d75e0cb 100644
--- a/main.cc
+++ b/main.cc
@@ -44,6 +44,7 @@ void update_state() {
         check_collisions();
     for (unsigned int i = 0; i < n_balls; ++i)
         ball_update_state(balls + i);
+    polygons_update_state();
     spaceship_update_state();
 }
 
diff --git a/matrix.h b/matrix.h
new file mode 100644
index 0000000..bb2a621
--- /dev/null
+++ b/matrix.h
@@ -0,0 +1,15 @@
+#ifndef MATRIX_H_INCLUDED
+#define MATRIX_H_INCLUDED
+
+#include "vec2d.h"
+
+class matrix {
+  public:
+    vec2d b1, b2;
+};
+
+inline vec2d operator*(matrix m, vec2d v) {
+    return vec2d{v.x * m.b1.x + v.y * m.b2.x, v.x * m.b1.y + v.y * m.b2.y};
+}
+
+#endif
diff --git a/polygon_generator.cc b/polygon_generator.cc
index 0eb828d..fad40e5 100644
--- a/polygon_generator.cc
+++ b/polygon_generator.cc
@@ -3,27 +3,35 @@
 #include <cassert>
 #include <cmath>
 
-#define PI 3.141592653589793238462643323
-
 static double to_rad(double angle_in_deg) {
-    static double PI_180 = PI / 180;
+    static double PI_180 = M_PI / 180;
     return angle_in_deg * PI_180;
 }
 
 polygon poly_generate::rectangle(double width, double height) {
     assert(width > 0);
     assert(height > 0);
-    return polygon{
-        {0, 0}, 0, {{0, 0}, {width, 0}, {width, height}, {0, height}}};
+    return polygon{{0, 0},
+        0,
+        {{-width / 2, -height / 2},
+            {width / 2, -height / 2},
+            {width / 2, height / 2},
+            {-width / 2, height / 2}}};
 }
 
 polygon poly_generate::triangle(double side1, double side2, double angle) {
     assert(side1 > 0);
     assert(side2 > 0);
-    return polygon{{0, 0},
-        0,
-        {{0, 0},
-            {side1, 0},
-            {side2 * std::cos(to_rad(angle)),
-                side2 * std::sin(to_rad(angle))}}};
+    vec2d points[] = {{0, 0},
+        {side1, 0},
+        {side2 * std::cos(to_rad(angle)), side2 * std::sin(to_rad(angle))}};
+
+    vec2d barycenter = {
+        (points[0].x + points[1].x + points[2].x) / 3,
+        (points[0].y + points[1].y + points[2].y) / 3,
+    };
+
+    for (unsigned int i = 0; i < 3; ++i)
+        points[i] -= barycenter;
+    return polygon{{0, 0}, 0, {std::begin(points), std::end(points)}};
 }
diff --git a/polygons.cc b/polygons.cc
index d0d3ffe..9208fa6 100644
--- a/polygons.cc
+++ b/polygons.cc
@@ -1,7 +1,9 @@
 #include "polygons.h"
 
+#include "matrix.h"
 #include "polygon_generator.h"
 
+#include <cmath>
 #include <iostream>
 
 polygon* polygons = nullptr;
@@ -10,19 +12,43 @@ uint n_polygons = 3;
 void polygons_init_state() {
     polygons = new polygon[n_polygons];
 
-    polygons[0] = poly_generate::triangle(200, 200, 30).set_center({300, 200});
-    polygons[1] = poly_generate::square(200).set_center({100, 400});
-    polygons[2] = poly_generate::rectangle(200, 100).set_center({400, 400});
+    polygons[0] = poly_generate::triangle(150, 150, 30)
+                      .set_center({400, 300})
+                      .set_angle(90);
+    polygons[1] = poly_generate::square(200).set_center({200, 600});
+    polygons[2] = poly_generate::rectangle(200, 100).set_center({600, 600});
+}
+
+static double to_rad(double angle_in_deg) {
+    static double PI_180 = M_PI / 180;
+    return angle_in_deg * PI_180;
+}
+
+void polygons_update_state() {
+    static double angle = 0;
+    for (polygon* p = polygons; p != polygons + n_polygons; ++p) {
+        p->rotate(1);
+        p->translate({2 * std::cos(angle), 0});
+    }
+    angle -= .03;
 }
 
 void polygon::draw(cairo_t* cr) const {
     const vec2d& center = this->center;
     cairo_set_source_rgb(cr, 1, 1, 1);
 
-    for (auto& point : this->points)
-        cairo_line_to(cr, center.x + point.x, center.y + point.y);
-    cairo_line_to(
-        cr, center.x + this->points[0].x, center.y + this->points[0].y);
+    double cos_theta = std::cos(to_rad(this->angle));
+    double sin_theta = std::sin(to_rad(this->angle));
+
+    matrix rotation = matrix{{cos_theta, sin_theta}, {-sin_theta, cos_theta}};
+
+    vec2d final_point;
+    for (auto& point : this->points) {
+        final_point = rotation * point;
+        cairo_line_to(cr, center.x + final_point.x, center.y + final_point.y);
+    }
+    final_point = rotation * this->points[0];
+    cairo_line_to(cr, center.x + final_point.x, center.y + final_point.y);
     cairo_stroke(cr);
 }