got the speed working (yay) but the angular velocity that results is superrrr low, thus not creating any rotation after impact, wierd...

Makefile

@@ -11,7 +11,7 @@ CXXFLAGS=-Wall -g -O2 $(PROFILING_CFLAGS) $(GTK_CFLAGS)
 LIBS=$(GTK_LIBS) -lm
 
 PROGS=balls
-OBJS=balls.o c_index.o game.o gravity.o spaceship.o main.o polygons.o polygon_generator.o
+OBJS=balls.o c_index.o game.o gravity.o spaceship.o main.o polygons.o polygon_generator.o collisions.o
 
 # dependencies (gcc -MM *.cc)
 balls.o: balls.cc game.h balls.h vec2d.h gravity.h
@@ -23,6 +23,7 @@ spaceship.o: spaceship.cc balls.h vec2d.h game.h
 stats.o: stats.cc
 polygons.o: polygons.cc polygons.h vec2d.h polygon_generator.h
 polygon_generator.o: polygon_generator.cc polygon_generator.h
+collisions.o: collisions.cc collisions.h vec2d.h
 
 
 .PHONY: run

collisions.cc

@@ -0,0 +1,123 @@
+#include "collisions.h"
+
+#include <algorithm>
+#include <iostream>
+#include <vector>
+
+static std::vector<vec2d> edges_of(polygon& p) {
+    std::vector<vec2d> edges;
+    edges.reserve(p.global_points.size());
+
+    for (uint i = 0; i < p.global_points.size(); ++i)
+        edges.push_back(p.global_points[(i + 1) % p.global_points.size()] -
+                        p.global_points[i]);
+    return edges;
+}
+
+static bool separating_axis(
+    vec2d& axis, polygon& p, polygon& q, vec2d* pv, vec2d* impact_point) {
+    double min_p, max_p, min_q, max_q;
+    min_p = min_q = INFINITY;
+    max_p = max_q = -INFINITY;
+
+    double projection;
+    vec2d min_p_point, max_p_point;
+    for (auto& point : p.global_points) {
+        projection = vec2d::dot(point, axis);
+
+        if (projection < min_p) {
+            min_p = projection;
+            min_p_point = point;
+        }
+
+        if (projection > max_p) {
+            max_p = projection;
+            max_p_point = point;
+        }
+    }
+
+    for (auto& point : q.global_points) {
+        projection = vec2d::dot(point, axis);
+
+        min_q = std::min(min_q, projection);
+        max_q = std::max(max_q, projection);
+    }
+
+    if (max_p >= min_q && max_q >= min_p) {
+        double d;
+        if (max_q - min_p < max_p - min_q) {
+            d = max_q - min_p;
+            *impact_point = min_p_point;
+        } else {
+            d = max_p - min_q;
+            *impact_point = max_p_point;
+        }
+        // push a bit more than needed so the shapes do not overlap in future
+        // tests due to float precision
+        double d_over_o_squared = d / vec2d::dot(axis, axis) + 1e-10;
+        *pv = d_over_o_squared * axis;
+        return false;
+    }
+
+    return true;
+}
+
+static uint get_smallest_vec_index(std::vector<vec2d> vs) {
+    uint ret, i = 0;
+    double min = INFINITY;
+    for (auto& v : vs) {
+        double dot = vec2d::dot(v, v);
+        if (dot < min) {
+            ret = i;
+            min = dot;
+        }
+        i++;
+    }
+    return ret;
+}
+
+static collision convex_collides(polygon& p, polygon& q) {
+    collision ret{false};
+
+    std::vector<vec2d> edges_p = edges_of(p);
+    std::vector<vec2d> edges_q = edges_of(q);
+    std::vector<vec2d> edges;
+    edges.reserve(edges_p.size() + edges_q.size());
+    edges.insert(edges.end(), edges_p.begin(), edges_p.end());
+    edges.insert(edges.end(), edges_q.begin(), edges_q.end());
+    std::vector<vec2d> orthogonals;
+    orthogonals.reserve(edges.size());
+    for (auto& v : edges)
+        orthogonals.push_back(v.orthogonal());
+
+    std::vector<vec2d> push_vectors;
+    push_vectors.reserve(orthogonals.size());
+    std::vector<vec2d> impact_points;
+    push_vectors.reserve(orthogonals.size());
+
+    vec2d push_vector;
+    vec2d impact_point;
+    for (auto& o : orthogonals) {
+        if (separating_axis(o, p, q, &push_vector, &impact_point))
+            // the axis is separating (the projections don't overlap)
+            return ret;
+        push_vectors.push_back(push_vector);
+        impact_points.push_back(impact_point);
+    }
+    // if no axis is sperating, then they must be colliding
+    ret.collides = true;
+    uint i = get_smallest_vec_index(push_vectors);
+    ret.n = vec2d::normalize(push_vectors[i]);
+    ret.impact_point = impact_points[i];
+
+    // assert that p pushes away from q
+    vec2d d = q.centroid() - p.centroid();
+    if (vec2d::dot(ret.n, d) > 0)
+        ret.n *= -1;
+
+    return ret;
+}
+
+collision collides(polygon& p, polygon& q) {
+    return convex_collides(p, q);
+}

collisions.h

@@ -0,0 +1,15 @@
+#ifndef COLLISIONS_H_INCLUDED
+#define COLLISIONS_H_INCLUDED
+
+#include "polygons.h"
+#include "vec2d.h"
+
+struct collision {
+    bool collides;
+    vec2d n; // minimum push vector
+    vec2d impact_point;
+};
+
+extern collision collides(polygon& p, polygon& q);
+
+#endif

polygon_generator.cc

@@ -8,23 +8,30 @@ static double to_rad(double angle_in_deg) {
     return angle_in_deg * PI_180;
 }
 
-polygon poly_generate::rectangle(double width, double height) {
+polygon poly_generate::rectangle(double width, double height, double mass) {
     assert(width > 0);
     assert(height > 0);
+    static const double one_over_twelve = 1. / 12;
     return polygon{{0, 0},
         0,
         {{-width / 2, -height / 2},
-            {width / 2, -height / 2},
+            {-width / 2, height / 2},
             {width / 2, height / 2},
-            {-width / 2, height / 2}}};
+            {width / 2, -height / 2}},
+        one_over_twelve * mass * width * std::pow(height, 3),
+        mass};
 }
 
-polygon poly_generate::triangle(double side1, double side2, double angle) {
+polygon poly_generate::triangle(
+    double side1, double side2, double angle, double mass) {
     assert(side1 > 0);
     assert(side2 > 0);
-    vec2d points[] = {{0, 0},
-        {side1, 0},
-        {side2 * std::cos(to_rad(angle)), side2 * std::sin(to_rad(angle))}};
+    static const double one_over_36 = 1. / 36;
+    double base, height;
+    base = side1;
+    height = side2 * std::sin(to_rad(angle));
+    vec2d points[] = {
+        {0, 0}, {side1, 0}, {side2 * std::cos(to_rad(angle)), height}};
 
     vec2d barycenter = {
         (points[0].x + points[1].x + points[2].x) / 3,
@@ -33,5 +40,9 @@ polygon poly_generate::triangle(double side1, double side2, double angle) {
 
     for (unsigned int i = 0; i < 3; ++i)
         points[i] -= barycenter;
-    return polygon{{0, 0}, 0, {std::begin(points), std::end(points)}};
+    return polygon{{0, 0},
+        0,
+        {std::begin(points), std::end(points)},
+        one_over_36 * mass * base * std::pow(height, 3),
+        mass};
 }

polygon_generator.h

@@ -7,14 +7,14 @@
 
 namespace poly_generate {
 
-    polygon rectangle(double width, double height);
+    polygon rectangle(double width, double height, double mass = 1);
 
-    inline polygon square(double width) {
+    inline polygon square(double width, double mass = 1) {
         assert(width > 0);
-        return rectangle(width, width);
+        return rectangle(width, width, mass);
     };
 
-    polygon triangle(double side1, double side2, double angle);
+    polygon triangle(double side1, double side2, double angle, double mass = 1);
 
 }; // namespace poly_generate
 #endif

polygons.cc

@@ -1,43 +1,184 @@
 #include "polygons.h"
 
 #include "cairo.h"
+#include "collisions.h"
 #include "game.h"
 #include "matrix.h"
 #include "polygon_generator.h"
 
 #include <iostream>
+#include <utility>
 
 polygon* polygons = nullptr;
-uint n_polygons = 1;
+uint n_polygons = 2;
 
 void polygons_init_state() {
     polygons = new polygon[n_polygons];
 
-    std::cout << "width" << width << std::endl;
-    // polygons[0] = poly_generate::square(200)
-    //                   .set_center({400, 600})
-    //                   .set_angle(37)
-    //                   .set_speed({1, -1});
-    polygons[0] = poly_generate::triangle(150, 150, 30)
-                      .set_center({400, 300})
-                      .set_angle(45)
-                      .set_speed({3, 2});
-    // polygons[2] = poly_generate::rectangle(200, 100).set_center({600, 600});
+    polygons[0] = poly_generate::square(100, 1)
+                      .set_center({200, 530})
+                      .set_angle(-30)
+                      .set_angular_speed(0)
+                      .set_speed({200, -200});
+    // polygons[0] = poly_generate::triangle(150, 150, 30)
+    //                   .set_center({200, 400})
+    //                   .set_angle(13)
+    //                   .set_angular_speed(10)
+    //                   .set_speed({200, 50});
+    polygons[1] = poly_generate::rectangle(50, height / 2., INFINITY)
+                      .set_center({25 + width * 1. / 2, height / 2.})
+                      .set_angle(0);
 }
 
 static double to_rad(double angle_in_deg) {
-    static double PI_180 = M_PI / 180;
+    static double PI_180 = M_PI / 180.;
     return angle_in_deg * PI_180;
 }
 
+static double to_deg(double angle_in_rad) {
+    static double PI_180 = 180. / M_PI;
+    return angle_in_rad * PI_180;
+}
+
+static bool is_point_inside_rect(rect rect, vec2d point) {
+    vec2d tl = rect.first, br = rect.second;
+    return point.x > tl.x && point.x < br.x && point.y > tl.y && point.y < br.y;
+}
+
+static bool bounding_rects_collide(rect cur_bound, rect other_bound) {
+    vec2d other_tl = other_bound.first, other_br = other_bound.second;
+    return is_point_inside_rect(cur_bound, other_tl) ||
+           is_point_inside_rect(cur_bound, {other_tl.x, other_br.y}) ||
+           is_point_inside_rect(cur_bound, {other_br.x, other_tl.y}) ||
+           is_point_inside_rect(cur_bound, other_br);
+}
+
+static double impulse_parameter(vec2d v_ab1,
+    vec2d n,
+    double m_a,
+    double m_b,
+    vec2d r_ap,
+    vec2d r_bp,
+    double I_a,
+    double I_b,
+    double e) {
+    double nominator = -(1 + e) * vec2d::dot(v_ab1, n);
+    double denominator = 1 / m_a + 1 / m_b +
+                         std::pow(vec2d::cross(r_ap, n), 2) / I_a +
+                         std::pow(vec2d::cross(r_bp, n), 2) / I_b;
+    return nominator / denominator;
+}
+
+static void handle_collision(collision& c, polygon* a, polygon* b) {
+    // see https://www.myphysicslab.com/engine2D/collision-en.html for the
+    // formulas
+
+    double omega_a1 = to_rad(a->angular_speed);
+    double omega_b1 = to_rad(b->angular_speed);
+
+    vec2d r_ap = c.impact_point - a->centroid();
+    vec2d v_ap1 = a->speed + vec2d::cross(omega_a1, r_ap);
+    std::cout << "  "
+              << "r_ap = " << r_ap << std::endl;
+    std::cout << "  "
+              << "v_ap1 = " << v_ap1 << std::endl;
+
+    vec2d r_bp = c.impact_point - b->centroid();
+    vec2d v_bp1 = b->speed + vec2d::cross(omega_b1, r_bp);
+    std::cout << "  "
+              << "r_bp = " << r_bp << std::endl;
+    std::cout << "  "
+              << "v_bp1 = " << v_bp1 << std::endl;
+
+    vec2d v_ab1 = v_ap1 - v_bp1;
+    std::cout << "    "
+              << "v_ab1 = " << v_ab1 << std::endl;
+
+    double I_a = a->inertia, I_b = b->inertia;
+    std::cout << "  Parameters for j: " << std::endl;
+    std::cout << "    "
+              << "v_ab1 = " << v_ab1 << std::endl;
+    std::cout << "    "
+              << "n = " << c.n << std::endl;
+    std::cout << "    "
+              << "m_a = " << a->mass << std::endl;
+    std::cout << "    "
+              << "m_b = " << b->mass << std::endl;
+    std::cout << "    "
+              << "r_ap = " << r_ap << std::endl;
+    std::cout << "    "
+              << "r_bp = " << r_bp << std::endl;
+    std::cout << "    "
+              << "I_a = " << I_a << std::endl;
+    std::cout << "    "
+              << "I_b = " << I_b << std::endl;
+
+    double j = impulse_parameter(
+        v_ab1, c.n, a->mass, b->mass, r_ap, r_bp, I_a, I_b, 1);
+    std::cout << "====> j = " << j << std::endl;
+
+    vec2d v_a2 = a->speed + j * c.n / a->mass;
+    vec2d v_b2 = b->speed - j * c.n / b->mass;
+    std::cout << "  "
+              << "v_a2 = " << v_a2 << std::endl;
+    std::cout << "  "
+              << "v_b2 = " << v_b2 << std::endl;
+
+    double omega_a2 = omega_a1 + vec2d::cross(r_ap, j * c.n) / I_a;
+    double omega_b2 = omega_b1 - vec2d::cross(r_bp, j * c.n) / I_b;
+    std::cout << "  "
+              << "omega_a2 = " << omega_a2 << std::endl;
+    std::cout << "  "
+              << "omega_b2 = " << omega_b2 << std::endl;
+
+    a->speed = v_a2;
+    a->angular_speed = to_deg(omega_a2);
+
+    b->speed = v_b2;
+    b->angular_speed = to_deg(omega_b2);
+}
+
+static void check_collisions(polygon* current_p) {
+    rect cur_bound = current_p->get_bounding_box();
+
+    for (polygon* other_p = polygons; other_p != polygons + n_polygons;
+         ++other_p) {
+        if (other_p == current_p) // polygons don't collide with themselves
+            continue;
+        rect other_bound = other_p->get_bounding_box();
+        if (bounding_rects_collide(cur_bound, other_bound) ||
+            bounding_rects_collide(other_bound, cur_bound)) {
+            // std::cout << "Bounding boxes do collide" << std::endl;
+            collision c = collides(*current_p, *other_p);
+            if (c.collides) {
+                std::cout << "colliding" << std::endl;
+                std::cout << "speed before: " << current_p->speed << std::endl;
+                std::cout << "angular speed before: "
+                          << current_p->angular_speed << std::endl;
+                handle_collision(c, current_p, other_p);
+                std::cout << "speed after: " << current_p->speed << std::endl;
+                std::cout << "angular speed after: " << current_p->angular_speed
+                          << std::endl;
+                std::cout << std::endl;
+            }
+        }
+    }
+}
+
 static void check_border_collision(polygon* p) {
     for (auto& point : p->global_points) {
-        if (point.x <= 0 || point.x >= width) {
+        bool hit_vert_wall = point.x <= 0 || point.x >= width;
+        bool hit_hori_wall = point.y <= 0 || point.y >= width;
+
+        if (hit_vert_wall || hit_hori_wall) {
+            p->set_angular_speed(-p->angular_speed); // this is not accurate,
+                                                     // but avoids bugs for now
+
+            if (hit_vert_wall)
                 p->speed.x *= -1;
-            break;
-        }
-        if (point.y <= 0 || point.y >= height) {
+            if (hit_hori_wall)
                 p->speed.y *= -1;
+
             break;
         }
     }
@@ -45,9 +186,12 @@ static void check_border_collision(polygon* p) {
 
 void polygons_update_state() {
     for (polygon* p = polygons; p != polygons + n_polygons; ++p) {
-        p->rotate(1);
+        if (p->mass == INFINITY) // immovable objects don't need to be updated
+            continue;
         check_border_collision(p);
-        p->translate(p->speed);
+        check_collisions(p);
+        p->rotate(delta * p->angular_speed);
+        p->translate(delta * p->speed);
     }
 }
 
@@ -67,13 +211,13 @@ void polygon::draw_bounding_rect(cairo_t* cr) const {
     cairo_set_dash(cr, dashes, 2, 0);
 
     auto bb = this->get_bounding_box();
-    vec2d min = bb.first, max = bb.second;
+    vec2d tl = bb.first, br = bb.second;
 
-    cairo_line_to(cr, min.x, min.y);
-    cairo_line_to(cr, min.x, max.y);
-    cairo_line_to(cr, max.x, max.y);
-    cairo_line_to(cr, max.x, min.y);
-    cairo_line_to(cr, min.x, min.y);
+    cairo_line_to(cr, tl.x, tl.y);
+    cairo_line_to(cr, tl.x, br.y);
+    cairo_line_to(cr, br.x, br.y);
+    cairo_line_to(cr, br.x, tl.y);
+    cairo_line_to(cr, tl.x, tl.y);
     cairo_stroke(cr);
     cairo_set_dash(cr, 0, 0, 0); // disable dashes
 }
@@ -88,6 +232,13 @@ void polygon::draw(cairo_t* cr) const {
 
     cairo_line_to(cr, this->global_points[0].x, this->global_points[0].y);
     cairo_stroke(cr);
+
+    // draw centroid
+    vec2d centroid = this->centroid();
+    cairo_translate(cr, centroid.x, centroid.y);
+    cairo_arc(cr, 0, 0, 1, 0, 2 * M_PI);
+    cairo_stroke(cr);
+    cairo_translate(cr, -centroid.x, -centroid.y);
 }
 
 void polygons_draw(cairo_t* cr) {

polygons.h

@@ -8,6 +8,8 @@
 #include <utility>
 #include <vector>
 
+typedef std::pair<vec2d, vec2d> rect;
+
 class polygon {
   private:
     void update_global_points();
@@ -16,30 +18,32 @@ class polygon {
     vec2d center;
     double angle;
     std::vector<vec2d> points;
+    double inertia;
+    double mass;
+
     std::vector<vec2d> global_points = points;
 
     vec2d speed;
     double angular_speed;
-    double mass = 1;
 
     void draw(cairo_t* cr) const;
     void draw_bounding_rect(cairo_t* cr) const;
 
-    std::pair<vec2d, vec2d> get_bounding_box() const {
-        vec2d min{INFINITY, INFINITY}, max{-INFINITY, -INFINITY};
+    rect get_bounding_box() const {
+        vec2d tl{INFINITY, INFINITY}, tr{-INFINITY, -INFINITY};
 
         for (auto& point : this->global_points) {
-            if (point.x < min.x)
-                min.x = point.x;
-            if (point.y < min.y)
-                min.y = point.y;
+            if (point.x < tl.x)
+                tl.x = point.x;
+            if (point.y < tl.y)
+                tl.y = point.y;
 
-            if (point.x > max.x)
-                max.x = point.x;
-            if (point.y > max.y)
-                max.y = point.y;
+            if (point.x > tr.x)
+                tr.x = point.x;
+            if (point.y > tr.y)
+                tr.y = point.y;
         }
-        return {min, max};
+        return {tl, tr};
     }
 
     polygon& set_center(vec2d c) {
@@ -64,6 +68,11 @@ class polygon {
         return *this;
     }
 
+    polygon& set_mass(double m) {
+        mass = m;
+        return *this;
+    }
+
     polygon& translate(vec2d delta) {
         center += delta;
         update_global_points();
@@ -75,6 +84,14 @@ class polygon {
         update_global_points();
         return *this;
     }
+
+    vec2d centroid() const {
+        double x = 0, y = 0;
+        for (auto& p : global_points)
+            x += p.x, y += p.y;
+
+        return vec2d{x, y} / points.size();
+    }
 };
 
 extern polygon* polygons;

vec2d.h

@@ -41,6 +41,10 @@ class vec2d {
         return vec2d{x - other.x, y - other.y};
     }
 
+    vec2d operator-() const {
+        return vec2d{-x, -y};
+    }
+
     vec2d operator*(double l) const {
         return vec2d{x * l, y * l};
     }
@@ -59,12 +63,28 @@ class vec2d {
         return *this;
     }
 
+    vec2d orthogonal() {
+        return {-y, x};
+    }
+
     static double dot(const vec2d& a, const vec2d& b) {
         return a.x * b.x + a.y * b.y;
     }
 
     static double cross(const vec2d& a, const vec2d& b) {
-        return a.x * b.x + a.y * b.y;
+        return a.x * b.y - a.y * b.x;
+    }
+
+    static vec2d cross(const double omega, const vec2d& v) {
+        return {-omega * v.y, omega * v.x};
+    }
+
+    static double norm(const vec2d& v) {
+        return std::sqrt(dot(v, v));
+    }
+
+    static vec2d normalize(const vec2d& v) {
+        return v / norm(v);
     }
 };