inelastic collisions, controllable restitution coefficient

balls.cc

@@ -18,6 +18,55 @@ unsigned int v_angle_max = 100;
 ball * balls = nullptr;
 unsigned int n_balls = 50;
 
+// Coefficient of restitution:
+// C_r == 1.0 ==> perfectly elastic collisions
+// C_r == 0.0 ==> perfectly inelastic collisions
+//
+static double C_r = 1.0;
+static int c_r_display_countdown = 0;
+static int c_r_display_init = 300;
+
+void restitution_coefficient_set (double c) {
+    C_r = c;
+    if (C_r > 1.0)
+	C_r = 1.0;
+    else if (C_r < 0.0)
+	C_r = 0.0;
+}    
+
+double restitution_coefficient_get () {
+    return C_r;
+}
+
+void restitution_coefficient_change (double d) {
+    C_r += d;
+    if (C_r > 1.0)
+	C_r = 1.0;
+    else if (C_r < 0.0)
+	C_r = 0.0;
+    restitution_coefficient_show ();
+}
+
+void restitution_coefficient_show () {
+    c_r_display_countdown = c_r_display_init;
+};
+
+void restitution_coefficient_draw (cairo_t * cr) {
+    static const double margin = 20;
+    if (c_r_display_countdown != 0) {
+	cairo_save(cr);
+	cairo_new_path(cr);
+	cairo_move_to(cr, margin, margin);
+	cairo_line_to(cr, margin + (width - 2*margin)*C_r, margin);
+	cairo_set_source_rgb(cr, 1.0, 1.0, 0.0);
+	cairo_set_line_width(cr, margin/2);
+	cairo_stroke(cr);
+	if (c_r_display_countdown > 0)
+	    --c_r_display_countdown;
+	cairo_restore(cr);
+    }
+}
+
 static vec2d random_velocity() {
     double r2;
     vec2d v;
@@ -49,43 +98,45 @@ void balls_init_state () {
     }
 }
 
+void ball_walls_collision (ball * p) {
+    if (p->position.x + p->radius > width) { /* right wall */
+	if (p->velocity.x > 0) {
+	    p->position.x -= p->position.x + p->radius - width;
+	    p->velocity.x = -C_r*p->velocity.x;
+	}
+    } else if (p->position.x < p->radius) { /* left wall */
+	if (p->velocity.x < 0) {
+	    p->position.x += p->radius - p->position.x;
+	    p->velocity.x = -C_r*p->velocity.x;
+	}
+    } 
+    if (p->position.y + p->radius > height) { /* bottom wall */
+	if (p->velocity.y > 0) {
+	    p->position.y -= p->position.y + p->radius - height;
+	    p->velocity.y = -C_r*p->velocity.y;
+	}
+    } else if (p->position.y < p->radius) { /* top wall */
+	if (p->velocity.y < 0) {
+	    p->position.y += p->radius - p->position.y;
+	    p->velocity.y = -C_r*p->velocity.y;
+	}
+    }
+}
+
 void ball_update_state (ball * p) {
     vec2d g = gravity_vector (p);
 
     p->position += delta*p->velocity + delta*delta*g/2.0;
     p->velocity += delta*g;
-
-    if (p->position.x + p->radius > width) { /* right wall */
-	if (p->velocity.x > 0) {
-	    p->position.x -= p->position.x + p->radius - width;
-	    p->velocity.x = -p->velocity.x;
-	}
-    } else if (p->position.x < p->radius) { /* left wall */
-	if (p->velocity.x < 0) {
-	    p->position.x += p->radius - p->position.x;
-	    p->velocity.x = -p->velocity.x;
-	}
-    } 
-
-    if (p->position.y + p->radius > height) { /* bottom wall */
-	if (p->velocity.y > 0) {
-	    p->position.y -= p->position.y + p->radius - height;
-	    p->velocity.y = -p->velocity.y;
-	}
-    } else if (p->position.y < p->radius) { /* top wall */
-	if (p->velocity.y < 0) {
-	    p->position.y += p->radius - p->position.y;
-	    p->velocity.y = -p->velocity.y;
-	}
-    } 
     p->angle += delta*p->v_angle;
     while (p->angle >= 2*M_PI)
 	p->angle -= 2*M_PI;
     while (p->angle < 0)
 	p->angle += 2*M_PI;
+    ball_walls_collision (p);
 }
 
-void ball_elastic_collision (ball * p, ball * q) {
+void ball_ball_collision (ball * p, ball * q) {
     vec2d pq = q->position - p->position;
     double d2 = vec2d::dot(pq,pq);
     double r = p->radius + q->radius;
@@ -94,13 +145,19 @@ void ball_elastic_collision (ball * p, ball * q) {
 
 	double mp = p->radius * p->radius;
 	double mq = q->radius * q->radius;
+	double m_total = mp + mp;
+
+	double d = sqrt(d2);
+	vec2d pq_overlap = (r - d)/d*pq;
+	p->position -= pq_overlap*mq/m_total;
+	q->position += pq_overlap*mp/m_total;
 
 	double f = vec2d::dot(pq_v, pq);
 
 	if (f < 0) {
 	    f /= d2*(mp + mq);
-	    p->velocity += 2*mq*f*dp;
+	    p->velocity += 2*C_r*mq*f*pq;
-	    q->velocity -= 2*mp*f*dp;
+	    q->velocity -= 2*C_r*mp*f*pq;
 	}
     }
 }

balls.h

@@ -39,8 +39,14 @@ extern int face_rotation;
 extern void balls_init ();
 extern void balls_destroy ();
 extern void ball_update_state (ball * p);
-extern void ball_elastic_collision (ball * p, ball * q);
+extern void ball_ball_collision (ball * p, ball * q);
 extern void ball_reposition (ball * b);
 extern void balls_draw (cairo_t * cr);
 
+extern void restitution_coefficient_show ();
+extern void restitution_coefficient_draw (cairo_t * cr);
+extern void restitution_coefficient_set (double c);
+extern double restitution_coefficient_get ();
+extern void restitution_coefficient_change (double d);
+
 #endif

main.cc

@@ -21,23 +21,23 @@
 void check_collisions_simple () {
     for(unsigned int i = 0; i < n_balls; ++i)
 	for(unsigned int j = i + 1; j < n_balls; ++j)
-	    ball_elastic_collision(balls + i, balls + j);
+	    ball_ball_collision(balls + i, balls + j);
     for(unsigned int j = 0; j < n_balls; ++j)
-	ball_elastic_collision(&spaceship, balls + j);
+	ball_ball_collision(&spaceship, balls + j);
    gravity_collisions (balls, balls + n_balls);
    gravity_collisions (&spaceship, &spaceship + 1);
 }
 
 void check_collisions_with_index () {
     c_index_build();
-    c_index_check_collisions(ball_elastic_collision);
+    c_index_check_collisions(ball_ball_collision);
    for(unsigned int j = 0; j < n_balls; ++j)
-	ball_elastic_collision(&spaceship, balls + j);
+	ball_ball_collision(&spaceship, balls + j);
    gravity_collisions (balls, balls + n_balls);
    gravity_collisions (&spaceship, &spaceship + 1);
 }
 
-void (*check_collisions)() = 0;
+void (*check_collisions)() = check_collisions_simple;
 
 void update_state () {
     if (check_collisions)
@@ -66,6 +66,7 @@ gboolean draw_frame (GtkWidget * widget, cairo_t *cr, gpointer data) {
     cairo_set_source_rgba(cr, 0.0, 0.0, 0.0, 1.0);
     cairo_paint(cr);
     gravity_draw (cr);
+    restitution_coefficient_draw (cr);
     balls_draw (cr);
     spaceship_draw (cr);
     return FALSE;
@@ -100,6 +101,12 @@ gint keyboard_input (GtkWidget *widget, GdkEventKey *event) {
     case GDK_KEY_Right:
 	gravity_change (10, 0);
 	break;
+    case GDK_KEY_R:
+	restitution_coefficient_change (0.01);
+	break;
+    case GDK_KEY_r:
+	restitution_coefficient_change (-0.01);
+	break;
     case GDK_KEY_G:
     case GDK_KEY_g:
 	gravity_show ();
@@ -150,6 +157,7 @@ void print_usage (const char * progname) {
 	    "\tface=<filename>\n"
 	    "\tstats=<sample-count> :: rendering timing statitstics (0=disabled, default)\n"
 	    "\tcollisions=<C> :: n=no collisions, s=simple, i=index\n"
+	    "\trestitution=<C_r> :: restitution coefficient C_r\n"
 	    "\t-r :: activate face rotation\n",
 	    progname);
 }
@@ -247,6 +255,11 @@ int main (int argc, const char *argv[]) {
 	    face_rotation = 1;
 	    continue;
 	}
+	double c_r;
+	if (sscanf(argv[i], "restitution=%lf", &c_r) == 1) {
+	    restitution_coefficient_set (c_r);
+	    continue;
+	}
 	print_usage(argv[0]);
 	return 1;
     }