# Collisions

## Detecting collisions

REBOUND comes with several collision detection modules. These modules check for physical collisions, not close encounters. Particles need to have a finite radius for collisions to occur. By default, collision detection is turned off.

### No collisions

By default REBOUND does not search for collisions. You can manually set the collision routine to NONE with the following code:

struct reb_simulation* r = reb_create_simulation();
r->collision = REB_COLLISION_NONE;
sim = rebound.Simulation()
sim.collision = "none"

### Direct

The direct collision detection module is a brute force collision search and scales as $$O(N^2)$$. It checks for instantaneous overlaps between every particle pair. The following code enables this module:

struct reb_simulation* r = reb_create_simulation();
r->collision = REB_COLLISION_DIRECT;
sim = rebound.Simulation()
sim.collision = "direct"

Important

This method checks for instantaneous overlaps. It does this only after each timestep. This means that if the timestep is large enough for particles to pass completely through each other, then the collision will be missed.

### Line

This is a brute force collision search and scales as $$O(N^2)$$ but compared to the direct method described above, this algorithm checks for overlapping particles during the timestep (not just at the end). It assumes particles travelled along straight lines during the timestep and might therefore miss some collisions.

struct reb_simulation* r = reb_create_simulation();
r->collision = REB_COLLISION_LINE;
sim = rebound.Simulation()
sim.collision = "line"

### Tree

This method uses an oct-tree to check for overlapping particles at the end of the timestep. When a large number of particles $$N$$ is used, this method scales as $$O(N log(N))$$, rather than $$O(N^2)$$ for the direct search. Note that you need to initialize the simulation box whenever you want to use the tree. Below is an example on how to enable the tree based collision search.

struct reb_simulation* r = reb_create_simulation();
reb_configure_box(r, 10, 1, 1, 1); # confine the simulation to a box of size 10
r->collision = REB_COLLISION_TREE;
sim = rebound.Simulation()
sim.configure_box(10)   # confine the simulation to a box of size 10
sim.collision = "tree"

### Linetree

Similar to the tree method, this method also uses an oct-tree and has a scaling of $$O(N log(N))$$.
It checks for overlapping trajectories during the last timestep, not only for overlapping particles at the end of the timestep. It might still miss some collisions because it assumes that particles travel along straight lines.

Below is an example on how to enable the line-tree collision search.

struct reb_simulation* r = reb_create_simulation();
reb_configure_box(r, 10, 1, 1, 1); # confine the simulation to a box of size 10
r->collision = REB_COLLISION_LINETREE;
sim = rebound.Simulation()
sim.configure_box(10)   # confine the simulation to a box of size 10
sim.collision = "linetree"

## Resolving collisions

Once a collision has been detected, you have a choice on what to do next. You might just want to merge particles, let them bounce off each other, or simply keep a log of all collisions that occurred.

REBOUND comes with several built-in collision resolve functions. You can also write your own.

Internally this functionality is implemented using a function pointer. You can set this pointer to a function that should be called when a collision occurs, whether it be a built-in function or your own.

### Halt

This function resolves a collision by simply halting the integration and setting the status flag in the simulation to REB_EXIT_COLLISION. In python this will raise the Collision exception. This is the default. It can also be set manually using the following syntax:

struct reb_simulation* r = reb_create_simulation();
r->collision = REB_COLLISION_DIRECT;
r->collision_resolve = reb_collision_resolve_halt;
sim = rebound.Simulation()
sim.collision = "direct"
sim.collision_resolve = "halt"

### Hard-sphere

This assumes a hard-sphere collision. This uses the coefficient_of_restitution parameter in struct reb_simulation. It conserves momentum and mass. Depending on the coefficient of restitution, it also conserves energy.

The following example shows how to set up a hard-sphere collision resolve function and a direct collision detection routine.

struct reb_simulation* r = reb_create_simulation();
r->collision = REB_COLLISION_DIRECT;
r->coefficient_of_resitution = 0.5;
r->collision_resolve = reb_collision_resolve_hardsphere;
sim = rebound.Simulation()
sim.collision = "direct"
sim.coefficient_of_resitution = 0.5
sim.collision_resolve = "hardsphere"

### Merge

This function merges the two colliding particles. It conserves mass, momentum and volume, but not energy.
The particle with the higher index will be removed.

The following example shows how to set up a hard-sphere collision resolve function and a direct collision detection routine.

struct reb_simulation* r = reb_create_simulation();
r->collision = REB_COLLISION_DIRECT;
r->collision_resolve = reb_collision_resolve_merge;
sim = rebound.Simulation()
sim.collision = "direct"
sim.collision_resolve = "merge"

### Custom function

You can write your own collision resolve function. In your function, you can update the properties of the particles involved in the collision. The return value of your function determines if a particle gets removed.

• 0: don't remove either particle from the simulation
• 1: remove the first particle (p1) from the simulation
• 2: remove the second particle (p2) from the simulation
• 3: remove both particles from the simulation

Here is a short example on how to write a simple custom collision resolve function:

int collision_print_only(struct reb_simulation* const r, struct reb_collision c){
printf("%f\t", r->p);
printf("%f\t", r->particles[c.p1].x);    // x position of particle 1
printf("%f\n", r->particles[c.p2].x);    // x position of particle 2
return 0; // Don't remove either particle
}

int main(int argc, char* argv[]){
struct reb_simulation* r = reb_create_simulation();
r->collision = REB_COLLISION_DIRECT;
r->collision_resolve = collision_print_only;
}
def collision_print_only(sim_pointer, collision):
sim = sim_pointer.contents           # get simulation object from pointer
print(sim.t)                         # print time
print(sim.particles[collision.p1].x) # x position of particle 1
print(sim.particles[collision.p2].x) # x position of particle 2
return 0                             # Don't remove either particle

sim = rebound.Simulation()
sim.collision = "direct"
sim.collision_resolve = collision_print_only

The first argument of the collision resolve function is a pointer to the simulation. The second argument is a reb_collision structure. It contains information about which particles are involved in the collision and, for periodic or shear-periodic boundary conditions, if the collision occurred across a boundary:

int p1
Index corresponding to one of the colliding particles
int p2
Index corresponding to one of the colliding particles
struct reb_ghostbox gb
Shift of particle p1 due to a collision across periodic and shearing sheet boundaries. All entries are zero if a normal collision occurs.