I have very basic collision detection requirements, so, instead of a full library, I just tried to write up the most bare-bones algorithm I could. It *almost* works, and I've been staring at it for a while with no progress. Any help is appreciated.

Here's the resolution method:

void PhysicsSystem::resolve_collision(DynamicEntity& entity, int x, int y)
{
  Vector2f tile_pos(x, y);
  Vector2f nearest(entity.pos);
  Vector2f min(x, y), max(x + 1, y + 1);

  if (nearest.x() < min.x()) nearest.x() = min.x();
  else if (nearest.x() > max.x()) nearest.x() = max.x();

  if (nearest.y() < min.y()) nearest.y() = min.y();
  else if (nearest.y() > max.y()) nearest.y() = max.y();

  Vector2f ray(entity.pos - nearest);
  auto length = ray.norm();
  auto depth = entity.size - length;

  if (length != 0 && depth > 0)
  {
    ray.normalize();
    entity.pos += depth * ray;
  }
}

This produces a good response when colliding with a tile below and one to the right, but it collides one tile too soon coming from the other two directions.

Thanks, I added your suggestion and it does seem to be working a little better, but it still does something funny around the corners.

Here is the method now:

void PhysicsSystem::resolve_collision(DynamicEntity& entity, int x, int y)
{
  Vector2f tile_pos(x, y);
  Vector2f nearest(entity.pos);
  Vector2f min(x, y), max(x, y);

  if (entity.vel.x() < 0) 
    min.x() = x - 1;
  else 
    max.x() = x + 1;

  if (entity.vel.y() < 0) 
    min.y() = y - 1;
  else 
    max.y() = y + 1;

  if (nearest.x() < min.x()) nearest.x() = min.x();
  else if (nearest.x() > max.x()) nearest.x() = max.x();

  if (nearest.y() < min.y()) nearest.y() = min.y();
  else if (nearest.y() > max.y()) nearest.y() = max.y();

  Vector2f ray(entity.pos - nearest);
  auto length = ray.norm();
  auto depth = entity.size - length;

  if (length != 0 && depth > 0)
  {
    ray.normalize();
    entity.pos += depth * ray;
  }
}

Around the corners the collision goes out a little too far sometimes. I think I need to think about the math a little more, because I'm not even sure why your suggestion helped ; )