 Since the original  framework builds on a random sequential addition of particles enhanced with a level-set description , we first devise an analysis based on a connectivity graph of a tile set, resolving the question where should a particle be copied when it intersects a tile boundary.
<meaning-changed>  Since the original  framework builds on a random sequential addition of particles enhanced with a level-set description , we first devise an analysis based on a connectivity graph of a tile set, resolving the question where should a particle be copied when it intersects a tile boundary.
 Since the original framework builds on a random sequential addition of particles enhanced with an implicit representation of particle boundaries by the level-set description , we first devise an analysis based on a connectivity graph of a tile set, resolving the question where should a particle be copied when it intersects a tile boundary.