<H1>1. Introduction</H1>
      
      Collision handling in Computer Graphics has two phases. One is to detect collisions and the other is to resolve collisions. In cloth collision detection, the computation time to detect collisions is not negligible because the number of geometrical entities (nodes, faces, edges) the collision detection algorithm has to handle is considerable (over 10,000 particles for regular attire). For this reason, several approaches have tried to expedite the collision detection processes [ 16 , 3 ]. Collision resolution is to find the correct next positions and velocities of colliding objects. Cloth resolution methods so far have found non-penetrating positions, velocities and accelerations of cloth surface particles 
[ 14 , 3 , 15 ]. This scheme works fine for cloth-rigid collisions and for the special case of cloth-cloth collisions where the dynamic interactions between cloth surfaces in cloth-cloth collisions do not have to be noticeable. Volino et. al. [ 15 ]
 applied the conjugate gradient method to find the actual particles’ positions where a group of particles are colliding into each other. By preserving barycentric relationships of collision entities, their method resolves collisions where numerous cloth surfaces are colliding together as a group, which is a novel way to resolve multiple collisions at once. However it does not conserve the momentum of cloth surfaces in cloth-cloth collisions. Another method for cloth-cloth collisions has been proposed by Provot 
[ 12 ]
, which resolves collisions by giving an average velocity to all the particles of collisions. Provot’s method is easy to implement but it cannot give proper visual effect of collisions since we cannot get dynamic interactions between particles once the particles collide into each other. Cloth-cloth collision resolution is a special case of deformable N-body collision resolution. To solve deformable N-body collision resolutions, we propose a new collision resolution method which gives a visually reasonable response by ensuring the conservation of N-body momentums. Our cloth system is particle-based, as many systems are in other cloth research groups [ 14 , 6 , 12 , 3 ]. To resolve collisions, we first divide the colliding particles into parts and build a system of linear equations based on the collision relationships between these parts. Then we solve the whole system using the law of N-body momentum conservation. The system of equalities is based on the scheme adapted from the simultaneous resolution method for rigid N-body collisions proposed by Baraff 
[ 1 ]. However his original inequality relationships between relative velocities before and after collisions are purely heuristic, which may not be physically correct. Though this physical inaccuracy has been an inherent problem of simultaneous collision resolutions, it appears to give graphically agreeable results. Hence with the help of the law of N-body momentum conservation, we found the results of our resolutions are visually acceptable. In the next section, we discuss the issues involved in collision detection, especially to define a way to store collision information. In Sec. 3, we propose our collision resolution scheme. In Sec. 3.1 and 3.2, we examine some special cases of collisions which need some prior processes before we actually resolve collisions. From Sec. 3.3 to Sec. 3.5, the actual collision resolution method is presented. Finally Sec. 4 discusses results.
      
        