A Different Approach for Continuous Physics

"Motion" : physics engine of Ubisoft

Existing approach
 linear convex cast
   - occur : detecting this collision != handling it.

while(TOI found)
     - move at earliest line of impact
    - compute
    - solve

 costs lots of CPU

  speculative contact points
    :  ghost bug, stop the dynamic rigid body even if if it shouldn't.
    : doesn't prevent tunneling issues
    : can occur with rag doll

Robust:
    : few solver
    : handling variance frame rate
    : handling fast rotating bodies


Our method:  broad phrase, narrow phrase, constraint creation, solver

Broad phase
: body's linear velocity  compute to the trajectory
   detect the potential colliding bodies
               - consider trajectory
               - use the bodies AABB
Transfer volume and compute a segment intersection, add AABB to other AABB

Narrow phase:  Incremental manifold, provides one new contact point at each frame.
      full manifold: provides all contact points in one frame
            Distance -based full manifold: potential contact points in fill manifold
support shapes
   - shapes should on all rigid bodies
            - sphere
           - capsule
           - box
         
    Distance-based full manifold with a sphere:  can use GJK

     distance-based full manifold bw capsule and box: project capsule extremities on the box's plane.

     If the capsule is in the Voronoi edge region , use GJK

      distance-based full manifold bw a capsule and a triangle
           - Generalizing three triangle

       distance-based full manifold bw a box and a triangle
           Use edges that face he reference plane
        distance-based full manifold bw two convex
           
       Handle potential and real contact points at the same time

               - real contact points can generate fast rotation
             - potential one avoid tunneling in same frame
             - reuse geometry info.
             -  maximum  cache size
    Restituion
     - potential contact points
      -  at next frame the body reaches obstacle with reduce velocities
      - do not use the current velocities
      - use previous frame

    Solver: with Gauss Seidal solver, each constraint changes the velocity of buddy

   Limitation on the second impact
     
  Handling server gasset bodies
     
Handling several fast bodies





  Performance:  broad segment intersection with AABB
  - more body pairs are

Continuous physics cost
   - constraint create

CPU benchmark

memory cost
    other : 14mb
    continuous :150kb

    - solver

low additional cost for cpu
 Restitution handle correctly

Robust: no tunneling issue with fast rotate

limit:
 - server fast bodies
 - second impact