The following may hold the key to my flattening problem I got. However, I am still unable to figure out how the object can "spread out" during the flattening process. ------------------------------------------------------------- The state of each particle can be described in a 6D vector [x1, x2, x3 ,v1, v2, v3] where [x1, x2 , x3] is the particle's position and [v1, v2, v3] is the particle's velocity. The internal forces are imposed by the springs connecting particles when 2 particles move from their rest length. These forces are governed by the ideal Hookian spring to keep particles together. To flatten a surface, we apply a downward force (G = [0, 0, g]) and force a collision with a plane. If the collision is purely elastic, the new velocity is Vnew = Vold - 2(Vold.N).N where N is the normal to the plane. When colliding with the ground plane, the new velocity is Vnew = [v1, v2, -v3], with Vold = [v1,v2,v3] To speed up the stabilization of the system, a coefficient of restitution k(in the range of 0 to 1) is used such that Vnew = Vold - (1+k)(Vold.N).N Note that if k=1, it is a purely elastic. With the state initialized as [X0, V0], the flattening process becomes a calculation of the subsequent sequence of the states according to ODEs which can be approximate with Euler method. Source: Digtial restoration using volumetric scanning Author: W.Brent Seales and Yun Lin ------------------------------------------------------------ Based on the above, what I observed is that only v3 is changing, resulting in changes in x3. if we initialized v1, v2, v3 to 0 which is the case since the resting position should have 0 velocity, v1 and v2 will be 0 all the way. I hope someone can help me out here. I have thinking of this problem for days. Thanks.

Not true. You have the spring connecting each mass, so when it hits the surface, it moves outward, or inward, but it cannot just compress to nothing. Here's a scenario:

             /                 .            /                  .           /                   .          /                    .                               .                               .-----------------------------

Just imagine that the lines are springs and at the ends of each spring are masses. Gravity pulls it down:

                               .             /                 .            /                  .           /                   .          /                    .                               .-----------------------------                               .                               .             /                 .            /                  .           /                   .          /                    .-----------------------------

At this point there is a contact with the surface plane. The lowest spring will compress, but it cannot just compress to a point, at some point it will push back and slide out to one side.

                               .                               .                               .            /                  .           /                   .        __/                    .-----------------------------                               .                               .                               .                               .           /                   .     __ __/                    .-----------------------------                               .                               .                               .                               .                               .  __ __ __/                    .-----------------------------                               .                               .                               .                               .                               .__ __ __ __                    .-----------------------------

That is how it ends up being flat.

Hi Duncan

I agree with you on this. However what was described above did not help in determining the new velocity or displacement in the x/y direction. From the forumula, we can see the v1 and v2 remain unchanged for Vnew.

Well, you have crossed the boundary of my understanding (not to difficult from what I've heard, but don't tell anyone else :) ).