Animatable Pivot - Rolling Cube Demo

INTRODUCTION

During the production of "Deep" the movie, the rigging department had to design the rigs of ice cubes that some characters were pushing. In order to achieve this rolling cube the rig needed to dynamically change the rotation pivot.

I didnt have time to look further into it so i couldnt be of much help at the time. But since one of my interests is rigging i decided to dig deeper when i had enough time.

If you do a google search the problem of rolling cubes is something most Riggers and Character TDs have faced anytime. One of the most interesting articles on how it can be done is this one. But i wanted to do it my own way and in different ways. One using the Node Editor, Matrix Multiplication and Geometric Transformations and the other, by using constraints. I'll show both here.

The first approach is simple: animate the cube setting keys in the Rotate Pivot X,Y,Z  attributes. If you do that, you will notice that it doesnt work. Just when you change pivot, the cube suffers a translation due to the fact that the rotation is applied again but with the new pivot. This is, it doesnt remember the rotation you performed with the previous pivot.

So the solution is to calculate the translation difference between pivots and apply it to the top controller.

I started with the outliner configuration you can see above. This configuration is generic. It works for all kinds of meshes and any number of pivots, The cube pCube1 can be substitued by whatever mesh you want. Here to illustrate better, i have used a NURB Surface and positioned one in each corner of the cube.

The main transform group has an enum attribute to select the pivot. Once chosen, we calculate each pivots world position from the hierarchy and its local rotate pivot position. This is important because if you just simply use the pivots world rotate position you will cause a cycle in the transformations as it changes every time you rotate. The local rotate pivot position doesnt. So it becomes necessary to compute the world position traversing the hierarchy bottom-up. 

Here is the Node Graph.

Another way of doing it is, instead of using matrix multiplication, using the tools maya provides, this is by using constraints. We constrain from for example a locator to all the NURBS pivots. And instead of  using the Node Editor we manipulate the weights of the constraint of each of the pivots.

Both alternatives make use of scriptJobs. They are both here provided here.

The first one calculates the pivots difference in an accum buffer.

The second one modifies the contrain weights and applies the calculation to the Rotate Pivot of the transform group.

FURTHER DEVELOPMENT

I just wanted to play a bit with those concepts and figure out how i would tackle with the problem myself. Needless to say it still needs to be organised as most rigs are, which means being able to set keys in a Curve Control. This is not a big change though.

As I previously said, this configuration is generic. it would work for any kind of mesh and any number and distribution of pivots.

Here is the final video file.