Driving A Vector's Direction By Euler With Maya Node Editor

Introduction

Past thursday one my fellow mates at the office in charge of refining the shots and animating dynamics asked me to help him with a problem he was facing: he needed to map the euler rotation angles from a CTRL transform to the nucleus' gravity direction vector. In short: control with angles the direction of a vector.

He was trying with the "angleBetween" node looking for some way to solve his problem. I have to say that at first he wouldnt explain  to me correctly what he needed but that's because he was striving for it himself.

The next day, this is last friday, while at the bus in the morning to the office i remembered the conversation he had a couple of days earlier asking for this to my fellow riggers. They seemed to fill the expectations of my comrade in need with their answers. It wasnt clear for me but i was too busy with something else and didnt want to intercede.... Until now, where this was something that was puzzling him for quite a few days now.

So i started to suppose what was the problem and started to think how i would solve it with nodes.

Controlling Vectors through Rotation

In fact, once aware of the problem the solution is just applying some simple math. We have a curve/CTRL's transform that represents rotations with Euler angles.

Well, we need to apply the rotation of the control to the vector. In terms of maths, we need to get the matrix representation of the rotation. Maya's node editor has a ComposeMatrix node that generates a matrix with information on translation, rotation, scale, shear depending on what the input is.

Next step is to multiply this matrix by the vector we want to transform. Again, Maya has VectorProduct node for this that can do different operations such as Dot, Cross, VectorMatrix and PointMatrix.

v' = M * v

All that is left is just attach the output of the operation to the nucleus's gravity vector....and voilà!!!

Voilà????? Hold on a second, there is a little problem.

One little problem

The way i approached for the first time the node network i was convinced it had to work from the beginning since these are simple maths. But i was committing one error that stems from the fact that i was a little unaware of how nodes work.

I was using the current gravity vector direction to feed the operation and then the result attached back to the nucleus as input..... And i tried to test with known trigonometric values and i was getting a strange behaviour: the numbers just didn't correspond to a valid result.

My network suffered from a "cycle" that never stopped: i'm feeding the input of the attribute with the output of the same attribute after doing some calculation....

But i found one workaround for this.

Workaround

After trying inefficiently to break that cycle using an intermediate transform where i would store the result and pass it on again to nucleus i decided to write a post in a Maya forum convinced of the fact that this can be made without using a transform or any other supplemental entities.

But i kept thinking after the post, enbraved by the fact that i wasnt getting a quick question and i was stuck. Well, if all i need is the starting value of the nucleus how about putting that same initial value into a transform and use it instead of the nucleus to feed the calculation? That way  i can attach directly the result to the nucleus gravity vector. All i have to make sure is that both vector values: nucleus initial value and transform's value are the same!! It doesnt matter really which channels of the transfrom i use provided they represent the three vector componentes X, Y,Z. I decided to use the translate.

Additional Comments

It's worth noting that since the initial value of the vector is such that the module is 1.0, the results after the matrix multiplication must be also of module 1.0. Since a rotation matrix doesnt change the module of a vector. 

This was helpful to rapidly notice wrong numbers and therefore there was a problem. Also, testing with cosine and sine values of most known angles such as 0,30,45,60,90 degrees.... One is used to see numbers like 0.707 or 0.5 and 0.866 etc....

Also, note that because we are using the rotation the translation of the control/curve doesnt matter.