Calculate Distance Using Non-Uniform Scale

Hello, it's been a while since I've posted anything here, but it's not that I've abandoned it, and I still have several ideas to share. On this occasion, I'm going to share a problem I've been having lately while working with rigs. Calculating the distance between two points is a frequently used operation, and we almost always have to compensate for scale, since animators tend to scale the controls. However, this usually only works if everything is scaled uniformly; otherwise, the distance calculation will be altered.

Non-uniform scale does not work

I haven't found much information on this subject; we almost always limit ourselves to making it work only when we use uniform scales. Well, I set myself the task of finding a way to fix this error. I found two ways, both of which require a transformation node to calculate the scale. Here I describe them:

Orient and Scale:

One of the first things that came to mind was to find the orientation between the two points and scale in that orientation, thus preserving the distance. The idea is to find the orientation every time the points move; in other words, we have to apply an aimConstraint to make this work. However, to do this, many DAG nodes would have to be created, which would make it difficult. For this reason, I did everything directly with matrices. 

Connections in node editor

This aimMatrix does not require any input for an upVector, because we are looking the angle between them. We are using in the primary target vector of the aimMatrix (1,0,0), because that will be our primary axis, so in the multiplyDivide node we need to conect the distance in the input1X. It seems a bit long, but it works very well.

Local Space:

This method seems to be the most obvious, and I discovered it after trying the first method. It is quite simple; it basically works by making our distance calculations work in a local space, so you will never have the problem of scale.

Connections in node editor

As with the first method, our points that calculate distance need to be parented to the control. This parent does not necessarily have to be direct; it can have a zeroOut group, but this control is what will adjust the scale. Here is a demo of the first method, but the second should work equally.

Orient and Scale method

That's all, thanks for stopping by to read. Happy measuring!