Formula to maintain distance along the x-axis between an outer object and an inner object while scaling:
Outer cube dimensions = x=4.4, y=11.4, z=11
Inner cube dimensions = x=2.64, y=9.48, z=16.8
Example:
I have an object I would like to maintain a constant distance of 0.88 if scaled along the x-axis.
If I scale the object along the x-axis 3 times it gives me this.
see image below:
I'm trying to get cube / object along the x-axis to maintain the distance (in this example it's 0.88).
When I do this graphically it comes out the scale I should use to change the x-axis of the outer box should be 0.7339...How can I do this using a formula / equation?
I'm looking for a formula / equation due to the fact that this is going to be used to make "parametric" objects.
Suppose you want to scale the $\ x$-dimension of the inner object by a scale factor $\ s\ $, and keep the $\ x$-distance between the surfaces of the inner and outer objects fixed at $\ d\ $.
Let $\ w\ $ be the $\ x$-width of the inner object before scaling. Then the $\ x$-width of the outer object will be $\ w+2d\ $. After scaling, the $\ x$-width of the inner object will be $\ sw\ $, and the $\ x$-width of the outer object will have to be $\ sw+2d $. The outer object will thus have been scaled in the $ x$-direction by the factor $$ f=\frac{sw+2d}{w+2d}\ , $$ and if you've already scaled the outer object instead by the factor $\ s\ $, then you'll have to rescale it by the factor $\ \frac{f}{s}\ $ to obtain the right dimensions.
In your example, $\ w=2.64,$$\,d=0.88\ ,$ and $\ s=3\ $, and if we plug these into the above formula, we get $$ f=\frac{3\times2.64+2\times0.88}{2.64+2\times0.88}=\frac{11}{5} $$
Thus, after scaling the outer box up by a factor of $\ 3\ $, you need to rescale it by the factor $\ \frac{11}{15}\approx0.7333\ $ to get the right dimensions. I assume the digit $9$ appearing in the fourth decimal place of the scaling factor $\ 0.7339\dots\ $ you give is either a typo or rounding error.