MAINTAIN VOLUME Sample Project

This project demonstrates the use of expressions to maintain the volume of

a character.  It relates three properties, which are sub-properties of the same transform.  When expressions occur on a subproperty they are evaluated last.

In this case there is a simple channel controlling the y-scale of the model.

The x-scale and z-scale are each computed with an expression.  In this case

the x and z use the identical expression.  Since the volume stays constant as

if the model was scaled to 100% which equals 1.  The formula uses the equation:

 

x-scale * y-scale * z-scale = 1

 

In this case the y-scale is the known value, and the x-scale is the unknown.  We

will assume that the x-scale and z-scale  will be equal to one another.  So

 

x-scale * y-scale * x-scale = 1

 

Where x-scale is what we want to solve for, so:

 

x-scale ^ 2 * y-scale = 1

 

Divide both sides by y-scale yields:

 

x-scale ^ 2 = 1 / y-scale

 

Now take the square root:

 

x-scale = Sqrt( 1 / y-scale )

 

Since z-scale is the same:

 

z-scale = Sqrt( 1 / y-scale )

 

Have fun with expressions, Bob

 

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