This is a simple but very useful equation to blend between two values A and B.

( A * w ) + ( B * ( 1 – w ) )

w is a weight value.

When w = 0 the answer is B,
and when w = 1 the answer is A.

( A * 0 ) + ( B * ( 1 – 0 ) ) = A
( A * 1 ) + ( B * ( 1 – 1 ) ) = B

This equation is used all over computer graphics. It the basis of compositing pixels, and can be used to make controls for technical animation ( see this eye rig setup for 3dsMax )

Tutorial: Using the maths as an expression in Eyeon fusion.

In this tutorial I use an expression script to animate a blend between two changing positions. This allows the creation of a new point based on the current position of two other points.

You can download a sample file here

Note: using *  in algebra …

The convention is write equations concisely without the * for multiplication like this:

A w  + B ( 1 – w )

This is because hand written algebra tends to use single letters for variables, and multiplication signs can get confused with the variable x. While this form is easier to read, it can be confusing were people are  used to reading computer code, and are expecting * for multiplication and long variable names.