Measure tree for intervals

I need help understanding Union of Intervals based on Advanced Data Structures Book by Peter Brass. Attached is the section of the book that Im trying to Understand starting from the middle of the page 163 where it says "A fully dynamic structure to maintain the measure of a union of intervals..."

Im trying to make the Measure of all Unions of Intervals Calculate Properly.

This is basically what I understood,
1) Start with any Balanced Search Tree. Therefore I used height balanced search tree.
example, for interval [1,9], I insert a 1 into the tree. Then I Insert a 9 into the tree.

2) during insertion of for interval [1,9]
a) i record the path of 1 into a stack, insert 1 into the tree, rebalance the tree, use the stack to trace back to the root while calculating the leftmin, rightmax and measure.

-b) record the path of 9 into a stack, insert 1 into the tree, rebalance the tree, use the stack to trace back to the root while calculating the leftmin, rightmax and measure.

What's messing me up is it's associated nodes. I can't visualize it correctly.
Anyway, I implemented this in C and its not calculating right. Am I missing something?

Tags: C, GCC