[Closed] Local coordsys and inverse mesh transform confusion

The pivot point is a Node-level property. Object Space is independent of the pivot point. The pivot point offset is stored in a separate transformation matrix called the Object-Offset Transform. When the object space is transformed into world space, the vertex positions are multiplied by the object-offset, node transform and parent transform matrices. The combined matrix of these three is known as the object transform matrix.

Let’s see a sphere primitive as example:
The Base Object takes the position [0,0,0] as the center and creates N vertices at distances equal to the radius around this origin. When you access local vertex positions, they will always be relative to the object’s origin.

Then the vertices are passed up the stack – if there are any deformation modifiers like Bend and Twist, their positions will be affected in object space. Note that most modifiers have their own gizmo and center to define the modifier’s space, but by default they are aligned to the object space.

Then we come to the node level where the vertices are multiplied by the object-offset matrix (thus resulting in an offset relatively to the pivot point), then multiplied by the node transform which transforms the vertices AND the pivot in parent space, and finally by the transformation of the parent (or the identity matrix if child of the world) to reach the final destination in the world space.

Check out the “Using Node Transform Properties” topic in the MAXScript Reference.