TransformPoint and InverseTransformPoint

Questions & Answers
1

In the code below, what values are the first two variables being set to, and why?

This code is attached to the main character in the Unity 2D side scroller tutorial. For the purposes of this question assume the following Vector3 values:

Active Platform: (2,1,0)

Player: (1,2,0) The player is standing just on the edge of the platform, therefore his x coordinate is slightly off.

var newGlobalPlatformPoint = activePlatform.TransformPoint(activeLocalPlatformPoint);
activeLocalPlatformPoint = activePlatform.InverseTransformPoint (transform.position);
activeGlobalPlatformPoint = transform.position;
var moveDistance = (newGlobalPlatformPoint - activeGlobalPlatformPoint);
transform.position = transform.position + moveDistance;
2

We start with

transform.position = (1,2,0)
activePlatform.position = (2,1,0)

we then know that

activeLocalPlatformPoint = (-1,1,0)

that is, the transform's center relative to the platform's center (TransformPoint) and

activeGlobalPlatformPoint = (1,2,0)

that is, the global position of platform.position + aLPP

We'll now move the platform up one unit -

activePlatform.position = (2,2,0)

Then, going through the function:

var newGlobalPlatformPoint = activePlatform.TransformPoint(activeLocalPlatformPoint);
// nGPP = aP.TP(aLPP) : nGPP = (2,2,0).TP( (-1,1,0) ) : nGPP = (1,3,0)
activeLocalPlatformPoint = activePlatform.InverseTransformPoint (transform.position);
// inverseTransformPoint converts world coordinates to local
// aLPP = aP.ITP( t.p ) : aLPP = aP.ITP( (2,2,0) ) : aLPP = (-1,0,0)
activeGlobalPlatformPoint = transform.position;
// aGPP = (1,2,0)
var moveDistance = (newGlobalPlatformPoint - activeGlobalPlatformPoint);
// mD = ( (1,3,0) - (1,2,0) ) = (0,1,0)
transform.position = transform.position + moveDistance;

TransformPoint moves a point from world coordinates to an object's local coordinates (including rotation); InverseTransformPoint moves a point from local coordinates (including rotation) to world.

3

Actually it’s the opposite to what Loius said. The default values, as shown in the inspector, are local. Thus “transforming” mean changing to world and “inverse transforming” changing back to the default, local coordinates. From the docs:

Transform.TransformPoint:
Transforms the position x, y, z from local space to world space.

Transform.InverseTransformPoint:
Transforms the position x, y, z from world space to local space. The opposite of Transform.TransformPoint.