Shift
Shift (ST Actorname) [to] (Ve #4 position);
The Syntax of Shift is:
Shift "myActor" to [x,y,z,1];
It simply translates the vertices V of "myActor" by (x,y,z). The 4th component must be 1.
An important form of animation manipulates the actors in a scene while leaving the scene (and camera) coordinates fixed. This is why the named actors have names, so that scripts can manipulate them. The Shift Command is used to translate an individual actor without rotating it. The simplest and most straightforward use is to apply the command to an actor to move it discretely to a new location, with the same orientation. Variations on this command: ShiftSpin and SpinShift translate an actor, either post- or premultiplying a rotation.
Another sort of variation on Shift, DoShift, is used to move one or several actors through "continuous" sequences of translations simultaneously. There are also commands: DoShiftSpin and DoSpinShift that move sets of actors through more complex simultaneous motions, such as orbiting planets, or spinning tops.
Here, we discuss the simplest of these, the Shift Command. In order to understand the actor animation commands it is necessary to fix ideas on just what an actor is (and what it is not). First of all, we should observe that each actor is, ultimately, only a collection of vertices V in global coordinates (the "fixed stars"), together with the "geometry" that binds the vertices together (the lines, triangles, quadrilaterals, etc. ) This is true of all actors in Mathwright32, whether defined by equations, imported, or defined by OpenGL script.
Now, after the actor vertices are defined, the actor is positioned in a scene by actively transforming these vertices to scene coordinates (usually using Translate() and Rotate() in the Actor Script). The fact that these transformations commute with the navigation transformations (Move and Turn) means that these initial positions are independent of viewpoint. That is natural.
Note: In all of this discussion, we assume that Scale() transformations are not used in actor scripts. They are not orthogonal, hence do not belong in general, to the Euclidean group. All of the actors you may create or import into Mathwright32 may be scaled initially as you like to fit the scene without using the Scale() transformation in any case.
The transformations in the Actor Script define the initial position and orientation of the actor, the way it appears when selected into the scene, in terms of the global coordinate system. Together, they may be viewed as a rigid (Euclidean) transformation, I, from R3 to R3. We have already observed that each rigid transformation from R3 to R3 has unique representation as the composition of a rotation about the origin followed by a translation. This is a SpinShift. It also has a (usually different) unique representation as the composition of a translation first, followed by a rotation about the origin. This is a ShiftSpin
. We find it convenient sometimes to use one such representation, sometimes the other, because while, in principle, we can always translate from one to the other, the algebra is sometimes messy.
Each actor therefore has, attached to it two things: A set of vertices, V, referred to the global coordinate system, and a rigid transformation of the global coordinate system to itself that actively carries those vertices to the initial position, defined by its script. Call this initial transformation of R3: I. It is a permanent property of the actor (like the vertices V) as long as the actor script is not changed. "I" will also be called the "Initial Stage Transformation."
Before this initial stage transformation is applied, the actor is simply defined by its vertex coordinates, V. While you will only see an actor in this state before you script it, it will be important to be aware of what that state, V, is when you script motion for an actor, as we shall see. The important thing to understand is that, in order to move any given actor, we must define a Euclidean transformation of all of R3 -- a combination of a spin and a shift. That transformation will not affect other actors, but it will carry the vertices V of the current actor to new vertices, and we will see the effect of that transformation. The Initial Stage transformation, I, defined by each actor's script does just that, for each actor, individually.
This is all well and good. When navigation commands are issued, they affect all actors in the same way, maintaining all relative spatial relations. Now the question is: How do we change the position of a single actor, leaving the others alone? To do this, we define a new Euclidean stage transformation for the actor, one that temporarily replaces the Initial Stage transformation, (until the scene is Reset or Restored) and transforms V to its new destination.
Each of the commands: SpinShift, ShiftSpin, Spin, and Shift defines for the actor a new Stage Transformation. These do not accumulate. Each new one simply replaces the previous one. The actor is simply wherever the last command put it. Thus at any time, the actor's vertices are the image of V under the last SpinShift, ShiftSpin, Spin, or Shift that was called on the actor. In this way, your program "knows" at any time what the position and orientation of each actor is.
This is why it is important to remember what the vertex set V looks like for each actor. Every shift motion will transform that vertex set to the desired position and orientation.
If the Stage transformation is the initial one, I, the actor appears as the script initially dictated. If it is a Shift, it appears -- and remains under all navigation commands -- in the new position given by the last shift transformation. The orientation (rotational state) will be the same as that of the original vertex set V, and may not be that of I. Whenever the screen is Reset, using the Restore Button, the scene is restored to its original state and all Stage Transformations are restored to the original ones.
Therefore, each actor carries with it, first, the initial coordinates, V, defined by its vertices. Its script defines the initial transformation, I, into the global scene. This defines the initial position and orientation of the actor.
See Also