Purpose: To scale objects independently along x-and y-axes, about a userspecified center of scaling [1].Description : The rack is a modification of the two-axis trackball or the two-axis number wheel [2], and is designed to facilitate the scaling or stretching of objects.First the center of origin of the scaling operation must be determined, and then the magnitude of the scale factors can be established.To locate the scaling origin, the user picks a scale origin point on the screen (the + cue in Figure 1).The user is then given an "identity cue" (e) representing a scale of 1.0 in both x and y, along with the tablet tracker (*) and the origin cue.When the tablet tracker is superimposed on the identity cue, an identity scale factor results, and the resulting object is the same as the original.A transformation process is applied to both the x-and y-scales of the selected object.The x-scale is determined by Xscale = (Xtracker -Xorigin)/(Xidentity -Xorigin}.The y-scale is determined similarly.As the tracker is moved away from the identity cue in an x-direction, the x-scale increases (Figure 2).As the tracker moves back towards the origin, the x-scale diminishes to 0 (Figure 3).As the tracker moves past the origin in a negative direction, the result is a negative scale increasing in magnitude (Figure 4).This is equivalent to reflection about the y-axis followed by a scaling by the absolute value of Xscale.In this technique, the user's hand actions are tightly coupled to the scaling in the two directions.

The ability of the user of a graphics system to interactively control the motions of 3-D objects enhances his or her spatial perception and comprehension of those objects. This paper describes several logical devices based on the tablet, each particularly suited to control some type of interactive manipulation of 2-D and 3-D objects in real time. The “turntable” and the “stirrer” convert rotary motion of the tablet pen or puck into values for one-axis rotational control; the “rack”, a two-axis device, is used for scaling control; for three-axis rotational control, the tablet-based three-axis trackball is particularly suited.

A system for removing hidden edges in line displays of three dimensional scenes is described. The hardware system is relatively low cost, and operates on several hundred vectors in real-time. The system consists of a graphics peripheral connected to a PDP 11/55 computer and a software package to drive the peripheral.