The Rack
Peter P. Tanner, Kenneth B. Evans · ACM Transactions on Graphics · 1982
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.