The "tx, ty, and xy planes" window displays curves representing a plot of x(t) versus t in blue, y(t) versus t in red, and y versus x in magenta.  Sections of these curves are highlighted in green, and the lengths of the sections highlighted are determined by the choice of Delta in the control panel.  There are then semi-transparent rectangles of width epsilon/2, and in the xy-plane there is a cirle of radius epsilon.  The key fact is that if all of the selections of curves lie within the rectangles of width epsilon/2, then the selection of curve in the xy-plane will lie within the circle or radius epsilon implying the continuity of the function if this can be accomplished for any choice of epsilon.

The following three windows mentioned correspond to the "t, x(t)", "t,y(t)", and "Range" windows in the above Domain and Range demo.

The "t, x(t)" window displays x(t) versus t, so that the continuity of x(t) can be examined as in the rectangular case.

The "t, y(t)" window displays y(t) versus t, so that the continuity of y(t) can be examined as in the rectangular case.

The "t, x(t), y(t)" graphs these three quantities as the first, second, and third variables repsectively.  There is a circle and a square in plane with the point (T0,x(T0),y(T0)) holding t constant.  By pressing "x" in this window one obtains the same view as the "x(t),y(t) Projection" window.  If in this view the curve lies within the square of side length epsilon/2, then the curve will lie within the circle of radius epsilon implying continuity.

The "Close-up window gives a close-up view of the "x(t),y(t), Projection" window to help view for small epsilons and deltas.