The "Domain: f(x,y)" window shows the domain of the function f(x,y), together with the curve (x(t),y(t)) in green and the point (x(t0),y(t0)).  The blue curve is the curve (x(t),y(t)) such that |x-t| < delta.

The "Graph: f(x,y)" window shows the light gray graph of f(x,y) together with the green graph of the curve (x(t), y(t), f(x(t),y(t))).  The blue curve is the curve (x(t), y(t), f(x(t),y(t))) such that |x-t| < delta.  The pink planes are of distance epsilon/3 from the point (x(t0), y(t0), f(x(t0), y(t0))) in the x, y, and z- directions.  These pink planes determine the same cube that is shown in the "x(t),y(t),f(x(t),y(t))" window when the "Cube" checkbox is selected.

The "2D Projection" window shows the projection of the "Graph: f(x,y)" window into the xy-plane.  This allows one to determine the continuity of the curve (x(t), y(t)).  If the blue selection lies entirely within the red square (which can be made visible with the "Cube" checkbox) and consequently within the white circle (which can be made visible with the "Sphere" checkbox) and this can be accomplished for all choices of epsilon, then the curve is continuous in the xy-direction.

The "x(t),y(t),f(x(t),y(t))" window shows the graph of the curve along the surface without the surface.  The cube shown here is the same as the cube defined by the pink planes in the "Graph: f(x,y)" window.  If the blue section lies within this cube ( which can be made visible with the "Cube" checkbox) and consequently within the cyan sphere of radius epsilon (which can be made visible with the "Sphere" checkbox) and this can be accomplished for all choices of epsilon, then the curve is continuous.