LiveGraphics3D Example:
Two Surfaces

Plot3D Example

This example is taken from Stan Wagon's book "Mathematica in Action". The special feature of the plotted function f(x,y) = x y (x x - y y) / (x x + y y) and f(x,y) = 0 at (x,y) = (0,0) is the difference between its mixed partial derivatives at (0,0).

Apart from that this plot shows axes with labels and tick marks. (See below for more details about its creation.)

Sometimes LiveGraphics3D uses the color of the wrong face of a polygon; especially in this example because the polygons have four edges (not only three). This effect is however shared by Mathematica, thus I do not know whether I should try to remove it.

ParametricPlot3D Example

Another example from Stan Wagon's book: This time it is a Moebius tube.

This plot uses different "styles" (colors) for each polygon and "manually" chosen positions of the axes.

One unsolved problem of LiveGraphics3D is its bad hidden line/surface algorithm. In this case the y-axis seems to intersect the tube for some special points of view.


Martin Kraus, April 15, 2021