Scales and Axes of 3D Surface Plots

The scaling of 3D surface plots deviates somewhat from the usual approaches, since the basis of a 3D plot is a rectangular grid with integer coordinates. This grid forms the x-y-plane giving rise to discrete integer x- and y-coordinates. The z-coordinate is continuous and can be of any range. From this basis it is clear that the z-coordinate has to be handled differently to the x- and y-coordinates.

Note:

Please note that the terms "x-axis" and "x-coordinates" describe two different things. Whilst the "x-axis" being one of the rotational axes (see property ViewAngleX), the term "x-coordinates" denotes the scale along one side of the rectangular base grid (GridMat).

Plot3D provides two different classes of scaling parameters: First, the scaling parameters which influence the overall appearance of the plot, e.g. shrinking or magnifying one of the x-, y- and z-coordinates, or the plot as a whole. This class of parameters is controlled by the properties ScaleFactX, ScaleFactY, ScaleFactZ, and Magnification and the method AutoScale.  Secondly, there are six properties (RangeXLow, RangeXHigh, RangeYLow, RangeYHigh, RangeZLow, and RangeZHigh) and one method (SetRange) which control the scale of each coordinate. It's the second class of parameters which have to be handled differently for the x- and y-coordinates on one hand and the z-coordinate on the other hand.

The scales for the x- and y-coordinates are mere inscriptions drawn along the edges of the base rectangular grid (see figure above). Changing the parameters RangeXLow...RangeYHigh does not affect the display of the 3D surface, but changes only the values displayed on the scales of the axes (you can think of assigning some arbitrary values to the corners of the base matrix grid, while the grid itself keeps the same size). The scale of the z-coordinates, in contrast, does influence the display. The z-axis acts like a normal axis - if you change the range of the axis the corresponding data will show up differently.

The visibility of the scales can be controlled by the properties VisibleXCoords, VisibleYCoords, and VisibleZCoords. The number of decimal places and the number of scale ticks can be controlled by the properties DecPlaceX, DecPlaceY, DecPlaceZ, and MinTickX, MinTickY, MinTickZ, respectively.

Hint:

You may start the sample program Plotit3D to study the effects of the various scaling parameters.