Axes Entries

Use this panel to change the dimensions and subdivisions of the domain of the current function.

Limits Tab

Here are two boxes to define the axes extremes of the X and Z axes. The boxes assume positive integers only, but  the true value of the domain is twice the values you see. Thus, if the limit of the X-axis is set  to 3, then -3 <= x ,= 3. 

The numbers are also interpreted as absolute radians; thus, if the limit of the Z-axis is set to 2 then we can also interpret that the Z-axis goes from -2 radians to 2 radians. 

The values in radians and they conversion to angles are displayed in boxes below.

Limit of X

Here you use the left and right arrows to decrease or increase the X-dimension of the domain. You can also directly enter a value in the provided box. 

Limit of Z

Here you use the left and right arrows to decrease or increase the Z-dimension of the domain. You can also directly enter a value in the provided box

Subdivisions Tab

Here you use the left and right arrows to decrease or increase the subdivisions per unit of the domain. You can also directly enter a value in the provided box. 

The number of subdivisions applies to both axes at the same time. So, if the Divisions Per Unit is set to 5, every unit of the X-axis and every unit of the Z-axis is subdivided 5 times. Following this example, a unit radian subdivided 5 times is a 0.20 radian subdivision.

Remarks.

Since the domain is at the same time a rectangle, and this rectangle is further subdivided,  the total number of points of the domain is also displayed in box below.

Axes Orientation

The Axes View panel is used for pre viewing the rotation of the axes before drawing any surface or plot, or for selecting some preselected angle views. 

Special Views Tab

The option buttons are:

• Top. For a top view of the surface. The user sees the surface looking from the positive side of the Y-axis toward the origin.
• Lateral. For a lateral view. The user sees the surface looking from the positive side of the X-axis toward the origin.
• Frontal. For a frontal view. The user sees the surface looking from the positive side of the Z-axis toward the origin.
• Orthogonal.  For an orthogonal view.
• Axonometric. For an isometric view.

The Axes Entries button is to invoke the Axes Entries panel. 

Background Tab

This is a tab to make color changes to the background of the Special Views tab.

Angles Tab

In this panel the user can change the angles of rotation for some special  views of his/her interest. The angles are the following:

• Fi is the angle around an unmovable X-axis. This is shown in the panel as Fi = @^*X.
• Psi s the angle around an unmovable Y-axis. This is shown in the panel as Psi = @^*Y.
• Ji s the angle around an unmovable Z-axis. This is shown in the panel as Ji = @^*Z.

Some preset angles are also shown in color. The plus and minus symbol is used to change an angle value from positive to negative or vice versa.

Check the Draw on mouse release to see immediate results of changes in the axes. This may be a convenience or not depending of the amount of polygons to draw. For intricate or elaborated surfaces better uncheck this box.

Remarks

Counterclockwise rotations are positive and clockwise rotations are negative.

The frontal view assumes all angles are 0.

Complex Domain Table

The Domain And Range panel is used to present a table of the values used in the domain of the current function, and the results of the computations (the range).

The points of the domain are vertically shown in the first green column under the heading Original Complex (x, x). This column starts at the negative side of the X-axis and the negative side of the Z-axis.

The image under current transformation of each one of those points are shown in the next green column under the heading Transformed Complex (y, z).

Real Domain Table

The Real Domain And Range panel also consists of two columns, but this time the first column is of single numbers instead of an ordered pair. The reason is that real numbers are complex numbers with imaginary part zero, so, for example,  (-2, i0) = -2.

The first column is an extraction of the real numbers available in the chosen domain. This is equivalent to say that the first column shows the numbers of the real X-axis of the domain.

The second column are for the images under the current function of the real numbers available in the first column. 

The second column is maintained as ordered pairs because the function in use may generate complex numbers as images of real numbers. 

For example, the function f(x, iz) = x² +i produces a unitary displacement of the real parabolic curve y = x² along the positive side of the Z-axis for all values of the domain, even for the real numbers.

The displaced parabola produced by  f(x, iz) = x² +i is shown at right. The equations entered in the Equation Editor are: U(x, z) = x² and V(x, z) = 1.

Remarks.

If you make changes to the equations of the current function, or chose another function to plot, both tables must be closed and reopened to refresh the tables. The tables are also affected if you make changes to the domain values, like X-axis limit, Z-axis limit, or subdivisions per unit.

The tables are not affected by viewing rotations.