Polar Plotting in Mathcad

Polar Coordinates

Consider a point in space as defined in Figure 1.

In the Cartesian, or rectangular, coordinate system, the point can be located as noted below and shown in Figure 2:

  • Move x units to the right of the origin if x > 0or -x units to the left if x < 0.
  • Move y units up from this point, if y > 0 or -y units down if y < 0.

This same point can also be located by its polar coordinates, [r,theta], where r is the radius, or the distance from the point to the origin and theta is the angle from the positive x-axis to the radius as shown in Figure 3.

Conversely, given a point [r,theta], you can calculate the [x,y] coordinates, or use Mathcad's mapping functions to do these conversions for you. (Figure 4)

Inserting a Polar Plot

You can use the 2D polar plot operator to plot points in terms of their polar coordinates. To insert a polar plot into a Mathcad worksheet, choose Insert > Graph > Polar Plot, or choose the Polar Plot icon on the Graph toolbar. You see the shell of a polar plot with the placeholders shown in Figure 5.

You can plot a function, Figure 6, or a set of data, Figure 7. Data points are connected by a straight line by default. Use the plot formatting options, discussed below, to show symbols at each point or remove the lines connecting them. Just like X-Y plots, polar plots can have up to 16 traces.

Negative Radii

A feature in Mathcad 15 allows you to specify negative values for radii in polar plots, similar to the negative values allowed for the X and Y axes in X-Y plots. This is particularly useful when plotting in dB (log scale), which commonly occurs in the communications and antenna design industries. Review the calculations shown in Figure 8. Previously, Mathcad phase translated the negative radii and gave them a positive radius value. Show negative radii enabled on the radial axis produces the polar graph shown in Figure 9.

Units

Mathcad uses radians for angles. To display the result in degrees on the plot, include the unit 'deg' on the definition of , causing the point to appear at 15 degrees on the angular axis as shown in Figure 10.

Formatting Polar Plots

Double-click on a polar plot to format it. On the Traces tab you can choose the number and color of the gridlines for both the radial and angular axes. You can display or suppress the numbers on each axis. The radial axis can be set to log scale or have markers applied. A marker appears as the purple dashed circle at the specified radius (0.3 shown in Figure 11). There are three axis style options: Perimeter, Crossed, or None as shown in Figures 12, 13, and 14.

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