Polar Control

This chapter provides details on how the placement of control lines and the selection of polar parameters can be used to manipulate shapes within a PAM.

You can use the Polar control to define operations in the polar (angle, radius) coordinate system.

As with many controls, before you define the polar parameters, you must first identify the shape(s) that you want to effect and add a control line (construction line).

This control functions similarly to the Stretch and Repeat controls, but the way the polar control operates on shapes is dependent on the type of shape and the placement of the Polar control line (construction line).

Angle Sweep

You can set the angle of sweep to be in either radians or degrees . Because all AEL trig functions work in radians, the default is radians. If you want to use degrees, you must use the AEL function rad() each time you reference an angle in a trig function, to convert it to radians.

Start

The equation or value you enter in this field defines the starting value for the Angle sweep.

Stop

The equation or value you enter in this field defines the ending value for the Angle sweep. You can define a sweep as greater than 360° from the start. In that case, the sweep goes around more than once.

Step

The equation or value you enter in this field defines the resolution of Angle sweep. A very small step produces a smooth surface for a curved shape; a large step creates line segments.

Note The current value of Angle sweep is saved in the variable _angle , that can be used in expressions for the Radius , X offset , and Y offset parameters. For a list of the variables that can be used in these parameters, see Using_Variables_in_the_Radius__&__Offset__Parameters._For_more_details_on_using_expressions,_see_Defining Parameters.

Radius and Incremental Offset

The Radius and Incremental Offset parameters are unique in that these parameters are evaluated by the program more than once. Most parameters are evaluated once and then used, but these parameters are evaluated at each Step, and then used appropriately.

Radius as a Function of Angle

The equation or value you enter in the Radius field defines the change in radius from 0.0 to the initial position of the shape. To produce a spiral-like shape, define the radius as a function of Angle sweep.

Radius as a function of angle allows for some unique shapes to be defined. For example, these settings produce the illustrated shape:
Delete Ends: True
Units: Radians
Start: 0.0
Stop: PI*2
Step: PI/32
Radius: sin(2*_angle)*200 mil

Incremental Offset as a Function of Angle

The parameters you enter in the X offset and Y offset fields enable you to modify the location of each point that results from the angle and Radius parameters, specifically, the point at which each Step ends. In the square spiral in the following example, each corner is one of these points.

The first spiral is a radial spiral with a step size of PI/8.0. A smooth radial spiral requires a smaller step size; a square spiral, such as in this example, requires that you change the step size so that there are only four points per cycle: 2.0*PI/4.0 (2p = 360°).

This gives a four-sided spiral. But the spiral is not square because what works for a rounded spiral, where each point is placed at an ever-increasing radius from the center, does not work for a square spiral.

To square things up, you must use to X and Y offsets to apply a small delta (a function of the spiral parameters and the current angle) to each point (corner) to push each point along the direction of the side.

For more details on using offsets, see the section First Spiral Example.

Shape Response

The polar control acts like both the Stretch and Repeat controls, depending on various factors. The only two shapes that can be stretched are paths and polylines (shapes defined by a set of control points), and these shapes stretch only if they are touched or cut by a Polar control line (construction line).

All other shapes (those whose outline or size is defined by a set of vertex points), and paths/polylines not cut by a control line, are copied by the polar control.

Using Paths

Paths support three corner types: mitered, square, and curved. Mitered and curved corner types require a certain amount of distance between the control points to be drawn correctly. If the space is too small, the results are not ideal. Because of this, when working with paths, use the square corner for a Polar stretch with a small step.

Delete End-Points

In the context of a polar operation, Delete End-Points (toggled at the top of the Polar Control Definition dialog box) means to delete the end-points of a stretched, two-point path or polyline.

In general, a polar stretch on a path or polyline preserves the parts of the shape on either side of the polar control line. This is consistent with the way a normal stretch operates on shapes, but there may be times when you do not want this to happen. All initial shapes must have some size, but you may want to generate a shape that does not have any remnant of the initial starting shape. This is similar to using Offset in a Stretch control to compensate for the initial size of a shape (see Offset). In this case, if:

• the shape is a path or polyline,
  and
• the initial shape has only two points,
  and
• the operation is a stretch (the control line touches or cuts the shape),
  then the Delete End-Points option removes the initial points from the resulting shape.
  This feature is very useful when you create spiral-like shapes where you do not want the straight remnants from the initial path hanging on to the ends of the generated shape. Remember, though, that Delete End-Points works only on two-point paths and polylines.

Using Variables in the Radius & Offset Parameters

A number of temporary variables have been defined to hold commonly-needed values for use in the Radius and Offset parameters. These variables act as a shorthand so that you can use the variable in an expression rather than repeating the possibly lengthy expression that defines it.

• _angle (as calculated by the Angle expression for the current step)
• _radius (For use in the Offset field only) (as calculated by the Radius expression for the current step)
• _angle_start (as calculated by the Start expression)
• _angle_stop (as calculated by the Stop expression)
• _angle_step (as calculated by the Step expression)
• _angle_i (step number that increments from 0 to

The convention of a leading underscore (_) for global variables is the same as is used by the ADS Analog RF Simulator (ADSsim).

For more details on using expressions, see Defining Parameters.