#### QUESTION

I apologize if this is a obvious question and answer, I don't often use *Mathematica* to display plots or graphics in general to be honest. So, I was tutoring my cousin yesterday in relation to Polar functions and decided to bring up *Mathematica* to illustrate some of the ideas we were discussing. I quickly typed a one line command into *Mathematica* 8 and got an odd result. When rendering a polar function, *Mathematica* took a few seconds to make it smooth. Prior to this it has too many lines (see picture, before is on left and after is on the right.)

The code is:

```
Manipulate[PolarPlot[Sin[nS*t], {t, -5 Pi, 5 Pi}], {nS, 1, 20, 1}]
```

Does anyone know why this is happening and if there is a way to make Mathematica render smooth at first?

#### ANSWER

This is done intentionally to update the plot quickly as you move the slider. `Manipulate`

changes the setting for `PerformanceGoal`

(via `$PerformanceGoal`

) to `"Speed"`

while you move the slider, then to `"Quality"`

after you let go. This is seen in this simple demonstration:

```
Manipulate[{n, $PerformanceGoal}, {n, 0, 1}]
```

If you want the final quality while dragging at the expense of update speed you can give an explicit `PerformanceGoal -> "Quality"`

:

```
Manipulate[
PolarPlot[Sin[nS*t], {t, -5 π, 5 π},
PerformanceGoal -> "Quality"], {nS, 1, 20, 1}]
```

Alternatively you can take manual control of this process with `ControlActive`

, and specify the `PlotPoints`

that are used while dragging and after release:

```
Manipulate[
PolarPlot[Sin[nS*t], {t, -5 π, 5 π},
PlotPoints -> ControlActive[50, 150]], {nS, 1, 20, 1}]
```

You can turn off updating while dragging altogether using `ContinuousAction`

:

```
Manipulate[PolarPlot[Sin[nS*t], {t, -5 π, 5 π}],
{nS, 1, 20, 1}, ContinuousAction -> False]
```

As belisarius comments you range for `t`

is excessive: `{t, -π, π}`

will not run multiple circuits. This will allow the plot to update much more quickly. I leave the original value in the examples above so that the effect is easier to observe.