Plots and Sampled Objects

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Plots and Sampled Objects

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Certain mathematical objects in Sketchpad are plotted by connecting or combining many individual samples, just as you might plot a function on paper by connecting many individual plotted points.

In some cases, the samples are points; the points can be connected to make a continuous plot, or displayed separately to make a discrete plot.

In other cases the samples are other geometric objects or even portions of a picture; these samples are always displayed separately.

A locus is displayed by considering many locations or values of the driver on its domain; the samples are the corresponding locations of the driven object.

A function plot is displayed by calculating the dependent variable for many values of the independent variable; the samples are the corresponding plotted points.

A parametric plot is displayed by evaluating two functions for many values of an understood parameter; the samples are the corresponding plotted points.

A sampled transformed path is displayed by transforming many locations along the pre-image path; the samples are the transformed locations.

A sampled transformed picture is displayed by dividing the pre-image picture into many small parts; the samples are the transformed images of those small parts.

For all these objects, the Properties dialog box has a Plot panel that allows you to set the number of samples used to plot the object. The greater the number of samples, the smoother and more accurate the plot is. However, the greater the number of samples, the slower Sketchpad can be in calculating and displaying the plot. Choose Edit | Preferences | Sampling to set both the maximum allowed number of samples and the default number of samples for to newly constructed objects.

The properties panel for plots and other sampled objects include these settings:

Number of Samples: You can set the number of samples for any sampled object.

Continuous or Discrete: When the samples are points, they can be connected so that the plot appears continuous, or they can be displayed individually so that the plot appears as discrete points.

Show Arrowheads and Endpoints: When the samples are points and the domain is not a closed curve, the ends of the plot can show arrowheads when they’re adjustable and endpoints when they’re fixed.

Domain: When the driver is numeric, you can determine the domain numerically.

Allowable Distortion: For a transformed picture, this setting determines how much distortion is acceptable in a sample. Samples with more than this level of distortion are not shown.