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Using OneStone® Pebbles

The User Interface (UI) of the Curve Families Pebble is pictured at right; as described on the Pebbles Home page, all Pebbles UIs are similar, so the following procedure applies equally to them all. The procedure is also summarized in an animated .gif which can be seen here.

  • Start the Pebble by clicking the 'Launch...' link on that Pebble's web page. Pebbles are designed to download themselves on each use, as described here. This ensures you always run the latest version available. The size of each is around 200 KB so it should download in just a few seconds.
  • Enter an expression in the text box at upper left. There are individual restrictions on the expression a Pebble operates on; for instance, the Surfaces of Revolution Pebble only accepts the variables 'X' or 'Y', while the Curve Families Pebbles accepts 'Theta' and 'R', as well. These differences are noted on a particular Pebble's web page and in it's Help file. The list of operators recognized by all Pebbles appears below.
  • Select a constant from the drop-down list. The drop-down list below the expression is automatically loaded with any numeric constants present in the expression. The first constant in the list is automatically selected, appropriate minimum and maximum values are calculated, and the slider is set to the original value of the constant. These minimum, maximum and current values can all be edited directly, as well.
  • Drag the slider to vary the selected constant. The curves/surfaces will smoothly animate in response to the sliders motion. At the same time, the current value display will change to reflect the new value, and the full modified expression is shown below the slider with the selected constant highlighted.
  • Click and drag the 2D display window to shift the graphed region. Both displays update in real time as the 2D surface is dragged. Zoom controls below the modified expression display can also be used.
  • Click and drag the 3D display to change the viewing angle. The colors of visual elements can be changed, as well, to improve contrast/visibility.

Expression Syntax

The expressions accepted by Pebbles are case-insensitive ('SIN' works as well as 'sin'), but, as indicated below, both upper and lower case E's are valid operators ('E' is the exponential operator, shorthand for 'times ten to the power of', and 'e' is the natural log constant 2.71828...) so care must be taken. Blank spaces are accepted. Implied multiplication is recognized, but unequivocal use of parentheses is strongly encouraged.

The tables below list the operators accepted by all OneStone Pebbles.

Basic Math Operators

+ -
* /
( )
ln   log  
  E   ^
abs sqrt

Constants

  e  
pi

Trig Operators

sin arcsin
  cos     arccos  
tan arctan

Hyperbolic Trig Operators

sinh arcsinh
  cosh     arccosh  
tanh arctanh

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