StageTools - Documentation (CenterStage/Tutorial)

To make a new object, select the `New` item in the `Objects` menu. You should get a dialog box that lists various types of objects, with `Surface` the selected type. The `Object name` field is the title for the object; it will be `Surface` by default, which is fine. Hit the `OK` button. The name of the object (`Surface`) will appear in the object list at the right of `CenerStage`'s main window, and the default surface definition will appear in the definition area. If you hit the `Update` button, `CenerStage` will compute the object and display it in `Geomview`'s camera window. You have made your first object! To rotate it, press and drag the mouse button in `Geomview`'s camera window.

The information in the definition script tells `CenerStage` what the object looks like. `Surface` objects are parameterized surfaces, and you can see the definition of the function and its domain given here. The `Function` command first gives the two variables for the parametric surface (in this case, `u` and `v`). The rest of the function is a TCL script that computes the values of the variables `x`, `y` and `z` for a given set of values for the input parameters. These three values specify the position of the surface in space. In the example, we see that `x = u`, `y = v` and `z = u v`. The latter means that `z` is `u` times `v`; note that the space between `u` and `v` is required, otherwise `CenerStage` will think that this is the variable whose name is `uv`, and will report an error since that variable doesn't exist. This means that the surface is really the graph of the function f(u,v) = uv. It would also have been possible to specify this as

```    Function {u v} {
let x = u
let y = v
let z = u v
}
```
or even better, as
```     Function {x y} {
let z = x y
}
```
(Note that capitalization counts, so you must use `Function` not `function`, and the variable `X` is different from `x`).

The `Domain` command tells `CenerStage` what values of `u` and `v` to use when constructing the surface. In this case, `u` is to run from -1 to 1 and there will be 10 divisions along this direction, and similarly for `v`. This means that the domain for the surface is a 10ยด10 grid of squares forming a large square with corners at (-1,-1), (1,-1), (1,1) and (-1,1). By default, `CenerStage` will represent that domain as a solid patch, but you can change that to be any of a number of different styles using the `Domain` menu. For example, selecting the `Domain/Grid` menu would make the surface appear as a collection of lines rather than a solid surface.

In a similar way, you can change other surface attributes. For instance, setting `Shading` to `Smooth` in the `Appearance` menu tells `CenerStage` to use an interpolation method to color the faces so that the surface looks smoother. (You need to set `Domain` back to `Patch` to see this.) The transparency effect listed in this menu is not available in all implementations of `Geomview`, in particular, the X11 version.

You can control the coloring method via the `Color` menu. By default, the points on the object are colored by their height in the `z` direction, but you can change that to a number of other coloring schemes. Experimenting with these is left as an exercise for the reader.

 StageTools Documentation web pages Created: 08 Sep 2001 Last modified: 08 Sep 2001 15:58:33 Comments to: `dpvc@union.edu`