# Parametric surfaces: a simple introduction to visualization

Parametric surfaces are particularly handy if you are unable to find any data to play with right away. Parametric surfaces are surfaces parametrized typically by 2 variables, u and v. VTK has a bunch of classes that let users explore Parametric surfaces. This functionality is also available in Mayavi. The data is a 2D surface embedded in 3D. Scalar data is also available on the surface. More details on parametric surfaces in VTK may be obtained from Andrew Maclean’s Parametric Surfaces document.

> 1. After starting mayavi2, create a simple Parametric surface source by selecting File->Load data->Create Parametric Surface source. Once you create the data, you will see a new node on the Mayavi tree view on the left that says ParametricSurface. Note that you will not see anything visualized on the TVTK scene yet.

>    You can modify the nature of the parametric surface by clicking on the node for the ParametricSurface source object.

> 2. To see an outline (a box) of the data, navigate to the Visualize->Modules menu item and select the Outline module. You can also right-click on the ParametricSurface node to bring up a context menu and select Add Module->Surface. You will immediately see a wireframe cube on the TVTK scene. You should also see two new nodes on the tree view, one called Colors and legends and one underneath that called Outline.

> 3. You can change properties of the outline displayed by clicking on the Outline node on the left. This will create an object editor window on left bottom of the window (the object editor tab) below the tree view. Play with the settings here and look at the results. For example, to change the color of the outline box modify the value in the color field. If you double-click a node on the left it will pop up an editor dialog rather than show it in the embedded object editor.

> 4. To navigate the scene look at the section on Interaction with the scene section for more details. Experiment with these.

> 5. To view the actual surface create a Surface module by selecting Visualize->Modules->Surface. You can show contours of the scalar data on this surface by clicking on the Surface node on the left and switching on the Enable contours check-box.

> 6. To view the color legend (used to map scalar values to colors), click on the Modules node on the tree view. Then, on the ‘Scalar LUT’ tab, activate the Show scalar bar check-box. This will show you a legend on the TVTK scene. The legend can be moved around on the scene by clicking on it and dragging it. It can also be resized by clicking and dragging on its edges. You can change the nature of the color-mapping by choosing among different lookup tables on the object editor.

> 7. You can add as many modules as you like. Not all modules make sense for all data. Mayavi does not yet grey out (or disable) menu items and options if they are invalid for the particular data chosen. This will be implemented in the future. However making a mistake should not in general be disastrous, so go ahead and experiment.

> 8. You may add as many data sources as you like. It is possible to view two different parametric surfaces on the same scene by selecting the scene node and then loading another parametric surface source. Whether this makes sense or not is up to the user. You may also create as many scenes you want to and view anything in those. You can cut/paste/copy sources and modules between any nodes on the tree view using the right click options.

> 9. To delete the Outline module say, right click on the Outline node and select the Delete option. You may also want to experiment with the other options.

> 10. You can save the rendered visualization to a variety of file formats using the File->Save Scene As menu.

> 11. The visualization may itself be saved out to a file via the File->Save Visualization menu and reloaded using the Load visualization menu.

Shown below is example visualization made using the parametric source. Note that the positioning of the different surfaces were effected by moving the actors on screen using the actor mode of the scene via the ‘a’ key. For more details on this see the section on Interaction with the scene.