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## Tutorial VI - Transformations & Displacement

This tutorial will cover creating transformations and applying the transformations to primitives. We will create two primitives: a cylinder and a cone. The objective will be to orient and move the cone to the end of the cylinder.

Edit Transformations Dialog

This tutorial will utilize the Edit Transformations dialog which is divided into three panes: create, defined, and combine.

Create

Create pane allows the creation of the three basic transformations (scale, translate, rotate). After selecting the desired transformation from the option menu and entering the parameters, clicking the New button will create the transformation and add it to the Defined list. Basic transformations are automatically named with the type of transformation and the input data that was used to create it.

Defined

The Defined pane contains a list of all the transformations that have been previously created and are available to be applied to volumes. The Apply Matrix button will pre-multiply the selected transformation with the displacement matrix of the selected volumes. Likewise for the inverse of the selected transformation which can be applied with the Apply Inverse button.

Combine

The Combine pane is used to combine previously defined transformations into a single transformation. This is accomplished by selecting transformations in the Defined list and clicking the Add button. This will append the desired transformation to the end of the combine list. Clicking the Combine button will roll up the list of transformations into a new single transformation and prompt the user to assign the new transformation a name.

Creating the Primitives

On the CAD & Geometry panel, use the Cylinder and Cone facilities to enter the following data:

Primitives Panel Values
Cylinder First Axis Reference Point {-2, 0, 0}
Second Axis Point {2, 0, 0}
Radius 0.5
Cone Apex Reference Point {0, 0, -1}
Base Center {0, 0, 0}
Radius 0.5

The data in this table will create a cylinder with the apex of a cone protruding from the side of the cylinder. The cylinder and cone will be represented as Volume 1 and Volume 2 respectively in the Structure Tree. The following image illustrates the resulting geometry.

Creating the Transformations

To move the cone on the end of the cylinder in the positive X direction, we will need to create two transformations: a rotation about the Y-axis and then a translation in the X direction. Using the Create pane, enter the data from the following table:

Transformation Parameter Value
Rotation X 0.0
Y 1.0
Z 0.0
Angle 270.0
Translation X 2.0
Y 0.0
Z 0.0
After entering the data above, there will be two entries in the Defined list: "Rotate {0.000, 1.000, 0.000, 270.000}" and "Translate {2.000, 0.000, 0.000}".

Combining the Transformations

Basic transformations (as well as any other defined transformation) can be compiled into a single transformation matrix. This functionality provides a mechanism for building complex transformations from more primitive ones.

In our example, we want to create a single new transformation that will position the cone to the desired location. This will require the rotation and translation to be combined:

1. Select the Rotate transformation in the Defined pane.
2. Press the Add button.
3. Select the Translate transformation in the Defined pane.
4. Press the Add button.
5. Press the Combine button.
6. Enter "RotateAndTranslate" as the Transformation Name.
7. Press the Ok button.

These steps create a new transformation in the Defined pane named "RotateAndTranslate".

Applying the Transformations

Any defined transformation can be applied to any volume. Now lets apply the rolled up transformation to the cone geometry:

1. Select "RotateAndTranslate" from the Defined pane.
2. Select the volume for the cone, Volume 2.
3. Press the Apply Matrix button
The resulting geometry is displayed below.

 Responsible NASA Official: William T. Jones Site Curator: William T. Jones Comments and Questions Last Updated: Oct 2, 2003