Rotation Tab

Figure 3 shows the rotation tab GUI. The rotation interface has several sets of text boxes and slider controls organized into colorized groups based on whether the data is input or output. The input groups are colored brown, while the output groups are colored blue. The only input text boxes are for the Euler angles and for the vector to

be rotated. All other text boxes are read-only for displaying output. Changing the quaternion components can be done using the quaternion slider controls. Each Euler angle also has a slider control that can be used to vary the input angle. The nine rotation matrix sliders are read-only. All of the GUI slider controls automatically update to indicate the relative value of the quantity being displayed in the associated text box. The rotation quaternion is continuously normalized with any changes in the GUI input.

The upper and lower limits for the Euler angle sliders also vary depending on the rotation order choice. Those limits are set to ensure that there are no ambiguities when converting from the quaternion back to Euler angles. Euler angle singularities (i.e., gimbal lock) is properly handled by QuatView, and a red text box indicator is displayed whenever singularities occur as shown in Figure 4. When a singular condition does occur, then rotations about one Euler axis are frozen and the rotations about the remaining two Euler axes have an identical effect. This condition is commonly referred to as "gimbal lock", and is one major reason to avoid using Euler angles if the second angle is near ±90°. Note that the quaternion is not affected by the Euler angle singularity and all of the quaternion components can freely vary between -1 and +1 without any numerical instabilities.

The 3D orientation display shows a selectable 3D object with three colored lines that represent the rotated body (Frame B) coordinate axes. The body direction 1 axis is colored green, direction 2 is colored red, and direction 3 is colored blue. The quaternion axis is also displayed as a yellow line. The reference or fixed frame (Frame A) is displayed using black lines with the axes labeled 1, 2, and 3. The orientation of the 3D object and its Frame B axes changes as the Euler angles or quaternion components are varied by the user. The available 3D object geometries include a cube, cylinder, cone, and sphere.

The bottom left of the rotation GUI has a set of edit boxes where the user can enter a vector. This input vector is tied to Frame B by default. So as Frame B rotates the components of the vector as seen from Frame A will change. The group labeled "Vector Output (...)" then displays the rotated vector components from the perspective of the unrotated frame (Frame A). The user can also optionally specify the input vector to be tied to Frame A in which case the "Vector Output (...)" group will display the fixed vector components from the perspective of the rotated frame (Frame B). Optionally, the input vector can also be plotted in the 3D display.

The rotation tab GUI responds to the following mouse events: left mouse click, left mouse double click, right mouse click, and right mouse double click. The effects of these mouse events vary depending on the mouse location as described below.

Double clicking the left mouse button over the Euler angle input group results in all three angles being reset to zero. Likewise, double clicking over the quaternion input group results in the quaternion being reset to [1,0,0,0]. Double clicking over the 3D display group resets the reference coordinate system back to its default orientation.

A right mouse context menu provides copy and paste commands for any of the input or output groups. These copy and paste commands process all of the separate text box values at once. This allows the user to copy and paste a complete quaternion, rotation matrix, or set of Euler angles at once, instead of having to copy and paste the data from each individual text box.

The right mouse context menu also provides options for performing mathematical operations on the Euler angles, quaternion, and rotation matrix. These operations include negation, transpose, complex conjugate, reverse order, animation, and reset. Figure 5 shows the Euler angle context menu, and Figure 6 shows the DCM context menu.

A main context menu is displayed if the cursor is located outside any of the input or output groups when the right mouse button is pressed. The main context menu duplicates the six link buttons along the lower right of the GUI. This can be useful if on systems with small screen displays that are too small vertically to display all the link buttons along the bottom of the GUI.

The 3D orientation display responds to the left mouse move and right mouse move commands. The left mouse move rotates the reference coordinate system (Frame A) with axes labeled as 1, 2, and 3. The right mouse move scales the display. The mouse wheel, if available, also scales the 3D display. Double clicking restores the orientation and scale factor back to their default values.

Animation is activated using the Euler angle right mouse menu. This same menu starts and stops the animation. The animation can also be stopped by clicking "Stop Animation" link on the bottom portion of the GUI outside of the two tabbed regions. The animation speed for each of the three Euler axes is selected using the Options dialog shown in Figure 7. Setting the speed to zero for a given axis disables rotation about that axis. Two animation styles are available: continuous and bounce.

Pressing the Options link button will display the Options dialog as shown in Figure 7. This dialog allows the user to select the number of decimal digits to display, the animation speed for each Euler axis, the vector initial reference frame, the 3D object geometry, and whether or not to keep the Euler angles constant when changing the rotation order. An option is also available to plot the input vector and select a plot color for the vector.

All of the program options are automatically saved in a standard user configuration file so that the options are restored between program sessions. A reset link is provided just below the OK button so that the user can reset all the options to their default values.