Working with Vectors in the Vector Geometry Tool

STK Pro, STK Premium (Air), STK Premium (Space), or STK Enterprise
You can obtain the necessary licenses for this tutorial by contacting AGI Support at support@agi.com or 1-800-924-7244.

The results of the tutorial may vary depending on the user settings and data enabled (online operations, terrain server, dynamic Earth data, etc.). It is acceptable to have different results.

Capabilities covered

This lesson covers the following capabilities of the Ansys Systems Tool Kit® (STK®) digital mission engineering software:

  • STK Pro
  • Analysis Workbench

Problem statement

Engineers, analysts, and mission planners need to visualize geometric components with time-varying placement and/or orientation in 3D space for a variety of purposes. You are planning a satellite mission. You want to create both static and dynamic visual aids using vector geometry components of the vehicle's attitude, sensor pointing, and other phenomena of interest. You need a quick and easy way to visualize them clearly and intelligibly.

Solution

Use the Analysis Workbench capability's Vector Geometry tool to configure vector geometry components for the satellite. Then, use the 3D Attitude Graphics window to display an attitude sphere and other pre-built and custom components to create static and dynamic vector graphics for the mission.

What you will learn

Upon completion of this tutorial, you will understand the following:

  • How to use the Vector Geometry tool
  • How to open and use the 3D Attitude Graphics window
  • How to display vector geometry components in 3D Graphics and 3D Attitude Graphics windows
  • How to use the attitude sphere as a visualization aid
  • How to create a persistent vector display

Creating a new scenario

First, you must create a new scenario, and then build from there.

  1. Launch the STK application ().
  2. Click Create a Scenario in the Welcome to STK dialog box.
  3. Enter the following in the STK: New Scenario Wizard:
    4. Option Value
    Name AnalysisWorkbench_VGT
    Location Default
    Start Default
    Stop Default
  4. Click OK when you finish.
  5. Click Save () when the scenario loads.

    6. The STK application creates a folder with the same name as your scenario for you.

  6. Verify the scenario name and location in the Save As dialog box.
  7. Click Save.

Save () often during this scenario!

Disabling streaming terrain

By default, the STK application connects to the Ansys Geospatial Data Cloud to distribute Earth terrain data for analysis and visualization. Turn off streaming terrain, as it is not required for your analysis.

  1. Right-click on AnalysisWorkbench_VGT () in the Object Browser.
  2. Select Properties () in the shortcut menu.
  3. Select the Basic - Terrain page when the Properties Browser opens.
  4. Clear the Use terrain server for analysis check box in the Terrain Server panel.
  5. Click OK to confirm your change and to close the Properties Browser.

Modeling a satellite

For this scenario, you will model a notional satellite in a Molniya orbit. Molniya orbits are highly eccentric, meaning that there is a large difference between the altitude at apogee and the altitude of perigee. Molniya orbits are also critically inclined. This keeps the perigee of the orbit in the Southern Hemisphere. Molniya orbits also have a long dwell time in the extreme latitude regions of the Northern Hemisphere.

Inserting a Satellite object

A Satellite object models the properties and behavior of a vehicle in orbit around a central body.

  1. Bring the Insert STK Objects tool () to the front.
  2. Select Satellite () in the Select An Object To Be Inserted list.
  3. Select the Orbit Wizard () in the Select A Method list.
  4. Click Insert....

Using the Orbit Wizard

The Orbit Wizard is a satellite-level tool designed to assist you in creating any one of several standard orbits or designing your own satellite orbit.

  1. Open the Type drop-down list when the Orbit Wizard opens.
  2. Select Molniya.
  3. Enter Satellite in the Satellite Name field.
  4. Click OK to propagate the satellite and to close the Orbit Wizard.

Displaying vector graphics in the 3D Graphics window

You can control the display of geometric elements related to the satellite by updating its 3D Graphics - Vector properties.

Viewing the satellite in the 3D Graphics window

First, prepare your workspace and zoom to the Satellite object in the 3D Graphics window.

  1. Close the 2D Graphics window.

    2. It is not needed in this analysis.

  2. Right-click on Satellite () in the Object Browser.
  3. Select Zoom To in the shortcut menu.

Displaying the Velocity vector

The Analysis Workbench capability contributes an extensive list of predefined components to the STK application that you can use immediately. Start by adding the satellite's Velocity vector.

  1. Open Satellite's () Properties ().
  2. Select the 3D Graphics – Vector page when the Properties Browser opens.
  3. Select the Vectors tab.
  4. Select the Show check box for Velocity Vector in the list.

    5. The Velocity vector is defined in a Central Body Inertial (CBI) reference frame. All central bodies in the Vector Geometry tool support inertial axes.

  5. Enter 0.6000 in the Scale field in the Component Size panel, which itself is located in the Common Options panel.
  6. Click Apply to confirm your changes and to keep the Properties Browser open.

Adding a Velocity vector in a Central Body Fixed reference frame

The list on the 3D Graphics – Vector page shows only a subset of the available components. Add a Vector component defined in a Central Body Fixed (CBF) reference frame.

  1. Click Add....
  2. Select Velocity(CBF) (), located in the Installed Components () folder in the Components for: Satellite tree when the Add Components dialog box opens.

    3. Note the lock icon overlaid on the available vector components. The lock icon indicates components that come installed with the STK application. They are grouped into the Installed Components () folder and cannot be edited.

  3. Click OK to confirm your selection and to close the Add Components dialog box.

    4. Since you have added the new vector to the list, the STK application assumes that you want to display it. Therefore, the Show check box for Velocity(CBF) is already selected.

  4. Click Apply to confirm your changes and to keep the Property Browser open.

Viewing the vectors in the 3D Graphics window

View both vectors in the 3D Graphics window.

  1. Bring the 3D Graphics window to the front.
  2. Click Start () on the Animation toolbar to animate your scenario.

    3. Watch as the two vectors you defined separate, reflecting their differing reference frames (CBF and CBI).

  3. Click Pause () when the vectors have a wide degree of separation.

3D Graphics window VIEW

While you want your focus to be on the vector graphics, the display in the 3D Graphics window can be distracting: the satellite's orbit track, the lighting effects, the stars in the background, and other aspects of the 3D Graphics window can take away from the focus of your visualization. While you could customize the 3D Graphics window by modifying its properties, clear the display of imagery in the Globe Manager, and update the satellite's 3D Graphics properties to get a clearer, simplified view, there is a much easier way to achieve the desired result: by opening a 3D Attitude Graphics window.

Viewing vector graphics in the 3D Attitude Graphics window

The 3D Attitude Graphics window displays an object together with visualization aids such as vectors and an attitude sphere. It provides an easy way to visualize the attitude of a vehicle and the changes in its attitude over time. The advantage of the 3D Attitude Graphics window is that it is a simplified view: the Earth background, other scenario objects, lighting considerations, and so on are all removed in favor of a black background. You can open the 3D Attitude Graphics window with an individual object.

Opening the 3D Attitude Graphics window

Open the 3D Attitude Graphics window with the Satellite object.

  1. Right-click on Satellite () in the Object Browser.
  2. Select Satellite in the shortcut menu.
  3. Select New 3D Attitude Graphics Window () in the Satellite submenu.
  4. Use your mouse to get a look at the satellite when the 3D Attitude Graphics window opens.

    5. 3D Attitude Graphics window VIEW

    You can use your mouse to zoom and rotate in the 3D Attitude Graphics window just as you would in the 3D Graphics window. Note that the same components are simultaneously displayed for the satellite in the both the 3D Graphics and 3D Attitude Graphics windows.

Visualizing a plane

In addition to Vector components, you can also visualize Angles (), Axes (), Points (), and Planes () in the 3D Attitude Graphics window. Visualize the satellite’s body plane.

  1. Return to Satellite's () Properties ().
  2. Select the Planes tab.
  3. Select the Show check box for Body.XY Plane.

    4. The Body X-Y plane refers to the X-Y quadrant of the satellite's Body axes.

  4. Clear the Show Label check box.
  5. Enter 70 in the Translucent plane field.

    6. The plane will be 70 percent transparent.

  6. Click Apply to confirm your changes and to keep the Properties Browser open.
  7. Bring the 3D Attitude Graphics window to the front.

    8. Body XY Plane

    Note the plane's alignment with the body axes of the Satellite object.

  8. Return to Satellite's () Properties ().
  9. Clear the Show check box for Body.XY Plane.
  10. Click Apply to confirm your change and to keep the Properties Browser open.

Creating custom components with the Vector Geometry tool

The Analysis Workbench capability comprises four application-wide tools (the Vector Geometry tool, the Time tool, the Calculation tool, and the Spatial Analysis tool) that you can use to create custom components and insert them into your scenarios. They are designed to streamline, organize, and extend the fundamental computational capabilities of the STK software. You can use these tools to create components that suit your needs. The Vector Geometry tool creates geometry components with time-varying placement or orientation in 3D space, including Vectors (), Axes (), Points (), Systems (), Angles (), and Planes ().

Opening the Analysis Workbench

Access the Vector Geometry tool by opening the Analysis Workbench.

  1. Right-click on Satellite () in the Object Browser.
  2. Select Analysis Workbench... () in the shortcut menu.
  3. Select the Vector Geometry tab when the Analysis Workbench opens.

Creating a new Vector component

Create a velocity vector with the satellite body frame as its reference axes.

  1. Click Create new Vector () on the Vector Geometry toolbar.
  2. Click Type: Select... when the Add Geometry Component dialog box opens.
  3. Select Derivative () in the Select Component Type list when the Select Component Type dialog box opens.

    4. This will create a derivative of a vector computed with respect to specified axes.

  4. Click OK to confirm your selection and to close the Select Component Type dialog box.
  5. Enter Velocity(Body) in the Name field.

Viewing the base vector and reference axes

Take a look at the components that are selected for the vector and the reference axes.

  1. Click the Vector ellipsis ().
  2. Ensure Position () is selected in the Vectors for: Satellite tree when the Select Reference Vector dialog box opens.

    3. Position () is a displacement vector between the Earth's center point and the Satellite's center point.

  3. Click Cancel to close the Select Reference Vector dialog box without making any changes.
  4. Click the Reference Axes ellipsis ().
  5. Ensure Body () is selected in the Aces for: Satellite tree when the Select Reference Axes dialog box opens.
  6. Click Cancel to close the Select Reference Axes dialog box without making any changes.
  7. Click OK to confirm your changes and to close the Add Geometry Component dialog box.

The value of the Derivative vector is computed using analytic formulas.

Viewing the vector's dependency tree

The Analysis Workbench's shortcut menu provides options to examine dependencies of the selected component, which opens a new dialog box with a dependency tree that contains all components that depend on the selected component or, alternatively, all constituent components on which the selected component depends. View your new vector's dependencies using this method. While the dependency information will not be explicitly used in this exercise, you may want to make mental note of this tool for understanding and troubleshooting scenarios.

  1. Right-click on Velocity(Body) (), located in the My Components () folder in the Components for: Satellite tree.

    2. Vector components you create are editable and are grouped in the My Components () folder.

  2. Select Show Dependencies... in the shortcut menu.
  3. Note the Show dependents option is selected when the Dependency Tree opens.
  4. Note that only Satellite/Satellite Velocity(Body) () is listed in the Dependencies for Satellite Velocity(Body) Vector tree.
  5. Select the Show constituents option.

    6. The Show constituents option shows the reverse: everything on which the vector depends.

  6. Expand () all the elements in the Dependencies for Satellite Velocity(Body) Vector tree.

    7. Velocity(Body) vector Dependency Tree

    Note that there are a number of components that are automatically created when you created your Velocity(Body) vector.

  7. Click Close to close the Dependency Tree.
  8. Click Close to close the Analysis Workbench.

Displaying the Velocity(Body) vector in the 3D Attitude Graphics window

Update the satellite's 3D Graphics - Vector properties to display the Velocity(Body) vector in the 3D Attitude Graphics window.

  1. Return to Satellite's () Properties ().
  2. Select the Vectors tab.
  3. Click Add....
  4. Select Velocity(Body) (), located in the My Components () folder in the Components for: Satellite tree, when the Add Components dialog box opens.
  5. Click OK to confirm your selection and to close the Add Components dialog box.
  6. Click Apply to confirm your changes and to keep the Properties Browser open.
  7. Bring the 3D Attitude Graphics window to the front.

Velocity(Body) vector

The new vector now appears in the 3D Attitude Graphics window.

Creating a new Angle component

In addition to vectors and planes, you can display angles in the 3D Graphics and 3D Attitude Graphics windows. Use the Vector Geometry tool to create a new angle component.

  1. Return to Satellite's () Properties ().
  2. Select the Angles tab.
  3. Click Add....
  4. Click Create new Angle () on the Vector Geometry toolbar when the Add Components dialog box opens.
  5. Leave the Type set to Between Vectors when the Add Geometry Component dialog box opens.

    6. This type defines an angle between two vectors.

  6. Enter VelocityDifference in the Name field.

Selecting the angle's reference vectors

Choose the To and From vectors to define your Between Vectors angle.

  1. Click the From Vector ellipsis ().
  2. Select Velocity (), located in the Installed Components () folder in the Vectors for: Satellite tree, when the Select Reference Vector dialog box opens.
  3. Click OK to confirm your selection and to close the Select Reference Vector dialog box.
  4. Click the To Vector ellipsis ().
  5. Select Velocity(CBF) (), located in the Installed Components () folder in the Vectors for: Satellite tree, when the Select Reference Vector dialog box opens.
  6. Click OK to confirm your selection and to close the Select Reference Vector dialog box.
  7. Click OK to confirm your changes and to close the Add Geometry Component dialog box.
  8. Select VelocityDifference (), located in the My Components () folder in the Components for: Satellite tree.
  9. Click OK to confirm your changes and to close the Add Components dialog box.

Viewing the angle in the 3D Attitude Graphics window

Take a look at the angle in the 3D Attitude Graphics window.

  1. Ensure VelocityDifference Angle is selected in the list.
  2. Clear the Show label check box.
  3. Click Apply to confirm your changes and to keep the Properties Browser open.
  4. Bring the 3D Attitude Graphics window to the front.
  5. Click Start () on the Animation toolbar.
  6. Observe the changes in the angle value as the vectors defining it move apart and back together.

    7. VelocityDifference Angle

  7. Click Reset () when finished.

Adding another new angle

Now that you know how to create and display angles, add another angle between the Velocity vector and the Velocity(Body) vector.

  1. Return to Satellite's () Properties ().
  2. Click Add....
  3. Click Create new Angle () on the Vector Geometry toolbar when the Add Components dialog box opens.
  4. Leave the Type set to Between Vectors when the Add Geometry Component dialog box opens.
  5. Enter Velocity(Body)Difference in the Name field.

Selecting the angle's reference vectors

Choose the To and From vectors to define your angle.

  1. Click the From Vector ellipsis ().
  2. Select Velocity (), located in the Installed Components () folder in the Vectors for: Satellite tree, when the Select Reference Vector dialog box opens.
  3. Click OK to confirm your selection and to close the Select Reference Vector dialog box.
  4. Click the To Vector ellipsis ().
  5. Select Velocity(Body) (), located in the My Components () folder in the Vectors for: Satellite tree, when the Select Reference Vector dialog box opens.
  6. Click OK to confirm your selection and to close the Select Reference Vector dialog box.
  7. Click OK to confirm your changes and to close the Add Geometry Component dialog box.
  8. Select Velocity(Body)Difference (), located in the My Components () folder in the Components for: Satellite tree.
  9. Click OK to confirm your changes and to close the Add Components dialog box.

Viewing the angle in the 3D Attitude Graphics window

Take a look at the angle in the 3D Attitude Graphics window.

  1. Ensure Velocity(Body)Difference Angle is selected in the list.
  2. Clear the Show label check box.
  3. Click Apply to confirm your changes and to keep the Properties Browser open.
  4. Bring the 3D Attitude Graphics window to the front.
  5. Click Start () on the Animation toolbar.
  6. Observe the changes in the angles.

    7. Velocity(Body)Difference Angle

  7. Click Reset () when finished.
  8. Return to Satellite's () Properties ().
  9. Clear the Show check boxes for both VelocityDifference Angle and Velocity(Body)Difference Angle in the list.
  10. Click Apply to confirm your changes and to keep the Properties Browser open.

Using the Attitude Sphere

The attitude sphere is a visualization aid that the STK application can display in the 3D Graphics and 3D Attitude Graphics windows. It is a powerful tool for understanding an object's attitude and for tracking attitude changes over time.

Defining and displaying the attitude sphere

Update the satellite's 3D Graphics Attitude Sphere properties to display its attitude sphere.

  1. Select the 3D Graphics – Attitude Sphere page.
  2. Select the Show check box in the Attitude Sphere panel.
  3. Enter 0.700 in the Value field in the Scale panel.

    4. This is a logarithmic scaling factor for the sphere.

  4. Note the Sphere Color and Grid line width options.

    5. These control the appearance of the grid lines defining the sphere.

  5. Note the Zero Deg Color and Zero Deg line width options.

    6. These options are used to highlight the equator and prime meridian lines as desired.

  6. Note Satellite VVLH is selected for the Frame.

    7. The Frame field lets you select a reference frame for the sphere display. In the VVLH (Vehicle Velocity Local Horizontal) frame, the axes align the Z axis opposite to the position vector and the X axis toward the inertial velocity vector.

  7. Note that Earth, Sun, and Moon are selected to show in the Projections list.

    8. The Projections list lets you control the display the projection of the position of central bodies and other objects of interest on the surface of the attitude sphere. You can use projections on the Attitude Sphere to help you analyze the velocity of a satellite relative to other bodies, such as the Earth.

  8. Click Apply to confirm your changes and to keep the Properties Browser open.

Viewing the attitude sphere

As a representation of your reference frame, the Attitude Sphere may make it easier at times to understand the velocity, position, or attitude of an object. Take a look a the attitude sphere in the 3D Attitude Graphics window.

  1. Bring the 3D Attitude Graphics window to the front.
  2. Use your mouse to zoom out to get a better view of the Attitude Sphere around Satellite.
  3. Click Start () on the Animation toolbar.

    4. Attitude Sphere

  4. As the scenario animates, notice a blue circle that changes in size on the surface of the sphere.

    5. This is the projection of the Earth.

  5. Note the comparative sizes of the projections of the Sun and Moon.

    6. Unlike the Earth, the Sun and Moon projections are labeled. All three projections provide situational awareness of where they are located in respect to Satellite. For instance, if you were to draw a straight line from the center point of Satellite to the center point of the Sun, that line would pass through the middle of the Sun projection at all times.

  6. Click Reset () when finished.

Showing projection volume graphics

You can also display a projection in three dimensions.

  1. Return to Satellite's () Properties ().
  2. Select the Volume check box for Earth in the Projections panel list.
  3. Click Apply to confirm your selection and to keep the Properties Browser open.
  4. Bring the 3D Attitude Graphics window to the front.

    5. Attitude Sphere volume graphics

    The Earth's projection is now displayed as a cone.

  5. Click Start () on the Animation toolbar.
  6. Click Pause () when the satellite is at apogee.

    7. Attitude Sphere Vector graphics near apogee

    At apogee, the Earth-defined vectors (Velocity and Velocity(CBF)) will appear at approximate right angles to the Earth projection cone, as would be expected.

  7. Click Reset () when finished.
  8. Return to Satellite's () Properties ().
  9. Clear the Show check box for the attitude sphere to turn off its display.
  10. Click Apply to confirm your change and to keep the Properties Browser open.

Creating a persistent vector display

Use vector persistence options to control the way in which geometric elements appear in the 3D Graphics window as the animation time elapses and the position of those elements change.

Opening the 3D Graphics - Vector properties

You can set the vector persistence graphics on the satellite's 3D Graphics - Vector page.

  1. Select the 3D Graphics - Vector page.
  2. Select the Vectors tab.

Selecting the reference axes

Use the ICRF (International Celestial Reference Frame) for the axes that define the coordinate frame to which the display options are applied for the Velocity(CBF) and Velocity(Body) vectors. The International Celestial Reference Frame axes are defined as the inertial (i.e., kinematically nonrotating) axes associated with a general relativity frame centered at the solar system barycenter (often called the BCRF). The IAU (International Astronomical Union) is the authority for the definition of the ICRF. The ICRF is the best realization of an inertial frame constructed to date and thus represents an improvement upon the theory behind the J2000 frame. While the ICRF and J2000 frames themselves are very close, they are not identical; moreover, the J2000 frame rotates (very slowly) over time with respect to the ICRF frame. Recent star catalogs and celestial body ephemerides are most often expressed natively with respect to the ICRF frame.

  1. Clear the Show check box for Velocity(Body) Vector in the list.
  2. Select Velocity Vector in the list.
  3. Click the Axes ellipsis ().
  4. Select ICRF (), located in the Installed Components () folder in the Axes for: Satellite tree, when the Select Reference Axes dialog box opens.
  5. Click OK to confirm your selection and to close the Select Reference Axes dialog box.
  6. Select Velocity(CBF) Vector in the list.
  7. Click the Axes ellipsis ().
  8. Select ICRF (), located in the Installed Components () folder in the Axes for: Satellite tree, when the Select Reference Axes dialog box opens.
  9. Click OK to confirm your selection and to close the Select Reference Axes dialog box.

Setting the persistence options

Set the options to successively display geometric elements over a specified duration.

  1. Select Velocity Vector in the list.
  2. Select the Show check box in the Persistence panel.
  3. Select the Fade check box.

    4. When selecting the Fade option, earlier occurrences of a geometric element display will fade over time so that it is drawn as completely filled at the most recent animation time and fades as the animation moves forward.

  4. Enter 1 day in the Duration field.

    5. This sets the length of time during which the geometric element is visible.

  5. Note that Sweep is selected for the Connect option by default.

    6. When Sweep is selected, a continuous band of color representing the path of the element will be shown.

  6. Select Velocity(CBF) Vector in the list.
  7. Select the Show check box in the Persistence panel.
  8. Select the Fade check box.
  9. Enter 1 day in the Duration field.
  10. Click OK to confirm your changes and to close the Properties Browser.

Viewing the changes in the 3D Graphics window

View the changes in the 3D Graphics (not the 3D Attitude Graphics) window.

  1. Bring the 3D Graphics window to the front.
  2. Click Start () on the Animation toolbar.

    3. Persistent vector graphics

    Watch as the two velocity vectors sweep out their respective disks.

  3. Click Reset () when finished.

Changing the view direction

Update the view direction in the 3D Graphics window for a slightly different view of the action.

  1. Click View From/To () on the 3D Graphics window's 3D Graphics toolbar.
  2. Select the Along a Direction option when the View From/To dialog box opens.

    3. Using the Along a Direction viewing mode, you can set the view along an existing vector or a vector created in the Vector Geometry Tool.

  3. Ensure Satellite () is selected in the From Position list.
  4. Click Add Vector () in the Direction panel.
  5. Select Velocity (), located in the Installed Components () folder in the Vectors for: Satellite tree, when the Select Vector dialog box opens.
  6. Click OK to confirm your selection and to close the Select Vector dialog box.
  7. Select the Inward option.

    8. Selecting the Inward option will reverse the 'view from' position and the 'view direction'.

  8. Click OK to confirm your changes and to close the View From/To dialog box.

Viewing the changes in the 3D Graphics window

Animate your scenario to see the changes.

  1. Click Start () on the Animation toolbar.
  2. Use the mouse to rotate the view around the satellite.

    3. Persistent vector graphics in another reference frame

  3. Note that the Velocity vector sweeps out a flat disk while the Velocity(CBF) vector sweeps out a warped disk.

    4. This is expected, as these disks are drawn in an inertial frame.

  4. Watch as the satellite descends through its orbit.

    5. Recall that the satellite you created at the beginning of this tutorial in a Molniya orbit. On the descending side of its orbit, its motion relative to the rotating Earth is in the opposite direction to its motion on the ascending side. The motion of a vector defined in a CBF framework will reflect this difference.

  5. Click Reset () when finished.

Saving your work

Clean up and close out your scenario.

  1. Close any open tools and properties.
  2. Save () your work.

Summary

You began by inserting a notional Satellite object in a Molniya orbit. You used the Analysis Workbench capability's Vector Geometry tool, in conjunction with the satellite's 3D Graphics - Vector properties to display several built-in Vector Geometry components and to create and display custom Vector and Angle components in the 3D Attitude Graphics window. You explored the attitude sphere and its capabilities before exploring vector persistence graphics in the 3D Graphics window. Using the Vector Geometry tool, you were able to visualize the differences among vectors defined in different reference frames.