Introduction | Time Tool | Vector Geometry Tool | Calculation Tool | Spatial Analysis Tool

STK Analysis Workbench Tools

Vector Geometry Tool (VGT)

The Vector Geometry Tool includes components of the following basic types:

Vector Geometry Tool Components
Icon	Name	Description
	Vector	Defines direction in 3D space as well as magnitude.
	Axes	Defines orientation and rotational motion of a triad of mutually orthogonal unit vectors in three-dimensional space.
	Point	Defines location and translation motion in three-dimensional space.
	System	Defines location and translation motion of the origin and orientation and rotational motion of a triad of mutually orthogonal unit vectors in three-dimensional space.
	Angle	Defines angular separation between two vectors or planes.
	Plane	Defines location and translation motion of the origin and orientation and rotational motion of a two-dimensional plane in three-dimensional space.

All of these types define geometric components with time-varying placement and/or orientation in 3D space. The basic types of components in VGT and their use in STK remain unchanged since previous versions of STK. However, several new specific types of components have been added, in particular the ones that utilize components from the Time and Calculation tools.

Vector Geometry Tool Component Types

The Geometry Component Add/Edit windows enable you to specify various properties of a component that you have added or selected for modification.

Shared Component Properties

The components in STK's Analysis Workbench capability share a number of properties as listed below that you can access when adding or modifying components.

Component Properties
Option	Description
Type	Click Select... to display the list of available component types.
Name	Displays the name of the selected component or allows the naming of a newly created component. When naming new components, STK will replace spaces with an underscore and invalid characters with a hyphen.
Parent	Displays the component's parent object. Click Select... to change or select the component's parent object.
Description	This is an editable field that you may add descriptive text to.
Type Description	This is a read-only field that contains a short description of the component type.

Defining Vectors

The Vector Geometry Tool provides the following ways of defining a vector:

Type	Description
Acceleration	Defined as an acceleration vector along the trajectory of a specified point with respect to a reference system.
Angle Rate	Defined as an angular velocity vector orthogonal, in the right-handed sense, to changes in the specified angle.
Angular Velocity	Angular velocity vector of one set of axes computed with respect to the reference set. Click each Select... button and choose the desired sets of axes.
Apoapsis	Vector from the center of the specified central body to the farthest point of an elliptical orbit created from the motion of the specified point. At any time, the orbit is fit to the current motion of the specified point according to the specified type orbital elements. Available types are: osculating, Brouwer-Lyddane long and short, and Kozai.
Coning	Vector created by revolving the Reference vector around the About vector with the specified rate. The vector is aligned with the Reference vector at the specified epoch. After that, it revolves between the specified start and stop angles using either the unidirectional or bidirectional mode.
Cross Product	Cross product vector created from two specified vectors. Includes an option to either normalize or directly assign the resulting vector dimension.
Custom Inline Script	Vector using scripted inline function in MATLAB, VBScript, or JScript that defines values and rates. Inline functions are used for simple calculations. Click Set Arguments and Expressions... to supply the X, Y, and Z value functions and derivative functions to be evaluated, the arguments to be used by the functions, and the unit dimension of the calculated value. When computed, STK creates a function with the inputs listed under Arguments, returning the values computed by the value and derivative functions. For more information, see Setting Arguments and Expressions.
Custom Script	Customized vector components defined with respect to reference axes. Click Select... to choose the reference axes, vector script file, and initialization script file. The initialization script file is run once, at the beginning of calculation. You can use it, for example, to establish certain values that are not otherwise influenced by the vector script file that you select. See Vector Geometry Tool Plugin Points.
Derivative	Derivative of a vector computed with respect to specified axes. Click each Select... and choose the desired base vector and reference axes. The value of the Derivative is normally computed using analytic formulas. However, you can force the use of numerical differences using the checkbox. Numerical differences are always used to compute the derivative of this Derivative component. The differencing time step is used when computing the numerical differences. When possible, a second-order differencing formula is used (e.g., central differencing).
Displacement	Vector defined by its start and end points. Click each Select... and choose the terminal points. To take light speed delay into account, from the perspective of the start point, select the Apparent box, which will enable the Ignore Aberration, Signal Sense, and Reference System controls. Select Ignore Aberration if you don't want to calculate the aberration correction. Define the sense of the signal transmission at the start point using the Signal Sense field, and define the frame in which the light time delay is computed using the Reference System field.
Displacement on Surface	Vector defined at the origin VGT point in the direction of geodesic on the Central Body surface, connecting that point with the destination VGT point. The vector is defined as a sum of two vectors: one is in the local horizontal plane at the origin point directed along the initial geodesic direction connecting two points with magnitude equal to the surface distance along geodesic; the other is along local vertical at the origin point with magnitude defined by the difference in altitudes between two points.
File	A vector specified by data from a vector file (*.vd). Click the Filename field ellipsis (...) button and enter the desired path and filename.
Eccentricity	Vector directed from the center of the specified central body toward the nearest point of an elliptical orbit created from the motion of the specified point. At any time, the orbit is fit to the current motion of the specified point according to the specified type orbital elements. Available types are: osculating, Brouwer-Lyddane long and short, and Kozai. The vector’s magnitude is equal to the current eccentricity of the fit orbit.
Fixed at Epoch	Based on another vector fixed at a specified epoch. Enter the desired epoch in the provided textbox, and click Select... and choose the desired vector from the list.
Fixed at Time Instant	Defined by evaluating a source vector with respect to reference axes at a specified time instant.
Fixed in Axes	Vector fixed in reference axes. Click Select... and choose the desired reference axes. Select the Spherical coordinate type and enter Right Ascension, Declination, and Magnitude, or select Cartesian and enter the X, Y, and Z components.
Force Model	Vector representing force model components per unit mass. Set the Central Body and Scale Factor, and click Force Model... to set the force model parameters. The Scale Factor field enables you to scale the vector to ensure that it shows, as the forces modeled using this vector are often very small and may fall below the display threshold.
Intersection	Defined along the intersection of two planes. Click Select... to choose Planes A and B.
Line of Nodes	Unit vector along the line of nodes, the line of intersection of the osculating orbit plane and the equator fixed to the specified central body. The vector is directed along the cross product of the Z axis of the central body fixed coordinate system and the osculating orbit normal, which is the instantaneous osculating orbit of the specified point with respect to the specified central body.
Linear Combination	A vector defined as a linear combination of two specified vectors.
Linear Scalar Combination	A vector defined as a linear combination of two specified vectors additionally scaled by scalars.
Model Attachment	Unit vector along the specified pointable element of the object’s 3D model. The vector’s direction follows the model as well as any articulations that affect the specified pointable element. The Model Attachment type is not valid as a template.
Orbit Angular Momentum	Vector perpendicular to the plane of an elliptical orbit created from the motion of the specified point with respect to the center of the specified central body. At any time, the orbit is fit to the current motion of the specified point according to the specified type orbital elements. Available types are: osculating, Brouwer-Lyddane long and short, and Kozai. The vector’s magnitude is equal to the current orbit angular momentum of the specified point with respect to the specified central body.
Orbit Normal	Unit vector perpendicular to the plane of an elliptical orbit created from the motion of the specified point with respect to the center of the specified central body. At any time, the orbit is fit to the current motion of the specified point according to the specified type orbital elements. Available types are: osculating, Brouwer-Lyddane long and short, and Kozai. The unit vector is directed along the current orbit angular momentum of the specified point with respect to the specified central body.
Periapsis	Vector from the center of the specified central body to the nearest point of an elliptical orbit created from the motion of the specified point. At any time, the orbit is fit to the current motion of the specified point according to the specified type orbital elements. Available types are: osculating, Brouwer-Lyddane long and short, and Kozai.
Plugin	Vector based on a custom computation you defined implemented as a COM component. The Plugin type is not valid as a template.
Projection	A projection of a vector computed with respect to a reference plane. Click Select... to specify the Source Vector and Reference Plane.
Projection Along Vector	Defined as a projection of a specified vector onto a direction of reference vector.
Reflection	Incident vector reflected using a plane whose normal is the normal vector, scaled by a factor. The selected vector or its opposite can be reflected on just one or on both sides of the plane. Click Select... to specify the Incident Vector (the reflecting vector) and the Normal Vector (the reflection surface). Clear the Use Opposite of Selected Vector check box to set the direction of the Incident Vector to default. Set the Scale Factor to the desired value. Select the Allow Backside Reflections check box to reflect the incident vector on both sides of the plane.
Rotation Vector	A rotation vector represents the rotation from a reference set of axes to another set of axes. The direction of the vector specifies the rotation axis; the magnitude of the vector specifies the rotation angle, which is always nonnegative. If the rotation must be a minimum rotation, then the direction may need to flip to ensure that the angle remains less than or equal to180 degrees.
Scaled	This is the scaled version of the input vector. Enter a value for the scaling multiple; select Normalize to convert the input vector to a unit vector before scaling it.
Scaled by Scalar	Defined as an input reference vector scaled by scalar.
Scheduled	Defined by a schedule of switching between on and off vectors. Both on and off vectors must be simultaneously available for the scheduled vector to exist at that time. You can choose to apply a slew between them and also apply a timing condition. For more information, see Slew Options. If the resulting vector is set to be normalized, then the value of the vector is a unit vector along the On or Off scheduled vector, or the direction of the slew between them. If not normalized, the value being returned is the value from the On and Off vector or an interpolated value during slewing. For the magnitude of the vector during slewing, STK interpolates from the magnitudes at the beginning and end of the slew. STK assigns the dimension of the vector as that of the OnSchedule vector, even when using the value from the OffSchedule vector. When you use a condition, On schedule becomes the satisfaction time interval of the condition when evaluated over the Interval List set by the Schedule setting. The satisfaction intervals of the condition are a subset of the condition calculation scalar's availability intervals.
To Star	Defined with respect to a star object. For a star object to be available, you must first create one.
To Vector	A displacement vector between origin and destination object points. To Vectors are automatically generated by STK for all objects in your scenario. The vectors are stored in a separate folder labeled, To Vectors, unless a vector with the same name already exists (Earth or Sun). In scenarios with many objects, the To Vectors folder can be very large for each object; you can select whether or not to display the To Vectors using the Show To-Vectors check box.
Velocity	Defined as a velocity vector along the trajectory of a specified point with respect to a reference system.

Defining Axes

A set of axes can be defined in any of the following ways:

Type	Description
Aligned and Constrained	Axes aligned using two pairs of vectors. One vector in each pair is fixed in these axes and the other vector serves as an independent reference. For each pair of vectors: Click Select... and choose a reference vector. Select the desired orientation system (Spherical, Cartesian, Euler Angles or PR Angles) and specify the applicable parameters. To modify the labels (X, Y, and Z) of the axes, click Labels....
Angular Offset	Axes created by rotating the Reference axes about the Spin vector through the specified rotation angle plus the additional rotational offset.
B-Plane	This is the B-plane axes using the selected target body and reference vector. Define the Direction and Target Body using the dropdown lists, and Trajectory and Reference Vector by clicking Select....
Custom Inline Script	Axes using scripted inline function in MATLAB, VBScript, or JScript that defines values and rates. Inline functions are used for simple calculations. Click Set Arguments and Expressions... to supply the EulerA, EulerB, and EulerC value functions to be evaluated, and the arguments to be used by the functions. When computed, STK creates a function with the inputs listed under Arguments, returning the values computed by the value and derivative functions. For more information, see Setting Arguments and Expressions.
Custom Script	Customized axes offset with respect to a set of reference Axes. Click Select... and choose the reference axes. Click the ellipsis (...) button to select the desired MATLAB (.m ) or VB Script (.vbs) script file. See Vector Geometry Tool Plugin Points.
Fixed at Epoch	Axes based on another set fixed at a specified epoch. Enter the desired epoch in the provided textbox, and click Select... and choose the desired set of axes from the list.
Fixed at Time Instant	Defined by evaluating a source axes with respect to a reference axes at a specified time instant.
Fixed in Axes	These are axes fixed in reference axes. Click Select... and choose the desired reference axes. Select the desired orientation system (Quaternion, Euler Angles, or YPR Angles) and specify the applicable parameters.
File	These are axes specified by data from an attitude file (*.a). Click the Filename field ellipsis (...) button and enter the desired path and filename.
Libration	Libration point axes using one primary and multiple secondary central bodies. Set primary and secondary bodies, and point type.
Model Attachment	These are axes aligned with the specified pointable element of the object’s 3D model. The axes follow the model as well as any articulations that affect the specified pointable element. The Model Attachment type is not valid as a template.
Plugin	These are axes based on a custom computation you defined implemented as a COM component. The Plugin type is not valid as a template.
Scheduled	Defined by a schedule of switching between and On and Off axes. You can choose to apply a slew between them and use an additional timing condition. When you use a condition, the On schedule becomes the satisfaction time intervals of the condition when evaluated over the Interval List set by the Schedule setting. The condition's satisfaction intervals are a subset of the condition calculation scalar's availability intervals. For more information, see Slew Options.
Spinning	These are axes created by spinning the Reference axes about the Spin vector with the specified rate. The axes are aligned with the Reference axes at the specified epoch plus the additional rotational offset. After that the axes spins about the Spin vector with the specified rate.
Surface	These are topocentric axes defined at a surface location under a specified reference point.
Trajectory	These are axes based on the trajectory of a point relative to the reference coordinate system.

Defining Points

The following options are provided for the definition of points.

Type	Description
B-Plane	B-plane point using the selected target body. Define the Direction, Target Body, and Type using the dropdown lists, and Trajectory by clicking Select....
Central Body Grazing	The grazing point is the point on the central body surface at the horizon from the reference point, in the plane spanned by the position vector of the reference point and the direction vector, raised in altitude to the specified value. An altitude specification of zero indicates the horizon point itself. Prior to STK 10, this point type was named "CB Grazing".
Central Body Intersection	This intersection is based on intersecting a ray along a specified vector originating from a specified reference point with a selected Central Body. Includes options to handle intersections at altitude and on terrain as well as limiting intersections to be within specified ranges from the reference Point. Intersections of the surface from outside to inside are always reported. To report intersections from inside to outside, set the Allow Intersections From Below option to be true. This is appropriate when the surface is at an altitude above the central body shape. This option does not apply when terrain sets the intersection surface. Sensor and communication subobjects are automatically equipped with two instances of this type of point using Boresight Vector: one intersecting with Central Body ellipsoid and the other intersecting with terrain.
Custom Inline Script	Point using scripted inline function in MATLAB, VBScript, or JScript that defines values and rates. Inline functions are used for simple calculations. Click Set Arguments and Expressions... to supply the X, Y, and Z value functions and derivative functions to be evaluated, and the arguments to be used by the functions. When computed, STK creates a function with the inputs listed under Arguments, returning the values computed by the value and derivative functions. For more information, see Setting Arguments and Expressions.
Fixed at Epoch	Defined by evaluating a source point with respect to a reference system at a specified epoch.
Fixed at Time Instant	Defined by evaluating the source point with respect to a reference system at a specified time instant.
Fixed in System	This is a point fixed in a reference coordinate system. Click Select... and choose the desired reference system. Select the Spherical coordinate type and enter Right Ascension, Declination, and Magnitude, or select Cartesian and enter the X, Y, and Z components.
Fixed on Central Body	This is a point fixed with respect to selected central body using Detic or Centric coordinates. It includes options of using reference ellipsoid or terrain as references for these coordinates. Available for Central Bodies and STK Planet objects.
File	This is a point specified by data from an ephemeris file (*.e). Click the ellipsis (...) button and select the desired path and filename.
Glint	This is a point on central body surface that reflects from source to observer. Pick the central body from the drop-down menu, and click the Select... buttons to pick the Source and Observer points. For the glint point computation to converge, the angle between the line of sight from the central body to the source and from the central body to the observer must be greater than 0.01 degrees.
Intersection	This is a point on a plane located along a given direction looking from a given origin. Specify the Direction Vector, Reference Plane, and Origin Point.
Libration	This is a Libration point using one primary and multiple secondary central bodies. Set the central body, secondary central bodies, and point type.
Model Attachment	This is a point placed at the specified attachment point of the object’s 3D model. The point follows the model as well as any articulations that affect the specified attachment point. The Model Attachment type is not valid as a template.
Plugin	This is a point based on a custom computation you defined implemented as a COM component. The Plugin type is not valid as a template.
Position Covariance Grazing	The grazing point is the point of closest approach to the surface of the specified position covariance ellipsoid surface along a defined direction. Position covariance must be available for a vehicle object to be considered a possible target for this option. The position covariance ellipsoid is computed based on the specification of either a 3D probability level — probability that the true position is inside the ellipsoid boundary — or a scale factor that is applied to the one sigma ellipsoid. To define a grazing point, start by selecting the target object about which the covariance ellipsoid is centered and specify the means for computing the position covariance ellipsoid. Next, define a reference point that will serve as the starting location for the line along which the grazing point will be computed. Next, define a direction to be used in conjunction with the displacement vector from the selected target object to the reference point to define a plane in which the line will lie. The grazing point will be computed starting with the line aligned with the specified direction, then rotating the line in the plane until the point of closest approach to the covariance ellipsoid surface occurs at the specified distance. A distance specification of zero indicates that the line will “graze” the covariance ellipsoid. Prior to STK10, this Point type was named "Cov Grazing". The Position Covariance Grazing type is not valid as a template.
Projection	The projection of a point onto a reference plane. Specify the Source Point and Reference Plane.
SatelliteCollection	The point location is defined by a satellite within the SatelliteCollection.
Surface	The detic subpoint of the reference point as projected onto the central body.

Defining Coordinate Systems

The following options are provided for the definition of coordinate systems.

Type	Description
Assembled	This is a system assembled from an origin point and a set of reference axes. Click Select... and choose an origin point and a set of reference axes.
Surface	This is a system with an origin on the surface of the central body with topocentric axes rotated on a clock angle. Specify the central body, angle, and the latitude, longitude, and altitude of the origin.

Defining Angles

The following options are provided for the definition of angles with respect to vectors:

Type	Description
Between Planes	Defines an angle between two planes. Click each Select... button and choose the To and From planes.
Between Vectors	Defines an angle between two vectors. Click each Select... button and choose the To and From vectors.
Dihedral Angle	Defines an angle between two vectors about an axis. Click each Select... button and choose the From, To and About Vectors. The axis of rotation for the angle can be aligned with either Positive or Negative direction of the about vector. The angle is measured in the counterclockwise (or right-handed) sense about the selected direction of the axis. The range of values defined for the angle can be set either from 0 to 360 deg or from -180 to 180 deg.
Rotation	Defines the angle of the shortest rotation between the specified From and To axes. This rotation is the eigen- (or principal) rotation between the two axes. The arc of this rotation can be drawn between the specified X, Y, or Z axes of the two sets of axes.
To Plane	Defines an angle between a vector and a plane. Click Select… to choose the Reference Vector and the Reference Plane. The angle can be computed using Signed or Unsigned options. If Signed is selected, the angle can be measured as either Positive or Negative when the reference Vector is directed toward the plane’s normal. Otherwise, the angle is measured as positive regardless of on which side of the plane the reference vector is located.

Defining Planes

The following options are provided for the definition of elements that define a plane.

Type	Description
Containing Two Vectors	Define a plane containing two vectors and a given point. Specify Vector 1 (Reference Vector), Vector 2, a Reference Point, and Axes 1 and 2 labels.
Normal	Define a plane normal to a vector at a given point. Specify the Normal Vector, the Reference Vector, the Reference Point, and Axes 1 and 2 labels.
Quadrant	Select a Quadrant from a Reference System (e.g., XY, XZ, YZ, YX, ZX, ZY). The reference point in all cases is the origin of the coordinate system. The axes are defined along the two selected axes (Axis 1 and 2) of the coordinate system. You can modify the Axis 1 and 2 labels.
Trajectory	The plane is defined on the basis of a trajectory of a selected Point with respect to a Reference System. The two axes of the plane (Axis 1 and 2) are along the relative position and towards the relative velocity, respectively. You can modify the Axis 1 and 2 labels. A Rotation Offset can be specified (see below).
Triad	Select three points — Point A, Point B, and a Reference Point — and create a plane containing all three with the first axis (Axis 1) aligned with the direction from the Reference Point to Point A and the second axis (Axis 2) toward the direction from the Reference Point to Point B. You can modify the Axis 1 and 2 labels. A Rotation Offset can be specified (see below).

For a plane created using the Trajectory or Triad option, if you do not wish to use the default directions for the axes, you can specify a Rotation Offset, which is an angle measured from x (Axis 1) away from y (Axis 2).

STK Technical Notes are available for central body reference frames supported in STK, vehicle body frames, sensor pointing types, and Vector Geometry Tool (VGT) reference frames.