Directions¶
Direction
objects represent a rotation starting from an initial point in KSP‘s coordinate system where the initial state was looking down the \(+z\) axis, with the camera “up” being the \(+y\) axis. This exists primarily to enable automated steering.
In your thinking, you can largely think of Directions as being Rotations and Rotations as being Directions. The two concepts can be used interchangeably. Used on its own to steer by, a rotation from the default XYZ axes of the universe into a new rotation does in fact provide an absolute direction, thus the name Direction for these objects even though in reality they are just Rotations. It’s important to know that Directions are just rotations because you can use them to modify other directions or vectors.
Note
When dealing with Directions (which are Rotations) in kOS, it is important to remember that KSP uses a lefthanded coordinate system. This affects the convention of which rotation direction is positive when calculating angles.
Creation¶
Method  Description 

R(pitch,yaw,roll) 
Euler rotation 
Q(x,y,z,rot) 
Quaternion 
HEADING(dir,pitch,roll) 
Compass heading 
LOOKDIRUP(lookAt,lookUp) 
Looking along vector lookAt, rolled so that lookUp is upward. 
ANGLEAXIS(degrees,axisVector) 
A rotation that would rotate the universe around an axis 
ROTATEFROMTO(fromVec,toVec) 
A rotation that would go from vectors fromVec to toVec 
FACING  From SHIP or TARGET 
UP  From SHIP 
PROGRADE, etc.  From SHIP, TARGET or BODY 

R
(pitch,yaw,roll)¶ A
Direction
can be created out of a Euler Rotation, indicated with theR()
function, as shown below where thepitch
,yaw
androll
values are in degrees:SET myDir TO R( a, b, c ).

Q
(x,y,z,rot)¶ A
Direction
can also be created out of a Quaternion tuple, indicated with theQ()
function, passing it the x, y, z, w values of the Quaternion. The concept of a Quaternion uses complex numbers and is beyond the scope of the kOS documentation, which is meant to be simple to understand. It is best to not use the Q() function unless Quaternions are something you already understand.SET myDir TO Q( x, y, z, w ).

HEADING
(dir,pitch,roll)¶ A
Direction
can be created out of aHEADING()
function. The first parameter is the compass heading, and the second parameter is the pitch above the horizon:SET myDir TO HEADING(degreesFromNorth, pitchAboveHorizon).
The third parameter, roll, is optional. Roll indicates rotation about the longitudinal axis.

LOOKDIRUP
(lookAt,lookUp)¶ A
Direction
can be created with the LOOKDIRUP function by using two vectors. This is like converting a vector to a direction directly, except that it also provides roll information, which a single vector lacks. lookAt is a vector describing the Direction’s FORE orientation (its local Z axis), and lookUp is a vector describing the direction’s TOP orientation (its local Y axis). Note that lookAt and lookUp need not actually be perpendicualr to each other  they just need to be nonparallel in some way. When they are not perpendicular, then a vector resulting from projecting lookUp into the plane that is normal to lookAt will be used as the effective lookUp instead:// Aim up the SOI's north axis (V(0,1,0)), rolling the roof to point to the sun. LOCK STEERING TO LOOKDIRUP( V(0,1,0), SUN:POSITION ). // // A direction that aims normal to orbit, with the roof pointed down toward the planet: LOCK normVec to VCRS(SHIP:BODY:POSITION,SHIP:VELOCITY:ORBIT). // Crossproduct these for a normal vector LOCK STEERING TO LOOKDIRUP( normVec, SHIP:BODY:POSITION).

ANGLEAXIS
(degrees,axisVector)¶ A
Direction
can be created with the ANGLEAXIS function. It represents a rotation of degrees around an axis of axisVector. To know which way a positive or negative number of degrees rotates, remember this is a lefthanded coordinate system:// Pick a new rotation that is pitched 30 degrees from the current one, taking into account // the ship's current orientation to decide which direction is the 'pitch' rotation: // SET pitchUp30 to ANGLEAXIS(30,SHIP:STARFACING). SET newDir to pitchUp30*SHIP:FACING. LOCK STEERING TO newDir.
Note
The fact that KSP is using a lefthanded coordinate system is important to keep in mind when visualizing the meaning of an ANGLEAXIS function call. It affects which direction is positive when calculating angles.

ROTATEFROMTO
(fromVec,toVec)¶ A
Direction
can be created with theROTATEFROMTO
function. It is one of the infinite number of rotations that could rotate vector fromVec to become vector toVec (or at least pointing in the same direction as toVec, since fromVec and toVec need not be the same magnitude). Note the use of the phrase “infinite number of”. Because there’s no guarantee about the roll information, there are an infinite number of rotations that could qualify as getting you from one vector to another, because there’s an infinite number of roll angles that could result and all still fit the requirement:SET myDir to ROTATEFROMTO( v1, v2 ).

Suffix terms from other structures
A
Direction
can be made from many suffix terms of other structures, as shown below:SET myDir TO SHIP:FACING. SET myDir TO TARGET:FACING. SET myDir TO SHIP:UP.
Whenever a Direction
is printed, it always comes out showing its Euler Rotation, regardless of how it was created:
// Initializes a direction to prograde
// plus a relative pitch of 90
SET X TO SHIP:PROGRADE + R(90,0,0).
// Steer the vessel in the direction
// suggested by direction X.
LOCK STEERING TO X.
// Create a rotation facing northeast,
// 10 degrees above horizon
SET Y TO HEADING(45, 10).
// Steer the vessel in the direction
// suggested by direction X.
LOCK STEERING TO Y.
// Set by a rotation in degrees
SET Direction TO R(0,90,0).
Structure¶

structure
Direction
¶ The suffixes of a
Direction
cannot be altered, so to get a newDirection
you must construct a new one.Suffix Type Description PITCH
scalar
(deg)Rotation around \(x\) axis YAW
scalar
(deg)Rotation around \(y\) axis ROLL
scalar
(deg)Rotation around \(z\) axis FOREVECTOR
Vector
This Direction’s forward vector (z axis after rotation). VECTOR
Vector
Alias synonym for FOREVECTOR
TOPVECTOR
Vector
This Direction’s top vector (y axis after rotation). UPVECTOR
Vector
Alias synonym for TOPVECTOR
STARVECTOR
Vector
This Direction’s starboard vector (z axis after rotation). RIGHTVECTOR
Vector
Alias synonym for STARVECTOR
INVERSE
Direction
The inverse of this direction. 
(unary minus)Direction
Using the negation operator 
on a Direction does the same thing as using the :INVERSE suffix on it.The
Direction
object exists primarily to enable automated steering. You can initialize aDirection
using aVector
or aRotation
.Direction
objects represent a rotation starting from an initial point in KSP‘s coordinate system where the initial state was looking down the \(+z\) axis, with the camera “up” being the \(+y\) axis. So for example, aDirection
pointing along the \(x\) axis might be represented asR(0,90,0)
, meaning the initial \(z\)axis direction was rotated 90 degrees around the \(y\) axis.If you are going to manipulate directions a lot, it’s important to note that the order in which the rotations occur is:
 First rotate around \(z\) axis.
 Then rotate around \(x\) axis.
 Then rotate around \(y\) axis.
What this means is that if you try to
ROLL
andYAW
in the same tuple, like so:R(0,45,45)
, you’ll end up rolling first and then yawing, which might not be what you expected. There is little that can be done to change this as it’s the native way things are represented in the underlying Unity engine.Also, if you are going to manipulate directions a lot, it’s important to note how KSP‘s native coordinate system works.

Direction:
FOREVECTOR
¶ Type: Vector
Access: Get only Vector
of length 1 that is in the same direction as the “lookat” of this Direction. Note that it is the same meaning as “what the Z axis of the universe would be rotated to if this rotation was applied to the basis axes of the universe”. When you LOCK STEERING to a direction, that direction’s FOREVECTOR is the vector the nose of the ship will orient to. SHIP:FACING:FOREVECTOR is the way the ship’s nose is aimed right now.

Direction:
TOPVECTOR
¶ Type: Vector
Access: Get only Vector
of length 1 that is in the same direction as the “lookup” of this Direction. Note that it is the same meaning as “what the Y axis of the universe would be rotated to if this rotation was applied to the basis axes of the universe”. When you LOCK STEERING to a direction, that direction’s TOPVECTOR is the vector the roof of the ship will orient to. SHIP:FACING:TOPVECTOR is the way the ship’s roof is aimed right now.

Direction:
STARVECTOR
¶ Type: Vector
Access: Get only Vector
of length 1 that is in the same direction as the “starboard side” of this Direction. Note that it is the same meaning as “what the X axis of the universe would be rotated to if this rotation was applied to the basis axes of the universe”. When you LOCK STEERING to a direction, that direction’s STARVECTOR is the vector the right wing of the ship will orient to. SHIP:FACING:STARVECTOR is the way the ship’s right wing is aimed right now.
Operations and Methods¶
You can use math operations on Direction
objects as well. The next example uses a rotation of “UP” which is a system variable describing a vector directly away from the celestial body you are under the influence of:
Supported Direction Operators:
Direction Multiplied by Direction:  

// A direction pointing along compass heading 330, by rotating NORTH by 30 degrees around UP axis:
SET newDir TO ANGLEAXIS(30,SHIP:UP) * NORTH.


Direction Multiplied by Vector:  
// What would the velocity of your ship be if it was angled 20 degrees to your left?
SET Vel to ANGLEAXIS(20,SHIP:TOPVECTOR) * SHIP:VELOCITY:ORBIT.
// At this point Vel:MAG and SHIP:VELOCITY:MAG should be the same, but they don't point the same way


Direction Added to Direction:  
It’s supposed to perform a Euler rotation of one direction by another, but it’s preferred to use 
For vector operations, you may use the :VECTOR
suffix in combination with the regular vector methods:
SET dir TO SHIP:UP.
SET newdir TO VCRS(SHIP:PROGRADE:VECTOR, dir:VECTOR)
The Difference Between Vectors and Directions¶
There are some consequences when converting from a Direction
to a Vector
and vice versa which should not be overlooked.
AVector
and aDirection
can be represented with the exact same amount of information: a tuple of 3 floating point numbers. So you might wonder why it is that aVector
can hold information about the magnitude of the line segment, while aDirection
cannot, given that both have the same amount of information. The answer is that aDirection
does contain one thing aVector
does not. ADirection
knows which way is “up”, while aVector
does not. If you tell kOS toLOCK STEERING
to aVector
, it will be able to point the nose of the vessel in the correct direction, but won’t know which way you want the roof of the craft rotated to. This works fine for axial symmetrical rockets but can be a problem for airplanes.
Therefore if you do this:
SET MyVec to V(100,200,300).
SET MyDir to MyVec:DIRECTION.
Then MyDir
will be a Direction
, but it will be a Direction
where you have no control over which way is “up” for it.