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A rotation is a variable type comprising 4 floats used together as a single item. This data is interpreted as a quaternion. As with vectors, each component can be accessed via ‘.x’, ‘.y’, ‘.z’, and ‘.s’ (not ‘.w’).

Syntax:

```float x = 0.0;
float y = 0.0;
float z = 0.0;
float s = 1.0;
rotation rot_a = <0.0, 0.0, 0.0, 1.0>;//copies these values into the respecive values of the rotation.
rotation rot_b = <x,y,z,s>;//copies the values of the variable into the rot.
rotation rot_c = rot_b;//copies the value of rot_b into rot_c```

LSL/OSSL does do some implicit typecasting but the compiler does not actualy convert types or simplify code; it just makes implicit typecasts explicit. So while <0, 0, 0, 1> is valid, it will use more bytecode and be slower than <0.0, 0.0, 0.0, 1.0>. For this reason please be sure to use a decimal point. "0." is enough, you don’t need an extra zero. However, this does lack clarity.

There are a number of ways to visualize an arbitrary rotation in three dimensions. The simplest is to think of a rotation as being equivalent to a set of 3 rotations around the x, y, and z axes (known as the Euler representation). In LSL this can be represented using the vector type, where the x element specifies the roll (angle of rotation around the x-axis), the y element specifies the pitch (angle of rotation around the y-axis), and the z element specifies the yaw (angle of rotation around the z-axis). Also see Banking.

Unfortunately, the Euler representation has drawbacks when it comes to combining rotations (see below). To avoid these problems, LSL represents rotations using mathematical entities known as quaternions, which consists of 4 elements: x, y, z, and s. Note that the x, y, and z elements do not correspond to roll, pitch, and yaw. For more information on what they represent, see the page on quaternions.

However, you can use rotations without dealing with the individual elements of quaternions. LSL offers library calls that convert between a quaternion and a vector containing the equivalent Euler representation: llEuler2Rot and llRot2Euler.

Note: LSL expects angles to be specified in terms of radians rather than degrees. A radian is the angle reached if you were to take a string the length of a circle’s radius and lay it along the circumference, approximately equal to 57.296 degrees. This ratio means that a full circle, which contains 360 degrees, is equal to 2*PI radians. Similarly, a semicircle of 180 degrees equals PI radians. LSL defines the constants DEG_TO_RAD and RAD_TO_DEG to facilitate conversion to and from degrees.

Example:

```vector eul = <0,0,45>; //45 degrees around the z-axis, in Euler form
rotation quat = llEuler2Rot(eul); //convert to quaternion
llSetRot(quat); //rotate the object```

LSL/OSSL also defines the constants PI_BY_TWO, PI, and TWO_PI to let you specify common rotations in radians directly:

```vector x_ninety = <PI_BY_TWO,0,0>; //90 degrees around the x-axis
vector y_one_eighty = <0,PI,0>; //180 degrees around the y-axis```

LSL/OSSL defines the constant ZERO_ROTATION to represent a rotation of angle zero. Calling llSetRot( ZERO_ROTATION ) orients the object so that its local axes are aligned with the global axes. The value returned by llGetRot is the object’s current orientation relative to this null rotation.

### Combining Rotations

An object is rotated by multiplying its current orientation with the desired rotation. The order in which the operands are specified depends if a rotation is performed around the global axes or the local axes.

Example:

```// a rotation of 45 degrees around the x-axis
rotation x_45 = llEuler2Rot( <45 * DEG_TO_RAD, 0, 0> );

rotation new_rot = llGetRot() * x_45;  // compute global rotation
llSetRot(new_rot);                  // orient the object accordingly```

This rotates the object around the global x-axis (the axis which runs from west to east).

Now consider the following:

```rotation new_rot = x_45 * llGetLocalRot();  // compute local rotation
llSetLocalRot(new_rot);                   // orient the object accordingly```

This rotates the object around its local x-axis, which depends on its current orientation. Think of this as specifying the rotation from the object’s point of view, that is, relative to the direction it is currently facing.

This also works Inversely by Dividing two rotations:

```rotation new_rot = x_45 / llGetRot();  // compute local rotation
llSetRot(new_rot);                   // orient the object accordingly```

Like previously, this would rotate your object along the x-axis based on its current orientation, but in the opposite direction.

When rotating a vector, the rotation must appear to the right of the vector:

```vector new_vec = old_vec * x_45; // compiles
vector new_v = x_45 * old_v; // doesn't compile```

Note: An object can be rotated around an arbitrary point by multiplying a vector by a rotation in the manner described above. The vector should be the difference between the object’s current position and the desired “center-point” of rotation. Take the result of the multiplication and add it to the point of rotation. This vector will be the “new location” the object should be moved to.

```vector currentPos = llGetPos();
vector rotPoint = llGetPos() + <1, 1, 1>; // in global coordinates
vector newPos = rotPoint + ((currentPos - rotPoint) * x_45);
llSetPos(newPos);```

Bear in mind that any translation (position) operation can result in a vector that would put the object outside of the world, or require a move further than 10 meters–so plan for these possibilities.

#### Math Functions

 Function Name Purpose llAngleBetween Returns the angle between two rotations llAxes2Rot Converts three axes to a rotation llAxisAngle2Rot Returns the rotation made by rotating by an angle around an axis llEuler2Rot Converts a vector euler rotation into a quaternion rotation llList2Rot Returns rotation from an element of a list llRot2Angle Returns the angle of a rotation llRot2Axis Returns the axis of a rotation llRot2Euler Converts a quaternion into a euler rotation llRot2Fwd Returns a unit vector representing the forward axis after a rotation llRot2Left Returns a unit vector representing the horizontal axis after a rotation llRot2Up Returns a unit vector representing the vertical axis after a rotation llRotBetween Returns the smallest angle (as a rotation) between two vectors

#### World Functions

 Function Name Purpose llApplyRotationalImpulse Applies a rotational impulse llDetectedRot Returns the rotation of detected object or agent llGetCameraRot Gets the rotation of a user’s camera llGetLocalRot Gets the local rotation of the object llGetOmega Returns the current rotational velocity llGetPrimitiveParams Gets rotation as well as many other params llGetRootRotation Gets the global rotation of the root object llGetRot Gets the global rotation of the object llGetTextureRot Returns the texture rotation of a side of an object llGetStatus Get wheter an object can be rotated llLookAt Set the target for object to rotate to look at llRezAtRoot Rez an object, specifying rotation llRezObject Rez an object, specifying rotation llRotateTexture Sets the rotation of a texture a side of an object llRotLookAt Sets the target rotation of an object llRotTarget Set rotational target for an object llRotTargetRemove Remove rotational target for an object given its handle llSetForceAndTorque Set rotational and linear force of a physical object llSetLocalRot Sets the local rotation llSetPrimitiveParams Set rotation as well as many other params llSetRot Sets the global rotation llSetStatus Set whether object can be rotated, among other parameters llSetTorque Sets rotational force of a physical object llSetVehicleRotationParam Sets the vehicle rotation parameter llSitTarget Sets the sit target for an object, specifying rotation llStopLookAt Cancel rotation started by llLookAt or llRotLookAt llTargetOmega client-side smooth rotation

#### Events

 Event Name Purpose at_rot_target when object comes within target angle not_at_rot_target when rotation target is set but object is not there changed when texture is changed, but not when object rotates control when avatar rotates left or right

Q: Is there a non lossy way to convert a rotation to a string and then back to a rotation again so that the resulting rotation has the same value as the original rotation?
A: See: Serialization

Q: I see 1/rot sometimes. What does that mean, exactly?
A: Do you mean <0,0,0,1>/rot ? That inverts the quaternion. Or do you mean <0,0,1>/rot ? Which multiples the vector by the inverse quaternion.

Q: How do I use llTargetOmega to rotate an object about it’s local Z-axis?
A: Use llRot2Up(llGetRot()) as the axis. It’s automatically normalized to 1.

Credit to: Lslwiki.net (not working) with changes made for brevity and clarity.