Rotation

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
eul *= DEG_TO_RAD; //convert to radians
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

World Functions

Events

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