Math

LSL has integers and floats, plus vector and rotation types for 3D work. Rotations are quaternions; you rarely need their components, because conversion functions translate them to and from Euler angles, axes and angle-axis form.

These building blocks cover projectile trajectories, look-at rotations, simple inverse kinematics with trigonometry, noise and procedural patterns, and numeric integration for custom physics. Applying the results to objects is covered by Movement and Physics.

Concepts

Basic math: absolute values, rounding, powers, roots and logarithms
- Integer and float operators follow the usual rules; dividing integers truncates
- Statistics over a list of numbers in one call
Angles are in radians
- DEG_TO_RAD and RAD_TO_DEG convert
- PI, TWO_PI and PI_BY_TWO are constants
Vectors hold positions, velocities, scales and colors
- Length, normalisation and distance functions, plus the dot (*) and cross (%) operators, cover most vector math
Rotations (quaternions)
- Multiply rotations to combine them, and multiply a vector by a rotation to rotate it
- Convert to and from Euler angles, axes and angle-axis, and find the rotation between two directions
Random numbers
- llFrand returns a random float up to a limit
- Shuffle lists, and make unique identifiers
Interpolation and color
- Linear interpolation is a + (b - a) * t for floats, vectors and colors
- Convert colors between sRGB and linear space before blending them

Functions and events

`integer`	`llAbs(integer val)`
`float`	`llFabs(float val)`
`integer`	`llRound(float val)`
`float`	`llPow(float base, float exponent)`
`float`	`llSqrt(float val)`
`float`	`llSin(float theta)`
`float`	`llAtan2(float y, float x)`
`float`	`llVecMag(vector vec)`
`vector`	`llVecNorm(vector vec)`
`float`	`llVecDist(vector vec_a, vector vec_b)`
`rotation`	`llEuler2Rot(vector vec)`
`vector`	`llRot2Euler(rotation q)`
`rotation`	`llRotBetween(vector start_vec, vector end_vec)`
`float`	`llFrand(float mag)`

Rotations

Quaternions combine by multiplication; convert them with the Euler, axis and angle-axis functions.

Math on the wiki

The wiki’s category of math functions.

Scripting Details

Basic math

`integer`	`llAbs(integer val)` Returns the absolute (positive) integer value of val.
`float`	`llFabs(float val)` Returns the absolute (positive) value of val.
`integer`	`llRound(float val)` Returns val rounded to the nearest integer. Halfway values are rounded toward infinity.
`integer`	`llFloor(float val)` Returns val rounded toward negative infinity. In other words, returns the largest integer less than or equal to val.
`integer`	`llCeil(float val)` Returns val rounded toward positive infinity. In other words, returns the smallest integer greater than or equal to val.
`float`	`llPow(float base, float exponent)` Returns base raised to the power exponent. If result is imaginary, returns NaN.
`float`	`llSqrt(float val)` Returns the square root of val. If negative, return NaN.
`float`	`llLog(float val)` Returns natural (base e) logarithm of val. If negative, return 0.0.
`float`	`llLog10(float val)` Returns base-10 (common) logarithm of val. If negative, return 0.0.
`integer`	`llModPow(integer base, integer exponent, integer modulus)` Returns base raised to the power exponent, modulo modulus (i.e., (b^e)%m). All inputs are wrapped to unsigned 32-bit integer range [0..4294967295]. Output is wrapped to signed 32-bit integer range [-2147483648..2147483647]. Will never overflow, unlike (b^e), which can overflow to inf.
`float`	`llListStatistics(integer operation, list src)` Returns the numeric result of the statistical aggregate function operation (a LIST_STAT_* constant) on the numeric list src.

Angles and trigonometry

`float`	`llSin(float theta)` Returns the sine of theta. Theta is in radians.
`float`	`llCos(float theta)` Returns the cosine of theta. Theta is in radians.
`float`	`llTan(float theta)` Returns the tangent of theta. Theta is in radians.
`float`	`llAsin(float val)` Returns the arcsine of val in radians.
`float`	`llAcos(float val)` Returns the arccosine of val in radians.
`float`	`llAtan2(float y, float x)` Returns the arctangent of y/x in radians, using the signs to determine the quadrant. Note the argument order: Y is the first parameter, X is the second parameter.
`float`	`PI = 3.14159265` Mathematical constant pi, representing the number of radians in a half circle (semi-circle). When used in sensor functions, it specifies a full sphere scan.
`float`	`TWO_PI = 6.28318530` Mathematical constant pi*2, representing the number of radians in a full circle.
`float`	`PI_BY_TWO = 1.57079633` Mathematical constant pi/2, representing the number of radians in a quarter circle. When used in sensor functions, it specifies a hemisphere scan.
`float`	`DEG_TO_RAD = 0.017453293` Constant 0.017453293 (precise value is PI/180). Multiply a value in degrees by this number to convert it to radians.
`float`	`RAD_TO_DEG = 57.2957795` 180/PI. Multiply a value in radians by this number to convert it to degrees.

Vectors

`float`	`llVecMag(vector vec)` Returns the magnitude (geometric length) of vec.
`vector`	`llVecNorm(vector vec)` Returns the normalized unit vector pointing the same direction as vec. If <0, 0, 0>, return <0, 0, 0>.
`float`	`llVecDist(vector vec_a, vector vec_b)` Returns a float representing the undirected, non-negative distance between vectors vec_a and vec_b.
`vector`	`ZERO_VECTOR = <0.0, 0.0, 0.0>` A vector constant representing <0.0, 0.0, 0.0>. This is the default value for vector variables.

Rotations

`rotation`	`llEuler2Rot(vector vec)` Returns the quaternion representation of the Euler angles (in radians) within vec.
`vector`	`llRot2Euler(rotation q)` Returns a vector of Euler angles (roll, pitch, yaw) of q. The angles will be in radians.
`rotation`	`llAxisAngle2Rot(vector axis, float angle)` Returns the rotation that rotates angle radians around the axis vector.
`float`	`llRot2Angle(rotation q)` Returns the angle, in radians, that q rotates.
`vector`	`llRot2Axis(rotation q)` Returns the unit vector axis that q rotates around.
`rotation`	`llAxes2Rot(vector fwd, vector left, vector up)` Returns the rotation defined by the coordinate axes fwd, left, and up.
`vector`	`llRot2Fwd(rotation q)` Returns the unit vector pointing toward positive X (forward) in the coordinate space of rotation q. Equivalent to <1, 0, 0> * q.
`vector`	`llRot2Left(rotation q)` Returns the unit vector pointing toward positive Y (left) in the coordinate space of rotation q. Equivalent to <0, 1, 0> * q.
`vector`	`llRot2Up(rotation q)` Returns the unit vector pointing toward positive Z (up) in the coordinate space of rotation q. Equivalent to <0, 0, 1> * q.
`rotation`	`llRotBetween(vector start_vec, vector end_vec)` Returns the shortest-path quaternion that rotates start_vec onto end_vec.
`float`	`llAngleBetween(rotation start_rot, rotation end_rot)` Returns the angle, in radians, between rotations start_rot and and end_rot.
`rotation`	`ZERO_ROTATION = <0.0, 0.0, 0.0, 1.0>` A rotation constant representing an identity rotation (causes no change). This is the default value for rotation variables.

Random numbers

`float`	`llFrand(float mag)` Returns a pseudo-random float in the range [0.0, mag) or (mag, 0.0] depending on the sign of mag. The value is inclusive of 0.0 but exclusive of mag.
`list`	`llListRandomize(list src, integer stride)` Returns a randomized copy of the list src by blocks of size stride. If the list length is not perfectly divisible by stride, no randomization occurs.
`key`	`llGenerateKey()` Generates and returns a unique versioned UUID key (utilizing SHA-1 hashing). Due to being versioned, it will not return NULL_KEY; however, the exact UUID version is an implementation detail that should not be relied upon.

Color

`vector`	`llLinear2sRGB(vector color)` Returns a sRGB colorspace vector converted from the linear RGB colorspace argument.
`vector`	`llsRGB2Linear(vector color)` Returns a linear RGB colorspace vector converted from the sRGB colorspace argument.

See also Category Math TrigPlanned Recipe: simple inverse kinematics with trigonometry

See also Page vector type Category Vector Category Math 3DPlanned Recipe: projectile trajectories

See also Planned Recipe: Perlin noise maps

See also SL Wiki LSL Math Feature Physics Feature Movement Page Guide: interpolation and easingPlanned Recipe: numeric integration for custom physics

Math

Concepts

Functions and events

Rotations

Math on the wiki

Scripting Details

Basic math

Angles and trigonometry

Vectors

Rotations

Random numbers

Color

Related