# randrot

Uniformly distributed random rotations

Since R2020b

## Description

R = randrot returns a unit quaternion drawn from a uniform distribution of random rotations.

example

R = randrot(m) returns an m-by-m matrix of unit quaternions drawn from a uniform distribution of random rotations.

example

R = randrot(m1,...,mN) returns an m1-by-...-by-mN array of random unit quaternions, where m1,…, mN indicate the size of each dimension. For example, randrot(3,4) returns a 3-by-4 matrix of random unit quaternions.

R = randrot([m1,...,mN]) returns an m1-by-...-by-mN array of random unit quaternions, where m1,…, mN indicate the size of each dimension. For example, randrot([3,4]) returns a 3-by-4 matrix of random unit quaternions.

## Examples

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Generate a 3-by-3 matrix of uniformly distributed random rotations.

r = randrot(3)
r = 3x3 quaternion array
0.17446 +  0.59506i -  0.73295j +  0.27976k      0.69704 - 0.060589i +  0.68679j -  0.19695k      0.35191 +  0.74478i +  0.52322j -  0.21842k
0.21908 -  0.89875i -    0.298j +  0.23548k    -0.049744 +  0.59691i +  0.56459j +  0.56786k      0.17527 -  0.46955i +  0.52986j -  0.68414k
0.6375 +  0.49338i -  0.24049j +  0.54068k       0.2979 -  0.53568i +  0.31819j +  0.72323k     -0.30189 -  0.22864i -  0.83159j +  0.40626k

Create a vector of 500 random quaternions. Use rotatepoint to visualize the distribution of the random rotations applied to point (1, 0, 0).

q = randrot(500,1);

pt = rotatepoint(q, [1 0 0]);

figure
scatter3(pt(:,1), pt(:,2), pt(:,3))
axis equal

## Input Arguments

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Size of square quaternion matrix, specified as an integer value. If m is 0 or negative, then R is returned as an empty matrix.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

Size of each dimension, specified as two or more integer values. If the size of any dimension is 0 or negative, then R is returned as an empty array.

Example: randrot(2,3) returns a 2-by-3 matrix of random quaternions.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

Vector of size of each dimension, specified as a row vector of two or more integer values. If the size of any dimension is 0 or negative, then R is returned as an empty array.

Example: randrot([2,3]) returns a 2-by-3 matrix of random quaternions.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

## Output Arguments

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Random quaternions, returned as a quaternion or array of quaternions.

Data Types: quaternion

## References

[1] Shoemake, K. "Uniform Random Rotations." Graphics Gems III (K. David, ed.). New York: Academic Press, 1992.

## Version History

Introduced in R2020b