Module `Scad_ml.Quaternion`Source

Provides functions for the creation of and operations between quaternions. These can be used to create composable and interpolatable rotations to be applied to vectors (e.g. Vec3.t) directly, and Scad.t through MultMatrix.t.

Sourcetype t = float * float * float * float

Sourceval id : t

The identity quaternion: (0., 0., 0., 1.)

Sourceval make : Vec3.t -> float -> t

make ax angle

Create a quaternion representing a rotation of angle (in radians) around the vector ax.

Basic Arithmetic

Sourceval add : t -> t -> t

add a b

Hadamard (element-wise) addition of quaternions a and b.

Sourceval sub : t -> t -> t

sub a b

Hadamard (element-wise) subtraction of quaternion b from a.

Sourceval mul : t -> t -> t

mul a b

Quaternion multiplication of a and b.

Sourceval negate : t -> t

negate t

Negation of all elements of t.

Sourceval add_scalar : t -> float -> t

add_scalar t s

Add s to the magnitude of t, leaving the imaginary parts unchanged.

Sourceval sub_scalar : t -> float -> t

sub_scalar t s

Subtract s from the magnitude of t, leaving the imaginary parts unchanged.

Sourceval scalar_sub_quat : t -> float -> t

scalar_sub_quat t s

Negate the imaginary parts of t, and subtract the magnitude from s to obtain the new magnitude.

Sourceval mul_scalar : t -> float -> t

mul_scalar t s

Element-wise multiplication of t by s.

Sourceval div_scalar : t -> float -> t

div_scalar t s

Element-wise division of t by s.

Vector Math

Sourceval norm : t -> float

norm t

Calculate the vector norm (a.k.a. magnitude) of t.

Sourceval normalize : t -> t

normalize t

Normalize t to a quaternion for which the magnitude is equal to 1. e.g. norm (normalize t) = 1.

Sourceval dot : t -> t -> float

dot a b

Vector dot product of a and b.

Sourceval conj : t -> t

conj t

Take the conjugate of the quaternion t, negating the imaginary parts (x, y, and z) of t, leaving the magnitude unchanged.

Sourceval distance : t -> t -> float

distance a b

Calculate the magnitude of the difference (Hadamard subtraction) between a and b.

Matrix Conversions

Sourceval of_rotmatrix : RotMatrix.t -> t

Sourceval to_multmatrix : t -> MultMatrix.t

Utilities

Sourceval to_string : t -> string

Sourceval get_x : t -> float

Sourceval get_y : t -> float

Sourceval get_z : t -> float

Sourceval get_w : t -> float

Sourceval slerp : t -> t -> float -> t

slerp a b step

Spherical linear interpotation. Adapted from pyquaternion.

Vector Transformations

Sourceval rotate_vec3 : t -> Vec3.t -> Vec3.t

rotate_vec3 t v

Rotate v with the quaternion t.

Sourceval rotate_vec3_about_pt : t -> Vec3.t -> Vec3.t -> Vec3.t

rotate_vec3_about_pt t p v

Translates v along the vector p, rotating the resulting vector with the quaternion t, and finally, moving back along the vector p. Functionally, rotating about the point in space arrived at by the initial translation along the vector p.

Sourceval alignment : Vec3.t -> Vec3.t -> t

alignment a b

Calculate a quaternion that would bring a into alignment with b.

package scad_ml