module Quat: sig .. end
type Gg.quat
The type for quaternions.
Constructors, accessors and constants
val v : float -> float -> float -> float -> Gg.quat
v x y z w is the quaternion xi+ yj + zk + w.
val zero : Gg.quat
zero is the zero quaternion.
val id : Gg.quat
id is the identity quaternion 1.
Functions
val mul : Gg.quat -> Gg.quat -> Gg.quat
mul q r is the quaternion multiplication q * r.
val conj : Gg.quat -> Gg.quat
val unit : Gg.quat -> Gg.quat
unit q is the unit vector
q/|q| (same as
Gg.V4.unit).
val inv : Gg.quat -> Gg.quat
inv q is the quaternion inverse q-1.
val slerp : Gg.quat -> Gg.quat -> float -> Gg.quat
slerp q r t is the spherical linear interpolation between q
and r at t. Non commutative, torque minimal and constant
velocity.
val squad : Gg.quat -> Gg.quat -> Gg.quat -> Gg.quat -> float -> Gg.quat
squad q cq cr r t is the spherical cubic interpolation
between q and r at t. cq and cr indicate the tangent
orientations at q and r.
val nlerp : Gg.quat -> Gg.quat -> float -> Gg.quat
nlerp q r t is the normalized linear interpolation between q
and r at t. Commutative, torque minimal and inconstant
velocity.
val of_m3 : Gg.m3 -> Gg.quat
of_m3 m is the unit quaternion for the rotation in m.
val of_m4 : Gg.m4 -> Gg.quat
of_m4 m is the unit quaternion for the rotation in the 3x3
top left matrix in m.
val rot_map : Gg.v3 -> Gg.v3 -> Gg.quat
val rot_axis : Gg.v3 -> float -> Gg.quat
val rot_zyx : Gg.v3 -> Gg.quat
val to_rot_axis : Gg.quat -> Gg.v3 * float
to_rot_axis q is the rotation axis and angle of the unit
quaternion q.
val to_rot_zyx : Gg.quat -> Gg.v3
to_rot_zyx q is the x, y, z axis angles of the unit
quaternion q.
val apply3 : Gg.quat -> Gg.v3 -> Gg.v3
apply3 q v applies the 3D rotation of the unit quaternion
q to the vector (or point) v.
val apply4 : Gg.quat -> Gg.v4 -> Gg.v4
apply4 q v apply the 3D rotation of the unit quaternion
q to the homogenous vector (or point) v.