Schema and access model

• Quaternion values expose one marker field, QUATERNION, and one four-entry field, entries.
• @ (ordinal quaternion -- ref) returns Ref to the selected entry through entries.
• ! (value ordinal quaternion --) writes one selected entry through entries.
• fieldCount (quaternion -- count) always returns 4.
• vector (quaternion -- entries) returns a copied four-entry vector of the stored components.

Constructors and conversions

• axisAngleQuaternion: builds one quaternion from one axis-angle tuple.
• identityQuaternion: returns the identity quaternion of the selected real schema.
• quaternion: builds a quaternion either from four entries or from one 3×3 rotation matrix.
• quaternionCast: casts every entry to another real schema.
• rotationQuaternion: builds a quaternion from one rotation vector.
• rotationQuaternion with explicit threshold uses the identity quaternion when the rotation-vector length is below the selected threshold.

Algebraic operations

• *: scales a quaternion by one scalar, or composes two quaternions, depending on the argument schemas.
• +: adds quaternions entrywise.
• conj: returns the quaternion conjugate.
• dot: returns the quaternion dot product.
• squaredLength: returns the squared quaternion norm.
• unit: returns the normalized quaternion.
• matrix: returns the 3×3 rotation matrix represented by the quaternion.

Interpolation and stabilization

• unitChecked and unitCheckedWithThreshold return the identity quaternion when the input length is below the selected threshold.
• nlerp performs normalized linear interpolation.
• slerp performs spherical linear interpolation with the default epsilon.
• slerpWithEpsilon performs spherical linear interpolation with explicit epsilon handling.
• When the quaternion dot product is negative, interpolation uses the negated second quaternion so that interpolation follows the shorter quaternion path.

Examples

Schema access

"Quaternion.identityQuaternion" use
"Quaternion.fieldCount" use
"control" use

{} () {} [
  Real32 identityQuaternion fieldCount printStack _:;
] "main" exportFunction

Expected Output During Compilation

4

Zero-angle construction

"Quaternion.axisAngleQuaternion" use
"control" use

{} () {} [
  (0.0r32 0.0r32 1.0r32 0.0r32) axisAngleQuaternion printStack _:;
] "main" exportFunction

Expected Output During Compilation

{
  QUATERNION: ();
  entries: (0.0r32 0.0r32 0.0r32 1.0r32);
}

Matrix conversion

"Quaternion.identityQuaternion" use
"Quaternion.matrix" use
"control" use

{} () {} [
  q: Real32 identityQuaternion;
  q matrix printStack _:;
] "main" exportFunction

Expected Output During Compilation

((1.0r32 0.0r32 0.0r32) (0.0r32 1.0r32 0.0r32) (0.0r32 0.0r32 1.0r32))

Checked normalization fallback

"Quaternion.quaternion" use
"Quaternion.unitChecked" use
"control" use

{} () {} [
  q: (0.0r32 0.0r32 0.0r32 0.0r32) quaternion;
  q unitChecked printStack _:;
] "main" exportFunction

Expected Output During Compilation

{
  QUATERNION: ();
  entries: (0.0r32 0.0r32 0.0r32 1.0r32);
}

Runtime matrix check

"Quaternion.identityQuaternion" use
"Quaternion.matrix" use
"algebra" use
"String" use
"control" use

{} Int32 {} [
  q: Real32 identityQuaternion;
  m: q matrix;
  expected: ((1.0r32 0.0r32 0.0r32) (0.0r32 1.0r32 0.0r32) (0.0r32 0.0r32 1.0r32));
  m expected = print
  LF print
  0
] "main" exportFunction

Expected Output

TRUE

See also

• algebra: Algebraic operations, vectors, and matrix utilities.
• Pose: Rigid-transform helpers over position vectors and quaternions.