Quaternion Tools

Browse all available quaternion tools.

Available tools

Axis Angle to Unit Quaternion Record Quaternion order is scalar-first [w,x,y,z], Hamilton product and right-handed active rotations; convert an explicit nonzero axis and angle to a unit quaternion; axis is normalized, radians are not silently clamped.
Quaternion Component Layout Converter Convert explicit quaternion scalar-first to scalar-last ordering or the reverse under a caller source-layout flag; no normalization or rotation inference.
Quaternion Conjugate Components Quaternion order is scalar-first [w,x,y,z], Hamilton product and right-handed active rotations; conjugate vector components without assuming a unit norm or taking an inverse.
Quaternion Finite Scalar Scale Quaternion order is scalar-first [w,x,y,z], Hamilton product and right-handed active rotations; scale finite quaternion components without claiming the result remains a unit rotation.
Quaternion Hamilton Product Pair Quaternion order is scalar-first [w,x,y,z], Hamilton product and right-handed active rotations; multiply left then right algebraically without commuting operands or assuming unit rotations.
Quaternion Inverse Components Quaternion order is scalar-first [w,x,y,z], Hamilton product and right-handed active rotations; invert a nonzero quaternion as normalized conjugate divided by its norm; nonfinite/unsafe results reject.
Quaternion Normalized Components Quaternion order is scalar-first [w,x,y,z], Hamilton product and right-handed active rotations; normalize a nonzero finite quaternion with hypot-based norm, rejecting zero/overflowing norms.
Quaternion Rotation Canonical Sign Quaternion order is scalar-first [w,x,y,z], Hamilton product and right-handed active rotations; canonicalize unit quaternion sign by the first nonzero component being positive, including half-turn scalar-zero cases.
Quaternion Rotation Sign Equivalence Check Quaternion order is scalar-first [w,x,y,z], Hamilton product and right-handed active rotations; compare unit rotations under q and -q sign equivalence using explicit component-space tolerance.
Quaternion Squared Norm Quaternion order is scalar-first [w,x,y,z], Hamilton product and right-handed active rotations; compute finite component squared norm, not a normalized rotation magnitude.
Quaternion Unit Relative Rotation Quaternion order is scalar-first [w,x,y,z], Hamilton product and right-handed active rotations; compute the relative active rotation to * conjugate(from), normalized to remove numerical drift.
Quaternion Unit Validity Audit Quaternion order is scalar-first [w,x,y,z], Hamilton product and right-handed active rotations; audit unit norm against an explicit nonnegative tolerance; finite components alone do not prove a rotation.
Unit Quaternion Angular Separation Quaternion order is scalar-first [w,x,y,z], Hamilton product and right-handed active rotations; measure shortest rotation separation through absolute unit dot product, treating q and -q as identical.
Unit Quaternion Basis Vector Images Quaternion order is scalar-first [w,x,y,z], Hamilton product and right-handed active rotations; return the three active basis-vector images as columns-as-vectors, not a transposed row-major matrix convention.
Unit Quaternion Record to Axis Angle Quaternion order is scalar-first [w,x,y,z], Hamilton product and right-handed active rotations; convert a unit rotation to canonical shortest axis-angle; zero rotation has an unknown/null axis, not an invented direction.
Unit Quaternion Rotation Matrix Quaternion order is scalar-first [w,x,y,z], Hamilton product and right-handed active rotations; form a row-major 3x3 active rotation matrix from an explicitly validated unit quaternion.
Unit Quaternion Sample Sign Continuity Quaternion order is scalar-first [w,x,y,z], Hamilton product and right-handed active rotations; choose consecutive sample signs to keep dot products nonnegative, preserving the first input sign; no smoothing or missing-motion recovery.
Unit Quaternion Short Arc NLERP Quaternion order is scalar-first [w,x,y,z], Hamilton product and right-handed active rotations; perform shortest-sign normalized linear interpolation on the closed unit t domain; antipodal spelling is corrected, not interpolated through zero.
Unit Quaternion Short Arc SLERP Quaternion order is scalar-first [w,x,y,z], Hamilton product and right-handed active rotations; perform shortest-sign spherical interpolation with normalized linear fallback for near-identical inputs on the closed unit t domain; antipodal spelling is corrected, not interpolated through zero.
Unit Quaternion Vector Rotation Quaternion order is scalar-first [w,x,y,z], Hamilton product and right-handed active rotations; rotate a finite three-vector by a validated unit quaternion without applying translation.