Quaternion¶

Overview¶

Quaternion, see http://en.wikipedia.org/wiki/Quaternion

TODO #96 convert from JME-style parametrization into classical mathematical description?

@author Jonathan Olson <jonathan.olson@colorado.edu>

Class Quaternion¶

import { Quaternion } from 'scenerystack/dot';

Constructor¶

new Quaternion( x, y, z, w )¶

Instance Methods¶

setXYZW( x, y, z, w )¶

Sets the x,y,z,w values of the quaternion @public

@param {number} x @param {number} y @param {number} z @param {number} w

plus( quat )¶

Addition of this quaternion and another quaternion, returning a copy. @public

@param {Quaternion} quat @returns {Quaternion}

timesScalar( s )¶

Multiplication of this quaternion by a scalar, returning a copy. @public

@param {number} s @returns {Quaternion}

timesQuaternion( quat )¶

Multiplication of this quaternion by another quaternion, returning a copy. Multiplication is also known at the Hamilton Product (an extension of the cross product for vectors) The product of two rotation quaternions will be equivalent to a rotation by the first quaternion followed by the second quaternion rotation, @public

@param {Quaternion} quat @returns {Quaternion}

timesVector3( v )¶

Multiply this quaternion by a vector v, returning a new vector3 When a versor, a rotation quaternion, and a vector which lies in the plane of the versor are multiplied, the result is a new vector of the same length but turned by the angle of the versor. @public

@param {Vector3} v @returns {Vector3}

getMagnitude()¶

The magnitude of this quaternion, i.e. \(\sqrt{x^2+y^2+v^2+w^2}\), returns a non negative number @public

@returns {number}

getMagnitudeSquared()¶

The square of the magnitude of this quaternion, returns a non negative number @public

@returns {number}

normalized()¶

Normalizes this quaternion (rescales to where the magnitude is 1), returning a new quaternion @public

@returns {Quaternion}

negated()¶

Returns a new quaternion pointing in the opposite direction of this quaternion @public

@returns {Quaternion}

toRotationMatrix()¶

Convert a quaternion to a rotation matrix This quaternion does not need to be of magnitude 1 @public

@returns {Matrix3}

Static Methods¶

fromEulerAngles( yaw, roll, pitch )¶

Function returns a quaternion given euler angles @public

@param {number} yaw - rotation about the z-axis @param {number} roll - rotation about the x-axis @param {number} pitch - rotation about the y-axis @returns {Quaternion}

fromRotationMatrix( matrix )¶

Convert a rotation matrix to a quaternion, returning a new Quaternion (of magnitude one) @public

@param {Matrix3} matrix @returns {Quaternion}

getRotationQuaternion( a, b )¶

Find a quaternion that transforms a unit vector A into a unit vector B. There are technically multiple solutions, so this only picks one. @public

@param {Vector3} a - Unit vector A @param {Vector3} b - Unit vector B @returns {Quaternion} A quaternion s.t. Q * A = B

slerp( a, b, t )¶

spherical linear interpolation - blending two quaternions with a scalar parameter (ranging from 0 to 1). @public @param {Quaternion} a @param {Quaternion} b @param {number} t - amount of change , between 0 and 1 - 0 is at a, 1 is at b @returns {Quaternion}

Source Code¶

See the source for Quaternion.js in the dot repository.