Maths - Quaternion Code

individual methods

complete sfrotation class

This class can represent a 3D rotation. The class has 4 double numbers which represent the rotation as either quaternion, axis-angle or euler number depending on the cde int/enum

The class has methods to combine with other rotations. Also many other methods, including the ability to load and save to from VRML and x3d

There are 3 versions available depending on language:

See also the following related classes

The full source code is available on Sourceforge here:


public final void conjugate(Quat4d q1) {
x = -q1.x;
y = -q1.y;
z = -q1.z;
w = q1.w;

Normalising Quaternions

public final void normalise() {
double n = Math.sqrt(x*x + y*y + z*z + w*w);
x /= n;
y /= n;
z /= n;
w /= n;

Quaternion Scalar Multiplication

public final void scale(double s){
x *= s;
y *= s;
z *= s;
w *= s;

Quaternion Multiplication

public final void mul(Quat4d q1,Quat4d q2) {
x = q1.x * q2.w + q1.y * q2.z - q1.z * q2.y + q1.w * q2.x;
y = -q1.x * q2.z + q1.y * q2.w + q1.z * q2.x + q1.w * q2.y;
z = q1.x * q2.y - q1.y * q2.x + q1.z * q2.w + q1.w * q2.z;
w = -q1.x * q2.x - q1.y * q2.y - q1.z * q2.z + q1.w * q2.w;
Information about the equivalence of quaternion multiplication and orthogonal matrix multiplication.

Quaternion Add

public final void add(Quat4d q1,Quat4d q2) {
x = q1.x + q2.x;
y = q1.y + q2.y;
z = q1.z + q2.z;
w = q1.w + q2.w;

metadata block
see also:


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