More work on quaternions.

include/wrmath/geom/quaternion.h

@@ -4,7 +4,7 @@
 
 #include <cassert>
 #include <cmath>
-#include <initializer_list>
+#include <ostream>
 #include <wrmath/geom/vector.h>
 #include <wrmath/math.h>
 
@@ -16,30 +16,93 @@ namespace geom {
 template <typename T>
 class Quaternion {
 public:
-	// The default constructor returns the identity quaternion.
+	/**
+	 * The default Quaternion constructor returns an identity quaternion.
+	 */
 	Quaternion() : v(Vector<T, 3>()), w(1.0)
 	{
 		wr::math::DefaultEpsilon(this->eps);
+		this->w = std::fmod(this->w, this->maxRotation);
 	};
 
 
-	Quaternion(Vector<T, 3> axis, T angle) : v(axis), w(angle)
+	/**
+	 * A Quaternion may be initialised with a Vector<T, 3> axis of rotation
+	 * and an angle of rotation.
+	 * @param _axis A three-dimensional vector of the same type as the Quaternion.
+	 * @param _angle The angle of rotation about the axis of rotation.
+	 */
+	Quaternion(Vector<T, 3> _axis, T _angle) : v(_axis), w(_angle)
 	{
 		wr::math::DefaultEpsilon(this->eps);
+		this->w = std::fmod(this->w, this->maxRotation);
 	};
 
 
+	/**
+	 * Return the axis of rotation of this quaternion.
+	 * @return The axis of rotation of this quaternion.
+	 */
+	Vector<T, 3>
+	axis() const
+	{
+		return this->v;
+	}
+
+
+	/**
+	 * Return the angle of rotation of this quaternion.
+	 * @return the angle of rotation of this quaternion.
+	 */
+	T
+	angle() const
+	{
+		return this->w;
+	}
+
+
+	/**
+	 * Compute the norm of a quaternion. Treating the Quaternion as a
+	 * Vector<T, 4>, it's the same as computing the magnitude.
+	 * @return A non-negative real number.
+	 */
+	T
+	norm()
+	{
+		T	n = 0;
+
+		n += (this->v[0] * this->v[0]);
+		n += (this->v[1] * this->v[1]);
+		n += (this->v[2] * this->v[2]);
+		n += (this->w * this->w);
+
+		return std::sqrt(n);
+	}
+
+
+	Vector<T, 4>
+	asVector()
+	{
+		return Vector<T, 4> {this->v[0], this->v[1], this->v[2], this->w};
+	}
+
+
+	/**
+	 * Perform quaternion addition with another quaternion.
+	 * @param other The quaternion to be added with this one.
+	 * @return
+	 */
 	Quaternion
 	operator+(const Quaternion<T> &other) const
 	{
-		return Quaternion(this->v + other.v, (this->w + other.w) % this->maxRotation);
+		return Quaternion(this->v + other.v, this->w + other.w);
 	}
 
 
 	Quaternion
 	operator-(const Quaternion<T> &other) const
 	{
-	    return Quaternion(this->v - other.v, (this->w - other.w) % this->maxRotation);
+	    return Quaternion(this->v - other.v, this->w - other.w);
 	}
 
 
@@ -69,6 +132,14 @@ public:
 		return !(*this == other);
 	}
 
+
+	friend std::ostream&
+	operator<<(std::ostream& outs, const Quaternion<T>& q)
+	{
+		outs << q.w << " + " << q.v;
+		return outs;
+	}
+
 private:
 	static constexpr T	maxRotation = 4 * M_PI;