class Vector3D

The Vector3D class encapsulates a 3D vector.

class Vector3D : public Vec3D<TypeVector3D>

Vector3D::Set	Sets all three components of a vector.
Vector3D::Normalize	Normalizes a 3D vector.
Vector3D::Unitize	Unitizes the weight of a 3D vector.
Vector3D::RotateAboutX	Rotates a vector about the x axis.
Vector3D::RotateAboutY	Rotates a vector about the y axis.
Vector3D::RotateAboutZ	Rotates a vector about the z axis.
Vector3D::RotateAboutAxis	Rotates a vector about a given axis.

Vector3D();

Vector3D(float a, float b, float c);

template <typename type> explicit Vector3D(const Vec3D<type>& v);

a	The value of the x coordinate.
b	The value of the y coordinate.
c	The value of the z coordinate.
v	Another 3D vector, possibly with a different component type, that is converted to a Vector3D.

The Vector3D class is used to store a three-dimensional direction vector having floating-point components x, y, and z. A direction vector stored in this class is assumed to have a w coordinate of 0 whenever it needs to be converted to a four-dimensional representation. Three-dimensional points (for which the w coordinate is 1) should be stored using the Point3D class.

The default constructor leaves the components of the vector undefined. If the values a, b, and c are supplied, then they are assigned to the x, y, and z coordinates of the vector, respectively.

float& operator [](machine k);	Returns a reference to the k-th scalar component of a vector. The value of k must be 0, 1, or 2.
const float& operator [](machine k) const;	Returns a constant reference to the k-th scalar component of a vector. The value of k must be 0, 1, or 2.
Vector3D& operator +=(const Vector3D& v);	Adds the vector v.
Vector3D& operator -=(const Vector3D& v);	Subtracts the vector v.
Vector3D& operator *=(const Vector3D& v);	Calculates the componentwise product with the vector v.
Vector3D& operator *=(float n);	Multiplies by the scalar n.
Vector3D& operator /=(float n);	Divides by the scalar n.

bool operator ==(const Vector3D& v1, const Vector3D& v2) const;	Returns a boolean value indicating whether the two vectors v1 and v2 are equal.
bool operator !=(const Vector3D& v1, const Vector3D& v2) const;	Returns a boolean value indicating whether the two vectors v1 and v2 are not equal.
Vector3D operator -(const Vector3D& v);	Returns the negation of the vector v.
Vector3D operator +(const Vector3D& a, const Vector3D& b);	Returns the sum of the vectors a and b.
Vector3D operator -(const Vector3D& a, const Vector3D& b);	Returns the difference of the vectors a and b.
Vector3D operator *(const Vector3D& v, float n);	Returns the product of the vector v and the scalar n.
Vector3D operator *(float n, const Vector3D& v);	Returns the product of the vector v and the scalar n.
Vector3D operator /(const Vector3D& v, float n);	Returns the product of the vector v and the inverse of the scalar n.
Vector3D operator *(const Vector3D& a, const Vector3D& b);	Returns the componentwise product of the vectors a and b
float BulkNorm(const Vector3D& v);	Returns the bulk norm of the vector v.
float WeightNorm(const Vector3D& v);	Returns the weight norm of the vector v.
Point2D Unitize(const Vector3D& v);	Returns the 2D point represented by the vector v after unitization.
float Magnitude(const Vector3D& v);	Returns the magnitude of the vector v.
float InverseMag(const Vector3D& v);	Returns the inverse magnitude of the vector v.
float SquaredMag(const Vector3D& v);	Returns the squared magnitude of the vector v.
float Dot(const Vector3D& a, const Vector3D& b);	Returns the dot product between a and b.
Vector3D Cross(const Vector3D& a, const Vector3D& b);	Returns the cross product between a and b.
Vector3D Project(const Vector3D& a, const Vector3D& b);	Returns (a ⋅ b)b, which is the projection of a onto b under the assumption that the magnitude of b is one.
Vector3D Reject(const Vector3D& a, const Vector3D& b);	Returns a − (a ⋅ b)b, which is the rejection of a from b under the assumption that the magnitude of b is one.

Vec3D

Vectors use a generic base class to store their components.

Point3D

Vector4D