class Bivector3D

Defined in: TSBivector3D.h

The Bivector3D class encapsulates a 3D bivector.

Definition

class Bivector3D : public Antivec3D<TypeBivector3D>

Member Functions

Bivector3D::Set Sets all three components of a bivector.

Constructor

Bivector3D();

Bivector3D(float a, float b, float c);

Bivector3D(const Point2D& p, const Point2D& q);

Bivector3D(const Point2D& p, const Vector2D& v);

Parameters

`a`	The value of the e₂₃ coordinate.
`b`	The value of the e₃₁ coordinate.
`c`	The value of the e₁₂ coordinate.
`p,q`	Two 2D points that lie on the line.
`v`	A 2D direction vector.

Description

The Bivector3D class is used to store a three-dimensional bivector having three floating-point components named x, y, and z.

The default constructor leaves the components of the bivector undefined.

If points p and q are specified, then the bivector is initialized to the wedge product between homogeneous extensions of p and q with z coordinates set to 1, giving a representation of the 2D line containing both points. If the point p and the direction v are specified, then the line contains the point p and runs parallel to the direction v.

Overloaded Operators

`Bivector3D& operator +=(const Bivector3D& v);`	Adds the bivector `v`.
`Bivector3D& operator -=(const Bivector3D& v);`	Subtracts the bivector `v`.
`Bivector3D& operator *=(float n);`	Multiplies by the scalar `n`.
`Bivector3D& operator /=(float n);`	Multiplies by the inverse of the scalar `n`.

Nonmember Operations

`bool operator ==(const Bivector3D& a, const Bivector3D& b);`	Returns a boolean value indicating whether the two bivectors `a` and `b` are equal.
`bool operator !=(const Bivector3D& a, const Bivector3D& b);`	Returns a boolean value indicating whether the two bivectors `a` and `b` are not equal.
`Bivector3D operator !(const Vector3D& v);`	Returns the complement of the vector `v`.
`Vector3D operator !(const Bivector3D& v);`	Returns the complement of the bivector `v`.
`Bivector3D operator -(const Bivector3D& v);`	Returns the negation of the bivector `v`.
`Bivector3D operator +(const Bivector3D& a, const Bivector3D& b);`	Returns the sum of the bivectors `a` and `b`.
`Bivector3D operator -(const Bivector3D& a, const Bivector3D& b);`	Returns the difference of the bivectors `a` and `b`.
`Bivector3D operator *(const Bivector3D& v, float n);`	Returns the product of the bivector `v` and the scalar `n`.
`Bivector3D operator *(float n, const Bivector3D& v);`	Returns the product of the bivector `v` and the scalar `n`.
`Bivector3D operator /(const Bivector3D& v, float n);`	Returns the product of the bivector `v` and the inverse of the scalar `n`.
`bool operator ==(const Bivector3D& a, const Bivector3D& b);`	Returns a boolean value indicating whether the two bivectors `a` and `b` are equal.
`bool operator !=(const Bivector3D& a, const Bivector3D& b);`	Returns a boolean value indicating whether the two bivectors `a` and `b` are not equal.
`Bivector3D operator ^(const Vector3D& a, const Vector3D& b);`	Returns the wedge product of the vectors `a` and `b`.
`Bivector3D operator ^(const Point2D& p, const Point2D& q);`	Returns the wedge product of the 2D points `p` and `q`. The z coordinates of `p` and `q` are assumed to be 1.
`Bivector3D operator ^(const Point2D& p, const Vector2D& v);`	Returns the wedge product of the 2D point `p` and the 2D vector `v`. The z coordinate of `p` is assumed to be 1.
`Vector3D operator ^(const Bivector3D& a, const Bivector3D& b);`	Returns the antiwedge product of the bivectors `a` and `b`.
`float operator ^(const Bivector3D& a, const Vector3D& b);`	Returns the antiwedge product of the bivector `a` and the vector `b`.
`float operator ^(const Vector3D& a, const Bivector3D& b);`	Returns the antiwedge product of the vector `a` and the bivector `b`.
`Vector3D Project(const Vector3D& a, const Bivector3D& b);`	Returns (b̲ ∧ a) ∨ b, which is the projection of `a` onto `b` under the assumption that the magnitude of `b` is one.

Base Classes

Antivec3D Antivectors use a generic base class to store their components.