class Flector4D

The Flector4D class encapsulates a 4D reflection operator (flector). For more information about flectors, see the projective geometric algebra website.

class Flector4D

Flector4D::Set	Sets all eight components of a flector.
Flector4D::Unitize	Unitizes the weight of a flector.
Flector4D::MakeTransflection	Returns a flector that represents a translation and a reflection.
Flector4D::MakeRotoreflection	Returns a flector that represents a rotation and a reflection.
Flector4D::GetTransformMatrix	Converts a flector to its corresponding 4 × 4 matrix.
Flector4D::GetInverseTransformMatrix	Converts a flector to the inverse of its corresponding 4 × 4 matrix.
Flector4D::GetTransformMatrices	Converts a flector to its corresponding 4 × 4 matrix and its inverse simultaneously.
Flector4D::SetTransformMatrix	Converts a 4 × 4 matrix to its corresponding flector.

Flector4D();

Flector4D(float sx, float sy, float sz, float sw, float hx, float hy, float hz, float hw);

Flector4D(const Vector4D& v, const Plane3D& g);

Flector4D(const Point3D& p, const Plane3D& g);

explicit Flector4D(const Vector4D& v);

explicit Flector4D(const Point3D& p);

explicit Flector4D(const Plane3D& g);

sx,sy,sz,sw	The values of the e1, e2, e3, and e4 coordinates.
hx,hy,hz,hw	The values of the e234, e314, e124, and e321 coordinates.
g	A plane whose entries are copied to the e234, e314, e124, and e321 coordinates.
v	A vector whose entries are copied to the e1, e2, e3, and e4 coordinates.
p	A point whose entries are copied to the e1, e2, and e3 coordinates.

The Flector4D class encapsulates a reflection operator (flector) in the 4D projective geometric algebra. It has the general form s_xe₁ + s_ye₂ + s_ze₃ + s_we₄ + h_xe₂₃₄ + h_ye₃₁₄ + h_ze₁₂₄ + h_we₃₂₁.

The default constructor leaves the components of the flector undefined. If the vector v and plane g are specified, then their coordinates are assigned to the vector part and trivector part of the flector, respectively. If only one of the vector v and plane g are specified, then the other part is set to zero. If the point p is specified, then its w coordinate is assumed to be one.

Flector4D& operator *=(float n);	Multiplies by the scalar n.
Flector4D& operator /=(float n);	Multiplies by the inverse of the scalar n.

bool operator ==(const Flector4D& a, const Flector4D& b);	Returns a boolean value indicating whether the two flectors a and b are equal.
bool operator !=(const Flector4D& a, const Flector4D& b);	Returns a boolean value indicating whether the two flectors a and b are not equal.
Flector4D operator ~(const Flector4D& F);	Returns the antireverse of the flector F.
Flector4D operator -(const Flector4D& F);	Returns the negation of the flector F.
Flector4D operator *(const Flector4D& F, float n);	Returns the product of the flector F and the scalar n.
Flector4D operator *(float n, const Flector4D& F);	Returns the product of the flector F and the scalar n.
Flector4D operator /(const Flector4D& F, float n);	Returns the product of the flector G and the inverse of the scalar n.
Motor4D operator *(const Flector4D& a, const Flector4D& b);	Returns the geometric antiproduct of the flectors a and b, producing a motor.
Flector4D operator *(const Flector4D& a, const Motor4D& b);	Returns the geometric antiproduct of the flector a and the motor b, producing a flector.
Flector4D operator *(const Motor4D& a, const Flector4D& b);	Returns the geometric antiproduct of the motor a and the flector b, producing a flector.
float BulkNorm(const Flector4D& F);	Returns the bulk norm of the flector F.
float WeightNorm(const Flector4D& F);	Returns the weight norm of the flector F.
Vector3D Transform(const Vector3D& v, const Flector4D& F);	Transforms the vector v with the flector F.
Bivector3D Transform(const Bivector3D& v, const Flector4D& F);	Transforms the bivector v with the flector F.
Point3D Transform(const Point3D& p, const Flector4D& F);	Transforms the point p with the flector F.
Line3D Transform(const Line3D& l, const Flector4D& F);	Transforms the line l with the flector F.
Plane3D Transform(const Plane3D& g, const Flector4D& F);	Transforms the plane g with the flector F.

Motor4D

Point3D

Line3D

Plane3D