C++ Code Documentation | template <class A> math::Moebius

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template <class A> math::Moebius

File: BASE/math/Moebius.H

Moebius (fractional linear) transforms (a x + b)(c x + d)^(-1) Modified from code by J. Lawrence.

public:

typedef typename A::Real Real;
Moebius();
Moebius( Moebius const &f );
Moebius &operator=( Moebius const &f );
const A &a() const;

coefficeients (a x + b)(c x + d)^(-1)
const A &b() const;
const A &c() const;
const A &d() const;
void identity();

*this := 1
void mul( Moebius const &a );

*this := (*this) * a
void mul( Moebius const &a, Moebius const &b );

*this := a * b
void mulleft( Moebius const &a );

*this := a * (*this)
void invert( Moebius const &a );

*this := a^(-1)
void invert();

*this := (*this)^(-1)

void rotation( Real a, Real b, Real x, Real y, Real z );

	Sets *this to a rotation FLT This FLT is the element of SO(4) which rotates the (1,v) plane by the angle a and rotates the (1,v)-perp plane by the angle b The orientation of the FLT is positive with 1 rotating toward v NOTE: v = quat(0,x,y,z) must have length one

void rotation( Real a, Real b, A const &s, A const &t );

	Sets *this to a rotation FLT This FLT is the element of SO(4) which rotates the (s,t) plane by angle a and rotates the (s,t)-perp plane by angleb Tthe orientation of the FLT is positive with s rotating toward v NOTE: s, t must be orthonormal

void translation( Real r, Real x, Real y, Real z );

sets *this to a translation FLT {{1, q},{0, 1}}, where q = quat(r,x,y,z)
void inversion( Real r, Real x, Real y, Real z );

sets *this to an inversion FLT {{1, 0},{q, 1}}, where q = quat(r,x,y,z)
void scale( Real s );

sets *this to an scale FLT (a,b,c,d) = (s,0,0,1)
void apply( A &x );

apply *this to x
friend std::ostream &operator<< NULL_TMPL_ARGS ( std::ostream &, Moebius<A> const &);
A _a, _b, _c, _d;

protected:

private:

template <class A> math::Moebius

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