esve::engine::dim4::impl::Transform Class Reference

Implements engine::dim4::Transform. More...

#include <esve/engine/dim4/impl/Transform.hxx>

Inheritance diagram for esve::engine::dim4::impl::Transform:

List of all members.

Public Member Functions
void	left_act (const Transform &left)
	*this := left * (*this)
void	right_act (const Transform &right)
	*this := (*this) * right
void	act (const Transform &action, const Transform &basis)
	General differential action.
void	identity ()
	*this := 1
void	invert ()
	*this := (*this)^(-1)
void	assign (const Transform &h)
	*this := t
void	normalize ()
	Snap to upper-triangular with unitary diagonal elements.
bool	operator== (const Transform &h) const
	Equal by value.
bool	operator!= (const Transform &h) const
	Unequal by value.
	Transform ()
	Construct the identity.
	Transform (const types::quat &a, const types::quat &b, const types::quat &c, const types::quat &d)
	Construct with these matrix elements. See engine::dim4::Transform.
const types::quat &	a () const
	Upper-left.
void	a (const types::quat &a)
	Upper-left.
const types::quat &	b () const
	Upper-right.
void	b (const types::quat &b)
	Upper-right.
const types::quat &	c () const
	Lower-left.
void	c (const types::quat &c)
	Lower-left.
const types::quat &	d () const
	Lower-right.
void	d (const types::quat &d)
	Lower-right.
Actions
Relative actions on the current state. The basis argument is similarity-conjugated: *this := basis*action*(basis)^(-1)*(*this) basis == IDENTITY means left action. basis == *this means right action.
virtual void	rotate (types::real alpha, types::real beta, const types::quat &r, const types::quat &s, const Transform &basis=IDENTITY)=0
	Rotate by angle alpha in the (r, s) plane; rotate by angle beta in the (r, s)-complement plane.
virtual void	rotate (types::real alpha, types::real beta, const types::pure &u, const Transform &basis=IDENTITY)=0
	Rotate by angle alpha in the (1, u) plane; rotate by angle beta in the (1, u)-complement plane.
virtual void	translate (const types::quat &r, const Transform &basis=IDENTITY)=0
	Move the local origin from g to g' = g + r.
virtual void	invertate (const types::quat &r, const Transform &basis=IDENTITY)=0
	Move the local infinity from h to h' per the relation (h')^(-1) = h^(-1) + r.
virtual void	scalate (types::real gamma, const Transform &basis=IDENTITY)=0
	Scale from the current state by a factor of gamma.
Static Public Attributes
const Transform &	IDENTITY
	The group identity element.

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Detailed Description

Implements engine::dim4::Transform.

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Member Function Documentation

void esve::engine::dim4::impl::Transform::normalize (   )  [virtual]

Snap to upper-triangular with unitary diagonal elements. In other words, remove inversion and scaling, leaving only the rotation group with translations. After normalize(), the transformation will be of the form f(z) = a*z*conj(d) + b*conj(d) where a and d are unitary. Implements esve::engine::dim4::Transform.

virtual void esve::engine::dim4::Transform::rotate (  types::real  alpha, types::real  beta, const types::quat &  r, const types::quat &  s, const Transform &  basis = IDENTITY )  [pure virtual, inherited]

Rotate by angle alpha in the (r, s) plane; rotate by angle beta in the (r, s)-complement plane. Orientation is positive with r rotating toward s. Precondition: r, s must be orthonormal.

virtual void esve::engine::dim4::Transform::rotate (  types::real  alpha, types::real  beta, const types::pure &  u, const Transform &  basis = IDENTITY )  [pure virtual, inherited]

Rotate by angle alpha in the (1, u) plane; rotate by angle beta in the (1, u)-complement plane. Orientation is positive with 1 rotating toward u. Precondition: u is unit length.

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