Eagle::PhysicalSpace::OddMultiVector Class Reference

The combination of a vector and a trivector yields an odd multivector, which is dual to a rotor. More...

#include <elementary/eagle/rotor3.hpp>

Inheritance diagram for Eagle::PhysicalSpace::OddMultiVector:

Public Member Functions
	OddMultiVector (const trivector &V, const vector &v=vector(0.0, 0.0, 0.0))
	Construct rotor from trivector and vector.
	OddMultiVector (const vector &v, const trivector &V=trivector(0.0))
	Construct rotor from vector and trivector.
rotor &	operator* ()
	Applying the hodge star operator.
const rotor &	operator* () const
	Applying the hodge star operator.
trivector &	trivec ()
	Retrieve trivector component, modifyable.
const trivector &	trivec () const
	Retrieve trivector component, read-only.
vector &	vec ()
	Retrieve vector component, modifyable.
const vector &	vec () const
	Retrieve vector component, read-only.
Public Member Functions inherited from Eagle::Vector< double, 4 >
Base_t &	fixed_array ()
	Provide access to the base class, writable.
Vector &	operator*= (const double &value)
	Self-multiplication.
Vector &	operator+= (const Vector &v)
	Self-addition.
Vector &	operator-= (const Vector &v)
	Self-subtraction.
Vector &	operator/= (const double &value)
	Self-division.
Vector &	operator= (const Vector &src)
	Assignment operator.
void	set (const V &value)
	Assign all values to the same scalar.
constexpr	Vector ()
	Default constructor.
Public Member Functions inherited from Eagle::FixedArray< double, n >
void	expandMinMax (FixedArray &MinValues, FixedArray &MaxValues) const
	Expand a range given by MinValues,MaxValues to include the values of this array, done per component.
constexpr	FixedArray () noexcept
	Default constructor.
constexpr double &	get (int i)
	writable element access
constexpr const FixedArray< double, subsize > *	get_subarray () const
	Helper class for retrieve a subset of the current array.
constexpr const FixedArray< double, SIZE-1 > &	get_subdim () const
	Mainly introduced because of Interpolate::operator[].
const FixedArray_t &	getFixedArray () const noexcept
	convenience function for base classes
constexpr double	getMax () const
	Compute the maximum element value of this array.
constexpr double	getMin () const
	Compute the maximum element value of this array.
constexpr bool	operator!= (const FixedArray< T, N > &F) const
	Compare two arrays.
constexpr bool	operator== (const FixedArray< T, N > &F) const
	Compare two arrays.
constexpr double &	operator[] (int i)
	writeable element access operator
constexpr double *	ptr (int i=0) noexcept
	Return a pointer to the ith element, no range checking.
constexpr void	set (const Value &x)
	Set all array elements to the same value.
void	setFromArray (const double *x, int length=SIZE, int offset=0)
	Set all array elements to an array's element value.
void	sort (FixedArray< int, N > &I) const
	Sort the elements of an array into the index array.

Friends
OddMultiVector	operator+ (const OddMultiVector &L, const OddMultiVector &R)
	Sum of trivector and vector.
OddMultiVector	operator+ (const trivector &V, const vector &v)
	Sum of trivector and vector.
OddMultiVector	operator+ (const vector &v, const trivector &V)
	Sum of vector and trivector.

Additional Inherited Members
Public Types inherited from Eagle::Vector< double, 4 >
enum
	The number of elements in this array.
Public Types inherited from Eagle::FixedArray< double, n >
typedef FlattenedArray_t::value_type	Element_t
	The maximally reduced type of elements stored here.
typedef GetFixedArrayType< double >::result_t	ElementAsFixedArray_t
	Element type as fixed array, if it is convertible to a fixed array.
typedef FixedArray	FixedArray_t
	Exporting the type definition of this array cass type.
typedef FixedArrayFlattener< FixedArrayOfElements_t >	FixedArrayFlattener_t
	Internal helper class.
typedef FixedArray< ElementAsFixedArray_t, N >	FixedArrayOfElements_t
	If the value is derived from a fixed array type itself, then the FixedArrayOfElements_t is an FixedArray<FixedArray<>> type.
typedef FixedArrayFlattener_t::result_t	FlattenedArray_t
	Reduction of this array type, if it is nested, to an flattened type which contains elementary types.
typedef double	value_type
	Export the type of the respective element value type.
Static Public Member Functions inherited from Eagle::FixedArray< double, n >
static constexpr FixedArray	convert (const FixedArray< T, N > &F, const ConversionFunctor &CF)
	Perform a type conversion on a given fixed array into another basis type:
static constexpr dimension_t	size ()
	The number of elements here.
Protected Attributes inherited from Eagle::FixedArray< double, n >
double	data [SIZE]
	The actual data values, intentional no-initialization for data member, which increases performance on vector creation.

Detailed Description

The combination of a vector and a trivector yields an odd multivector, which is dual to a rotor.

The memory layout is compatible to a rotor, but the algebraic properties are not.

An odd multivector sums up the blades of odd grades, such as 1 (vectors) and 3 (trivectors). An odd multivector is dual to a rotor.