Gather general basic mathematic functions which are not available in cmath here. More...

Namespaces
namespace	PhysicalSpace
	Geometric algebra of the physical 3D-space, by which we mean the Clifford algebara over Euclidean, three-dimensional space.

namespace	Plane
	Geometric algebra of the plane, by which we mean the Clifford algebra over Euclidean, two-dimensional space.

namespace	STA
	Geometric algebra of spacetime, a.k.a.

Classes
struct	AnalyticFunctionBase
	Abstract base class for analytic functions, coordinate-independent. More...

class	AntiSymmetric

struct	AnyType

struct	Assert

struct	Assert< true >

struct	Assertion

struct	Assertion< true >

class	Assignment
	Convenience class to allow using the comma operator for assigning a sequence of elements to a given array-like class. More...

struct	BinaryOperatorFunctor

struct	BinaryOperatorNode
	Template node class to perform binary operations on evaluate-able nodes. More...

class	BoundingBall
	Bounding container implemented by a ball. More...

class	BoundingBox
	A coordinate-parallel bounding box in three dimensions. More...

class	CameraPath
	A camera path with movements, motions and various constraints. More...

struct	Cartesian3D

class	Christoffel
	Christoffel symbols. More...

class	Column
	A column vector. More...

class	ConstantNode
	A node that constructs a type from a constant value. More...

struct	ConstantVectorNode
	A node that implements a constant vector value. More...

class	ConstructorNode
	A node that constructs a vectorial type from three scalar values. More...

class	Context
	A set of variable names, with indices associated to each type. More...

struct	ContraVariant

struct	ContravariantIndexingScheme
	Indices are all upper indices, e.g. More...

struct	CoordinateInfo

struct	CoordinateInfo< void >

struct	CoVariant

struct	CovariantIndexingScheme
	Indices are all lower indices, e.g. More...

struct	DegeneratedMatrix

struct	DerivationTrait
	Template type trait class to compute analytical derivates. More...

struct	DerivationTrait< BinaryOperatorFunctor< NodeType, NodeType, NodeType, '+'> >
	Computes (u+v),x which is u,x+v,x. More...

struct	DerivationTrait< BinaryOperatorFunctor< NodeType, NodeType, NodeType, '-'> >
	Computes (u-v),x which is u,x-v,x. More...

struct	DerivationTrait< BinaryOperatorFunctor< ScalarNode, ScalarNode, ScalarNode, ' *'> >
	Computes (ab),x which is a,x b + a b,y. More...

struct	DerivationTrait< BinaryOperatorFunctor< ScalarNode, ScalarNode, ScalarNode, '+'> >
	Computes (a+b),x which is a,x+b,y. More...

struct	DerivationTrait< BinaryOperatorFunctor< ScalarNode, ScalarNode, ScalarNode, '-'> >
	Computes (a-b),x which is a,x-b,y. More...

struct	DerivationTrait< BinaryOperatorFunctor< ScalarNode, ScalarNode, ScalarNode, '/'> >
	Computes (a/b),x which is (a,x b - a b,y) / b^2. More...

struct	DerivationTrait< LocationComponent< Component > >
	Computes (v[i]),x. More...

struct	DerivationTrait< ScalarCube >
	Computes (y^3),x which is 3 y^2 y,x. More...

struct	DerivationTrait< ScalarPlusBivector >
	Computes (a+U),x which is a,x+U,v. More...

struct	DerivationTrait< ScalarSquare >
	Computes (y^2),x which is 2 y y,x. More...

struct	DerivationTrait< ScalarTimesVector >
	Computes (av),x which is a,x v + a * v,x. More...

struct	DerivationTrait< UnaryMinus< NodeType > >
	Computes (-v),x which is -(v,x) More...

struct	DerivationTrait< VectorDotProduct >
	Computes (uv),x which is u,x * v + u * v,x. More...

struct	DerivationTrait< VectorSquare >
	Computes (v^2),x which is 2 v v,x. More...

struct	DerivationTrait< VectorTimesScalar >
	Computes (av),x which is a,x v + a * v,x. More...

struct	DerivationTrait< VectorWedgeVector >
	Computes $(u\wedge v),x$ which is $(u,x)\wedge v + u\wedge(v,x)$ . More...

struct	Determinantor
	The determinantor recursively computes the determinant of a matrix. More...

struct	Determinantor< 1 >
	The trivial determinant of a 1x1 matrix. More...

struct	Determinantor< 2 >
	The simple determinant of a 2x2 matrix. More...

struct	Determinantor< 3 >

struct	Determinantor< 4 >

struct	DomainFunctions

struct	DomainFunctions< RGB, DomainVector >

struct	DomainFunctions< RGBA, DomainVector >

class	DomainVector
	A vector type that is bound to a certain domain, inheriting all vector space properties, but provides type-safety to only operate within the same domain. More...

class	DomainVector< ScalarType[N], Domain, ScalarType >

struct	ElementOfFunctor

struct	EvaluationContext
	Class providing numerical values from some context ID for the evaluation of function trees. More...

class	Evaluator
	Abstract base class providing numerical values from some context ID for the evaluation of function trees. More...

class	Eye

struct	FA_CONVERT

class	FixedArray
	A FixedArray is a simple copy-by-value array providing random access to its elements. More...

struct	FixedArrayFlattener
	A template metaprogram class (type trait) to compute the flattened version of a FixedArray. More...

struct	FixedArrayFlattener< FixedArray< FixedArray< T, M >, N > >

struct	FixedArrayFlattener< FixedArray< T, N > >

struct	FixedArrayType

struct	FixedArrayType< ElementType, 1 >

class	GaussSolver

struct	GE

struct	GetFixedArrayType
	A template metaprogram class to compute the an fixed array type of an homogeneous type. More...

struct	GT

class	Head
	Properties of a camera floating around in space, or, alternatively, an eagle's eye. More...

class	Interpol
	Interpolation of certain values. More...

struct	InversionOperation

struct	IVec4Packed

struct	KDInterface

class	KDTree
	A multidimensional KDTree data structure rewritten from c-code by John Tsiombikas (http://code.google.com/p/kdtree/). More...

struct	KDTreeCallBackFunctor

struct	KDTreeResult

struct	KDTreeResult< std::list< T > >

struct	KDTreeResult< std::map< double, T > >

struct	KDTreeResult< std::multimap< double, T > >

struct	KDTreeResult< std::set< T > >

struct	KDTreeResult< std::vector< T > >

struct	KeyValue
	Entry in interpolation table with some flags. More...

struct	LE

struct	LeibnitzRule
	Implements the Leibnitz rule for derivatives for binary operators o: [A o B ],x = [A,x o B + [A o B,x]. More...

struct	LocationComponent
	Extracts a component of a location. More...

class	LowerTriangular
	A symmetric matrix stored in lower triangular form. More...

struct	LT

class	Matrix
	Simple matrix class for performing fast operations on matrices of sizes known at compile-time. More...

struct	MetaInfo

struct	MetaInfo< bivector3 >

struct	MetaInfo< bivector3f >

struct	MetaInfo< Christoffel< N, Scalar_t > >

struct	MetaInfo< ColorSpace::RGBA::tvector >

struct	MetaInfo< Column< N, Scalar_t > >

struct	MetaInfo< Coordinates< Cartesian3D, double >::bivector >

struct	MetaInfo< Coordinates< Cartesian3D, double >::covector >

struct	MetaInfo< Coordinates< Cartesian3D, double >::point >

struct	MetaInfo< Coordinates< Cartesian3D, double >::vector >

struct	MetaInfo< covector3f >

struct	MetaInfo< DomainVector< Vector< ValueType, 3 >, RGB > >

struct	MetaInfo< DomainVector< Vector< ValueType, 4 >, RGBA > >

struct	MetaInfo< DomainVector< VectorType, Domain, scalar_t > >

struct	MetaInfo< FixedArray< T, N > >
	Implement the meta-information on fixed arrays. More...

struct	MetaInfo< LowerTriangular< N, Scalar_t > >

struct	MetaInfo< Matrix< R, C, Value > >

struct	MetaInfo< metric33 >

struct	MetaInfo< point3 >

struct	MetaInfo< point3f >

struct	MetaInfo< Row< N, Scalar_t > >

struct	MetaInfo< trivector3 >

struct	MetaInfo< tvector3 >

struct	MetaInfo< vector3f >

struct	MetaInfo< Vector< T, N > >

struct	MetaInfo< void >

struct	MetaInfoElementIndex
	For multidimensional types T of rank MetaInfo<T>::RANK, this class provides a mapping from index space to memory space. More...

struct	MetaInfoElementIndex< Christoffel< N, Scalar_t > >

struct	MetaInfoElementIndex< LowerTriangular< N, Scalar_t > >

struct	MetaInfoElementIndex< Matrix< R, C, Value > >

struct	MetaInfoIO
	Helper class which is provides some textual output for MetaInfo types. More...

struct	MetaInfoIO< MetaInfo< T > >

struct	MetaInfoNonTensor

struct	MetaInfoNonTensor< Christoffel< N, Scalar_t > >

class	MultiRange

class	MultiVector

struct	MyDataHolder

struct	Node
	Abstract base class for evaluation of arbitrary functions that have been parsed from some input. More...

struct	NotElementOfFunctor

class	OcTree

struct	OneNode
	A scalar node that always returns one. More...

struct	Operator
	An type-only template used as argument on computational constructors. More...

struct	Operator<' *','~'>
	Multiply with transpose. More...

struct	Operator<' *'>

struct	Operator<'&'>

struct	Operator<'+','='>

struct	Operator<'+'>

struct	Operator<'-'>

struct	Operator<'/'>

struct	Operator<'='>

struct	Operator<'~'>
	Transpose. More...

struct	OperatorBase

class	ParserContext
	Internal class for communicating with the Bison/Yacc Parser and Flexical Stanza Generator. More...

class	Quadratic
	An n x n matrix (i.e., a vector of length nn), stored row-wise: that is, A(i,j) = A[ij], where ij = in + j. More...

class	QuadTree

struct	Raster
	Class for computing triangle strips on a uniform 2D distribution of points within a plane. More...

struct	RGB

struct	RGBA

class	rgba_float_t

class	Row
	A row vector,. More...

struct	ScalarCube
	Compute . More...

struct	ScalarPlusBivector
	A node operator implementing creation of rotor from scalar and bivector. More...

struct	ScalarSquare

struct	ScalarTimesVector
	A node implementing scalar times vector multiplication. More...

struct	Spherical3D

class	SubMatrix
	SubMatrix is a Matrix with row R and column C deleted. More...

class	SubQuadratic

struct	SumDerivation
	Implements the derivation of a sum [A + B ],x = A,x + B,x. More...

class	Tensor3

struct	TensorBase
	Tensor experiments. More...

struct	TernaryOperatorNode
	Template node class to perform ternary operations on evaluate-able nodes. More...

class	Torsion
	Torsion Tensor. More...

class	TransposeOperation

struct	TriangleStrip
	Class to compute a contiguous triangle strip for a two-dimensional set of points. More...

struct	TypedNode
	Templatized trait class for Nodes that yield a specific return type. More...

struct	TypeIndexingScheme

struct	TypeIndexingScheme< bivector3 >

struct	TypeIndexingScheme< bivector3f >

struct	TypeIndexingScheme< ColorSpace::RGBA::tvector >

struct	TypeIndexingScheme< covector3 >

struct	TypeIndexingScheme< covector3f >

struct	TypeIndexingScheme< trivector3 >

struct	TypeIndexingScheme< tvector3 >

struct	TypeIndexingScheme< vector3f >

struct	TypeIndexingScheme< Vector< T, N > >

struct	UIVec4Packed

struct	UnaryMinus

struct	UnaryOperatorNode
	Template node class to perform unary operations on evaluate-able nodes. More...

struct	unit

struct	Unit
	http://en.wikipedia.org/wiki/Fundamental_unit In the SI system there are 7 fundamental units: kilogram, meter, candela, second, ampere, kelvin, and mole. More...

struct	VariableNode
	A node that references some variable which will be set by the Context of the Evaluator. More...

struct	Vec3Pack32bit
	Generic unpacking from 32-bit integer with bits per channel given explicitly. More...

struct	Vec3Pack64bit
	Generic unpacking from 64-bit integer with bits per channel given explicitly. More...

struct	Vec3Pack_10_11_11

union	Vec3Packed

struct	Vec3Packed.packed

class	Vector
	A Vector is an fixed-size array (see class FixedArray) with vector space operations, i.e. More...

struct	VectorDotProduct
	Dot product between tangential vectors. More...

struct	VectorizationTrait
	A trait class to specify which vectorizations are possible. More...

struct	VectorSquare
	Computes v^2 for vector v. More...

struct	VectorTimesScalar
	A node implementing vector times scalar multiplication. More...

struct	VectorWedgeVector
	A node operator implementing creation of a bivector from two vectors. More...

class	ViewPoints
	A set of priority-weighted view points, used to recommend view points for objects. More...

struct	YlmCoefficients

struct	ZeroNode
	A scalar node that always returns zero. More...

Typedefs
typedef unsigned short	color16_t
	Type for 16-bit colors.

typedef unsigned char	color8_t
	Type for 8-bit colors.

typedef ConstantNode< ScalarNode >	ConstantScalarNode
	A scalar-valued node that yields a constant value, independent from the evaluation context.

typedef int	OperatorID_t
	The type identifying an Operator.

typedef DomainVector< Vector< color16_t, 3 >, RGB >	rgb16_t
	16 bit RGB colors

using	rgb_half_t = DomainVector< Vector< half, 3 >, RGB >
	16 bit floating point RGB colors

typedef DomainVector< Vector< color8_t, 3 >, RGB >	rgb_t
	8 bit RGB colors

typedef DomainVector< Vector< color16_t, 4 >, RGBA >	rgba16_t
	16 bit RGB colors with alpha channel

using	rgba_half_t = DomainVector< Vector< half, 4 >, RGBA >
	16 bit floating point RGBA colors with alpha channel

typedef DomainVector< Vector< color8_t, 4 >, RGBA >	rgba_t
	8 bit RGB colors with alpha channel

typedef TypedNode< double >	ScalarNode
	Base class for evaluation of a scalar function that has been parsed from some input.

typedef VariableNode< double >	ScalarVariableNode
	A node that references some variable which will be set by the Context of the Evaluator.

typedef ConstructorNode< VectorNode >	VectorConstructorNode
	A node that constructs a vector from three scalar values.

typedef TypedNode< tvector3 >	VectorNode
	Base class for evaluation of a vector-valued function that has been parsed from some input.

Arguments for computational constructors
typedef Operator<'+'>	Add
	Addition.

typedef Operator<'-'>	Sub
	Subtraction.

typedef Operator<' *'>	Mult
	Multiplication.

typedef Operator<'/'>	Div
	Division.

typedef Operator<'~'>	Conj
	Conjugate.

typedef Operator<','>	Deriv
	Derivative.

typedef Operator<'&'>	BinaryAnd
	Bit operations.

Functions
MemCore::RefPtr< MemCore::Chunk< Eagle::point3f > >	computeNumericalShift (const MemCore::RefPtr< MemCore::TypedChunk< Eagle::point3 > > &RawData, const FixedArray< double, 3 > &TranslationVector)
	Compute a shifted, single-precision version of the given data chunk of double-precision point coordinates.

RefPtr< ScalarNode >	cube (const RefPtr< ScalarNode > &x)
	Compute .

template<class value >
value	Det (const Quadratic< 1, value > &M)
	Determinant of 1x1 matrix (trivial)

template<class value >
value	Det (const Quadratic< 2, value > &M)
	Determinant of 2x2 matrix (easy)

template<class value >
value	Det (const Quadratic< 3, value > &M)
	Determinant of 3x3 matrix (straightforward)

template<class value >
value	Det (const Quadratic< 4, value > &M)
	Determinant of 4x4 matrix (effortsome) http://www.cvl.iis.u-tokyo.ac.jp/~miyazaki/tech/teche23.html.

double	faculty (unsigned long n)
	Division of two faculties, i.e. n!/m!

double	faculty_div (unsigned long n, unsigned long m)
	Division of two faculties, i.e. n!/m!

template<dimension_t C, class Value >
const Column< C, Value > &	InterpretAsColumn (const Row< C, Value > &A)
	Explicit treatment of a row as column, pure type conversion, readonly.

template<dimension_t C, class Value >
Column< C, Value > &	InterpretAsColumn (Row< C, Value > &A)
	Explicit treatment of a row as column, pure type conversion.

bool	IntervalOverlap (double a0, double a1, double b0, double b1)
	Check whether two intervals [a0,a1] and [b0,b1] overlap.

bool	IntervalOverlap (std::array< double, 2 > a, std::array< double, 2 > b)
	Check whether two intervals a=[a0,a1] and b=[b0,b1] overlap.

template<class IntType >
IntType	intPow (IntType n)
	Compute n^n of unsigned.

template<class IntType >
IntType	intPow (IntType n, IntType m)
	Compute n^m of ints.

template<class IntType >
IntType	intPowRecursive (IntType n, IntType m, IntType c)
	A helper function for a recursive implementation of pow of int.

constexpr bool	isEqual (double A, double B, double precision=1E-10)
	Compare two doubles with limited precision.

template<dimension_t M, dimension_t R, dimension_t C, class ValueA , class ValueB >
constexpr auto	Matrix_mult (const Matrix< R, M, ValueA > &A, const Matrix< M, C, ValueB > &B)
	Matrix product, version as function.

int	minus_exponential (int m)
	Return .

double	norm (const PhysicalSpace::bivector &v)
	The norm of a bivector.

double	norm (const PhysicalSpace::tvector &v)
	Compute the Euclidan norm of a vector.

double	norm2 (const PhysicalSpace::bivector &v)
	Compute the squared norm of a bivector, which is the area spun by the plane.

double	norm2 (const PhysicalSpace::tvector &v)
	Compute the squared norm of a vector v, i.e. v.v.

parzival_API RefPtr< Node >	One ()
	A node that is always one (type OneNode).

template<dimension_t C, class Value >
Column< C, Value >	operator* (const Column< C, Value > &A, double V)
	Multiply column vector by double.

template<dimension_t C, class Value >
Row< C, Value >	operator* (const Row< C, Value > &A, const double &V)
	Multiply row vector by double.

template<int N, class Value >
Value	operator* (const Row< N, Value > &l, const Column< N, Value > &r)
	Contraction operation: multiply row by column.

parzival_API MemCore::RefPtr< BivectorNode >	operator^ (const MemCore::RefPtr< VectorNode > &, const MemCore::RefPtr< VectorNode > &)
	Wedge product of two 3-vectors, yielding a bivector.

template<int N, class value >
Quadratic< N, value >	operator~ (Quadratic< N, value > Q)
	Return the transposed n x n square matrix.

template<class ResultType >
MemCore::RefPtr< typename ResultType::TypedNode_t > *	RefNode (ResultType *N)
	ingroup parzival Create a new reference pointer appropriate for the class given.

template<typename T >
T	sinc (T x)
	The sinc(x) function, save for x=0, and numerically stable around x=0.

RefPtr< ScalarNode >	square (const RefPtr< ScalarNode > &x)
	Compute .

parzival_API RefPtr< Node >	Zero ()
	A node that is always zero (type ZeroNode).

<A HREF="http://www.astro.virginia.edu/~eww6n/math/LegendrePolynomial.html">Legendre polynom</A> of order l,m
double	P0 (double x)
	$P_{0,0}(x)$

double	P1 (double x)
	$P_{1,0}(x)$

double	Pn (int n, double x)
	$P_{n,0}(x)$

double	Plm (int l, int m, double x)
	$P_{l,m}(x)$

double	Laguerre (int k, double x)
	http://en.wikipedia.org/wiki/Laguerre_polynomials

double eagle_API	Re_Ylm (int l, int m, double costheta, double phi)
	Real part of spherical harmonics $Y_{lm}$ .

double eagle_API	Im_Ylm (int l, int m, double costheta, double phi)
	Imaginary part of spherical harmonics $Y_{lm}$ .

std::complex< double > eagle_API	Ylm (int l, int m, double costheta, double phi)
	Spherical harmonics, complex return value.

std::complex< double > eagle_API	Ylm_sincos (int l, int m, double costheta, double sin_mphi, double cos_mphi)
	Spherical harmonics, complex return value with precomputed .

double eagle_API	abs2_Ylm (int l, int m, double costheta, double phi)
	- square of norm of complex spherical harmonic

int	lm_to_A (int l, int m)
	Computation of linear index from (l,m) pair.

void	A_to_lm (int A, int &l, int &m)
	Computation of (l,m) pair from linear index.

Detailed Description

Gather general basic mathematic functions which are not available in cmath here.

The "Eagle" namespace contains classes that implement vector and geometric algebra as well as interpolation procedures that ultimately allow the construction of camera paths.

Meta-template math functions go to meta/Math.hpp

The naming of the namespace is inspired by the sharp eye of the eagle, that requires description by the mathematics of geometric algebra. A camera path's purpose is a smooth flight through a virtual scene, like an eagle smoothly flies through a real scene.

Class Documentation

◆ Eagle::AnyType

struct Eagle::AnyType

◆ Eagle::Assert

struct Eagle::Assert

template<bool>
struct Eagle::Assert< bool >

◆ Eagle::Assert< true >

struct Eagle::Assert< true >

◆ Eagle::Assertion

struct Eagle::Assertion

template<bool>
struct Eagle::Assertion< bool >

◆ Eagle::Assertion< true >

struct Eagle::Assertion< true >

◆ Eagle::DerivationTrait

struct Eagle::DerivationTrait

template<class BinaryFunctor>
struct Eagle::DerivationTrait< BinaryFunctor >

Template type trait class to compute analytical derivates.

For binary operators as template argument, they will have

typedef typename BinaryFunctor::LeftNode_t LeftNode_t;

typedef typename BinaryFunctor::RightNode_t RightNode_t;

and the function to be implemented is:

RefPtr<Node> compute(RefPtr<LeftNode_t>, RefPtr<RightNode_t>, const ScalarVariableNode&Variable);

MemCore::StrongPtr

A reference counting pointer class which keeps objects alive as long as strong pointers to these obje...

Definition RefPtr.hpp:405

Eagle::VariableNode

A node that references some variable which will be set by the Context of the Evaluator.

Definition TypedNode.hpp:108

For unary operators:

typedef typename Functor::SourceNode_t Source_t;

RefPtr<Node> compute(RefPtr<Source_t>, const ScalarVariableNode&Variable);

◆ Eagle::FA_CONVERT

struct Eagle::FA_CONVERT

◆ Eagle::IVec4Packed

struct Eagle::IVec4Packed

◆ Eagle::KDTreeResult

struct Eagle::KDTreeResult

template<class Container>
struct Eagle::KDTreeResult< Container >

◆ Eagle::Operator

struct Eagle::Operator

template<OperatorID_t CompType, OperatorID_t bop = 0>
struct Eagle::Operator< CompType, bop >

An type-only template used as argument on computational constructors.

Parameters

CompType A free parameter to select the operation, such as '+', '*', '-' etc.

◆ Eagle::TransposeOperation

class Eagle::TransposeOperation

◆ Eagle::UIVec4Packed

struct Eagle::UIVec4Packed

◆ Eagle::Vec3Packed.packed

struct Eagle::Vec3Packed.packed

Typedef Documentation

◆ OperatorID_t

typedef int Eagle::OperatorID_t

The type identifying an Operator.

See class Operator for usage.

◆ ScalarNode

typedef TypedNode<double> Eagle::ScalarNode

Base class for evaluation of a scalar function that has been parsed from some input.

RefPtr<ScalarNode>      MyNode = ...;
 
EvaluationContext       EV;
double  value = MyNode->eval(EV);

◆ VectorNode

typedef TypedNode<tvector3> Eagle::VectorNode

Base class for evaluation of a vector-valued function that has been parsed from some input.

using namespace Eagle;
 
RefPtr<VectorNode>      MyNode = ...;
 
EvaluationContext       EV;
PhysicalSpace::tvector value = MyNode->eval(EV);

Function Documentation

◆ A_to_lm()

void Eagle::A_to_lm	(	int	A,
		int &	l,
		int &	m
	)

inline

Computation of (l,m) pair from linear index.

$l = \sqrt{ A_{lm} }$

$m = A_{lm} - l^2 - l$

◆ IntervalOverlap() [1/2]

bool Eagle::IntervalOverlap	(	double	a0,
		double	a1,
		double	b0,
		double	b1
	)

inline

Check whether two intervals [a0,a1] and [b0,b1] overlap.

Source and explanation: https://fgiesen.wordpress.com/2011/10/16/checking-for-interval-overlap/

Referenced by IntervalOverlap().

◆ IntervalOverlap() [2/2]

bool Eagle::IntervalOverlap	(	std::array< double, 2 >	a,
		std::array< double, 2 >	b
	)

inline

Check whether two intervals a=[a0,a1] and b=[b0,b1] overlap.

Source and explanation: https://fgiesen.wordpress.com/2011/10/16/checking-for-interval-overlap/

References IntervalOverlap().

◆ lm_to_A()

int Eagle::lm_to_A	(	int	l,
		int	m
	)

inline

Computation of linear index from (l,m) pair.

$A_{lm} = l^2 + l + m$

◆ norm()

double Eagle::norm ( const PhysicalSpace::tvector & v )

inline

Compute the Euclidan norm of a vector.

Note that if just the square of the norm is required, then function norm2() is more efficient since the square root does not need to be taken.

References norm2().

Referenced by Wizt::LineDescriptionTentacle::activate(), Wizt::Brush::computeBoundingBoxInScreenOverlaySpace(), Wizt::VCameraLens::environment_render(), GeoCameraLens::environment_render(), Wizt::CrossSectionCam::environment_render(), Eagle::PhysicalSpace::rotor::exp(), Eagle::BoundingBall::expandBall(), Eagle::Quadratic< N, Value >::GaussDecompose(), Wizt::VRenderContext::ModelShift(), Eagle::PhysicalSpace::vector::normalize(), Eagle::PhysicalSpace::vector::ortho(), Eagle::PhysicalSpace::vector::Ortho(), Wizt::VRenderContext::setEyeView(), Wizt::VRenderContext::setTileAwarePerspective(), Eagle::PhysicalSpace::vector::unit(), Eagle::PhysicalSpace::bivector::unit(), Wizt::VCamera::untranslatedLookAt(), and Wizt::VCamera::untranslatedLookAt().

◆ operator*()

template<int N, class Value >

Value Eagle::operator*	(	const Row< N, Value > &	l,
		const Column< N, Value > &	r
	)

inline

Contraction operation: multiply row by column.

Note that the reverse operation, ie. multiplying a column by a row, is the tensor product and yields a $n\times n$ matrix.

◆ RefNode()

template<class ResultType >

MemCore::RefPtr< typename ResultType::TypedNode_t > * Eagle::RefNode ( ResultType * N )

ingroup parzival Create a new reference pointer appropriate for the class given.

This is a convenience function for the Quest parser, since that one can only deal with native C pointers in the main union data type. It is not supposed to be used anywhere else than in this specific context.

◆ sinc()

template<typename T >

T Eagle::sinc ( T x )

inline

The sinc(x) function, save for x=0, and numerically stable around x=0.

When the sine function is written as a taylor series,

$sin(x) = x - x^3/3! + x^5/5! - x^7/7!$

we get the sinc(x) function as

$sin(x)/x = 1 - x^2/(2*3) + x^4/(2*3*4*5) - \cdots = 1 - x^2 [ 1 - x^2 / 20 ] / 6$

Namespaces

Classes

Typedefs

Functions

Detailed Description

Class Documentation

◆ Eagle::AnyType

◆ Eagle::Assert

◆ Eagle::Assert< true >

◆ Eagle::Assertion

◆ Eagle::Assertion< true >

◆ Eagle::DerivationTrait

◆ Eagle::FA_CONVERT

◆ Eagle::IVec4Packed

◆ Eagle::KDTreeResult

◆ Eagle::Operator

◆ Eagle::TransposeOperation

◆ Eagle::UIVec4Packed

◆ Eagle::Vec3Packed.packed

Typedef Documentation

◆ OperatorID_t

◆ ScalarNode

◆ VectorNode

Function Documentation

◆ A_to_lm()

◆ IntervalOverlap() [1/2]

◆ IntervalOverlap() [2/2]

◆ lm_to_A()

◆ norm()

◆ operator*()

◆ RefNode()

◆ sinc()