3D torus function. The function is defined by the torus center, axis, and major and inner radii. The function presents a negative sign inside the torus, and positive outside. More...

#include <primitive_funcs_lib.hpp>

Inheritance diagram for qugar::impl::funcs::TorusBzr:

[legend]

Collaboration diagram for qugar::impl::funcs::TorusBzr:

[legend]

Public Member Functions
	TorusBzr (real major_radius, real minor_radius)
	Constructor.

	TorusBzr (real major_radius, real minor_radius, const Point< 3 > &center)
	Constructor.

	TorusBzr (real major_radius, real minor_radius, const Point< 3 > &center, const Point< 3 > &axis)
	Constructor.

Public Member Functions inherited from qugar::impl::funcs::TorusBase
	TorusBase (real major_radius, real minor_radius, const Point< 3 > &center, const Point< 3 > &axis)
	Constructor.

real	major_radius () const
	Gets the major radius of the torus.

real	minor_radius () const
	Gets the minor radius of the torus.

const Point< 3 > &	center () const
	Gets the center of the plane.

const Point< 3 > &	axis () const
	Gets the axis of the plane.

Public Member Functions inherited from qugar::impl::BezierTP< 3, 1 >
	BezierTP (const TensorSizeTP< dim > &order)
	Constructor.

	BezierTP (const TensorSizeTP< dim > &order, const CoefsType &value)
	Constructs a constant value Bezier tensor product.

	BezierTP (const TensorSizeTP< dim > &order, const std::vector< CoefsType > &coefs)
	Constructor.

	BezierTP (const BezierTP< dim, range > &bezier)
	Copy constructor.

	BezierTP (const MonomialsTP< dim, range > &monomials)
	Constructor.

virtual Value< real >	operator() (const Point< dim > &point) const final
	Evaluator operator.

virtual Value< Interval< dim > >	operator() (const Point< dim, Interval< dim > > &point) const final
	Evaluator operator.

virtual Gradient< real >	grad (const Point< dim > &point) const final
	Gradient evaluator operator.

virtual Gradient< Interval< dim > >	grad (const Point< dim, Interval< dim > > &point) const final
	Gradient evaluator operator.

virtual Hessian< real >	hessian (const Point< dim > &point) const final
	Hessian evaluator operator.

const ::algoim::xarray< CoefsType, dim > &	get_xarray () const
	Gets a constant reference to the stored xarray view of the polynomial coefficients.

std::shared_ptr< BezierTP< dim - 1, range > >	extract_facet (const int local_facet_id) const

std::shared_ptr< BezierTP< dim, range > >	raise_order (const TensorSizeTP< dim > &new_order) const
	Raises the order of the Bezier tensor product.

std::shared_ptr< BezierTP< dim, range > >	negate () const
	Creates a new Bezier tensor product (TP) object that is the negation of the current object.

void	rescale_domain (const BoundBox< dim > &new_domain)
	Recomputes (in-place) the Bezier coefficients for a new domain (that may not be [0, 1]).

FuncSign	sign () const
	Returns the sign of the function represented by the Bézier tensor-product using the properties of the control points convex hull.

std::shared_ptr< BezierTP< dim, range > >	operator* (const BezierTP< dim, range > &rhs) const
	Product of two Beziers.

std::shared_ptr< BezierTP< dim, range > >	operator+ (const BezierTP< dim, range > &rhs) const
	Addition of two Beziers.

std::shared_ptr< BezierTP< dim, range > >	operator- (const BezierTP< dim, range > &rhs) const
	Subtraction of two Beziers.

std::shared_ptr< BezierTP< sub_dim, range > >	compose (const BezierTP< sub_dim, dim > &rhs) const
	Composes the current Bezier with the given Bezier `rhs`.

Public Member Functions inherited from qugar::impl::PolynomialTP< dim, range >
	PolynomialTP (const TensorSizeTP< dim > &order)
	Constructor.

	PolynomialTP (const TensorSizeTP< dim > &order, const CoefsType &value)
	Constructs a constant value PolynomialTP object with the specified order.

	PolynomialTP (const TensorSizeTP< dim > &order, const std::vector< CoefsType > &coefs)
	Constructor.

std::size_t	get_num_coefs () const
	Get the number of coeficients.

const std::vector< CoefsType > &	get_coefs () const
	Gets the polynomial coefficients.

const TensorSizeTP< dim > &	get_order () const
	Gets the polynomial order along the parametric directions.

int	get_order (int dir) const
	Gets the polynomial order (degree + 1) along the direction `dir`.

const CoefsType &	get_coef (int index) const
	Retrieves the coefficients at the specified index.

CoefsType &	get_coef (int index)
	Retrieves the coefficients at the specified index.

const CoefsType &	get_coef (const TensorIndexTP< dim > &index) const
	Retrieves the coefficient associated with the given tensor index.

CoefsType &	get_coef (const TensorIndexTP< dim > &index)
	Retrieves the coefficient associated with the given tensor index.

int	get_degree (int dir) const
	Gets the polynomial degree (order - 1) along the direction `dir`.

void	transform_image (const BoundBox< range > &old_domain, const BoundBox< range > &new_domain)
	Transforms (in place) the coefficients of the polynomial from `old_domain` to `new_domain`.

void	coefs_linear_transform (const real scale, const CoefsType &shift)
	Applies a linear transformation to every coefficient.

Public Member Functions inherited from qugar::impl::DomainFunc< dim, range >
	DomainFunc ()=default
	Default constructor.

	DomainFunc (const DomainFunc &)=default
	Default copy constructor.

	DomainFunc (DomainFunc &&)=default
	Default move constructor.

DomainFunc &	operator= (const DomainFunc &)=default
	Default copy assignment operator.

DomainFunc &	operator= (DomainFunc &&)=default
	Default move assignment operator.

virtual	~DomainFunc ()=default
	Default virtual destructor.

Static Private Member Functions
static std::shared_ptr< MonomialsTP< 3, 1 > >	create_monomials (real major_radius, real minor_radius, const Point< 3 > &center, const Point< 3 > &axis)
	Creates a polynomial representation based on monomials for the given radii, center, and axis.

Additional Inherited Members
Public Types inherited from qugar::impl::BezierTP< 3, 1 >
using	Parent
	Parent type.

using	CoefsType
	Coefs type.

using	Value
	Value type.

using	Gradient
	Gradient type.

using	Hessian
	Hessian type.

using	Interval
	Algoim's interval alias.

Public Types inherited from qugar::impl::PolynomialTP< dim, range >
using	CoefsType = std::conditional_t<range == 1, real, Point<range>>
	Coefs type.

Public Types inherited from qugar::impl::DomainFunc< dim, range >
template<int N>
using	Interval = ::algoim::Interval<N>
	Algoim's interval alias.

template<typename T >
using	Value = std::conditional_t<range == 1, T, Vector<T, range>>
	Value type.

template<typename T >
using	Gradient = Vector<Value<T>, dim>
	Gradient type.

template<typename T >
using	Hessian = Vector<Value<T>, num_hessian>
	Hessian (symmetric type).

Static Public Member Functions inherited from qugar::impl::BezierTP< 3, 1 >
static Value< T >	casteljau (const Point< dim, T > &point, typename std::vector< CoefsType >::const_iterator &coefs, const Vector< int, dim > &order)
	Evaluates a Bezier polynomial using the Casteljau's algorithm.

static Vector< Value< T >, dim+1 >	casteljau_der (const Point< dim, T > &point, typename std::vector< CoefsType >::const_iterator &coefs, const Vector< int, dim > &order)
	Evaluates the gradient Bezier polynomial using the Casteljau's algorithm.

Static Public Attributes inherited from qugar::impl::DomainFunc< dim, range >
static const int	num_hessian = dim * (dim + 1) / 2
	Number of Hessian (symmetric) components.

Static Protected Member Functions inherited from qugar::impl::funcs::TorusBase
static Point< 3 >	get_default_center ()
	Gets the default center of the torus. It is set to the center of the Cartesian coordinate system.

static Point< 3 >	get_default_axis ()
	Gets the default axis of the torus. It is set to the z-axis of the Cartesian coordinate system.

Protected Attributes inherited from qugar::impl::funcs::TorusBase
real	major_radius_
	Major radius of the torus.

real	minor_radius_
	Minor radius of the torus.

Point< 3 >	center_
	Center of the torus.

Point< 3 >	axis_
	Axis of the torus.

Protected Attributes inherited from qugar::impl::PolynomialTP< dim, range >
TensorSizeTP< dim >	order_
	Order of the polynomial along each parametric direction.

std::vector< CoefsType >	coefs_

Detailed Description

3D torus function. The function is defined by the torus center, axis, and major and inner radii. The function presents a negative sign inside the torus, and positive outside.

Note: Bezier version.

Constructor & Destructor Documentation

◆ TorusBzr() [1/3]

qugar::impl::funcs::TorusBzr::TorusBzr	(	real	major_radius,
		real	minor_radius )

Constructor.

Center is set to (0,0,0) and axis to (0,0,1).

Parameters

major_radius	Radius of the major circle.
minor_radius	Radius of the inner circle.

◆ TorusBzr() [2/3]

qugar::impl::funcs::TorusBzr::TorusBzr	(	real	major_radius,
		real	minor_radius,
		const Point< 3 > &	center )

Constructor.

The axis is set to (0,0,1).

Parameters

major_radius	Radius of the major circle.
minor_radius	Radius of the inner circle.
center	Torus' center.

◆ TorusBzr() [3/3]

qugar::impl::funcs::TorusBzr::TorusBzr	(	real	major_radius,
		real	minor_radius,
		const Point< 3 > &	center,
		const Point< 3 > &	axis )

Constructor.

Parameters

major_radius	Radius of the major circle.
minor_radius	Radius of the inner circle.
center	Torus' center.
axis	Torus' axis (perpendicular to the major circle plane).

Member Function Documentation

◆ create_monomials()

static std::shared_ptr< MonomialsTP< 3, 1 > > qugar::impl::funcs::TorusBzr::create_monomials	(	real	major_radius,
		real	minor_radius,
		const Point< 3 > &	center,
		const Point< 3 > &	axis )

staticnodiscardprivate

Creates a polynomial representation based on monomials for the given radii, center, and axis.

Parameters

major_radius	Radius of the major circle.
minor_radius	Radius of the inner circle.
center	Torus' center.
axis	Torus' axis (perpendicular to the major circle plane).

The documentation for this class was generated from the following file:

/__w/qugar/qugar/cpp/include/qugar/primitive_funcs_lib.hpp

Public Member Functions

Static Private Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ TorusBzr() [1/3]

◆ TorusBzr() [2/3]

◆ TorusBzr() [3/3]

Member Function Documentation

◆ create_monomials()