Package org.robwork.sdurw_geometry

Class QuadraticSurface

java.lang.Object

org.robwork.sdurw_geometry.QuadraticSurface

public class QuadraticSurface
extends java.lang.Object

A quadratic surface.

The general quadratic surface is described as an implicit surface of the form:

x^T A x + 2 a^T x + u = 0

where

A is a symmetric matrix, A \in \mathbb{R}^{3\times3} , and a \in \mathbb{R}^3, u \in \mathbb{R}

Constructor Summary

Constructors

Constructor	Description
QuadraticSurface(long cPtr, boolean cMemoryOwn)
QuadraticSurface(SWIGTYPE_p_Eigen__DiagonalMatrixT_double_3_3_t A, SWIGTYPE_p_Eigen__Vector3d a, double u)	Eigen::Diagonal<Eigen::Matrix3d>&, const Eigen::Vector3d&, double, const std::vector<TrimmingRegion>&)
QuadraticSurface(SWIGTYPE_p_Eigen__DiagonalMatrixT_double_3_3_t A, SWIGTYPE_p_Eigen__Vector3d a, double u, SWIGTYPE_p_std__vectorT_rw__core__PtrT_rw__geometry__ImplicitSurface_const_t_t conditions)	Eigen::Diagonal<Eigen::Matrix3d>&, const Eigen::Vector3d&, double, const std::vector<TrimmingRegion>&)
QuadraticSurface(SWIGTYPE_p_Eigen__DiagonalT_Eigen__Matrix3d_t A, SWIGTYPE_p_Eigen__Vector3d a, double u)	Construct new quadratic surface of the implicit form x^T A x + 2 a^T x + u = 0 when A is diagonal. Some functions, such as #getTriMesh and #extremums, work on a diagonalized surface. When this constructor is used, some effort is saved as the surface is already known to be diagonalized. For a diagonalized surface, all scaled, cloned and translated surfaces will also be diagonalized surfaces.
QuadraticSurface(SWIGTYPE_p_Eigen__DiagonalT_Eigen__Matrix3d_t A, SWIGTYPE_p_Eigen__Vector3d a, double u, SWIGTYPE_p_std__vectorT_rw__core__PtrT_rw__geometry__ImplicitSurface_const_t_t conditions)	Construct new quadratic surface of the implicit form x^T A x + 2 a^T x + u = 0 when A is diagonal. Some functions, such as #getTriMesh and #extremums, work on a diagonalized surface. When this constructor is used, some effort is saved as the surface is already known to be diagonalized. For a diagonalized surface, all scaled, cloned and translated surfaces will also be diagonalized surfaces.
QuadraticSurface(SWIGTYPE_p_Eigen__SelfAdjointViewT_Eigen__Matrix3d_const_Eigen__Lower_t A, SWIGTYPE_p_Eigen__Vector3d a, double u)	Construct new quadratic surface of the implicit form x^T A x + 2 a^T x + u = 0 when A is non-diagonal.
QuadraticSurface(SWIGTYPE_p_Eigen__SelfAdjointViewT_Eigen__Matrix3d_const_Eigen__Lower_t A, SWIGTYPE_p_Eigen__Vector3d a, double u, SWIGTYPE_p_std__vectorT_rw__core__PtrT_rw__geometry__ImplicitSurface_const_t_t conditions)	Construct new quadratic surface of the implicit form x^T A x + 2 a^T x + u = 0 when A is non-diagonal.
QuadraticSurface(SWIGTYPE_p_Eigen__SelfAdjointViewT_Eigen__Matrix3d_const_Eigen__Upper_t A, SWIGTYPE_p_Eigen__Vector3d a, double u)	Construct new quadratic surface of the implicit form x^T A x + 2 a^T x + u = 0 when A is non-diagonal.
QuadraticSurface(SWIGTYPE_p_Eigen__SelfAdjointViewT_Eigen__Matrix3d_const_Eigen__Upper_t A, SWIGTYPE_p_Eigen__Vector3d a, double u, SWIGTYPE_p_std__vectorT_rw__core__PtrT_rw__geometry__ImplicitSurface_const_t_t conditions)	Construct new quadratic surface of the implicit form x^T A x + 2 a^T x + u = 0 when A is non-diagonal.
QuadraticSurface(SWIGTYPE_p_Eigen__SelfAdjointViewT_Eigen__Matrix3d_Eigen__Lower_t A, SWIGTYPE_p_Eigen__Vector3d a, double u)	Eigen::SelfAdjointView<const Eigen::Matrix3d, Eigen::Lower>&, const Eigen::Vector3d&, double, const std::vector<TrimmingRegion>&)
QuadraticSurface(SWIGTYPE_p_Eigen__SelfAdjointViewT_Eigen__Matrix3d_Eigen__Lower_t A, SWIGTYPE_p_Eigen__Vector3d a, double u, SWIGTYPE_p_std__vectorT_rw__core__PtrT_rw__geometry__ImplicitSurface_const_t_t conditions)	Eigen::SelfAdjointView<const Eigen::Matrix3d, Eigen::Lower>&, const Eigen::Vector3d&, double, const std::vector<TrimmingRegion>&)
QuadraticSurface(SWIGTYPE_p_Eigen__SelfAdjointViewT_Eigen__Matrix3d_Eigen__Upper_t A, SWIGTYPE_p_Eigen__Vector3d a, double u)	Eigen::SelfAdjointView<const Eigen::Matrix3d, Eigen::Upper>&, const Eigen::Vector3d&, double, const std::vector<TrimmingRegion>&)
QuadraticSurface(SWIGTYPE_p_Eigen__SelfAdjointViewT_Eigen__Matrix3d_Eigen__Upper_t A, SWIGTYPE_p_Eigen__Vector3d a, double u, SWIGTYPE_p_std__vectorT_rw__core__PtrT_rw__geometry__ImplicitSurface_const_t_t conditions)	Eigen::SelfAdjointView<const Eigen::Matrix3d, Eigen::Upper>&, const Eigen::Vector3d&, double, const std::vector<TrimmingRegion>&)

Method Summary

Modifier and Type	Method	Description
SWIGTYPE_p_Eigen__Vector3d	a()	Get the 3d vector for the first order term in the implicit formulation.
SWIGTYPE_p_Eigen__Matrix3d	A()	Get the 3 x 3 symmetric matrix for the second order term in the implicit formulation.
void	addTrimmingCondition(ImplicitSurfaceCPtr condition)	Add a trimming condition to this surface.
double	call(Vector3D in)
QuadraticSurfacePtr	clone()
void	delete()
double	determinantA()	Get the determinant of the \mathbf{A} matrix.
SWIGTYPE_p_std__pairT_rw__geometry__QuadraticSurface_rw__math__Rotation3DT_t_t	diagonalize()	Get a diagonalization of the surface.
boolean	diagonalized()	Check if this surface is diagonalized.
pair_d_d	extremums(Vector3D direction)
static long	getCPtr(QuadraticSurface obj)
TriMeshPtr	getTriMesh()
TriMeshPtr	getTriMesh(SWIGTYPE_p_std__vectorT_rw__math__Vector3DT_double_t_t border)
SWIGTYPE_p_std__vectorT_rw__core__PtrT_rw__geometry__ImplicitSurface_const_t_t	getTrimmingConditions()	Get the trimming conditions for the surface.
Vector3D	gradient(Vector3D x)
boolean	insideTrimmingRegion(Vector3D P)
static QuadraticSurfacePtr	makeCircularCone(double a, double b)
static QuadraticSurfacePtr	makeCircularCylinder(double radius)
static QuadraticSurfacePtr	makeCircularCylinder(double radius, boolean outward)
static QuadraticSurfacePtr	makeCircularHyperboloidOneSheet(double a, double b)
static QuadraticSurfacePtr	makeCircularHyperboloidTwoSheets(double a, double b)
static QuadraticSurfacePtr	makeCircularParaboloid(double a)
static QuadraticSurfacePtr	makeEllipsoid(double a, double b, double c)
static QuadraticSurfacePtr	makeEllipticCone(double a, double b, double c)
static QuadraticSurfacePtr	makeEllipticCylinder(double a, double b)
static QuadraticSurfacePtr	makeEllipticHyperboloidOneSheet(double a, double b, double c)
static QuadraticSurfacePtr	makeEllipticHyperboloidTwoSheets(double a, double b, double c)
static QuadraticSurfacePtr	makeEllipticParaboloid(double a, double b)
static QuadraticSurfacePtr	makeHyperbolicCylinder(double a, double b)
static QuadraticSurfacePtr	makeHyperbolicParaboloid(double a, double b)
static QuadraticSurfacePtr	makeParabolicCylinder(double a)
static QuadraticSurfacePtr	makePlane(Vector3D n, double d)	Represent a plane as a QuadraticSurface. A plane is a particularly simple type of quadratic surface, where \mathbf{A}=\mathbf{0} . Even though a plane is not strictly a quadratic surface, is is often convenient to be able to treat it like a quadratic surface.
static QuadraticSurfacePtr	makeSphere(double radius)
static QuadraticSurfacePtr	makeSpheroid(double a, double b)
Vector3D	normal(Vector3D x)
QuadraticSurfacePtr	normalize()	Normalize the implicit expression such that the largest coefficient becomes one. For a quadratic surface, a scaling of \mathbf{A}, \mathbf{a} and u with a common factor, will give the exact same surface.
void	reuseTrimmingRegions(ImplicitSurfacePtr surface)
QuadraticSurfacePtr	scale(double factor)
void	setDiscretizationResolution(double resolution)
void	setTrimmingConditions(SWIGTYPE_p_std__vectorT_rw__core__PtrT_rw__geometry__ImplicitSurface_const_t_t conditions)	Set the trimming conditions of this surface.
boolean	SurfaceEqual(Surface surface, double threshold)
QuadraticSurfacePtr	transform(Transform3D T)	rw::math::Transform3D<double>&) const
QuadraticSurfacePtr	transform(Vector3D P)	rw::math::Vector3D<double>&) const
double	u()	Get the scalar for the zero order term in the implicit formulation.

Methods inherited from class java.lang.Object

equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

QuadraticSurface

public QuadraticSurface(long cPtr,
                        boolean cMemoryOwn)

QuadraticSurface

public QuadraticSurface(SWIGTYPE_p_Eigen__DiagonalT_Eigen__Matrix3d_t A,
                        SWIGTYPE_p_Eigen__Vector3d a,
                        double u,
                        SWIGTYPE_p_std__vectorT_rw__core__PtrT_rw__geometry__ImplicitSurface_const_t_t conditions)

Construct new quadratic surface of the implicit form x^T A x + 2 a^T x + u = 0 when A is diagonal.

Some functions, such as #getTriMesh and #extremums, work on a diagonalized surface.
When this constructor is used, some effort is saved as the surface is already known to be
diagonalized.

For a diagonalized surface, all scaled, cloned and translated surfaces will also be
diagonalized surfaces.

Parameters:

A - [in] the diagonal of the A matrix.

a - [in] the vector a \in \mathbb{R}^3 .

u - [in] the scalar offset u \in \mathbb{R} .

conditions - [in] (optional) list of trimming conditions.

QuadraticSurface

public QuadraticSurface(SWIGTYPE_p_Eigen__DiagonalT_Eigen__Matrix3d_t A,
                        SWIGTYPE_p_Eigen__Vector3d a,
                        double u)

Construct new quadratic surface of the implicit form x^T A x + 2 a^T x + u = 0 when A is diagonal.

Some functions, such as #getTriMesh and #extremums, work on a diagonalized surface.
When this constructor is used, some effort is saved as the surface is already known to be
diagonalized.

For a diagonalized surface, all scaled, cloned and translated surfaces will also be
diagonalized surfaces.

Parameters:

A - [in] the diagonal of the A matrix.

a - [in] the vector a \in \mathbb{R}^3 .

u - [in] the scalar offset u \in \mathbb{R} .

QuadraticSurface

public QuadraticSurface(SWIGTYPE_p_Eigen__DiagonalMatrixT_double_3_3_t A,
                        SWIGTYPE_p_Eigen__Vector3d a,
                        double u,
                        SWIGTYPE_p_std__vectorT_rw__core__PtrT_rw__geometry__ImplicitSurface_const_t_t conditions)

Eigen::Diagonal<Eigen::Matrix3d>&, const Eigen::Vector3d&, double, const std::vector<TrimmingRegion>&)

QuadraticSurface

public QuadraticSurface(SWIGTYPE_p_Eigen__DiagonalMatrixT_double_3_3_t A,
                        SWIGTYPE_p_Eigen__Vector3d a,
                        double u)

Eigen::Diagonal<Eigen::Matrix3d>&, const Eigen::Vector3d&, double, const std::vector<TrimmingRegion>&)

QuadraticSurface

public QuadraticSurface(SWIGTYPE_p_Eigen__SelfAdjointViewT_Eigen__Matrix3d_const_Eigen__Upper_t A,
                        SWIGTYPE_p_Eigen__Vector3d a,
                        double u,
                        SWIGTYPE_p_std__vectorT_rw__core__PtrT_rw__geometry__ImplicitSurface_const_t_t conditions)

Construct new quadratic surface of the implicit form x^T A x + 2 a^T x + u = 0 when A is non-diagonal.

Parameters:

A - [in] a view of the upper part of the symmetric matrix A \in \mathbb{R}^{3\times3} . Use the Eigen function A.selfadjointView<Eigen::Upper>() to
extract the upper part.

a - [in] the vector a \in \mathbb{R}^3 .

u - [in] the scalar offset u \in \mathbb{R} .

conditions - [in] (optional) list of trimming conditions.

QuadraticSurface

public QuadraticSurface(SWIGTYPE_p_Eigen__SelfAdjointViewT_Eigen__Matrix3d_const_Eigen__Upper_t A,
                        SWIGTYPE_p_Eigen__Vector3d a,
                        double u)

Construct new quadratic surface of the implicit form x^T A x + 2 a^T x + u = 0 when A is non-diagonal.

Parameters:

A - [in] a view of the upper part of the symmetric matrix A \in \mathbb{R}^{3\times3} . Use the Eigen function A.selfadjointView<Eigen::Upper>() to
extract the upper part.

a - [in] the vector a \in \mathbb{R}^3 .

u - [in] the scalar offset u \in \mathbb{R} .

QuadraticSurface

public QuadraticSurface(SWIGTYPE_p_Eigen__SelfAdjointViewT_Eigen__Matrix3d_Eigen__Upper_t A,
                        SWIGTYPE_p_Eigen__Vector3d a,
                        double u,
                        SWIGTYPE_p_std__vectorT_rw__core__PtrT_rw__geometry__ImplicitSurface_const_t_t conditions)

Eigen::SelfAdjointView<const Eigen::Matrix3d, Eigen::Upper>&, const Eigen::Vector3d&, double, const std::vector<TrimmingRegion>&)

QuadraticSurface

public QuadraticSurface(SWIGTYPE_p_Eigen__SelfAdjointViewT_Eigen__Matrix3d_Eigen__Upper_t A,
                        SWIGTYPE_p_Eigen__Vector3d a,
                        double u)

Eigen::SelfAdjointView<const Eigen::Matrix3d, Eigen::Upper>&, const Eigen::Vector3d&, double, const std::vector<TrimmingRegion>&)

QuadraticSurface

public QuadraticSurface(SWIGTYPE_p_Eigen__SelfAdjointViewT_Eigen__Matrix3d_const_Eigen__Lower_t A,
                        SWIGTYPE_p_Eigen__Vector3d a,
                        double u,
                        SWIGTYPE_p_std__vectorT_rw__core__PtrT_rw__geometry__ImplicitSurface_const_t_t conditions)

Construct new quadratic surface of the implicit form x^T A x + 2 a^T x + u = 0 when A is non-diagonal.

Parameters:

A - [in] a view of the lower part of the symmetric matrix A \in \mathbb{R}^{3\times3} . Use the Eigen function A.selfadjointView<Eigen::Lower>() to
extract the lower part.

a - [in] the vector a \in \mathbb{R}^3 .

u - [in] the scalar offset u \in \mathbb{R} .

conditions - [in] (optional) list of trimming conditions.

QuadraticSurface

public QuadraticSurface(SWIGTYPE_p_Eigen__SelfAdjointViewT_Eigen__Matrix3d_const_Eigen__Lower_t A,
                        SWIGTYPE_p_Eigen__Vector3d a,
                        double u)

Construct new quadratic surface of the implicit form x^T A x + 2 a^T x + u = 0 when A is non-diagonal.

Parameters:

A - [in] a view of the lower part of the symmetric matrix A \in \mathbb{R}^{3\times3} . Use the Eigen function A.selfadjointView<Eigen::Lower>() to
extract the lower part.

a - [in] the vector a \in \mathbb{R}^3 .

u - [in] the scalar offset u \in \mathbb{R} .

QuadraticSurface

public QuadraticSurface(SWIGTYPE_p_Eigen__SelfAdjointViewT_Eigen__Matrix3d_Eigen__Lower_t A,
                        SWIGTYPE_p_Eigen__Vector3d a,
                        double u,
                        SWIGTYPE_p_std__vectorT_rw__core__PtrT_rw__geometry__ImplicitSurface_const_t_t conditions)

Eigen::SelfAdjointView<const Eigen::Matrix3d, Eigen::Lower>&, const Eigen::Vector3d&, double, const std::vector<TrimmingRegion>&)

QuadraticSurface

public QuadraticSurface(SWIGTYPE_p_Eigen__SelfAdjointViewT_Eigen__Matrix3d_Eigen__Lower_t A,
                        SWIGTYPE_p_Eigen__Vector3d a,
                        double u)

Eigen::SelfAdjointView<const Eigen::Matrix3d, Eigen::Lower>&, const Eigen::Vector3d&, double, const std::vector<TrimmingRegion>&)

Method Detail

getCPtr

public static long getCPtr(QuadraticSurface obj)

delete

public void delete()

transform

public QuadraticSurfacePtr transform(Transform3D T)

rw::math::Transform3D<double>&) const

transform

public QuadraticSurfacePtr transform(Vector3D P)

rw::math::Vector3D<double>&) const

scale

public QuadraticSurfacePtr scale(double factor)

clone

public QuadraticSurfacePtr clone()

extremums

public pair_d_d extremums(Vector3D direction)

getTriMesh

public TriMeshPtr getTriMesh(SWIGTYPE_p_std__vectorT_rw__math__Vector3DT_double_t_t border)

getTriMesh

public TriMeshPtr getTriMesh()

setDiscretizationResolution

public void setDiscretizationResolution(double resolution)

SurfaceEqual

public boolean SurfaceEqual(Surface surface,
                            double threshold)

call

public double call(Vector3D in)

insideTrimmingRegion

public boolean insideTrimmingRegion(Vector3D P)

normal

public Vector3D normal(Vector3D x)

gradient

public Vector3D gradient(Vector3D x)

reuseTrimmingRegions

public void reuseTrimmingRegions(ImplicitSurfacePtr surface)

A

public SWIGTYPE_p_Eigen__Matrix3d A()

Get the 3 x 3 symmetric matrix for the second order term in the implicit formulation.

a

public SWIGTYPE_p_Eigen__Vector3d a()

Get the 3d vector for the first order term in the implicit formulation.

u

public double u()

Get the scalar for the zero order term in the implicit formulation.

determinantA

public double determinantA()

Get the determinant of the \mathbf{A} matrix.

Returns:

the determinant.

normalize

public QuadraticSurfacePtr normalize()

Normalize the implicit expression such that the largest coefficient becomes one.

For a quadratic surface, a scaling of \mathbf{A}, \mathbf{a} and u with a common
factor, will give the exact same surface. This means that the numerical values can get
arbitrarily big or small. This functions scales the expression such that the largest
element becomes 1.

Returns:

a mathematically identical surface, where the coefficients of the defining
equation is normalized.

getTrimmingConditions

public SWIGTYPE_p_std__vectorT_rw__core__PtrT_rw__geometry__ImplicitSurface_const_t_t getTrimmingConditions()

Get the trimming conditions for the surface.

Returns:

ImplicitSurface vector specifying the boundary of the surface. If surface is
unbounded, the length of the vector is zero.

setTrimmingConditions

public void setTrimmingConditions(SWIGTYPE_p_std__vectorT_rw__core__PtrT_rw__geometry__ImplicitSurface_const_t_t conditions)

Set the trimming conditions of this surface.

Parameters:

conditions - [in] a vector of conditions.

addTrimmingCondition

public void addTrimmingCondition(ImplicitSurfaceCPtr condition)

Add a trimming condition to this surface.

Parameters:

condition - [in] the condition to add.

diagonalize

public SWIGTYPE_p_std__pairT_rw__geometry__QuadraticSurface_rw__math__Rotation3DT_t_t diagonalize()

Get a diagonalization of the surface.

Returns:

the diagonalized surface, and the rotation transforming this surface into the
diagonalized surface.

diagonalized

public boolean diagonalized()

Check if this surface is diagonalized.

Returns:

true if A is digaonalized, false otherwise.

makeEllipsoid

public static QuadraticSurfacePtr makeEllipsoid(double a,
                                                double b,
                                                double c)

makeSpheroid

public static QuadraticSurfacePtr makeSpheroid(double a,
                                               double b)

makeSphere

public static QuadraticSurfacePtr makeSphere(double radius)

makeEllipticParaboloid

public static QuadraticSurfacePtr makeEllipticParaboloid(double a,
                                                         double b)

makeCircularParaboloid

public static QuadraticSurfacePtr makeCircularParaboloid(double a)

makeHyperbolicParaboloid

public static QuadraticSurfacePtr makeHyperbolicParaboloid(double a,
                                                           double b)

makeEllipticHyperboloidOneSheet

public static QuadraticSurfacePtr makeEllipticHyperboloidOneSheet(double a,
                                                                  double b,
                                                                  double c)

makeCircularHyperboloidOneSheet

public static QuadraticSurfacePtr makeCircularHyperboloidOneSheet(double a,
                                                                  double b)

makeEllipticHyperboloidTwoSheets

public static QuadraticSurfacePtr makeEllipticHyperboloidTwoSheets(double a,
                                                                   double b,
                                                                   double c)

makeCircularHyperboloidTwoSheets

public static QuadraticSurfacePtr makeCircularHyperboloidTwoSheets(double a,
                                                                   double b)

makeEllipticCone

public static QuadraticSurfacePtr makeEllipticCone(double a,
                                                   double b,
                                                   double c)

makeCircularCone

public static QuadraticSurfacePtr makeCircularCone(double a,
                                                   double b)

makeEllipticCylinder

public static QuadraticSurfacePtr makeEllipticCylinder(double a,
                                                       double b)

makeCircularCylinder

public static QuadraticSurfacePtr makeCircularCylinder(double radius,
                                                       boolean outward)

makeCircularCylinder

public static QuadraticSurfacePtr makeCircularCylinder(double radius)

makeHyperbolicCylinder

public static QuadraticSurfacePtr makeHyperbolicCylinder(double a,
                                                         double b)

makeParabolicCylinder

public static QuadraticSurfacePtr makeParabolicCylinder(double a)

makePlane

public static QuadraticSurfacePtr makePlane(Vector3D n,
                                            double d)

Represent a plane as a QuadraticSurface.

A plane is a particularly simple type of quadratic surface, where
\mathbf{A}=\mathbf{0} .

Even though a plane is not strictly a quadratic surface, is is often convenient to be
able to treat it like a quadratic surface.

Parameters:

n - [in] the normal of the plane.

d - [in] the distance from the plane to the origo.

Returns:

a QuadraticSurface representing a plane.