Cone< Precision > Class Template Reference

A representation of a cone. More...

#include <gz/math/Cone.hh>

Public Member Functions
	Cone ()=default
	Default constructor. The default radius and length are both zero. The default rotational offset is Quaternion<Precision>::Identity.
	Cone (const Precision _length, const Precision _radius, const Material &_mat, const Quaternion< Precision > &_rotOffset=Quaternion< Precision >::Identity)
	Construct a cone with a length, radius, material and optionally a rotational offset.
	Cone (const Precision _length, const Precision _radius, const Quaternion< Precision > &_rotOffset=Quaternion< Precision >::Identity)
	Construct a cone with a length, radius, and optionally a rotational offset.
std::optional< Vector3< Precision > >	CenterOfVolumeBelow (const Plane< Precision > &_plane) const
	Center of volume below the plane. This is useful for example when calculating where buoyancy should be applied.
Vector3< Precision >	Centroid () const
	Get the centroid of the cone in its reference frame (defined in the class description): on the axis of symmetry, a quarter of the length from the base toward the vertex, i.e. (0, 0, -length/4) rotated by the rotational offset. This is the standard solid cone centroid; see for example the centroid tables in the CRC Standard Mathematical Tables and Formulae.
Precision	DensityFromMass (const Precision _mass) const
	Compute the cone's density given a mass value. The cone is assumed to be solid with uniform density. This function requires the cone's radius and length to be set to values greater than zero. The Material of the cone is ignored.
Precision	Length () const
	Get the length in meters.
std::optional< MassMatrix3< Precision > >	MassMatrix () const
	Get the mass matrix for this cone. This function is only meaningful if the cone's radius, length, and material have been set. Optionally, set the rotational offset.
bool	MassMatrix (MassMatrix3d &_massMat) const
	Get the mass matrix for this cone. This function is only meaningful if the cone's radius, length, and material have been set. Optionally, set the rotational offset.
const Material &	Mat () const
	Get the material associated with this cone.
bool	operator== (const Cone &_cone) const
	Check if this cone is equal to the provided cone. Radius, length, and material properties will be checked.
Precision	Radius () const
	Get the radius in meters.
Quaternion< Precision >	RotationalOffset () const
	Get the rotational offset. By default, a cone's length is aligned with the Z axis. The rotational offset encodes a rotation from the z axis.
bool	SetDensityFromMass (const Precision _mass)
	Set the density of this cone based on a mass value. Density is computed using Precision DensityFromMass(const Precision _mass) const. The cone is assumed to be solid with uniform density. This function requires the cone's radius and length to be set to values greater than zero. The existing Material density value is overwritten only if the return value from this true.
void	SetLength (const Precision _length)
	Set the length in meters.
void	SetMat (const Material &_mat)
	Set the material associated with this cone.
void	SetRadius (const Precision _radius)
	Set the radius in meters.
void	SetRotationalOffset (const Quaternion< Precision > &_rotOffset)
	Set the rotation offset.
Precision	Volume () const
	Get the volume of the cone in m^3.
Precision	VolumeBelow (const Plane< Precision > &_plane) const
	Get the volume of the cone below a given plane in m^3. It is assumed that the center of the cone is on the origin.

Detailed Description

template<typename Precision>
class gz::math::Cone< Precision >

A representation of a cone.

The cone class supports defining a cone with a radius, length, rotational offset, and material properties. Radius and length are in meters. See Material for more on material properties.

A reference frame is defined with an origin on the axis of symmetry equidistant from the vertex and the circular base, with XYZ coordinate axes defined with the Z axis parallel to the axis of symmetry and pointing toward the vertex of the cone. This frame is consistent with the SDFormat cone shape. The rotational offset encodes an additional rotation of the cone relative to this frame.

Constructor & Destructor Documentation

Cone() [1/3]

template<typename Precision >

Cone ( )

default

Default constructor. The default radius and length are both zero. The default rotational offset is Quaternion<Precision>::Identity.

Cone() [2/3]

template<typename Precision >

Cone	(	const Precision	_length,
		const Precision	_radius,
		const Quaternion< Precision > &	_rotOffset = Quaternion< Precision >::Identity
	)

Construct a cone with a length, radius, and optionally a rotational offset.

Parameters

[in]	_length	Length of the cone.
[in]	_radius	Radius of the cone.
[in]	_rotOffset	Rotational offset of the cone.

Cone() [3/3]

template<typename Precision >

Cone	(	const Precision	_length,
		const Precision	_radius,
		const Material &	_mat,
		const Quaternion< Precision > &	_rotOffset = Quaternion< Precision >::Identity
	)

Construct a cone with a length, radius, material and optionally a rotational offset.

Parameters

[in]	_length	Length of the cone.
[in]	_radius	Radius of the cone.
[in]	_mat	Material property for the cone.
[in]	_rotOffset	Rotational offset of the cone.

Member Function Documentation

CenterOfVolumeBelow()

template<typename Precision >

std::optional< Vector3< Precision > > CenterOfVolumeBelow

(

const Plane< Precision > &

_plane

)

const

Center of volume below the plane. This is useful for example when calculating where buoyancy should be applied.

Parameters

[in]

_plane

The plane which slices this cone, expressed in the cone's reference frame.

Returns

The center of volume if there is anything below the plane, otherwise return a std::nullopt. Expressed in the cone's reference frame.

Centroid()

template<typename Precision >

Vector3< Precision > Centroid

(

)

const

Get the centroid of the cone in its reference frame (defined in the class description): on the axis of symmetry, a quarter of the length from the base toward the vertex, i.e. (0, 0, -length/4) rotated by the rotational offset. This is the standard solid cone centroid; see for example the centroid tables in the CRC Standard Mathematical Tables and Formulae.

Returns

The centroid, expressed in the cone's reference frame.

DensityFromMass()

template<typename Precision >

Precision DensityFromMass

(

const Precision

_mass

)

const

Compute the cone's density given a mass value. The cone is assumed to be solid with uniform density. This function requires the cone's radius and length to be set to values greater than zero. The Material of the cone is ignored.

Parameters

[in]

_mass

Mass of the cone, in kg. This value should be greater than zero.

Returns

Density of the cone in kg/m^3. A negative value is returned if radius, length or _mass is <= 0.

Length()

template<typename Precision >

Precision Length

(

)

const

Get the length in meters.

Returns

The length of the cone in meters.

MassMatrix() [1/2]

template<typename Precision >

std::optional< MassMatrix3< Precision > > MassMatrix

(

)

const

Get the mass matrix for this cone. This function is only meaningful if the cone's radius, length, and material have been set. Optionally, set the rotational offset.

Returns

The computed mass matrix if parameters are valid (radius > 0), (length > 0) and (density > 0). Otherwise std::nullopt is returned.

MassMatrix() [2/2]

template<typename Precision >

bool MassMatrix

(

MassMatrix3d &

_massMat

)

const

Get the mass matrix for this cone. This function is only meaningful if the cone's radius, length, and material have been set. Optionally, set the rotational offset.

Parameters

[out]

_massMat

The computed mass matrix will be stored here.

Returns

False if computation of the mass matrix failed, which could be due to an invalid radius (<=0), length (<=0), or density (<=0).

Mat()

template<typename Precision >

const Material & Mat

(

)

const

Get the material associated with this cone.

Returns

The material assigned to this cone

operator==()

template<typename Precision >

bool operator==

(

const Cone< Precision > &

_cone

)

const

Check if this cone is equal to the provided cone. Radius, length, and material properties will be checked.

Radius()

template<typename Precision >

Precision Radius

(

)

const

Get the radius in meters.

Returns

The radius of the cone in meters.

RotationalOffset()

template<typename Precision >

Quaternion< Precision > RotationalOffset

(

)

const

Get the rotational offset. By default, a cone's length is aligned with the Z axis. The rotational offset encodes a rotation from the z axis.

Returns

The cone's rotational offset.

See also

void SetRotationalOffset(const Quaternion<Precision> &_rot)

SetDensityFromMass()

template<typename Precision >

bool SetDensityFromMass

(

const Precision

_mass

)

Set the density of this cone based on a mass value. Density is computed using Precision DensityFromMass(const Precision _mass) const. The cone is assumed to be solid with uniform density. This function requires the cone's radius and length to be set to values greater than zero. The existing Material density value is overwritten only if the return value from this true.

Parameters

[in]

_mass

Mass of the cone, in kg. This value should be greater than zero.

Returns

True if the density was set. False is returned if the cone's radius, length, or the _mass value are <= 0.

See also

Precision DensityFromMass(const Precision _mass) const

SetLength()

template<typename Precision >

void SetLength

(

const Precision

_length

)

Set the length in meters.

Parameters

[in]

_length

The length of the cone in meters.

SetMat()

template<typename Precision >

void SetMat

(

const Material &

_mat

)

Set the material associated with this cone.

Parameters

[in]

_mat

The material assigned to this cone

SetRadius()

template<typename Precision >

void SetRadius

(

const Precision

_radius

)

Set the radius in meters.

Parameters

[in]

_radius

The radius of the cone in meters.

SetRotationalOffset()

template<typename Precision >

void SetRotationalOffset

(

const Quaternion< Precision > &

_rotOffset

)

Set the rotation offset.

Parameters

[in]

_rotOffset

rotational offset quaternion. See Quaternion<Precision> RotationalOffset() for details on the rotational offset.

See also

Quaternion<Precision> RotationalOffset() const

Volume()

template<typename Precision >

Precision Volume

(

)

const

Get the volume of the cone in m^3.

Returns

Volume of the cone in m^3.

VolumeBelow()

template<typename Precision >

Precision VolumeBelow

(

const Plane< Precision > &

_plane

)

const

Get the volume of the cone below a given plane in m^3. It is assumed that the center of the cone is on the origin.

Parameters

[in]

_plane

The plane which slices this cone, expressed in the cone's reference frame.

Returns

Volume below the plane in m^3.

---

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

• Cone.hh