Utility functions for calculating properties of geometry. More...

#include <GeometryUtil.hpp>

Static Public Member Functions
static double	estimateVolume (const std::vector< rw::core::Ptr< rw::geometry::Geometry >> &geoms)
	Estimates the volume of a list of geometries. More...

static double	estimateVolume (const rw::geometry::TriMesh &trimesh)
	Estimates the volume of a trimesh. More...

static std::pair< rw::math::Vector3D< double >, rw::math::InertiaMatrix<> >	estimateInertiaCOG (double mass, const std::vector< rw::core::Ptr< rw::geometry::Geometry >> &geoms, const rw::core::Ptr< rw::kinematics::Frame > ref, const rw::kinematics::State &state, const rw::math::Transform3D<> &reftrans=rw::math::Transform3D<>::identity())
	Estimates the inertia and center of gravity (COG) of a list of geometries. More...

static rw::math::InertiaMatrix	estimateInertia (double mass, const std::vector< rw::core::Ptr< rw::geometry::Geometry >> &geoms, const rw::core::Ptr< rw::kinematics::Frame > ref, const rw::kinematics::State &state, const rw::math::Transform3D<> &reftrans=rw::math::Transform3D<>::identity())
	Estimates the inertia of a list of geometries. More...

static rw::math::InertiaMatrix	estimateInertia (double mass, const std::vector< rw::core::Ptr< rw::geometry::Geometry >> &geoms, const rw::math::Transform3D<> &reftrans=rw::math::Transform3D<>::identity())
	Estimates the inertia of a list of geometries. More...

template<class T >
static std::pair< rw::math::Rotation3D< T >, rw::math::Vector3D< T > >	calculatePrincipalInertia (const rw::math::InertiaMatrix< T > &inertia)
	Find the principal axes and the principal inertia. More...

static rw::math::Vector3D< double >	estimateCOG (const std::vector< rw::core::Ptr< rw::geometry::Geometry >> &geoms)
	Estimates the center of gravity (COG) of a list of geometries. More...

static rw::math::Vector3D< double >	estimateCOG (const std::vector< rw::core::Ptr< rw::geometry::Geometry >> &geoms, const rw::core::Ptr< rw::kinematics::Frame > ref, const rw::kinematics::State &state)
	Estimates the center of gravity (COG) of a list of geometries. More...

static rw::math::Vector3D< double >	estimateCOG (const TriMesh &trimesh, const rw::math::Transform3D<> &t3d=rw::math::Transform3D<>::identity())
	Estimates the center of gravity (COG) of a triangle mesh. More...

static double	calcMaxDist (const std::vector< rw::core::Ptr< rw::geometry::Geometry >> &geoms, const rw::math::Vector3D< double > center, rw::core::Ptr< rw::kinematics::Frame > ref, const rw::kinematics::State &state)
	calculates the max distance to any triangle in the geoms, from some point center More...

static std::vector< rw::kinematics::Frame * >	getAnchoredFrames (rw::kinematics::Frame &f, const rw::kinematics::State &state)
	util function that locates all frames that is staticly connected to f and that has geometry information.

static std::vector< rw::kinematics::Frame * >	getAnchoredChildFrames (rw::core::Ptr< rw::kinematics::Frame > parent, const rw::kinematics::State &state)
	util function that locates all frames in the sub tree of parent that is staticly connected and that has geometry information.

template<std::size_t N>
static double	simplexVolume (const std::vector< rw::math::VectorND< N >> &vertices)
	calculates volume of k-simplex More...

static std::pair< rw::math::Vector3D< double >, rw::math::Vector3D< double > >	getExtremumDistances (rw::core::Ptr< TriMesh > trimesh, const rw::math::Transform3D<> &t3d=rw::math::Transform3D<>::identity())
	Returns the extremum distances for the vertices of the TriMesh given the specified transformation. More...

static rw::math::Vector3D< double >	getDimensions (rw::core::Ptr< rw::geometry::Geometry > geometry)
	Returns the dimensions of geometry. More...

static rw::math::Vector3D< double >	getDimensions (rw::core::Ptr< TriMesh > trimesh)
	Returns the dimensions of trimesh. More...

template<std::size_t N>
static double	actualSimplexVolume (const std::vector< rw::math::VectorND< N >> &vertices)
	Calculates the volume of a N-simplex. Volume of a N-simplex is calculated as: \( V_{Simplex} = \frac{\|W\|}{N!} \), where: More...

Detailed Description

Utility functions for calculating properties of geometry.

The methods for calculation of volume, inertia, and the center of gravity, is as described in [1].

[1]: Fast and Accurate Computation of Polyhedral Mass Properties, Brian Mirtich. Journal of Graphics Tools, Vol.1, pages 31-58, 1996

Member Function Documentation

◆ actualSimplexVolume()

static double actualSimplexVolume ( const std::vector< rw::math::VectorND< N >> & vertices )

inlinestatic

Calculates the volume of a N-simplex. Volume of a N-simplex is calculated as: \( V_{Simplex} = \frac{|W|}{N!} \), where:

\( W \) is the N*N matrix \( [v_{1}-v_{0} , \:v_{i}-v_{0}\:\cdots\: , v_{N}-v_{0}] \) Where \( v_{i} \) is the i'th vertic given. This function can be supplied with N and N+1 vertices. If only N vertices are given, then the volume is calculated with the origo as the remaining vertex. (See https://en.wikipedia.org/wiki/Simplex#Volume)

◆ calcMaxDist()

static double calcMaxDist	(	const std::vector< rw::core::Ptr< rw::geometry::Geometry >> &	geoms,
		const rw::math::Vector3D< double >	center,
		rw::core::Ptr< rw::kinematics::Frame >	ref,
		const rw::kinematics::State &	state
	)

static

calculates the max distance to any triangle in the geoms, from some point center

Parameters

geoms	[in] the geometries containing the triangles
center	[in] the point to calculate the distance from
ref	[in] the reference frame.
state

Returns: the maximum distance to any triangle in the geometries

◆ calculatePrincipalInertia()

static std::pair<rw::math::Rotation3D<T>, rw::math::Vector3D<T> > calculatePrincipalInertia ( const rw::math::InertiaMatrix< T > & inertia )

inlinestatic

Find the principal axes and the principal inertia.

Parameters

inertia [in] the inertia matrix to calculate principal values for.

Returns: a rotation matrix giving the principal axes, and a vector of principal inertia values for these axes.

◆ estimateCOG() [1/3]

static rw::math::Vector3D<double> estimateCOG ( const std::vector< rw::core::Ptr< rw::geometry::Geometry >> & geoms )

static

Estimates the center of gravity (COG) of a list of geometries.

The COG will be found relative to the geometry frame.

Note: The geometries should be defined relative to the same frame - otherwise the result will not make sense.

Parameters

geoms [in] the list of geometries.

Returns: the center of gravity for the geometries.

◆ estimateCOG() [2/3]

static rw::math::Vector3D<double> estimateCOG	(	const std::vector< rw::core::Ptr< rw::geometry::Geometry >> &	geoms,
		const rw::core::Ptr< rw::kinematics::Frame >	ref,
		const rw::kinematics::State &	state
	)

static

Estimates the center of gravity (COG) of a list of geometries.

The COG will be given relative to the given reference frame.

Parameters

geoms	[in] the list of geometries.
ref	[in] the reference frame.
state	[in] the state which gives the position of the geometries relative to the reference frame.

Returns: the center of gravity for the geometries.

◆ estimateCOG() [3/3]

static rw::math::Vector3D<double> estimateCOG	(	const TriMesh &	trimesh,
		const rw::math::Transform3D<> &	t3d = `rw::math::Transform3D<>::identity()`
	)

static

Estimates the center of gravity (COG) of a triangle mesh.

Parameters

trimesh	[in] the triangle mesh.
t3d	[in] (optional) make a transformation of the trimesh.

Returns: the center of gravity of the mesh.

◆ estimateInertia() [1/2]

static rw::math::InertiaMatrix estimateInertia	(	double	mass,
		const std::vector< rw::core::Ptr< rw::geometry::Geometry >> &	geoms,
		const rw::core::Ptr< rw::kinematics::Frame >	ref,
		const rw::kinematics::State &	state,
		const rw::math::Transform3D<> &	reftrans = `rw::math::Transform3D<>::identity()`
	)

static

Estimates the inertia of a list of geometries.

The inertia is described relative to the ref coordinate system The reftrans parameter can however be used to transform the geometries.

Parameters

mass	[in] the total mass of all geometries.
geoms	[in] the list of geometries.
ref	[in] the reference frame for the geometries (if NULL, it is assumed that the geometries are defined relative to the same frame).
state	[in] state used to retrieve the current location of geometries relative to the reference frame (only used if ref is given).
reftrans	[in] (optional) used to transform the geometry before calculation of the inertia.

Returns: the inertia around relative to the ref frame.

◆ estimateInertia() [2/2]

static rw::math::InertiaMatrix estimateInertia	(	double	mass,
		const std::vector< rw::core::Ptr< rw::geometry::Geometry >> &	geoms,
		const rw::math::Transform3D<> &	reftrans = `rw::math::Transform3D<>::identity()`
	)

static

Estimates the inertia of a list of geometries.

The inertia is described relative to the geometry reference frame. The reftrans parameter can however be used to transform the geometries.

Note: The geometries should be defined relative to the same frame - otherwise the result will not make sense.

Parameters

mass	[in] the total mass of all geometries.
geoms	[in] the list of geometries.
reftrans	[in] (optional) used to transform the geometry before calculation of the inertia.

Returns: the inertia matrix relative to the reference frame.

◆ estimateInertiaCOG()

static std::pair<rw::math::Vector3D<double>, rw::math::InertiaMatrix<> > estimateInertiaCOG	(	double	mass,
		const std::vector< rw::core::Ptr< rw::geometry::Geometry >> &	geoms,
		const rw::core::Ptr< rw::kinematics::Frame >	ref,
		const rw::kinematics::State &	state,
		const rw::math::Transform3D<> &	reftrans = `rw::math::Transform3D<>::identity()`
	)

static

Estimates the inertia and center of gravity (COG) of a list of geometries.

The inertia is described relative to the ref coordinate system translated to COG. The reftrans parameter can however be used to transform the geometries.

Parameters

mass	[in] the total mass of all geometries.
geoms	[in] the list of geometries.
ref	[in] the reference frame for the geometries (if NULL, it is assumed that the geometries are defined relative to the same frame).
state	[in] state used to retrieve the current location of geometries relative to the reference frame (only used if ref is given).
reftrans	[in] (optional) used to transform the geometry before calculation of the inertia.

Returns: the center of gravity relative to the ref frame and the inertia around the center of gravity (in the coordinate frame of the ref frame).

◆ estimateVolume() [1/2]

static double estimateVolume ( const rw::geometry::TriMesh & trimesh )

static

Estimates the volume of a trimesh.

Parameters

trimesh [in] the trimesh.

Returns: the total volume of the trimesh.

◆ estimateVolume() [2/2]

static double estimateVolume ( const std::vector< rw::core::Ptr< rw::geometry::Geometry >> & geoms )

static

Estimates the volume of a list of geometries.

Note: If geometries are overlapping, the overlapping regions will count twice in the volume.

Parameters

geoms [in] the list of geometries.

Returns: the total volume of the geometries.

◆ getDimensions() [1/2]

static rw::math::Vector3D<double> getDimensions ( rw::core::Ptr< rw::geometry::Geometry > geometry )

static

Returns the dimensions of geometry.

Parameters

geometry [in] Geometry to analyse

Returns: Dimensions in the x,y and z directions.

◆ getDimensions() [2/2]

static rw::math::Vector3D<double> getDimensions ( rw::core::Ptr< TriMesh > trimesh )

static

Returns the dimensions of trimesh.

Parameters

trimesh [in] TriMesh to analyse

Returns: Dimensions in the x,y and z directions.

◆ getExtremumDistances()

static std::pair<rw::math::Vector3D<double>, rw::math::Vector3D<double> > getExtremumDistances	(	rw::core::Ptr< TriMesh >	trimesh,
		const rw::math::Transform3D<> &	t3d = `rw::math::Transform3D<>::identity()`
	)

static

Returns the extremum distances for the vertices of the TriMesh given the specified transformation.

Parameters

trimesh	[in] TriMesh to find extremum distances for
t3d	[in] Transformation of the vertices

Returns: Pair containing the lower and upper extremum distances of the vertices.

◆ simplexVolume()

static double simplexVolume ( const std::vector< rw::math::VectorND< N >> & vertices )

inlinestatic

calculates volume of k-simplex

Warning: What is meant by volume is not really volume, see "actualSimplexVolume" - if you want the volume. Read the documentation (preferably code), to make sure you get what you want.

Volume of k-dimensional simplex (triangle is 2-simplex) is calculated as: \( V(S) = \frac{1}{k!} \sqrt{W W^T}\), where:

\( W \) is a matrix consisting of rows

\(w_i = [v_{i,1}-v_{0,1}\:v_{i,2}-v_{0, 2}\:\cdots\:v_{i,k+1}-v_{0,k+1}] \)

of i-th vertex coordinates. (taken from: http://www.math.niu.edu/~rusin/known-math/97/volumes.polyh) (dead link)

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

GeometryUtil.hpp

Static Public Member Functions

Detailed Description

Member Function Documentation

◆ actualSimplexVolume()

◆ calcMaxDist()

◆ calculatePrincipalInertia()

◆ estimateCOG() [1/3]

◆ estimateCOG() [2/3]

◆ estimateCOG() [3/3]

◆ estimateInertia() [1/2]

◆ estimateInertia() [2/2]

◆ estimateInertiaCOG()

◆ estimateVolume() [1/2]

◆ estimateVolume() [2/2]

◆ getDimensions() [1/2]

◆ getDimensions() [2/2]

◆ getExtremumDistances()

◆ simplexVolume()