Interface for implicit surfaces. An implicit surface is given by an expression of the form \( F(\mathbf{x})=0, \mathbf{x} \in \mathbb{R}^3\). More...

#include <ImplicitSurface.hpp>

Inherits Surface.

Inherited by ImplicitTorus, and QuadraticSurface.

Public Types
typedef rw::core::Ptr< ImplicitSurface >	Ptr
	Smart pointer type for ImplicitSurface.

typedef rw::core::Ptr< const ImplicitSurface >	CPtr
	Smart pointer type for const ImplicitSurface.

Public Types inherited from Surface
typedef rw::core::Ptr< Surface >	Ptr
	Smart pointer type for Surface.

typedef rw::core::Ptr< const Surface >	CPtr
	Smart pointer type for const Surface.

Public Member Functions
	ImplicitSurface ()
	Constructor.

virtual	~ImplicitSurface ()
	Destructor.

ImplicitSurface::Ptr	transform (const rw::math::Transform3D< double > &T) const
	Move the surface. More...

ImplicitSurface::Ptr	transform (const rw::math::Vector3D< double > &P) const
	Move the surface without rotation. More...

ImplicitSurface::Ptr	scale (double factor) const
	Get a scaled version of the surface. More...

ImplicitSurface::Ptr	clone () const
	Clone the surface. More...

virtual std::pair< double, double >	extremums (const rw::math::Vector3D< double > &direction) const =0
	Find the extent of the surface along a specific direction. More...

virtual rw::core::Ptr< TriMesh >	getTriMesh (const std::vector< rw::math::Vector3D< double >> &border=std::vector< rw::math::Vector3D< double >>()) const =0
	Discretize the surface into a triangle mesh representation. More...

virtual void	setDiscretizationResolution (double resolution)=0
	Set the resolution used for discretization in the getTriMesh function. More...

virtual bool	equals (const Surface &surface, double threshold) const =0
	Check if this surface is identical to other surface . More...

virtual double	operator() (const rw::math::Vector3D< double > &x) const =0
	Evaluate the implicit function, \( F(\mathbf{x}) \), for the surface. More...

virtual bool	insideTrimmingRegion (const rw::math::Vector3D< double > &P) const
	Check if point, P, on surface lies inside the trimming region. More...

virtual rw::math::Vector3D< double >	normal (const rw::math::Vector3D< double > &x) const
	Get the normal of the surface at a specific point, x, lying on the surface. More...

virtual rw::math::Vector3D< double >	gradient (const rw::math::Vector3D< double > &x) const =0
	Get the gradient, \(\nabla \mathbf{F}\), of the surface at a specific point, x, lying on the surface. More...

virtual void	reuseTrimmingRegions (ImplicitSurface::Ptr surface) const
	Let other surface reuse this surfaces trimming regions, if there are identical region definitions. More...

Public Member Functions inherited from Surface
	Surface ()
	Constructor.

virtual	~Surface ()
	Destructor.

Surface::Ptr	transform (const rw::math::Transform3D< double > &T) const
	Move the surface. More...

Surface::Ptr	transform (const rw::math::Vector3D< double > &P) const
	Move the surface without rotation. More...

Surface::Ptr	scale (double factor) const
	Get a scaled version of the surface. More...

Surface::Ptr	clone () const
	Clone the surface. More...

Detailed Description

Interface for implicit surfaces. An implicit surface is given by an expression of the form \( F(\mathbf{x})=0, \mathbf{x} \in \mathbb{R}^3\).

Member Function Documentation

◆ clone()

ImplicitSurface::Ptr clone ( ) const

inline

Clone the surface.

Returns: pointer to copy of surface.

◆ equals()

virtual bool equals	(	const Surface &	surface,
		double	threshold
	)		const

pure virtual

Check if this surface is identical to other surface .

Parameters

surface	[in] other surface to compare to.
threshold	[in] threshold for when surfaces can be considered identical.

Returns: true if identical, false otherwise.

Implements Surface.

Implemented in QuadraticSurface, and ImplicitTorus.

◆ extremums()

virtual std::pair<double, double> extremums ( const rw::math::Vector3D< double > & direction ) const

pure virtual

Find the extent of the surface along a specific direction.

If the surface has no lower bound, the value -std::numeric_limits<double>::max() can be returned to indicate that the surface has unbounded minimum value in the given direction.

If the surface has no upper bound, the value std::numeric_limits<double>::max() can be returned to indicate that the surface has unbounded maximum value in the given direction.

Parameters

direction [in] a normalized direction vector.

Returns: the minimum and maximum values along the given direction.

Note: This function does not take trimming conditions into account. For trimmed surfaces, create a Face with the boundary curves and use Face::extremums.

Implements Surface.

Implemented in QuadraticSurface, and ImplicitTorus.

◆ getTriMesh()

virtual rw::core::Ptr<TriMesh> getTriMesh ( const std::vector< rw::math::Vector3D< double >> & border = std::vector< rw::math::Vector3D< double >>() ) const

pure virtual

Discretize the surface into a triangle mesh representation.

If the border of a trimmed surface must fit with other surface triangulations, a discretized border must be given to this triangulation function.

If the same border points are used for different surfaces for their common edges, the triangulations will fit together.

Parameters

border [in] (optional) an ordered list of points on the surface, that forms the border of the patch to triangulate.

Returns: a new TriMesh.

Implements Surface.

Implemented in QuadraticSurface, and ImplicitTorus.

◆ gradient()

virtual rw::math::Vector3D<double> gradient ( const rw::math::Vector3D< double > & x ) const

pure virtual

Get the gradient, \(\nabla \mathbf{F}\), of the surface at a specific point, x, lying on the surface.

The gradient is the vector of partial derivatives \( \nabla \mathbf{F} = \begin{bmatrix}\frac{\partial F}{\partial x} & \frac{\partial F}{\partial y} & \frac{\partial F}{\partial z} \end{bmatrix}^T \)

Parameters

x	[in] a point on the surface.

Returns: the gradient, \(\nabla \mathbf{F}\), of the surface at x .

See also: the normal function to find the normal to the surface (the normalized gradient).

Implemented in QuadraticSurface, and ImplicitTorus.

◆ insideTrimmingRegion()

virtual bool insideTrimmingRegion ( const rw::math::Vector3D< double > & P ) const

inlinevirtual

Check if point, P, on surface lies inside the trimming region.

Parameters

P	[in] the point to check.

Returns: true if the points lies inside the trimming region.

Reimplemented in QuadraticSurface, and ImplicitTorus.

◆ normal()

virtual rw::math::Vector3D<double> normal ( const rw::math::Vector3D< double > & x ) const

inlinevirtual

Get the normal of the surface at a specific point, x, lying on the surface.

For the point on the implicit surface, where \( F(\mathbf{x})=0 \) , the normal is the direction of the gradient \(\frac{\nabla \mathbf{F}}{\|\nabla \mathbf{F}\|}\) .

Parameters

x	[in] a point on the surface.

Returns: the normal to the surface at x .

See also: the gradient function to find the gradient.

Reimplemented in QuadraticSurface, and ImplicitTorus.

◆ operator()()

virtual double operator() ( const rw::math::Vector3D< double > & x ) const

pure virtual

Evaluate the implicit function, \( F(\mathbf{x}) \), for the surface.

Parameters

x	[in] the point to evaluate.

Returns: the value of the implicit function. If smaller than zero, x lies inside the surface. If larger than zero, x lies outside the surface.

Implemented in QuadraticSurface, and ImplicitTorus.

◆ reuseTrimmingRegions()

virtual void reuseTrimmingRegions ( ImplicitSurface::Ptr surface ) const

inlinevirtual

Let other surface reuse this surfaces trimming regions, if there are identical region definitions.

This allows for some implementations to save a small amount of memory.

Parameters

surface [in/out] the other surface.

Reimplemented in QuadraticSurface, and ImplicitTorus.

◆ scale()

ImplicitSurface::Ptr scale ( double factor ) const

inline

Get a scaled version of the surface.

Parameters

factor [in] the factor to scale with.

Returns: a new scaled surface.

◆ setDiscretizationResolution()

virtual void setDiscretizationResolution ( double resolution )

pure virtual

Set the resolution used for discretization in the getTriMesh function.

The meaning of this parameter depends on the type of surface.

Parameters

resolution [in] the resolution parameter.

Implements Surface.

Implemented in QuadraticSurface, and ImplicitTorus.

◆ transform() [1/2]

ImplicitSurface::Ptr transform ( const rw::math::Transform3D< double > & T ) const

inline

Move the surface.

Parameters

T	[in] the transform to the new surface.

Returns: pointer to a new surface.

See also: transform(const rw::math::Vector3D<double>&) const if there is no rotation. This will preserve some nice properties for certain types of surfaces.

◆ transform() [2/2]

ImplicitSurface::Ptr transform ( const rw::math::Vector3D< double > & P ) const

inline

Move the surface without rotation.

If there is no rotation, this function is better to use than transform(const rw::math::Transform3D<>&) const for some surfaces. This is because certain properties can be preserved.

Parameters

P	[in] the translation vector to the new surface.

Returns: pointer to a new surface.

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

ImplicitSurface.hpp

Public Types

Public Member Functions

Detailed Description

Member Function Documentation

◆ clone()

◆ equals()

◆ extremums()

◆ getTriMesh()

◆ gradient()

◆ insideTrimmingRegion()

◆ normal()

◆ operator()()

◆ reuseTrimmingRegions()

◆ scale()

◆ setDiscretizationResolution()

◆ transform() [1/2]

◆ transform() [2/2]