A class representing a spherical harmonics object. More...

#include <shape_spherical_harmonics.hpp>

Inheritance diagram for netdem::SphericalHarmonics:

Public Member Functions
	SphericalHarmonics ()
	Default constructor.

	SphericalHarmonics (int n)
	Constructor with specified degree.

nlohmann::json	PackJson () override
	Pack the SphericalHarmonics object into a JSON structure.

void	InitFromJson (nlohmann::json const &js) override
	Initialize the SphericalHarmonics object from a JSON structure.

void	InitFromSTL (std::string const &file)
	Initialize the SphericalHarmonics object from an STL file.

void	InitFromSTL (STLModel const &stl_model)
	Initialize the SphericalHarmonics object from an STL model.

void	InitFromSurfacePoints (VecXT< Vec3d > const surf_points)
	Initialize the SphericalHarmonics object from a list of surface points.

void	Init ()
	Initialize the SphericalHarmonics object.

void	UpdateSurfaceNodes () override
	Update the surface nodes of the SphericalHarmonics object.

void	UpdateShapeProperties () override
	Update the shape properties of the SphericalHarmonics object.

void	SetSize (double d) override
	Set the size of the SphericalHarmonics object.

STLModel	GetSTLModel (int num_nodes=200) override
	Generate an STL model for the SphericalHarmonics object.

Shape *	Clone () const override
	Clone the SphericalHarmonics object.

double	SignedDistance (Vec3d const &pos) const override
	Compute the signed distance between a point and the SphericalHarmonics object.

Vec3d	SurfacePoint (Vec3d const &pos) override
	Compute the surface point of the SphericalHarmonics object closest to a given point.

Vec3d	SurfaceNormal (Vec3d const &pos)

Vec2d	SurfaceCurvature (Vec3d const &pos)

Vec3d	SurfaceNormal (double theta, double phi)

Vec2d	SurfaceCurvature (double theta, double phi)

double	CalculateRho (double theta, double phi) const
	Calculate the rho value for a given theta and phi.

double	CalculateRho (Vec3d const &dir) const
	Calculate the rho value for a given direction vector.

Public Member Functions inherited from netdem::Shape
virtual void	InitFromJsonFile (std::string const &js_file)
	Initializes the shape instance from a JSON file.

virtual double	GetSize () const
	Return shape size, which is defined as the diameter of equal-volume sphere.

virtual double	GetVolume () const
	Return the volume of the shape.

virtual Mat3d const &	GetInertia () const
	Return the inertia of the shape.

Vec3d	GetInertiaPrincipal () const
	Return the principal inertia of the shape.

virtual double	GetBoundSphereRadius () const
	Return the inertia of the shape.

virtual std::tuple< Vec3d, Vec3d >	GetBoundAABB () const
	Gets the boundary AABB of the shape instance.

virtual std::tuple< Vec3d, Vec3d >	GetBoundAABB (Vec3d const &pos, Vec4d const &quat) const
	Gets the boundary AABB of the shape instance.

virtual double	GetSkin () const
	Return skin size of the shape.

virtual double	GetSkinFactor () const
	Return skin factor of the shape.

virtual double	GetSurfaceNodeNum () const
	Return number of surface nodes of the shape.

virtual VecXT< Vec3d > const &	GetSurfaceNodes () const
	Return surface nodes of the shape.

virtual VecXT< double > const &	GetSurfaceNodeAreas () const
	Return surface area associated with each surface node.

virtual double	GetSurfaceNodeSpacing () const
	Return spacing of surface nodes.

const STLModel &	GetRenderMesh () const
	Return the surface mesh for rendering.

bool	CheckConvexity ()
	Return the convexity of the shape.

virtual void	Translate (Vec3d const &pos)
	Translates the shape instance to a new position.

virtual void	UpdateRenderMesh (int num_nodes=200)
	Initializes the surface mesh for rendering.

virtual void	SetSkin (double sk)
	Set skin size of the shape.

virtual void	SetSkinFactor (double sk_factor)
	Set skin size factor (skin = size by skin size factor) of the shape.

virtual void	EnableSurfaceNodes ()
	Enable the use of surface nodes.

virtual void	DisableSurfaceNodes ()
	Disable the use of surface nodes.

virtual bool	IsSurfaceNodesEnabled ()
	Check if the use of surface nodes is enabled.

virtual void	SetSurfaceNodeNum (int num)
	Set number of surface nodes of the shape.

virtual void	SetSurfaceNodes (VecXT< Vec3d > const &nodes)
	Set the surface nodes of the shape.

virtual void	SetSurfaceNodes (STLModel const &surf_stl)
	Set the surface nodes of the shape.

virtual void	SaveAsVTK (std::string const &filename)
	Saves the shape instance as a VTK file.

virtual void	SaveAsSTL (std::string const &filename)
	Saves the shape instance as an STL file.

virtual Vec3d	SupportPoint (Vec3d const &dir)
	Gets the support point in a given direction for the shape instance.

virtual VecXT< Vec3d >	SupportPoints (Vec3d const &dir)
	Gets the set of support points in a given direction for the shape instance.

virtual bool	CheckEnclose (Vec3d const &pos) const
	Determines whether a given point is enclosed within the shape instance.

virtual bool	CheckPrincipal () const
	Determines whether the shape is in principal configuration.

virtual void	Print ()
	Prints the properties of the shape instance.

virtual	~Shape ()
	Destructor for the Shape class.

Static Public Member Functions
static VecXT< double >	CalculateYnm (double theta, double phi, int deg)
	Calculate the spherical harmonics terms for a given theta, phi, and degree.

static VecXT< VecXT< double > >	CalculateYnm (const VecXT< double > &theta, const VecXT< double > &phi, int deg)
	Calculate the spherical harmonics terms for given theta, phi vectors, and degree.

static VecXT< double >	CalculateYnm_Fast (double theta, double phi, int deg)
	Calculate the spherical harmonics terms for a given theta, phi, and degree using pre-calculated values.

static VecXT< VecXT< double > >	CalculateYnm_Fast (const VecXT< double > &theta, const VecXT< double > &phi, int deg)
	Calculate the spherical harmonics terms for given theta, phi vectors, and degree using pre-calculated values.

static VecXT< double >	CalculateYnm_Fast (Vec3d const &dir, int deg)

static VecXT< VecXT< double > >	CalculateYnm_Fast (const VecXT< Vec3d > &dir_list, int deg)

Static Public Member Functions inherited from netdem::Shape
static MatNd< 8, 3 >	VerticesOfAABB (Vec3d const &bmin, Vec3d const &bmax)
	Gets the vertices of the boundary AABB of the shape instance.

Public Attributes
int	degree {8}
	The degree of the SphericalHarmonics object.

VecXT< double >	a_nm

Public Attributes inherited from netdem::Shape
int	id {0}
	ID of the shape instance.

std::string	label {"default"}
	Label of the shape instance.

Type	shape_type {Type::none}
	Type of the shape instance.

std::string	shape_name {"shape"}
	Name of the shape instance.

bool	use_customized_solver {false}
	Determines whether to use a customized contact solver or not.

STLModel	render_mesh
	Surface mesh for rendering.

Additional Inherited Members
Public Types inherited from netdem::Shape
enum	Type { none , point_sphere , sphere , spherical_harmonics , trimesh , trimesh_convex , ellipsoid , polybezier , triangle , plane , cylinder , poly_super_ellipsoid , poly_super_quadrics , level_set , netsdf , coded_netsdf , num_shapes }
	Enumeration for different types of shapes. More...

Protected Attributes inherited from netdem::Shape
double	size {1.0}
	Size and volume of the shape instance.

double	volume {0.5236}
	Volume of the shape instance.

Mat3d	inertia {{{0.05236, 0, 0}, {0, 0.05236, 0}, {0, 0, 0.05236}}}
	Inertia tensor of the shape instance.

double	bound_sphere_radius {0.5}
	Radius of the bounding sphere used for broad-phase contact detection.

double	skin {0.025}
	Skin thickness used for broad-phase contact detection.

double	skin_factor {0.05}
	Factor used to adjust the skin thickness.

Vec3d	bound_aabb_min {-0.5, -0.5, -0.5}
	Minimum bounds of the AABB used for broad-phase contact detection.

Vec3d	bound_aabb_max {0.5, 0.5, 0.5}
	Maximum bounds of the AABB used for broad-phase contact detection.

bool	is_convex {true}
	Determines whether the shape instance is convex or not.

bool	use_surface_nodes {false}
	Determines whether to use nodes for the contact solver.

int	surface_node_num {1000}
	Number of nodes used for the contact solver.

double	surface_node_spacing {std::sqrt(Math::PI / 1000.0)}
	Spacing between nodes used for the contact solver.

VecXT< Vec3d >	surface_nodes
	Surface nodes of the shape instance used for the contact solver.

VecXT< double >	surface_node_areas
	Area associated with each surface node.

Detailed Description

A class representing a spherical harmonics object.

This class provides methods for generating, initializing, and computing operations on a SphericalHarmonics object. The object is defined by its degree, radius, and coefficients for each term in the harmonics expansion. In particular, it provides methods for computing signed distance, surface point, and generating an STL model. It also provides various options for calculating the spherical harmonics terms, including basic, fast, and with pre-calculated values.

Examples: 00_contact_test_sphere.cpp, 00_sdf_demo.cpp, 01_contact_test_trimesh.cpp, 02_energy_test.cpp, 03_friction_test_sphere.cpp, 04_friction_test_trimesh.cpp, 10_contact_test_sphere.cpp, 11_contact_test_trimesh.cpp, 16_test_latent_space.cpp, 2_sdf_solver.cpp, 3_hybrid_solver.cpp, 90_packing_demo.cpp, 91_triaixal_comp_trimesh.cpp, 92_angle_repose_trimesh.cpp, 93_triaixal_comp_trimesh.cpp, and 94_angle_repose_trimesh.cpp.

Constructor & Destructor Documentation

◆ SphericalHarmonics() [1/2]

SphericalHarmonics::SphericalHarmonics ( )

Default constructor.

◆ SphericalHarmonics() [2/2]

SphericalHarmonics::SphericalHarmonics ( int n )

Constructor with specified degree.

Parameters

n	The degree of the SphericalHarmonics object.

Member Function Documentation

◆ CalculateRho() [1/2]

double SphericalHarmonics::CalculateRho	(	double	theta,
		double	phi ) const

Calculate the rho value for a given theta and phi.

This method calculates the rho value for a given theta and phi using the SphericalHarmonics expansion coefficients.

Parameters

theta	The polar angle theta.
phi	The azimuthal angle phi.

Returns: The rho value for the given input.

◆ CalculateRho() [2/2]

double SphericalHarmonics::CalculateRho ( Vec3d const & dir ) const

Calculate the rho value for a given direction vector.

This method calculates the rho value for a given direction vector using the SphericalHarmonics expansion coefficients.

Parameters

dir	The direction vector to compute the rho value for.

Returns: The rho value for the given input.

◆ CalculateYnm() [1/2]

VecXT< VecXT< double > > SphericalHarmonics::CalculateYnm	(	const VecXT< double > &	theta,
		const VecXT< double > &	phi,
		int	deg )

static

Calculate the spherical harmonics terms for given theta, phi vectors, and degree.

This method calculates the spherical harmonics expansion terms for given theta, phi vectors, and degree using the basic method.

Parameters

theta	A vector of polar angles theta.
phi	A vector of azimuthal angles phi.
deg	The degree of the expansion.

Returns: A matrix containing the expansion terms for the given input.

◆ CalculateYnm() [2/2]

VecXT< double > SphericalHarmonics::CalculateYnm	(	double	theta,
		double	phi,
		int	deg )

static

Calculate the spherical harmonics terms for a given theta, phi, and degree.

This method calculates the spherical harmonics expansion terms for a given theta, phi, and degree using the basic method.

Parameters

theta	The polar angle theta.
phi	The azimuthal angle phi.
deg	The degree of the expansion.

Returns: A vector containing the expansion terms for the given input.

◆ CalculateYnm_Fast() [1/4]

VecXT< VecXT< double > > SphericalHarmonics::CalculateYnm_Fast	(	const VecXT< double > &	theta,
		const VecXT< double > &	phi,
		int	deg )

static

Calculate the spherical harmonics terms for given theta, phi vectors, and degree using pre-calculated values.

This method calculates the spherical harmonics expansion terms for given theta, phi vectors, and degree using pre-calculated values to speed up computation.

Parameters

theta	A vector of polar angles theta.
phi	A vector of azimuthal angles phi.
deg	The degree of the expansion.

Returns: A matrix containing the expansion terms for the given input.

◆ CalculateYnm_Fast() [2/4]

VecXT< VecXT< double > > SphericalHarmonics::CalculateYnm_Fast	(	const VecXT< Vec3d > &	dir_list,
		int	deg )

static

◆ CalculateYnm_Fast() [3/4]

VecXT< double > SphericalHarmonics::CalculateYnm_Fast	(	double	theta,
		double	phi,
		int	deg )

static

Calculate the spherical harmonics terms for a given theta, phi, and degree using pre-calculated values.

This method calculates the spherical harmonics expansion terms for a given theta, phi, and degree using pre-calculated values to speed up computation.

Parameters

theta	The polar angle theta.
phi	The azimuthal angle phi.
deg	The degree of the expansion.

Returns: A vector containing the expansion terms for the given input.

◆ CalculateYnm_Fast() [4/4]

VecXT< double > SphericalHarmonics::CalculateYnm_Fast	(	Vec3d const &	dir,
		int	deg )

static

◆ Clone()

Shape * SphericalHarmonics::Clone ( ) const

overridevirtual

Clone the SphericalHarmonics object.

This method creates a copy of the SphericalHarmonics object.

Returns: A pointer to the cloned SphericalHarmonics object.

Reimplemented from netdem::Shape.

◆ GetSTLModel()

STLModel SphericalHarmonics::GetSTLModel ( int num_nodes = 200 )

overridevirtual

Generate an STL model for the SphericalHarmonics object.

This method generates an STLModel object representing the SphericalHarmonics object with the specified number of nodes for each surface triangle.

Parameters

num_nodes The number of nodes to use for each surface triangle (default: 200).

Returns: An STLModel object representing the SphericalHarmonics object.

Reimplemented from netdem::Shape.

Examples: 01_contact_test_trimesh.cpp, 11_contact_test_trimesh.cpp, and 16_test_latent_space.cpp.

◆ Init()

void SphericalHarmonics::Init ( )

Initialize the SphericalHarmonics object.

This method initializes the SphericalHarmonics object by updating its nodes and shape properties.

◆ InitFromJson()

void SphericalHarmonics::InitFromJson ( nlohmann::json const & js )

overridevirtual

Initialize the SphericalHarmonics object from a JSON structure.

This method initializes the SphericalHarmonics object from a JSON structure previously generated by PackJson().

Parameters

js	The JSON structure to load.

Reimplemented from netdem::Shape.

◆ InitFromSTL() [1/2]

void netdem::SphericalHarmonics::InitFromSTL ( std::string const & file )

Initialize the SphericalHarmonics object from an STL file.

This method initializes the SphericalHarmonics object from an STL file by generating surface points and calling InitFromSurfacePoints().

Parameters

file	The path to the STL file to load.

Examples: 01_contact_test_trimesh.cpp, 02_energy_test.cpp, 04_friction_test_trimesh.cpp, 11_contact_test_trimesh.cpp, 2_sdf_solver.cpp, 3_hybrid_solver.cpp, 90_packing_demo.cpp, 91_triaixal_comp_trimesh.cpp, 92_angle_repose_trimesh.cpp, 93_triaixal_comp_trimesh.cpp, and 94_angle_repose_trimesh.cpp.

◆ InitFromSTL() [2/2]

void SphericalHarmonics::InitFromSTL ( STLModel const & stl_model )

Initialize the SphericalHarmonics object from an STL model.

This method initializes the SphericalHarmonics object from an STL model by generating surface points and calling InitFromSurfacePoints().

Parameters

stl_model The STLModel object to load.

◆ InitFromSurfacePoints()

void SphericalHarmonics::InitFromSurfacePoints ( VecXT< Vec3d > const surf_points )

Initialize the SphericalHarmonics object from a list of surface points.

This method initializes the SphericalHarmonics object from a list of surface points by computing the coefficients for each term in the SphericalHarmonics expansion.

Parameters

surf_points The list of surface points to use.

Examples: 16_test_latent_space.cpp.

◆ PackJson()

nlohmann::json SphericalHarmonics::PackJson ( )

overridevirtual

Pack the SphericalHarmonics object into a JSON structure.

This method packs the SphericalHarmonics object into a JSON structure for serialization and storage.

Returns: The packed JSON structure.

Reimplemented from netdem::Shape.

◆ SetSize()

void SphericalHarmonics::SetSize ( double d )

overridevirtual

Set the size of the SphericalHarmonics object.

This method sets the radius of the SphericalHarmonics object to a new value.

Parameters

d	The new radius to use.

Reimplemented from netdem::Shape.

Examples: 01_contact_test_trimesh.cpp, 02_energy_test.cpp, 04_friction_test_trimesh.cpp, 11_contact_test_trimesh.cpp, 2_sdf_solver.cpp, 3_hybrid_solver.cpp, 90_packing_demo.cpp, 91_triaixal_comp_trimesh.cpp, 92_angle_repose_trimesh.cpp, 93_triaixal_comp_trimesh.cpp, and 94_angle_repose_trimesh.cpp.

◆ SignedDistance()

double SphericalHarmonics::SignedDistance ( Vec3d const & pos ) const

overridevirtual

Compute the signed distance between a point and the SphericalHarmonics object.

This method computes the signed distance between a point and the SphericalHarmonics object, which is positive if the point is outside the object and negative if it is inside.

Parameters

pos	The point to compute the signed distance from.

Returns: The signed distance between the point and the SphericalHarmonics object.

Reimplemented from netdem::Shape.

◆ SurfaceCurvature() [1/2]

Vec2d SphericalHarmonics::SurfaceCurvature	(	double	theta,
		double	phi )

◆ SurfaceCurvature() [2/2]

Vec2d SphericalHarmonics::SurfaceCurvature ( Vec3d const & pos )

◆ SurfaceNormal() [1/2]

Vec3d SphericalHarmonics::SurfaceNormal	(	double	theta,
		double	phi )

◆ SurfaceNormal() [2/2]

Vec3d SphericalHarmonics::SurfaceNormal ( Vec3d const & pos )

◆ SurfacePoint()

Vec3d SphericalHarmonics::SurfacePoint ( Vec3d const & pos )

overridevirtual

Compute the surface point of the SphericalHarmonics object closest to a given point.

This method computes the surface point of the SphericalHarmonics object closest to a given point using a binary search algorithm.

Parameters

pos	The point to find the closest surface point to.

Returns: The surface point of the SphericalHarmonics object closest to the specified point.

Reimplemented from netdem::Shape.

◆ UpdateShapeProperties()

void SphericalHarmonics::UpdateShapeProperties ( )

overridevirtual

Update the shape properties of the SphericalHarmonics object.

This method updates the shape properties of the SphericalHarmonics object, such as its volume and surface area.

Reimplemented from netdem::Shape.

Examples: 00_contact_test_sphere.cpp, 02_energy_test.cpp, 03_friction_test_sphere.cpp, and 10_contact_test_sphere.cpp.

◆ UpdateSurfaceNodes()

void SphericalHarmonics::UpdateSurfaceNodes ( )

overridevirtual

Update the surface nodes of the SphericalHarmonics object.

This method updates the surface nodes of the SphericalHarmonics object based on its radius and center position.

Reimplemented from netdem::Shape.

Member Data Documentation

◆ a_nm

VecXT<double> netdem::SphericalHarmonics::a_nm

The coefficients of each term in the SphericalHarmonics expansion. Please run Init() if a_nm is modified.

Examples: 00_contact_test_sphere.cpp, 02_energy_test.cpp, 03_friction_test_sphere.cpp, and 10_contact_test_sphere.cpp.

◆ degree

int netdem::SphericalHarmonics::degree {8}

The degree of the SphericalHarmonics object.

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

/Users/lzhshou/Documents/Research/myProjects/apaam/repo/netdem/src/shape/shape_spherical_harmonics.hpp
/Users/lzhshou/Documents/Research/myProjects/apaam/repo/netdem/src/shape/shape_spherical_harmonics.cpp

Public Member Functions

Static Public Member Functions

Public Attributes

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ SphericalHarmonics() [1/2]

◆ SphericalHarmonics() [2/2]

Member Function Documentation

◆ CalculateRho() [1/2]

◆ CalculateRho() [2/2]

◆ CalculateYnm() [1/2]

◆ CalculateYnm() [2/2]

◆ CalculateYnm_Fast() [1/4]

◆ CalculateYnm_Fast() [2/4]

◆ CalculateYnm_Fast() [3/4]

◆ CalculateYnm_Fast() [4/4]

◆ Clone()

◆ GetSTLModel()

◆ Init()

◆ InitFromJson()

◆ InitFromSTL() [1/2]

◆ InitFromSTL() [2/2]

◆ InitFromSurfacePoints()

◆ PackJson()

◆ SetSize()

◆ SignedDistance()

◆ SurfaceCurvature() [1/2]

◆ SurfaceCurvature() [2/2]

◆ SurfaceNormal() [1/2]

◆ SurfaceNormal() [2/2]

◆ SurfacePoint()

◆ UpdateShapeProperties()

◆ UpdateSurfaceNodes()

Member Data Documentation

◆ a_nm

◆ degree