A class representing a poly superellipsoid with two different orders and three different axes. More...

#include <shape_poly_super_ellipsoid.hpp>

Inheritance diagram for netdem::PolySuperEllipsoid:

Public Member Functions
	PolySuperEllipsoid ()
	Default constructor.

	PolySuperEllipsoid (double am, double ap, double bm, double bp, double cm, double cp, double nab, double nc)
	Constructor that sets the size and order parameters of the PolySuperEllipsoid object.

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

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

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

void	Init ()
	Initialize the PolySuperEllipsoid object.

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

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

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

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

Vec3d	SupportPoint (Vec3d const &dir) override
	Compute the support point of the PolySuperEllipsoid object in a given direction.

VecXT< Vec3d >	SupportPoints (Vec3d const &dir) override
	Compute the support points of the PolySuperEllipsoid object in a given direction.

double	SignedDistance (Vec3d const &pos) const override
	Compute the signed distance from a given position to the surface of the PolySuperEllipsoid object.

Vec3d	SurfacePoint (Vec3d const &pos) override
	Compute the surface point on the PolySuperEllipsoid object closest to a given position.

Vec3d	ParametrizationPoint (Vec3d const &dir)
	Compute the parameterization point on the PolySuperEllipsoid object in a given direction.

void	Print () override
	Print information about the PolySuperEllipsoid object.

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 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	~Shape ()
	Destructor for the Shape class.

Public Attributes
Vec2d	axis_a {0.5, 0.5}

Vec2d	axis_b {0.5, 0.5}

Vec2d	axis_c {0.5, 0.5}

double	order_ab {1.0}

double	order_c {1.0}

Vec3d	pos_ref {0, 0, 0}

Vec4d	quat_ref {1, 0, 0, 0}

Vec4d	quat_conj {1, 0, 0, 0}

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...

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.

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 poly superellipsoid with two different orders and three different axes.

This class provides methods for setting and updating the position of the poly superellipsoid, computing its surface properties, generating STL models for visualization, and calculating signed distances and surface points.

Additionally, the PolySuperEllipsoid class is a subclass of the Shape class, which allows it to be used in combination with other shapes in compound objects.

The poly superellipsoid is defined by the following equation: ( ( x / axis_a )^( 2 / order_ab ) + ( y / axis_b )^( 2 / order_ab ) ) ^ ( order_ab / oder_c ) + ( z / axis_c )^( 2 / order_c ) = 1 m and p indicate minus and plus to guarantee convexity, order should be in (0, 2)

Examples: 00_sdf_demo.cpp, 01_sdf_error.cpp, 1_gjk_solver.cpp, 2_sdf_solver.cpp, 3_hybrid_solver.cpp, 90_packing_demo.cpp, and 91_packing_ellipsoid.cpp.

Constructor & Destructor Documentation

◆ PolySuperEllipsoid() [1/2]

PolySuperEllipsoid::PolySuperEllipsoid ( )

Default constructor.

◆ PolySuperEllipsoid() [2/2]

PolySuperEllipsoid::PolySuperEllipsoid	(	double	am,
		double	ap,
		double	bm,
		double	bp,
		double	cm,
		double	cp,
		double	nab,
		double	nc )

Constructor that sets the size and order parameters of the PolySuperEllipsoid object.

Parameters

am	The minus value of the x-axis scaling factor.
ap	The plus value of the x-axis scaling factor.
bm	The minus value of the y-axis scaling factor.
bp	The plus value of the y-axis scaling factor.
cm	The minus value of the z-axis scaling factor.
cp	The plus value of the z-axis scaling factor.
nab	The order parameter for the x/y axes.
nc	The order parameter for the z axis.

Member Function Documentation

◆ Clone()

Shape * PolySuperEllipsoid::Clone ( ) const

overridevirtual

Clone the PolySuperEllipsoid object.

This method creates a copy of the PolySuperEllipsoid object.

Returns: A pointer to the cloned PolySuperEllipsoid object.

Reimplemented from netdem::Shape.

◆ GetSTLModel()

STLModel PolySuperEllipsoid::GetSTLModel ( int num_nodes = 200 )

overridevirtual

Generate an STL model of the PolySuperEllipsoid object.

This method generates an STL model of the PolySuperEllipsoid object using 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 PolySuperEllipsoid object.

Reimplemented from netdem::Shape.

Examples: 01_sdf_error.cpp.

◆ Init()

void PolySuperEllipsoid::Init ( )

Initialize the PolySuperEllipsoid object.

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

◆ InitFromJson()

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

overridevirtual

Initialize the PolySuperEllipsoid object from a JSON structure.

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

Parameters

js	The JSON structure to load.

Reimplemented from netdem::Shape.

◆ PackJson()

nlohmann::json PolySuperEllipsoid::PackJson ( )

overridevirtual

Pack the PolySuperEllipsoid object into a JSON structure.

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

Returns: The packed JSON structure.

Reimplemented from netdem::Shape.

◆ ParametrizationPoint()

Vec3d PolySuperEllipsoid::ParametrizationPoint ( Vec3d const & dir )

Compute the parameterization point on the PolySuperEllipsoid object in a given direction.

This method computes the parameterization point on the PolySuperEllipsoid object in a given direction.

Parameters

dir	The direction in which to compute the parameterization point.

Returns: The parameterization point on the PolySuperEllipsoid object in the specified direction.

◆ Print()

void PolySuperEllipsoid::Print ( )

overridevirtual

Print information about the PolySuperEllipsoid object.

This method prints basic information about the PolySuperEllipsoid object, including its position, rotation, size, volume, and surface area.

Reimplemented from netdem::Shape.

◆ SetSize()

void PolySuperEllipsoid::SetSize ( double d )

overridevirtual

Set the size of the PolySuperEllipsoid object.

This method sets the size of the PolySuperEllipsoid object by scaling its axes uniformly.

Parameters

d	The diameter of the PolySuperEllipsoid object.

Reimplemented from netdem::Shape.

Examples: 1_gjk_solver.cpp, 2_sdf_solver.cpp, 3_hybrid_solver.cpp, 90_packing_demo.cpp, and 91_packing_ellipsoid.cpp.

◆ SignedDistance()

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

overridevirtual

Compute the signed distance from a given position to the surface of the PolySuperEllipsoid object.

This method computes the signed distance from a given position to the surface of the PolySuperEllipsoid object using its center point and scaling factors.

Parameters

pos	The position for which to compute the signed distance.

Returns: The signed distance from the specified position to the surface of the PolySuperEllipsoid object.

Reimplemented from netdem::Shape.

Examples: 01_sdf_error.cpp.

◆ SupportPoint()

Vec3d PolySuperEllipsoid::SupportPoint ( Vec3d const & dir )

overridevirtual

Compute the support point of the PolySuperEllipsoid object in a given direction.

This method computes the support point of the PolySuperEllipsoid object in a given direction, which is the point on the surface farthest in the specified direction.

Parameters

dir	The direction in which to compute the support point.

Returns: The support point of the PolySuperEllipsoid object in the specified direction.

Reimplemented from netdem::Shape.

◆ SupportPoints()

VecXT< Vec3d > PolySuperEllipsoid::SupportPoints ( Vec3d const & dir )

overridevirtual

Compute the support points of the PolySuperEllipsoid object in a given direction.

This method computes the support points of the PolySuperEllipsoid object in a given direction, which are two opposite points on the surface farthest along the specified direction.

Parameters

dir	The direction in which to compute the support points.

Returns: A vector containing the two support points of the PolySuperEllipsoid object in the specified direction.

Reimplemented from netdem::Shape.

◆ SurfacePoint()

Vec3d PolySuperEllipsoid::SurfacePoint ( Vec3d const & pos )

overridevirtual

Compute the surface point on the PolySuperEllipsoid object closest to a given position.

This method computes the surface point on the PolySuperEllipsoid object closest to a given position by finding the point on the surface that has the minimum distance to the specified position.

Parameters

pos	The position for which to compute the closest surface point.

Returns: The surface point on the PolySuperEllipsoid object closest to the specified position.

Reimplemented from netdem::Shape.

◆ UpdateShapeProperties()

void PolySuperEllipsoid::UpdateShapeProperties ( )

overridevirtual

Update the shape properties of the PolySuperEllipsoid object.

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

Reimplemented from netdem::Shape.

◆ UpdateSurfaceNodes()

void PolySuperEllipsoid::UpdateSurfaceNodes ( )

overridevirtual

Update the surface nodes of the PolySuperEllipsoid object.

This method updates the surface nodes of the PolySuperEllipsoid object based on its current position and rotation.

Reimplemented from netdem::Shape.

Member Data Documentation

◆ axis_a

Vec2d netdem::PolySuperEllipsoid::axis_a {0.5, 0.5}

◆ axis_b

Vec2d netdem::PolySuperEllipsoid::axis_b {0.5, 0.5}

◆ axis_c

Vec2d netdem::PolySuperEllipsoid::axis_c {0.5, 0.5}

◆ order_ab

double netdem::PolySuperEllipsoid::order_ab {1.0}

◆ order_c

double netdem::PolySuperEllipsoid::order_c {1.0}

◆ pos_ref

Vec3d netdem::PolySuperEllipsoid::pos_ref {0, 0, 0}

◆ quat_conj

Vec4d netdem::PolySuperEllipsoid::quat_conj {1, 0, 0, 0}

◆ quat_ref

Vec4d netdem::PolySuperEllipsoid::quat_ref {1, 0, 0, 0}

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

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

Public Member Functions

Public Attributes

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ PolySuperEllipsoid() [1/2]

◆ PolySuperEllipsoid() [2/2]

Member Function Documentation

◆ Clone()

◆ GetSTLModel()

◆ Init()

◆ InitFromJson()

◆ PackJson()

◆ ParametrizationPoint()

◆ Print()

◆ SetSize()

◆ SignedDistance()

◆ SupportPoint()

◆ SupportPoints()

◆ SurfacePoint()

◆ UpdateShapeProperties()

◆ UpdateSurfaceNodes()

Member Data Documentation

◆ axis_a

◆ axis_b

◆ axis_c

◆ order_ab

◆ order_c

◆ pos_ref

◆ quat_conj

◆ quat_ref