TreeNormal Class Reference

Generic skeletal element based on the Euclidean distance. More...

#include <blobtree.h>

Inheritance diagram for TreeNormal:

Public Member Functions
	TreeNormal (BlendCompact *=nullptr)
	Creates a skeletal element given a blending function.
virtual	~TreeNormal ()
	Destroys a skeletal element.
virtual double	R (const Vector &) const
	Computes the squared Euclidean distance to the skeleton. More...
virtual double	Intensity (const Vector &) const
	Compute the intensity at a given point. More...
virtual Vector	Gradient (const Vector &) const
	Compute the gradient at a given point. More...
virtual void	IntensityGradient (const Vector &, double &, Vector &) const
	Compute the field value and the gradient of the field function at a given point in space. More...
virtual Vector	Normal (const Vector &) const =0
	Computes the normal vector between the skeleton and the argument point in space.
virtual double	K (const Segment &) const
	Compute the Lipschitz constant on a segment. More...
virtual double	K (const RayStep &) const
	Compute the Lipschitz constant on a segment. More...
virtual double	K (const Sphere &) const
	Compute the Lipschitz constant inside a sphere. More...
Public Member Functions inherited from TreeElement
	TreeElement (BlendCompact *=nullptr)
	Creates a new element given a blending function.
virtual	~TreeElement ()
	Destroys an element. More...
double	K () const
	Returns the Lipschitz constant of the element. More...
double	K (const Box &) const
	Returns a local Lipschitz constant within a box domain. More...
double	K (const Ray &) const
	Returns a local Lipschitz constant along a ray. More...
TreeNode *	Cut (const Box &) const
	Cuts the node to simplify its structure inside a box. More...
Public Member Functions inherited from TreeNode
	TreeNode ()
	Create a virtual node of the Blob-Tree structure.
virtual	~TreeNode ()
	Destroys a node.
virtual TreeNode *	Blend (TreeNode *)
	Insert a blending node that blends the old and the new sub-tree together. More...
virtual TreeNode *	Union (TreeNode *)
	Insert a union node that unions the old and the new sub-tree together. More...
virtual TreeNode *	Difference (TreeNode *)
	Insert a difference node. More...
virtual TreeNode *	Translate (const Vector &)
	Insert a translation node. More...
virtual TreeNode *	Rotate (const Matrix &)
	Insert a rotation node. More...
virtual TreeNode *	Scale (const Vector &)
	Insert a scaling node. More...
virtual TreeNode *	Copy () const =0
	Creates a deep copy of the node, recursively traversing the whole structure.
Box	GetBox () const
	Return the bounding box of the node.
virtual void	SetThreshold (const double &)
	Set the threshold value. More...
virtual Color	GetMaterial (const Vector &, const Vector &=Vector::Null) const
	Gets the color of a node at a point. More...
virtual int	Nodes () const
	Compute the number of nodes of the sub-tree.
virtual int	Depth () const
	Compute the dpeth of the sub-tree.
virtual Vector	Dichotomy (Vector, Vector, double, double, double, const double &=1.0e-4)
	Compute the intersection between the implicit surface and a segment. More...

Additional Inherited Members
Protected Attributes inherited from TreeNode
Box	box = Box::Null
	Bounding box of the node.
double	T = 0.5
	Threshold value.
Static Protected Attributes inherited from TreeNode
static const double	Epsilon = 1e-6
	Epsilon value for gradient computation.

Detailed Description

Generic skeletal element based on the Euclidean distance.

This class provides the following generic implementation of TreeNormal::Gradient().

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Member Function Documentation

Gradient()

Vector TreeNormal::Gradient ( const Vector &  p ) const

virtual

Compute the gradient at a given point.

This function relies on the TreeNormal::Normal() function.

Parameters

p

Point.

Reimplemented from TreeNode.

Reimplemented in TreeVertex, and TreeConeSphere.

Intensity()

double TreeNormal::Intensity ( const Vector &  p ) const

virtual

Compute the intensity at a given point.

This function relies on the TreeNormal::R() function.

Parameters

p

Point.

Implements TreeNode.

Reimplemented in TreeTetra, TreeVertex, TreeSphere, TreePyramid, TreeOctahedron, TreeBubble, TreeEdge, TreeCylinder, TreeTubular, TreeBox, TreeHollowBox, TreeCylinderBox, TreeCircle, TreeCircleArc, TreeRectangle, TreeRectangleDisc, TreeTorus, TreeHalfTorus, TreeDisc, TreeQuadricCurve, TreeTriangle, TreeCone, TreeConeSphere, and TreeQuadric.

IntensityGradient()

void TreeNormal::IntensityGradient ( const Vector &  p, double &  value, Vector &  gradient  ) const

virtual

Compute the field value and the gradient of the field function at a given point in space.

This function first call TreeNormal::Normal() function and derives the field value and the gradient from this vector.

See also

TreeVertex::IntensityGradient

Parameters

p	Point.
value	Returned field value.
gradient	Returned gradient.

Reimplemented from TreeNode.

Reimplemented in TreeVertex.

K() [1/3]

double TreeNormal::K ( const RayStep &  raystep ) const

virtual

Compute the Lipschitz constant on a segment.

Parameters

raystep

Segment.

Reimplemented from TreeNode.

Reimplemented in TreeVertex, TreeSphere, TreeEdge, and TreeBox.

K() [2/3]

double TreeNormal::K ( const Segment &  s ) const

virtual

Compute the Lipschitz constant on a segment.

Parameters

s

Segment.

Reimplemented from TreeElement.

Reimplemented in TreeVertex, TreeSphere, TreeEdge, and TreeBox.

K() [3/3]

double TreeNormal::K ( const Sphere &  s ) const

virtual

Compute the Lipschitz constant inside a sphere.

Parameters

s	The sphere.

Reimplemented from TreeElement.

R()

double TreeNormal::R ( const Vector &  p ) const

virtual

Computes the squared Euclidean distance to the skeleton.

This virtual member function calls TreeNormal::Normal() function. It is inefficient and should be reimplemented whenever possible.

Parameters

p

Point.

Reimplemented in TreeEdge, TreeQuadricCurve, TreeTriangle, and TreeConeSphere.