TreeElement Class Reference

Generic primitives. More...

#include <blobtree.h>

Inheritance diagram for TreeElement:

Public Member Functions
	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 Segment &) const
	Returns a local Lipschitz constant along a segment. More...
double	K (const Sphere &) const
	Returns a local Lipschitz constant in a sphere. 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 double	Intensity (const Vector &) const =0
	Compute the field function value at a given point in space.
virtual void	IntensityGradient (const Vector &, double &, Vector &) const
	Computes the field value and the gradient at a given point in space. More...
virtual Vector	Gradient (const Vector &) const
	Computes the gradient of the field function at a given point in space. More...
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.
virtual double	K (const RayStep &) const
	Compute the Lipschitz constant along an optimized ray-stepping segment. More...
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 primitives.

This class serves as a top level model for all primitives that are created using a potential function.

For elements with a symmetry axis, some optimization for computing the field function could be considered: first preprocess the primitive using:

// Box
if (!box.Intersect(ray))
{
  type = 0;
  return 0;
}
 
Vector pa = c - ray.Origin();
 
double dx = ray.Direction()*axis;
double pax = pa * axis;
double dpa = ray.Direction()*pa;
 
er = Quadric(ray.Direction()*ray.Direction() - dx * dx, 2.0*(dx*pax - dpa), pa*pa - pax * pax);
ea = Linear(-dx, pax);

This code preprocesses the primitive and computes quadric distance to the axis er.

Constructor & Destructor Documentation

~TreeElement()

TreeElement::~TreeElement ( )

virtual

Destroys an element.

This function takes care of deleting the blending function.

Member Function Documentation

Cut()

TreeNode * TreeElement::Cut ( const Box &  box ) const

virtual

Cuts the node to simplify its structure inside a box.

Parameters

box

The box.

Implements TreeNode.

K() [1/5]

double TreeElement::K ( ) const

virtual

Returns the Lipschitz constant of the element.

Basically returns the Lipschitz constant of the potential function.

Implements TreeNode.

Reimplemented in TreeNoiseSphere.

K() [2/5]

double TreeElement::K ( const Box &  b ) const

virtual

Returns a local Lipschitz constant within a box domain.

Returns the Lipschitz constant of the element if argument bounding box intersects the element's bounding box.

Parameters

b

Box.

Implements TreeNode.

Reimplemented in TreeBox.

K() [3/5]

double TreeElement::K ( const Ray &  ray ) const

virtual

Returns a local Lipschitz constant along a ray.

Returns the Lipschitz constant of the element if argument ray intersects the element's bounding box.

Parameters

ray

The ray.

Implements TreeNode.

Reimplemented in TreeNoiseSphere, TreeVertex, TreeSphere, TreeEdge, TreeCylinder, TreeCircle, and TreeDisc.

K() [4/5]

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

virtual

Returns a local Lipschitz constant along a segment.

Returns the Lipschitz constant of the element if segment intersects the element's bounding box.

Parameters

s

Segment.

Reimplemented from TreeNode.

Reimplemented in TreeNormal, TreeNoiseSphere, TreeVertex, TreeSphere, TreeEdge, and TreeBox.

K() [5/5]

double TreeElement::K ( const Sphere &  sphere ) const

virtual

Returns a local Lipschitz constant in a sphere.

Parameters

sphere

Sphere.

Reimplemented from TreeNode.

Reimplemented in TreeNormal.