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.
double	K () const
	Returns the Lipschitz constant of the element.
double	K (const Box &) const
	Returns a local Lipschitz constant within a box domain.
double	K (const Segment &) const
	Returns a local Lipschitz constant along a segment.
double	K (const Sphere &) const
	Returns a local Lipschitz constant in a sphere.
double	K (const Ray &) const
	Returns a local Lipschitz constant along a ray.
TreeNode *	Cut (const Box &) const
	Cuts the node to simplify its structure inside a box.
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 double	Omega (const Vector &) const
	Return the squared distance to the compact support of the node.
virtual void	IntensityGradient (const Vector &, double &, Vector &) const
	Computes the field value and the gradient at a given point in space.
virtual Vector	Gradient (const Vector &) const
	Computes the gradient of the field function at a given point in space.
virtual TreeNode *	Blend (TreeNode *)
	Insert a blending node that blends the old and the new sub-tree together.
virtual TreeNode *	Union (TreeNode *)
	Insert a union node that unions the old and the new sub-tree together.
virtual TreeNode *	Difference (TreeNode *)
	Insert a difference node.
virtual TreeNode *	Translate (const Vector &)
	Insert a translation node.
virtual TreeNode *	Rotate (const Matrix &)
	Insert a rotation node.
virtual TreeNode *	Scale (const Vector &)
	Insert a scaling node.
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.
Box	GetBox () const
	Return the bounding box of the node.
virtual void	SetThreshold (const double &)
	Set the threshold value.
virtual Color	GetMaterial (const Vector &, const Vector &=Vector::Null) const
	Gets the color of a node at a point.
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 QString	Show (int=0) const
	Show the tree hierarchy.
virtual Vector	Dichotomy (Vector, Vector, double, double, double, const double &=1.0e-4)
	Compute the intersection between the implicit surface and a segment.

Protected Attributes
BlendCompact *	blend = nullptr
	Falloff function.
Protected Attributes inherited from TreeNode
Box	box = Box::Null
	Bounding box of the node.
double	T = 0.5
	Threshold value.

Additional Inherited Members
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

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.

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.

K() [3/5]

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, TreeSphere, and TreeVertex.

K() [4/5]

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.

K() [5/5]

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 TreeSphere, and TreeVertex.

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.