The generic nodes with some pure virtual functions. More...

#include <blobtree.h>

Inheritance diagram for TreeNode:

Public Member Functions
	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 =0
	Compute the Lipschitz constant of the node.

virtual double	K (const Box &) const =0
	Compute the local Lipschitz constant in a box.

virtual double	K (const Ray &) const =0
	Compute the local Lipschitz along a ray.

virtual double	K (const Segment &) const
	Compute the Lipschitz constant along a segment.

virtual double	K (const RayStep &) const
	Compute the Lipschitz constant along an optimized ray-stepping segment.

virtual double	K (const Sphere &) const
	Compute the Lipschitz constant in a sphere.

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 TreeNode *	Cut (const Box &) const =0
	Cuts the node to simplify its structure inside a box.

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
Box	box = Box::Null
	Bounding box of the node.

double	T = 0.5
	Threshold value.

Static Protected Attributes
static const double	Epsilon = 1e-6
	Epsilon value for gradient computation.

Detailed Description

The generic nodes with some pure virtual functions.

All nodes include a Box to accelerate queries in the Blob-Tree such as ray-intersections, field function or gradient evaluation.

Member Function Documentation

◆ Omega()

double TreeNode::Omega ( const Vector & p ) const

virtual

Return the squared distance to the compact support of the node.

Parameters

p Point.

Reimplemented in TreeBox, TreeCylinder, TreeEdge, TreeHemisphereDisc, TreeSphere, TreeTorus, TreeTriangle, and TreeVertex.

◆ IntensityGradient()

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

virtual

Computes the field value and the gradient at a given point in space.

This virtual function computes the gradient and the field values separately, calling TreeNode::Intensity and TreeNode::Gradient respectively. This technique is slower however than some specific implementations which can be optimized for some primitives, in particular distance based primitives.

See also: TreeVertex::IntensityGradient

Parameters

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

Reimplemented in TreeBlend, TreeNormal, and TreeVertex.

◆ Gradient()

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

virtual

Computes the gradient of the field function at a given point in space.

If the closed form expression of the gradient is not implemented in derivatives of TreeNode, use this approximation instead.

Parameters

p Point.

Reimplemented in TreeAlpha, TreeBlend, TreeBlendSquared, TreeBlendUnion, TreeCloneFrame, TreeCloneTranslate, TreeConeSphere, TreeDifference, TreeFrame, TreeHyperBlend, TreeInstantiate, TreeIntersection, TreeNormal, TreeRotate, TreeScale, TreeTaper, TreeTexture, TreeTranslate, TreeTwist, TreeUnion, and TreeVertex.

◆ Blend()

TreeNode * TreeNode::Blend ( TreeNode * e )

virtual

Insert a blending node that blends the old and the new sub-tree together.

Parameters

e Element.

Reimplemented in TreeBlend.

◆ Union()

TreeNode * TreeNode::Union ( TreeNode * e )

virtual

Insert a union node that unions the old and the new sub-tree together.

Parameters

e Element.

◆ Difference()

TreeNode * TreeNode::Difference ( TreeNode * e )

virtual

Insert a difference node.

Parameters

e Element.

◆ Translate()

TreeNode * TreeNode::Translate ( const Vector & t )

virtual

Insert a translation node.

Parameters

t	Translation vector.

Reimplemented in TreeBlend, TreeBubble, TreeCone, TreeConic, TreeCubic, TreeCylinder, TreeEdge, TreeQuadric, TreeRectangleDisc, TreeSphere, TreeTranslate, and TreeVertex.

◆ Rotate()

TreeNode * TreeNode::Rotate ( const Matrix & r )

virtual

Insert a rotation node.

Parameters

r	Rotation matrix.

Reimplemented in TreeBlend, TreeBubble, TreeCone, TreeConic, TreeCubic, TreeCylinder, TreeEdge, TreeQuadric, TreeRectangleDisc, TreeRotate, TreeSphere, and TreeVertex.

◆ Scale()

TreeNode * TreeNode::Scale ( const Vector & s )

virtual

Insert a scaling node.

Parameters

s	Scaling vector.

Reimplemented in TreeEdge, TreeQuadric, TreeScale, and TreeVertex.

◆ K() [1/3]

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

virtual

Compute the Lipschitz constant along a segment.

By default return the Lipchitz constant of the bounding box of the segment.

Parameters

s	The segment.

Reimplemented in TreeAlpha, TreeBlend, TreeBlendSquared, TreeBlendUnion, TreeBox, TreeCloneFrame, TreeCloneTranslate, TreeContact, TreeDifference, TreeEdge, TreeElement, TreeFrame, TreeHyperBlend, TreeInstantiate, TreeIntersection, TreeNormal, TreeRotate, TreeScale, TreeSphere, TreeTaper, TreeTexture, TreeTranslate, TreeTwist, TreeUnion, and TreeVertex.

◆ K() [2/3]

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

virtual

Compute the Lipschitz constant along an optimized ray-stepping segment.

By default return the Lipchitz constant of the segment, i.e. do not use optimized algorithms with pre-computed data in RayStep.

Parameters

raystep The step.

Reimplemented in TreeBlend, TreeBox, TreeCloneFrame, TreeCloneTranslate, TreeDifference, TreeEdge, TreeInstantiate, TreeIntersection, TreeNormal, TreeRotate, TreeScale, TreeSphere, TreeTaper, TreeTexture, TreeTranslate, TreeTwist, TreeUnion, and TreeVertex.

◆ K() [3/3]

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

virtual

Compute the Lipschitz constant in a sphere.

By default return the Lipchitz constant of the bounding box of the sphere.

Parameters

s	The sphere.

Reimplemented in TreeAlpha, TreeBlend, TreeBlendSquared, TreeCloneFrame, TreeCloneTranslate, TreeContact, TreeDifference, TreeElement, TreeFrame, TreeInstantiate, TreeIntersection, TreeNormal, TreeRotate, TreeScale, TreeTaper, TreeTexture, TreeTranslate, TreeTwist, and TreeUnion.

◆ SetThreshold()

void TreeNode::SetThreshold ( const double & T )

virtual

Set the threshold value.

The threshold which may be needed for the direct evaluation of the surface under some specific circumstances.

Parameters

T	Threshold.

Reimplemented in TreeBinary, TreeCloneFrame, TreeCloneTranslate, TreeInstantiate, TreeOperator, and TreeUnary.

◆ GetMaterial()

Color TreeNode::GetMaterial	(	const Vector &	,
		const Vector &	= Vector::Null ) const

virtual

Gets the color of a node at a point.

This function returns a default black material.

Reimplemented in TreeAlpha, TreeBlend, TreeBlendRUnion, TreeBlendSquared, TreeBlendUnion, TreeCloneFrame, TreeCloneTranslate, TreeContact, TreeDifference, TreeFrame, TreeHyperBlend, TreeInstantiate, TreeIntersection, TreeNoise, TreeRotate, TreeScale, TreeTaper, TreeTexture, TreeTranslate, TreeTwist, TreeUnion, and TreeWarp.

◆ Show()

QString TreeNode::Show ( int space = 0 ) const

virtual

Show the tree hierarchy.

Parameters

space Number of spaces.

Reimplemented in TreeBlend, TreeCloneFrame, TreeCloneTranslate, TreeConeSphere, TreeCylinder, TreeDifference, TreeDisc, TreeEdge, TreeHemisphere, TreeHyperBlend, TreeIntersection, TreePoly, TreeRectangle, TreeTorus, and TreeUnion.

◆ Dichotomy()

Vector TreeNode::Dichotomy	(	Vector	a,
		Vector	b,
		double	va,
		double	vb,
		double	length,
		const double &	epsilon = 1.0e-4 )

virtual

Compute the intersection between the implicit surface and a segment.

Parameters

a,b	Segment vertices.
va,vb	Field value at segment vertices.
length	Distance between a and b.
epsilon	Accuracy.

Public Member Functions

Protected Attributes

Static Protected Attributes

Detailed Description

Member Function Documentation

◆ Omega()

◆ IntensityGradient()

◆ Gradient()

◆ Blend()

◆ Union()

◆ Difference()

◆ Translate()

◆ Rotate()

◆ Scale()

◆ K() [1/3]

◆ K() [2/3]

◆ K() [3/3]

◆ SetThreshold()

◆ GetMaterial()

◆ Show()

◆ Dichotomy()