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 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 =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. More...

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

virtual double	K (const Sphere &) const
	Compute the Lipschitz constant in a sphere. 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 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 Vector	Dichotomy (Vector, Vector, double, double, double, const double &=1.0e-4)
	Compute the intersection between the implicit surface and a segment. More...

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

◆ 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.

◆ 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.

◆ Difference()

TreeNode * TreeNode::Difference ( TreeNode * e )

virtual

Insert a difference node.

Parameters

e Element.

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

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

◆ 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.

◆ K() [1/3]

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

◆ K() [2/3]

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

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

◆ Rotate()

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

virtual

Insert a rotation node.

Parameters

r	Rotation matrix.

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

◆ Scale()

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

virtual

Insert a scaling node.

Parameters

s	Scaling vector.

Reimplemented in TreeVertex, TreeEdge, TreeQuadric, and TreeScale.

◆ 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, TreeUnary, TreeCloneTranslate, TreeCloneFrame, and TreeOperator.

◆ Translate()

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

virtual

Insert a translation node.

Parameters

t	Translation vector.

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

◆ Union()

TreeNode * TreeNode::Union ( TreeNode * e )

virtual

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

Parameters

e Element.

Public Member Functions

Protected Attributes

Static Protected Attributes

Detailed Description

Member Function Documentation

◆ Blend()

◆ Dichotomy()

◆ Difference()

◆ GetMaterial()

◆ Gradient()

◆ IntensityGradient()

◆ K() [1/3]

◆ K() [2/3]

◆ K() [3/3]

◆ Rotate()

◆ Scale()

◆ SetThreshold()

◆ Translate()

◆ Union()