TreeQuadricCurve Class Reference

Quadric curve skeletal element. More...

#include <blobtree.h>

Inheritance diagram for TreeQuadricCurve:

Public Member Functions
	TreeQuadricCurve (const QuadricCurve &, BlendCompact *)
	Creates a quadric polynomial curve skeletal element.
virtual	~TreeQuadricCurve ()
	Destroys a curve.
virtual TreeNode *	Copy () const
	Creates a deep copy of curve element.
int	Memory () const
	Compute the size of a node.
double	Intensity (const Vector &) const
	Compute the intensity at a given point.
Public Member Functions inherited from TreeNormal
	TreeNormal (BlendCompact *=nullptr)
	Creates a skeletal element given a blending function.
virtual	~TreeNormal ()
	Destroys a skeletal element.
virtual Vector	Gradient (const Vector &) const
	Compute the gradient at a given point.
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.
virtual double	K (const Segment &) const
	Compute the Lipschitz constant on a segment.
virtual double	K (const RayStep &) const
	Compute the Lipschitz constant on a segment.
virtual double	K (const Sphere &) const
	Compute the Lipschitz constant inside a sphere.
Public Member Functions inherited from TreeElement
	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 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	Omega (const Vector &) const
	Return the squared distance to the compact support of the node.
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.
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 Member Functions
Vector	Normal (const Vector &) const
	Compute the distance vector between a point in space and the curve.
double	R (const Vector &) const
	Compute the squared distance between a point in space and the quadric curve.

Protected Attributes
QuadricCurve	c
	Quadric polynomials defining the curve.
Quadric	xyz
	Quadric constant coefficients used to speed-up ray-tracing.
Vector	b
	End vertices of the curve.
Protected Attributes inherited from TreeElement
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

Quadric curve skeletal element.

The evaluation of the field function is computationally less intensive than the TreeCubicCurve primitive: the computation of the distance to the skeleton requires finding the roots of a cubic polynomial only.

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Constructor & Destructor Documentation

TreeQuadricCurve()

TreeQuadricCurve::TreeQuadricCurve	(	const QuadricCurve &	c,
		BlendCompact *	blend )

Creates a quadric polynomial curve skeletal element.

Parameters

c	Quadric curve.
blend	Falloff function.

Member Function Documentation

Intensity()

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

virtual

Compute the intensity at a given point.

Parameters

p

Point.

Reimplemented from TreeNormal.

Normal()

Vector TreeQuadricCurve::Normal ( const Vector & p ) const

protectedvirtual

Compute the distance vector between a point in space and the curve.

This function computes the projection of a point p onto the curve by minimizing the distance function along the curve, expressed as a cubic. As most of the coefficients are constant, they are pre-processed in the constructor.

Speed-ups come from pre-processing constant coefficients and invoking an inline normalized cubic solver.

Parameters

p

Point.

Implements TreeNormal.

R()

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

protectedvirtual

Compute the squared distance between a point in space and the quadric curve.

This function computes the projection of a point p onto the curve by minimizing the distance function along the curve, expressed as a cubic polynomial. As most of the coefficients of this cubic polynomial are constant, they are pre-processed in the constructor.

Parameters

p

Point.

Reimplemented from TreeNormal.