The BlobTree model. More...

#include <blobtree.h>

Inheritance diagram for BlobTree:

Public Member Functions
	BlobTree (TreeNode *=nullptr, const double &=0.5)
	Creates a BlobTree. More...

virtual	~BlobTree ()
	Destroys the BlobTree structure, recursively exploring the nodes of the BlobTree.

	BlobTree (const BlobTree &)
	Overloaded.

BlobTree &	operator= (const BlobTree &)
	Overloaded.

TreeNode *	GetRoot () const
	Returns the root. More...

double	GetThreshold () const
	Returns the threshold value. More...

virtual double	Value (const Vector &) const
	Computes the field function value at a point. More...

virtual Vector	Gradient (const Vector &) const
	Computes the gradient of the field function at a point. More...

virtual void	IntensityGradient (const Vector &, double &, Vector &) const
	Overloaded to minimize function calls. More...

virtual double	Volume (int=5) const
	Computes the volume of the BlobTree. More...

virtual double	Volume (const Box &, int) const
	Compute the volume of a BlobTree object. More...

virtual double	Volume (const Box &, int, double &) const
	Compute the volume of a BlobTree object. More...

virtual Sphere	Center (int) const
	Computes the gravity center of the BlobTree. More...

virtual Sphere	Center (const Box &, int) const
	Compute the center of gravity of the BlobTree. More...

virtual BlobTree *	Copy () const
	Deep copy. More...

virtual double	K () const
	Computes the Lipschitz constant over the whole domain. More...

virtual double	K (int) const
	Computes the Lipschitz constant. More...

virtual double	K (const Box &) const
	Computes the Lipschitz constant of the field function in a limited region of space. More...

virtual double	K (const Ray &) const
	Computes the Lipschitz constant of the function along a ray. More...

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

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

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

virtual bool	SphereTrace (const Ray &, const double &, const double &, const double &, double &, int &, const double &=1e-4) const
	Find the first intersection between a ray and an implicit surface on a given interval, using sphere tracing. More...

virtual bool	SphereTrace (const Ray &, const double &, const double &, const double &, const double &, double &, int &, const double &=1e-4) const
	Find the first intersection between a ray and an implicit surface on a given interval, using sphere tracing. More...

virtual bool	SphereBoxTrace (const Ray &, const double &, const double &, const double &, double &, int &, const double &=1e-4) const
	Find the first intersection between a ray and an implicit surface on a given interval, using sphere tracing. More...

virtual bool	SphereSegmentTrace (const Ray &, const double &, const double &, const double &, double &, int &, const double &=1e-4) const
	Find the first intersection between a ray and an implicit surface on a given interval, using sphere tracing. More...

virtual bool	RayStepSegmentTrace (const Ray &, const double &, const double &, const double &, double &, int &, const double &=1e-4) const
	Find the first intersection between a ray and the implicit surface.

virtual bool	BinarySearch (const Ray &ray, const double &a, const double &b, double &t, int &x, const double &=1e-4, bool=false) const
	Compute the intersection with a ray, using binary search. More...

virtual bool	BinarySearch (const Ray &ray, const double &a, const double &b, const Vector &pa, const Vector &pb, const double &va, const double &vb, double &t, int &, const double &=1e-4, bool=false) const
	Compute the intersection with a ray, using binary search. More...

virtual Box	GetBox () const
	Return the bounding box of the BlobTree structure. More...

virtual Voxel	EmptyVoxels (int) const
	Step along the ray. More...

virtual Color	GetMaterial (const Vector &, const Vector &=Vector::Null) const
	Computes the surface parameters at a point. More...

BlobTree *	Cut (const Box &) const
	Cuts the BlobTree to simplify its structure inside a box. More...

void	Rotate (const Matrix &)
	Creates a union node at the top node of the BlobTree. More...

void	Translate (const Vector &)
	Creates a union node at the top node of the BlobTree. More...

void	Scale (const Vector &)
	Creates a union node at the top node of the BlobTree. More...

void	Blend (TreeNode *)
	Creates a union node at the top node of the BlobTree. More...

void	Difference (TreeNode *)
	Creates a difference node at the top node of the BlobTree. More...

void	Intersection (TreeNode *)
	Creates an intersection node at the top node of the BlobTree. More...

void	Union (TreeNode *)
	Creates a union node at the top node of the BlobTree. More...

BlobTree *	CenterBox ()
	Centers the BlobTree at the origin.

BlobTree *	ScaleBox ()
	Scales the BlobTree to a unit bounding box. More...

int	Memory () const
	Compute the size of the BlobTree.

int	Nodes () const
	Compute the number of nodes of the BlobTree.

int	Depth () const
	Compute the depth of the BlobTree.

Static Public Member Functions
static void	ResetCalls ()
	Reset the number of function calls.

static int	Calls ()
	Get the number of function calls. More...

static int	Oversteps ()
	Return the number of overstep fails.

static TreeNode *	SplineVertex (const Vector &, const double &, const Vector &, const double &, const Vector &, const double &, const Vector &, const double &, const double &, int)
	Create a spline of TreeVertex primitives. More...

static BlobTree *	CreateCandlestick ()
	Create a candlestick.

static BlobTree *	CreateAmphora (const double &=0.02)
	Creates an amphora. More...

static BlobTree *	CreateVase ()
	Creates a vase.

static BlobTree *	CreateBear ()
	Creates a soft-toy like bear.

static BlobTree *	CreateBird ()
	Creates a soft-toy like bird.

static BlobTree *	CreateElk ()
	Creates a soft-toy like elk.

static BlobTree *	CreateFlask ()
	Create a liquor flask.

static BlobTree *	CreateFlaskGlass (bool=false, bool=false)
	Creates a flask. More...

static BlobTree *	ChessRook ()
	Creates a rook.

static BlobTree *	ChessQueen ()
	Creates a queen.

static BlobTree *	ChessKing ()
	Creates a king.

static BlobTree *	CreateCube ()
	Sphere pierced by three boxes.

static BlobTree *	Column (bool=false)
	Create a colum. More...

static BlobTree *	CreateCandle ()
	Candle.

static BlobTree *	ScotchGlass ()
	A simple glass.

static BlobTree *	WaterGlass ()
	Creates a simple water glass.

static BlobTree *	Mechanic ()
	Create a mechanical shape.

static BlobTree *	Candelabra ()
	Creates the candelabra.

static BlobTree *	Chandelier3 ()
	Create a candlestick.

static BlobTree *	ChampagneGlass ()
	Create a simple twisted shape.

static BlobTree *	Stalactite (const Vector &, const double &, const double &)
	Create a stalactite. More...

Protected Attributes
double	T
	Threshold value.

TreeNode *	root
	Root node.

Static Protected Attributes
static int	calls = 0
	Number of calls to Value().

static int	oversteps = 0
	Number of oversteps failed in ray marching.

Detailed Description

The BlobTree model.

Constructor & Destructor Documentation

◆ BlobTree()

BlobTree::BlobTree	(	TreeNode *	node = `nullptr`,
		const double &	T = `0.5`
	)

explicit

Creates a BlobTree.

Parameters

node	Root node.
T	Threshold.

Member Function Documentation

◆ BinarySearch() [1/2]

bool BlobTree::BinarySearch	(	const Ray &	ray,
		const double &	a,
		const double &	b,
		const Vector &	pa,
		const Vector &	pb,
		const double &	va,
		const double &	vb,
		double &	t,
		int &	x,
		const double &	e = `1e-4`,
		bool	uk = `false`
	)		const

virtual

Compute the intersection with a ray, using binary search.

Parameters

ray	The ray.
a,b	Interval.
pa,pb	Points.
va,vb	Field function values.
t	Intersection depth.
x	Returned number of steps.
e	Epsilon value.
uk	Boolean, local segment Lipschitz bound if true, global Lipschitz bound otherwise.

◆ BinarySearch() [2/2]

bool BlobTree::BinarySearch	(	const Ray &	ray,
		const double &	a,
		const double &	b,
		double &	t,
		int &	x,
		const double &	e = `1e-4`,
		bool	uk = `false`
	)		const

virtual

Compute the intersection with a ray, using binary search.

Parameters

ray	The ray.
a,b	Interval.
t	Intersection depth.
x	Returned number of steps.
e	Epsilon value.
uk	Boolean, local segment Lipschitz bound if true, global Lipschitz bound otherwise.

◆ Blend()

void BlobTree::Blend ( TreeNode * node )

Creates a union node at the top node of the BlobTree.

Parameters

node	Sub-tree node.

◆ Calls()

int BlobTree::Calls ( )

static

Get the number of function calls.

This function returns the number of calls to BlobTree::Value() since the creation of the BlobTree. It can be reset to using ResetCalls().

◆ Center() [1/2]

Sphere BlobTree::Center	(	const Box &	box,
		int	depth
	)		const

virtual

Compute the center of gravity of the BlobTree.

Parameters

box	Initial box.
depth	Recursion depth.

See also: BlobTree::Center(int)

◆ Center() [2/2]

Sphere BlobTree::Center ( int depth ) const

virtual

Computes the gravity center of the BlobTree.

This function returns a sphere, the center is the center of gravity, and the radius is the volume.

Parameters

depth Recursion depth.

◆ Column()

BlobTree * BlobTree::Column ( bool type = false )

static

Create a colum.

Parameters

type	Carvings, set to true if carvings are wanted.

◆ Copy()

BlobTree * BlobTree::Copy ( ) const

virtual

Deep copy.

Returns: Copy of the BlobTree.

◆ CreateAmphora()

BlobTree * BlobTree::CreateAmphora ( const double & thickness = 0.02 )

static

Creates an amphora.

Parameters

thickness The thickness of the amphora.

◆ CreateFlaskGlass()

BlobTree * BlobTree::CreateFlaskGlass	(	bool	type = `false`,
		bool	side = `false`
	)

static

Creates a flask.

Parameters

type	Creates a hole in the flask is set to true
side	Adds the handle.

◆ Cut()

BlobTree * BlobTree::Cut ( const Box & b ) const

Cuts the BlobTree to simplify its structure inside a box.

Parameters

b Box.

◆ Difference()

void BlobTree::Difference ( TreeNode * node )

Creates a difference node at the top node of the BlobTree.

Parameters

node	Sub-tree node.

◆ EmptyVoxels()

Voxel BlobTree::EmptyVoxels ( int n ) const

virtual

Step along the ray.

Compute a voxel whose cells are defined as empty if the statisfy the Lipschitz condition, or (possibly) non empty otherwise.

Parameters

n	Maximum subdivision.

◆ GetBox()

Box BlobTree::GetBox ( ) const

virtual

Return the bounding box of the BlobTree structure.

Returns: The box.

Reimplemented from AnalyticScalarField.

◆ GetMaterial()

Color BlobTree::GetMaterial	(	const Vector &	p,
		const Vector &	n = `Vector::Null`
	)		const

virtual

Computes the surface parameters at a point.

Parameters

p	Point.
n	Normal.

Returns: Color.

Reimplemented from AnalyticScalarField.

◆ GetRoot()

TreeNode * BlobTree::GetRoot ( ) const

Returns the root.

Returns: Root node.

◆ GetThreshold()

double BlobTree::GetThreshold ( ) const

Returns the threshold value.

Returns: Threshold value.

◆ Gradient()

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

virtual

Computes the gradient of the field function at a point.

Parameters

p Point.

Returns: Gradient.

See also: TreeNode::Gradient()

Reimplemented from AnalyticScalarField.

◆ IntensityGradient()

void BlobTree::IntensityGradient	(	const Vector &	p,
		double &	intensity,
		Vector &	normal
	)		const

virtual

Overloaded to minimize function calls.

Parameters

p	Point.
intensity	Returned field value.
normal	Returned gradient.

◆ Intersection()

void BlobTree::Intersection ( TreeNode * node )

Creates an intersection node at the top node of the BlobTree.

Parameters

node	Sub-tree node.

◆ K() [1/7]

double BlobTree::K ( ) const

virtual

Computes the Lipschitz constant over the whole domain.

See also: BlobTree::K(int)

Returns: Lipschitz constant.

Reimplemented from AnalyticScalarField.

◆ K() [2/7]

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

virtual

Computes the Lipschitz constant of the field function in a limited region of space.

The implementation prunes the whole tree data structure, combining the Lipschitz constants of the nodes as needed if the bounding box of the node intersects the argument box.

Parameters

b The box.

Returns: Lipschitz constant.

Reimplemented from AnalyticScalarField.

◆ K() [3/7]

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

virtual

Computes the Lipschitz constant of the function along a ray.

The implementation prunes the whole tree data structure, combining the Lipschitz constants of the nodes on the fly as needed.

Parameters

ray The ray.

Returns: Lipschitz constant.

◆ K() [4/7]

double BlobTree::K ( const RayStep & s ) const

virtual

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

Parameters

s	The ray-stepping segment.

Returns: Lipschitz constant.

◆ K() [5/7]

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

virtual

Computes the Lipschitz constant along a segment.

Parameters

s	The segment.

Returns: Lipschitz constant.

Reimplemented from AnalyticScalarField.

◆ K() [6/7]

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

virtual

Computes the Lipschitz constant in a sphere.

Parameters

s	The sphere.

Returns: Lipschitz constant.

Reimplemented from AnalyticScalarField.

◆ K() [7/7]

double BlobTree::K ( int n ) const

virtual

Computes the Lipschitz constant.

Divides the domain into a grid, and compute the maximum of the local constants.

Returns: Lipschitz constant.

◆ Rotate()

void BlobTree::Rotate ( const Matrix & r )

Creates a union node at the top node of the BlobTree.

Parameters

r	Rotation matrix.

◆ Scale()

void BlobTree::Scale ( const Vector & s )

Creates a union node at the top node of the BlobTree.

Parameters

s	Scaling vector.

◆ ScaleBox()

BlobTree * BlobTree::ScaleBox ( )

Scales the BlobTree to a unit bounding box.

This is a convenience function, which simply computes the bounding box of the blobtree and inserts a new scaling node.

◆ SphereBoxTrace()

bool BlobTree::SphereBoxTrace	(	const Ray &	ray,
		const double &	a,
		const double &	b,
		const double &	c,
		double &	t,
		int &	s,
		const double &	epsilon = `1e-4`
	)		const

virtual

Find the first intersection between a ray and an implicit surface on a given interval, using sphere tracing.

Parameters

ray	The ray
a,b	Interval where intersection is tracked.
c	Acceleration factor defining the stepping distance increase factor [1.0,100.0], using 1.5 is fine.
s	Returned number of steps.
t	Nearest root, if exists
epsilon	Precision for detecting ray-surface intersection.

The function is almost the same as normal sphere-tracing. Instead of marching along the ray with valid steps, the magnitude of the step is slighly over estimated by a factor e.

See also: BlobTree::SphereTrace(const Ray&, const double&, const double& , const double& , double&, int& ,const double& ) const

◆ SphereSegmentTrace()

bool BlobTree::SphereSegmentTrace	(	const Ray &	ray,
		const double &	a,
		const double &	b,
		const double &	c,
		double &	t,
		int &	s,
		const double &	epsilon = `1e-4`
	)		const

virtual

Find the first intersection between a ray and an implicit surface on a given interval, using sphere tracing.

Parameters

ray	The ray
a,b	Interval where intersection is tracked.
c	Acceleration factor defining the stepping distance increase factor [1.0,100.0], using 1.5 is fine.
s	Returned number of steps.
t	Nearest root, if exists
epsilon	Precision for detecting ray-surface intersection.

The function is almost the same as normal sphere-tracing. Instead of marching along the ray with valid steps, the magnitude of the step is slighly over estimated by a factor e.

See also: BlobTree::SphereTrace(const Ray&, const double&, const double& , const double& , double&, int& ,const double& ) const

◆ SphereTrace() [1/2]

bool BlobTree::SphereTrace	(	const Ray &	ray,
		const double &	k,
		const double &	a,
		const double &	b,
		const double &	e,
		double &	t,
		int &	s,
		const double &	epsilon = `1e-4`
	)		const

virtual

Find the first intersection between a ray and an implicit surface on a given interval, using sphere tracing.

Parameters

ray	The ray
k	Lipschitz constant.
a,b	Interval where intersection is tracked.
e	Overstep factor, should be within interval [1.0,2.0], using 1.25 is fine.
s	Returned number of steps.
t	Nearest root, if exists
epsilon	Precision for detecting ray-surface intersection.

The function is almost the same as normal sphere-tracing. Instead of marching along the ray with valid steps, the magnitude of the step is slighly over estimated by a factor e.

See also: BlobTree::SphereTrace(const Ray&, const double&, const double& , const double& , double&, int& ,const double& ) const

◆ SphereTrace() [2/2]

bool BlobTree::SphereTrace	(	const Ray &	ray,
		const double &	k,
		const double &	a,
		const double &	b,
		double &	t,
		int &	s,
		const double &	epsilon = `1e-4`
	)		const

virtual

Find the first intersection between a ray and an implicit surface on a given interval, using sphere tracing.

Parameters

ray	The ray
k	Lipschitz constant.
a,b	Interval where intersection is tracked.
s	Return number of steps.
t	Nearest root, if exists
epsilon	Precision for detecting ray-surface intersection.

Simply march along the ray using adaptive steps depending on the magnitude of the field function at point samples. Intersection occurs if the absolute value of the field function gets lower than epsilon.

In practice, if the Lipschitz constant is unknown, it may be accurately defined with the member function BlobTree::K(const Ray&). Thus, the code could be as follows:

double t;
double a,b;
int s;
if (blobtree->GetBox().Intersect(ray,a,b))
{
bool r=blobtree->SphereTrace(ray,blobtree->K(ray),a,b,t,s,1.0e-6);
}

Reimplemented from AnalyticScalarField.

◆ SplineVertex()

TreeNode * BlobTree::SplineVertex	(	const Vector &	a,
		const double &	ra,
		const Vector &	na,
		const double &	fa,
		const Vector &	b,
		const double &	rb,
		const Vector &	nb,
		const double &	fb,
		const double &	It,
		int	n
	)

static

Create a spline of TreeVertex primitives.

Parameters

a,b	Control points.
na,nb	Control directions.
ra,rb	Control radii.
fa,fb	Control length of directions.
It	Intensity.
n	Number of elements.

◆ Stalactite()

BlobTree * BlobTree::Stalactite	(	const Vector &	a,
		const double &	length,
		const double &	r
	)

static

Create a stalactite.

Parameters

a	Starting position.
length	Targent length of the stalactite, the generated model be slightly shorter.
r	Initial radius.

◆ Translate()

void BlobTree::Translate ( const Vector & t )

Creates a union node at the top node of the BlobTree.

Parameters

t	Translation vector.

◆ Union()

void BlobTree::Union ( TreeNode * node )

Creates a union node at the top node of the BlobTree.

Parameters

node	Sub-tree node.

◆ Value()

double BlobTree::Value ( const Vector & p ) const

virtual

Computes the field function value at a point.

If the root of the BlobTree is empty, this function returns -T.

Parameters

p Point.

Returns: Intensity.

Reimplemented from AnalyticScalarField.

◆ Volume() [1/3]

double BlobTree::Volume	(	const Box &	box,
		int	depth
	)		const

virtual

Compute the volume of a BlobTree object.

Parameters

box	Cube where volume computations will be performed.
depth	Recursion depth.

◆ Volume() [2/3]

double BlobTree::Volume	(	const Box &	box,
		int	depth,
		double &	e
	)		const

virtual

Compute the volume of a BlobTree object.

Parameters

box	Cube where volume computations will be performed.
depth	Recursion depth.
e	Error, i.e., amount of volume that could not be classified as inside or outside.

See also: BlobTree::Volume(const Box&,int) const

◆ Volume() [3/3]

double BlobTree::Volume ( int depth = 5 ) const

virtual

Computes the volume of the BlobTree.

Create an octree subdivision of space and check the differents cells of the octree using a Lipschitz criterion to determine whether cells are inside, outside or straddling the object.

Parameters

depth Recursion depth in the creation of the octree.

Public Member Functions

Static Public Member Functions

Protected Attributes

Static Protected Attributes

Detailed Description

Constructor & Destructor Documentation

◆ BlobTree()

Member Function Documentation

◆ BinarySearch() [1/2]

◆ BinarySearch() [2/2]

◆ Blend()

◆ Calls()

◆ Center() [1/2]

◆ Center() [2/2]

◆ Column()

◆ Copy()

◆ CreateAmphora()

◆ CreateFlaskGlass()

◆ Cut()

◆ Difference()

◆ EmptyVoxels()

◆ GetBox()

◆ GetMaterial()

◆ GetRoot()

◆ GetThreshold()

◆ Gradient()

◆ IntensityGradient()

◆ Intersection()

◆ K() [1/7]

◆ K() [2/7]

◆ K() [3/7]

◆ K() [4/7]

◆ K() [5/7]

◆ K() [6/7]

◆ K() [7/7]

◆ Rotate()

◆ Scale()

◆ ScaleBox()

◆ SphereBoxTrace()

◆ SphereSegmentTrace()

◆ SphereTrace() [1/2]

◆ SphereTrace() [2/2]

◆ SplineVertex()

◆ Stalactite()

◆ Translate()

◆ Union()

◆ Value()

◆ Volume() [1/3]

◆ Volume() [2/3]

◆ Volume() [3/3]