This map is composed of three steps. First it will take a box of size (Lx X Ly X Lz) defined by a member data bounding box and map it into a frustum with near plane (1 X Ly/Lx) and prescribed depth Then this frustum is transformed by an internal second map: most often a uniform scale, but other effects can be achieved by accumulating translation, shear and rotation: these are all applied to the second map. More...

#include <openvdb/math/Maps.h>

Inherits MapBase.

Public Types
using	Ptr = SharedPtr< NonlinearFrustumMap >

using	ConstPtr = SharedPtr< const NonlinearFrustumMap >

using	MapFactory) = Ptr(*)(

Public Member Functions
	NonlinearFrustumMap ()

	NonlinearFrustumMap (const BBoxd &bb, double taper, double depth)
	Constructor that takes an index-space bounding box to be mapped into a frustum with a given depth and taper (defined as ratio of nearplane/farplane). More...

	NonlinearFrustumMap (const BBoxd &bb, double taper, double depth, const MapBase::Ptr &secondMap)
	Constructor that takes an index-space bounding box to be mapped into a frustum with a given depth and taper (defined as ratio of nearplane/farplane). More...

	NonlinearFrustumMap (const NonlinearFrustumMap &other)

	NonlinearFrustumMap (const Vec3d &position, const Vec3d &direction, const Vec3d &up, double aspect, double z_near, double depth, Coord::ValueType x_count, Coord::ValueType z_count)
	Constructor from a camera frustum. More...

	~NonlinearFrustumMap () override=default

MapBase::Ptr	copy () const override
	Return a MapBase::Ptr to a deep copy of this map. More...

MapBase::Ptr	inverseMap () const override
	Not implemented, since there is currently no map type that can represent the inverse of a frustum. More...

Name	type () const override
	Return `NonlinearFrustumMap`. More...

bool	isLinear () const override
	Return `false` (a NonlinearFrustumMap is never linear). More...

bool	hasUniformScale () const override
	Return `false` (by convention false) More...

bool	isIdentity () const
	Return `true` if the map is equivalent to an identity. More...

bool	isEqual (const MapBase &other) const override
	Return `true` if this map is equal to the given map. More...

bool	operator== (const NonlinearFrustumMap &other) const

bool	operator!= (const NonlinearFrustumMap &other) const

Vec3d	applyMap (const Vec3d &in) const override
	Return the image of `in` under the map. More...

Vec3d	applyInverseMap (const Vec3d &in) const override
	Return the pre-image of `in` under the map. More...

Vec3d	applyJacobian (const Vec3d &in) const override
	Return the Jacobian of the linear second map applied to `in`. More...

Vec3d	applyJacobian (const Vec3d &in, const Vec3d &isloc) const override
	Return the Jacobian defined at `isloc` applied to `in`. More...

Vec3d	applyInverseJacobian (const Vec3d &in) const override
	Return the Inverse Jacobian of the map applied to in (i.e. inverse map with out translation) More...

Vec3d	applyInverseJacobian (const Vec3d &in, const Vec3d &isloc) const override
	Return the Inverse Jacobian defined at `isloc` of the map applied to in. More...

Vec3d	applyJT (const Vec3d &in, const Vec3d &isloc) const override
	Return the Jacobian Transpose of the map applied to vector `in` at `indexloc`. More...

Vec3d	applyJT (const Vec3d &in) const override
	Return the Jacobian Transpose of the second map applied to `in`. More...

Vec3d	applyIJT (const Vec3d &in) const override
	Return the transpose of the inverse Jacobian of the linear second map applied to `in`. More...

Vec3d	applyIJT (const Vec3d &d1_is, const Vec3d &ijk) const override

Mat3d	applyIJC (const Mat3d &in) const override
	Return the Jacobian Curvature for the linear second map. More...

Mat3d	applyIJC (const Mat3d &d2_is, const Vec3d &d1_is, const Vec3d &ijk) const override

double	determinant () const override
	Return the determinant of the Jacobian of linear second map. More...

double	determinant (const Vec3d &loc) const override

Vec3d	voxelSize () const override
	Return the size of a voxel at the center of the near plane. More...

Vec3d	voxelSize (const Vec3d &loc) const override
	Returns the lengths of the images of the three segments from loc to loc + (1,0,0), from loc to loc + (0,1,0) and from loc to loc + (0,0,1) More...

AffineMap::Ptr	getAffineMap () const override

void	setTaper (double t)
	set the taper value, the ratio of nearplane width / far plane width More...

double	getTaper () const
	Return the taper value. More...

void	setDepth (double d)
	set the frustum depth: distance between near and far plane = frustm depth * frustm x-width More...

double	getDepth () const
	Return the unscaled frustm depth. More...

double	getGamma () const

const BBoxd &	getBBox () const
	Return the bounding box that defines the frustum in pre-image space. More...

const AffineMap &	secondMap () const
	Return MapBase::Ptr& to the second map. More...

bool	isValid () const

bool	hasSimpleAffine () const
	Return `true` if the second map is a uniform scale, Rotation and translation. More...

void	read (std::istream &is) override
	read serialization More...

void	write (std::ostream &os) const override
	write serialization More...

std::string	str () const override
	string serialization, useful for debuging More...

MapBase::Ptr	preRotate (double radians, Axis axis=X_AXIS) const override
	Return a MapBase::Ptr to a new map that is the result of prepending the given rotation to the linear part of this map. More...

MapBase::Ptr	preTranslate (const Vec3d &t) const override
	Return a MapBase::Ptr to a new map that is the result of prepending the given translation to the linear part of this map. More...

MapBase::Ptr	preScale (const Vec3d &s) const override
	Return a MapBase::Ptr to a new map that is the result of prepending the given scale to the linear part of this map. More...

MapBase::Ptr	preShear (double shear, Axis axis0, Axis axis1) const override
	Return a MapBase::Ptr to a new map that is the result of prepending the given shear to the linear part of this map. More...

MapBase::Ptr	postRotate (double radians, Axis axis=X_AXIS) const override
	Return a MapBase::Ptr to a new map that is the result of appending the given rotation to the linear part of this map. More...

MapBase::Ptr	postTranslate (const Vec3d &t) const override
	Return a MapBase::Ptr to a new map that is the result of appending the given translation to the linear part of this map. More...

MapBase::Ptr	postScale (const Vec3d &s) const override
	Return a MapBase::Ptr to a new map that is the result of appending the given scale to the linear part of this map. More...

MapBase::Ptr	postShear (double shear, Axis axis0, Axis axis1) const override
	Return a MapBase::Ptr to a new map that is the result of appending the given shear to the linear part of this map. More...

template<typename MapT >
bool	isType () const
	Return `true` if this map is of concrete type `MapT` (e.g., AffineMap). More...

Static Public Member Functions
static MapBase::Ptr	create ()
	Return a MapBase::Ptr to a new NonlinearFrustumMap. More...

static bool	isRegistered ()

static void	registerMap ()

static Name	mapType ()
	Return `NonlinearFrustumMap`. More...

Static Protected Member Functions
template<typename MapT >
static bool	isEqualBase (const MapT &self, const MapBase &other)

Detailed Description

This map is composed of three steps. First it will take a box of size (Lx X Ly X Lz) defined by a member data bounding box and map it into a frustum with near plane (1 X Ly/Lx) and prescribed depth Then this frustum is transformed by an internal second map: most often a uniform scale, but other effects can be achieved by accumulating translation, shear and rotation: these are all applied to the second map.

Member Typedef Documentation

using ConstPtr = SharedPtr<const NonlinearFrustumMap>

using MapFactory = Ptr (*)(

inherited

using Ptr = SharedPtr<NonlinearFrustumMap>

Constructor & Destructor Documentation

NonlinearFrustumMap ( )

inline

NonlinearFrustumMap	(	const BBoxd &	bb,
		double	taper,
		double	depth
	)

inline

Constructor that takes an index-space bounding box to be mapped into a frustum with a given depth and taper (defined as ratio of nearplane/farplane).

NonlinearFrustumMap	(	const BBoxd &	bb,
		double	taper,
		double	depth,
		const MapBase::Ptr &	secondMap
	)

inline

Constructor that takes an index-space bounding box to be mapped into a frustum with a given depth and taper (defined as ratio of nearplane/farplane).

This frustum is further modifed by the secondMap, intended to be a simple translation and rotation and uniform scale

NonlinearFrustumMap ( const NonlinearFrustumMap & other )

inline

NonlinearFrustumMap	(	const Vec3d &	position,
		const Vec3d &	direction,
		const Vec3d &	up,
		double	aspect,
		double	z_near,
		double	depth,
		Coord::ValueType	x_count,
		Coord::ValueType	z_count
	)

inline

Constructor from a camera frustum.

Parameters

position	the tip of the frustum (i.e., the camera's position).
direction	a vector pointing from position toward the near plane.
up	a non-unit vector describing the direction and extent of the frustum's intersection on the near plane. Together, up must be orthogonal to direction.
aspect	the aspect ratio of the frustum intersection with near plane defined as width / height
z_near,depth	the distance from position along direction to the near and far planes of the frustum.
x_count	the number of voxels, aligned with left, across the face of the frustum
z_count	the number of voxels, aligned with direction, between the near and far planes

~NonlinearFrustumMap ( )

overridedefault

Member Function Documentation

Mat3d applyIJC ( const Mat3d & in ) const

inlineoverridevirtual

Return the Jacobian Curvature for the linear second map.

Implements MapBase.

Mat3d applyIJC	(	const Mat3d &	d2_is,
		const Vec3d &	d1_is,
		const Vec3d &	ijk
	)		const

inlineoverridevirtual

Return the Jacobian Curvature: all the second derivatives in range space

Parameters

d2_is	second derivative matrix computed in index space
d1_is	gradient computed in index space
ijk	the index space location where the result is computed

Implements MapBase.

Vec3d applyIJT ( const Vec3d & in ) const

inlineoverridevirtual

Return the transpose of the inverse Jacobian of the linear second map applied to in.

Implements MapBase.

Vec3d applyIJT	(	const Vec3d &	d1_is,
		const Vec3d &	ijk
	)		const

inlineoverridevirtual

Return the transpose of the inverse Jacobain (at locW applied to in. ijk is the location in the pre-image space (e.g. index space)

Implements MapBase.

Vec3d applyInverseJacobian ( const Vec3d & in ) const

inlineoverridevirtual

Return the Inverse Jacobian of the map applied to in (i.e. inverse map with out translation)

Implements MapBase.

Vec3d applyInverseJacobian	(	const Vec3d &	in,
		const Vec3d &	isloc
	)		const

inlineoverridevirtual

Return the Inverse Jacobian defined at isloc of the map applied to in.

Implements MapBase.

Vec3d applyInverseMap ( const Vec3d & in ) const

inlineoverridevirtual

Return the pre-image of in under the map.

Implements MapBase.

Vec3d applyJacobian ( const Vec3d & in ) const

inlineoverridevirtual

Return the Jacobian of the linear second map applied to in.

Implements MapBase.

Vec3d applyJacobian	(	const Vec3d &	in,
		const Vec3d &	isloc
	)		const

inlineoverridevirtual

Return the Jacobian defined at isloc applied to in.

Implements MapBase.

Vec3d applyJT	(	const Vec3d &	in,
		const Vec3d &	isloc
	)		const

inlineoverridevirtual

Return the Jacobian Transpose of the map applied to vector in at indexloc.

This tranforms range-space gradients to domain-space gradients.

Implements MapBase.

Vec3d applyJT ( const Vec3d & in ) const

inlineoverridevirtual

Return the Jacobian Transpose of the second map applied to in.

Implements MapBase.

Vec3d applyMap ( const Vec3d & in ) const

inlineoverridevirtual

Return the image of in under the map.

Implements MapBase.

MapBase::Ptr copy ( ) const

inlineoverridevirtual

Return a MapBase::Ptr to a deep copy of this map.

Implements MapBase.

static MapBase::Ptr create ( )

inlinestatic

Return a MapBase::Ptr to a new NonlinearFrustumMap.

double determinant ( ) const

inlineoverridevirtual

Return the determinant of the Jacobian of linear second map.

Implements MapBase.

double determinant ( const Vec3d & loc ) const

inlineoverridevirtual

Return the determinate of the Jacobian evaluated at loc loc is a location in the pre-image space (e.g., index space)

Implements MapBase.

AffineMap::Ptr getAffineMap ( ) const

inlineoverridevirtual

Implements MapBase.

const BBoxd& getBBox ( ) const

inline

Return the bounding box that defines the frustum in pre-image space.

double getDepth ( ) const

inline

Return the unscaled frustm depth.

double getGamma ( ) const

inline

double getTaper ( ) const

inline

Return the taper value.

bool hasSimpleAffine ( ) const

inline

Return true if the second map is a uniform scale, Rotation and translation.

bool hasUniformScale ( ) const

inlineoverridevirtual

Return false (by convention false)

Implements MapBase.

MapBase::Ptr inverseMap ( ) const

inlineoverridevirtual

Not implemented, since there is currently no map type that can represent the inverse of a frustum.

Exceptions

NotImplementedError

Implements MapBase.

bool isEqual ( const MapBase & other ) const

inlineoverridevirtual

Return true if this map is equal to the given map.

Implements MapBase.

static bool isEqualBase	(	const MapT &	self,
		const MapBase &	other
	)

inlinestaticprotectedinherited

bool isIdentity ( ) const

inline

Return true if the map is equivalent to an identity.

bool isLinear ( ) const

inlineoverridevirtual

Return false (a NonlinearFrustumMap is never linear).

Implements MapBase.

static bool isRegistered ( )

inlinestatic

bool isType ( ) const

inlineinherited

Return true if this map is of concrete type MapT (e.g., AffineMap).

bool isValid ( ) const

inline

Return true if the the bounding box in index space that defines the region that is maped into the frustum is non-zero, otherwise false

static Name mapType ( )

inlinestatic

Return NonlinearFrustumMap.

bool operator!= ( const NonlinearFrustumMap & other ) const

inline

bool operator== ( const NonlinearFrustumMap & other ) const

inline

MapBase::Ptr postRotate	(	double	radians,
		Axis	axis = `X_AXIS`
	)		const

inlineoverridevirtual

Return a MapBase::Ptr to a new map that is the result of appending the given rotation to the linear part of this map.

Implements MapBase.

MapBase::Ptr postScale ( const Vec3d & s ) const

inlineoverridevirtual

Return a MapBase::Ptr to a new map that is the result of appending the given scale to the linear part of this map.

Implements MapBase.

MapBase::Ptr postShear	(	double	shear,
		Axis	axis0,
		Axis	axis1
	)		const

inlineoverridevirtual

Return a MapBase::Ptr to a new map that is the result of appending the given shear to the linear part of this map.

Implements MapBase.

MapBase::Ptr postTranslate ( const Vec3d & t ) const

inlineoverridevirtual

Return a MapBase::Ptr to a new map that is the result of appending the given translation to the linear part of this map.

Implements MapBase.

MapBase::Ptr preRotate	(	double	radians,
		Axis	axis = `X_AXIS`
	)		const

inlineoverridevirtual

Return a MapBase::Ptr to a new map that is the result of prepending the given rotation to the linear part of this map.

Implements MapBase.

MapBase::Ptr preScale ( const Vec3d & s ) const

inlineoverridevirtual

Return a MapBase::Ptr to a new map that is the result of prepending the given scale to the linear part of this map.

Implements MapBase.

MapBase::Ptr preShear	(	double	shear,
		Axis	axis0,
		Axis	axis1
	)		const

inlineoverridevirtual

Return a MapBase::Ptr to a new map that is the result of prepending the given shear to the linear part of this map.

Implements MapBase.

MapBase::Ptr preTranslate ( const Vec3d & t ) const

inlineoverridevirtual

Return a MapBase::Ptr to a new map that is the result of prepending the given translation to the linear part of this map.

Implements MapBase.

void read ( std::istream & is )

inlineoverridevirtual

read serialization

Implements MapBase.

static void registerMap ( )

inlinestatic

const AffineMap& secondMap ( ) const

inline

Return MapBase::Ptr& to the second map.

void setDepth ( double d )

inline

set the frustum depth: distance between near and far plane = frustm depth * frustm x-width

void setTaper ( double t )

inline

set the taper value, the ratio of nearplane width / far plane width

std::string str ( ) const

inlineoverridevirtual

string serialization, useful for debuging

Implements MapBase.

Name type ( ) const

inlineoverridevirtual

Return NonlinearFrustumMap.

Implements MapBase.

Vec3d voxelSize ( ) const

inlineoverridevirtual

Return the size of a voxel at the center of the near plane.

Implements MapBase.

Vec3d voxelSize ( const Vec3d & loc ) const

inlineoverridevirtual

Returns the lengths of the images of the three segments from loc to loc + (1,0,0), from loc to loc + (0,1,0) and from loc to loc + (0,0,1)

Parameters

loc	a location in the pre-image space (e.g., index space)

Implements MapBase.

void write ( std::ostream & os ) const

inlineoverridevirtual

write serialization

Implements MapBase.

Public Types

Public Member Functions

Static Public Member Functions

Static Protected Member Functions

Detailed Description

Member Typedef Documentation

Constructor & Destructor Documentation

Member Function Documentation