/**
@mainpage OpenVDB

The @b OpenVDB library comprises a hierarchical data structure and a suite
of tools for the efficient manipulation of sparse, possibly time-varying,
volumetric data discretized on a three-dimensional grid.  It is based on
VDB, which was developed by Ken Museth at DreamWorks Animation, and it
offers an effectively infinite 3D index space, compact storage (both in
memory and on disk), fast data access (both random and sequential), and
a collection of algorithms specifically optimized for the data structure
for common tasks such as filtering, CSG, compositing, sampling and 
voxelization from other geometric representations. The technical details 
of VDB are described in the paper <a href="http://www.museth.org/Ken/Publications.html">&ldquo;VDB:&nbsp;High-Resolution Sparse Volumes with Dynamic Topology&rdquo;</a>.

@b OpenVDB is maintained by
<A HREF="http://www.dreamworksanimation.com">DreamWorks Animation</A>
and was developed primarily by
- Ken Museth
- Peter Cucka
- Mihai Ald&eacute;n
- David Hill

See the @subpage overview "Overview" for an introduction to the library.

See @subpage transformsAndMaps "Transforms and Maps" for more
discussion of the transforms used in @b OpenVDB.

See the @subpage faq "FAQ" for frequently asked questions about @b OpenVDB.

See the @subpage codeExamples "Cookbook" to get started using @b OpenVDB.

See @subpage python "Using OpenVDB in Python" to get started with the @b OpenVDB
Python module.

See the @subpage changes "Release Notes" for what's new in this version
of @b OpenVDB.

Contributors, please familiarize yourselves with our
@subpage codingStyle "coding standards".



@page overview OpenVDB Overview

@section Contents
- @ref secOverview
- @ref secTree
  - @ref subsecTreeConfig
- @ref secSparsity
  - @ref subsecValues
  - @ref subsecInactive
- @ref secSpaceAndTrans
  - @ref subsecVoxSpace
  - @ref subsecWorSpace
  - @ref subsecTrans
- @ref secGrid
- @ref secToolUtils
- @ref secIterator
  - @ref subsecTreeIter
  - @ref subsecNodeIter
  - @ref subsecValueAccessor
  - @ref subsecTraversal
<!-- - @ref secRegistry -->


@section secOverview Introduction

This document is a high-level summary of the terminology and basic
components of the OpenVDB library and is organized around two key
motivating concepts.  First, OpenVDB is designed specifically to
work efficiently with sparse volumetric data locally sampled at a high
spatial frequency, although it will function well for dense volumetric
data.  From this follows the need for a memory efficient representation of
this sparsity and the need for fast iterators (and other tools) that
respect sparsity.  Second, data storage is separated from data
interpretation.  OpenVDB uses unit-less three-dimensional integer
coordinates to address the sparse data, but introduces a unit-less
continuous index space for interpolation, along with a transform to
place the data in physical space.

When manipulating data in OpenVDB, the three essential objects are (1) the
@vdblink::tree::Tree Tree@endlink, a B-tree-like three-dimensional data
structure; (2) the @vdblink::math::Transform Transform@endlink, which relates
voxel indices @ijk to physical locations @xyz in @ref subsecWorSpace
"world" space; and (3) the @vdblink::Grid Grid@endlink, a container
that associates a @c Tree with a @c Transform and additional metadata.
For instancing purposes (i.e., placing copies
of the same volume in multiple locations), the same tree may be referenced
(via smart pointers) by several different <TT>Grid</TT>s, each having a
unique transform.

We now proceed to discuss the @c Tree and ideas of sparsity in some
detail, followed by a briefer description of the different spaces and
transforms as well as some of the tools that act on the sparse data.


@section secTree The Tree

In OpenVDB the @c Tree data structure exists to answer the question
<I>What value is stored at location @ijk in three-dimensional index
space?</I>  Here <I>i</I>, <I>j</I> and <I>k</I> are arbitrary signed 32-bit
integers, and the data type of the associated value (<TT>float</TT>,
<TT>bool</TT>, vector, etc.) is the same for all @ijk.  While the @c Tree
serves the same purpose as a large three-dimensional array, it is a
specially designed data structure that, given sparse unique values,
minimizes the overall memory footprint while retaining fast access times.
This is accomplished, as the name suggests, via a tree-based acceleration
structure comprising a @vdblink::tree::RootNode RootNode@endlink,
@vdblink::tree::LeafNode LeafNodes@endlink and usually one or more levels
of @vdblink::tree::InternalNode InternalNodes@endlink with prescribed
branching factors. 
  
@subsection subsecTreeConfig Tree Configuration

The tree-based acceleration structure can be configured in various ways,
but with the restriction that for a given tree all the <TT>LeafNode</TT>s
are at the same depth.  Conceptually, the @c RootNode and
@c InternalNodes increasingly subdivide the three-dimensional index
space, and the <TT>LeafNode</TT>s hold the actual unique voxels.  

The type of a @c Tree encodes both the type of the data to be
stored in the tree (<TT>float</TT>, <TT>bool</TT>, etc.) and the
tree's node configuration.  In practice a four-level (root,
internal, internal, leaf) configuration is standard, and several
common tree types are defined in openvdb.h.  For example,
@code
typedef tree::Tree4<float, 5, 4, 3>::Type FloatTree;
typedef tree::Tree4<bool, 5, 4, 3>::Type  BoolTree;
@endcode
These predefined tree types share the same branching factors, which dictate
the number of children of a given node.  The branching factors (5, 4, 3)
are specified as base two logarithms and should be read backwards from the
leaf nodes up the tree.

In the default tree configuration, each @c LeafNode holds a
three-dimensional grid of 2<SUP>3</SUP> voxels on a side (i.e., an
@f$8\times8\times8@f$ voxel grid).  Internally, the @c LeafNode is said
to be at "level 0" of the tree.  At "level 1" of this tree is the first
@c InternalNode, and it indexes a @f$2^4\times2^4\times2^4 =
16\times16\times16@f$ grid, each entry of which is either a @c LeafNode
or a constant value that represents an @f$8\times8\times8@f$ block of
voxels.  At "level 2" is the second @c InternalNode in this
configuration; it in turn indexes a @f$2^5\times2^5\times2^5 =
32\times32\times32@f$ grid of level-1 <TT>InternalNode</TT>s and/or values,
and so the @c InternalNode at level 2 subsumes a three-dimensional
block of voxels of size @f$32\times16\times8 = 4096@f$ on a side.  Unlike
the <TT>InternalNode</TT>s and <TT>LeafNode</TT>s, the @c RootNode ("level
3" for the default configuration) is not explicitly restricted in the number 
of children it may have, so the overall index space is limited only by the 
range of the integer indices, which are 32-bit by default. 


@section secSparsity Sparse Values and Voxels

Like a tree's node configuration, the type of data held by a tree is
determined at compile time. Conceptually the tree itself 
employs two different notions of data sparsity to reduce the memory footprint
and at the same time accelerate access to its contents.  The first is largely 
hidden from the user and concerns ways in which large regions of uniform values 
are compactly represented, and the second allows for fast sequential iteration, 
skipping user-specified "uninteresting" regions (that may or may not have 
uniform values). 

@subsection subsecValues Tile, Voxel, and Background Values

Although the data in a tree is accessed and set on a per-voxel level
(i.e., the value at @ijk) it need not be internally stored in that way.
To reduce the memory footprint and accelerate data access, data values are
stored in three distinct forms internal to the tree: <B>voxel values</B>,
<B>tile values</B>, and a <B>background value</B>.  A voxel value is a unique
value indexed by the location of a voxel and is stored in the @c LeafNode
responsible for that voxel.  A tile value is a uniform value assigned to all
voxels subsumed by a given node.  (For example, a tile Value belonging to an
@c InternalNode at level 1 is equivalent to a constant-value cube of voxels
of the same size, @f$8\times8\times8@f$, as a @c LeafNode.)  The tile value
is returned when a request is made for the data associated with any @ijk
location within the uniform tile.  The background value is a unique value 
(stored at the root level) that is returned when accessing any @ijk location 
that does not resolve to either a tile or a @c LeafNode. 

 
@subsection subsecInactive Active and Inactive Voxels

Any voxel or tile can be classified as either @b active or @b inactive.
The interpretation of this state is application-specific, but generally
active voxels are "interesting", and inactive somehow less so. The locations
of active values may be sparse in the overall voxel topology, and OpenVDB
provides @ref secIterator "iterators" that access active values only (as
well as iterators over inactive values, all values, and general topology).
An example of active vs. inactive: the voxels used to store the distance
values of a narrow-band level set (i.e., close to a given surface) will be
marked as active while the other ("far") voxel locations will be marked as
inactive and will generally represent regions of space with constant distance 
values (e.g., two constant distance values of opposite sign to distinguish 
the enclosed inside region from the infinite outside or background embedding).

The @vdblink::tree::Tree::prune() prune()@endlink method replaces
with tile values any nodes that subsume voxels with the same values
and active states.
The resulting tree represents the same volume, but more sparsely.

@section secSpaceAndTrans Coordinate Systems and Transforms

The sampled data in the tree is accessed using signed <B>index coordinates</B>
@ijk, but associating each indicial coordinate with a specific physical
location is a job for a @c Transform. A simple linear transform assumes
a lattice-like structure with a fixed physical distance @f$\Delta@f$ between
indices, so that @f$(x,y,z) = (\Delta i, \Delta j, \Delta k)@f$.   

@subsection subsecVoxSpace Index Space

To simplify transformations between physical space and lattice index
coordinates, a continuous generalization of the index lattice points called
<B>index space</B> is used.
For example, index space coordinate (1.0, 1.0, 1.0) corresponds to the same
point as (1,1,1) in the index lattice, but (1.5,1.0,1.0) also has meaning as
halfway between the index coordinates (1,1,1) and (2,1,1).  Index space can
be used in constructing interpolated data values: given an arbitrary
location in physical space, one can use a transform to compute the point in
index space (which need not fall on an exact integer index) that maps to that
location and locally interpolate from values with neighboring index
coordinates.

@subsection subsecWorSpace World Space

The interpretation of the data in a tree takes place in <B>world
space</B>.  For example, the tree might hold data sampled at discrete
physical locations in world space.  @c Transform methods such as
@vdblink::math::Transform::indexToWorld() indexToWorld() @endlink
and its inverse @vdblink::math::Transform::worldToIndex()
worldToIndex() @endlink
may be used to relate coordinates in the two continuous spaces. In 
addition, methods such as @vdblink::math::Transform::worldToIndexCellCentered()
worldToIndexCellCentered()@endlink actually return lattice points. 

@subsection subsecTrans Transforms and Maps
A @vdblink::math::Transform Transform @endlink provides a context for
interpreting the information held in a tree by associating a location
in world space with each entry in the tree.
The actual implementation of the @c Transform is managed by a 
@vdblink::math::MapBase Map@endlink object, which is an
encapsulation of a continuous, mostly invertible function of three
variables.  A @c Map is required to provide
@vdblink::math::MapBase::applyMap() applyMap()@endlink and
@vdblink::math::MapBase::applyInverseMap() applyInverseMap()@endlink
methods to relate locations in its domain to its range and vice versa.
A @c Map is also required to provide information about its local derivatives.
For more on these classes, see the
@subpage transformsAndMaps "Transforms and Maps" page.


@section secGrid The Grid

For many applications, it might not be necessary ever to operate directly on
trees, though there are often significant performance improvements to be
gained by exploiting the tree structure.
The @vdblink::Grid Grid@endlink, however, is the preferred interface through
which to manage voxel data, in part because a grid associates with a tree
additional and often necessary information that is not accessible through
the tree itself.

A @vdblink::Grid Grid@endlink contains smart pointers to a
@vdblink::tree::Tree Tree@endlink object and a
@vdblink::math::Transform Transform@endlink object, either or both of which
might be shared with other grids.
As mentioned above, the transform provides for the interpretation of voxel
locations.  Other grid metadata, notably the <B>grid class</B>, the
<B>vector type</B> and the world&nbsp;space/local space toggle, affect
the interpretation of voxel values.

OpenVDB is particularly well-suited (though by no means exclusively so)
to the representation of <B>narrow-band level sets</B> and
<B>fog volumes</B>.
A narrow-band level set is represented by three distinct regions of voxels:
an @b outside (or background) region of inactive voxels having a constant,
positive distance from the level set surface; an @b inside region of inactive
voxels having a constant, negative distance; and a thin band of active voxels
(normally three voxels wide on either side of the surface) whose values are
signed distances.
Similarly, a fog volume is represented by an outside region of inactive
voxels with value zero, an inside region of active voxels with value one,
and a thin band of active voxels, with values typically varying linearly
between zero and one, that separates the inside from the outside.
Identifying a grid as a level set or a fog volume, by setting its
@vdblink::GridClass grid class@endlink with
@vdblink::Grid::setGridClass() setGridClass@endlink, allows tools to invoke
alternative implementations that are better-suited or better-optimized
for those classes.
For example, resampling (in particular, scaling) a level set should normally
not be done without updating its signed distance values.
The @vdblink::tools::resampleToMatch() resampleToMatch@endlink tool
automatically recomputes signed distances for grids that are identified
as level sets.
(The lower-level @vdblink::tools::GridResampler GridResampler@endlink does not,
but it is optimized for level set grids in that it transforms only voxels
in the narrow band and relies on
@vdblink::Grid::signedFloodFill() signed flood fill@endlink to reconstruct
the inside and outside regions.)
Other tools whose behavior is affected by the grid class include the
@vdblink::tools::divergence() divergence@endlink operator (which has an
alternative implementation for @ref sStaggered "staggered velocity" grids),
the @vdblink::tools::volumeToMesh() volume to mesh@endlink converter, and
the @vdblink::tools::fillWithSpheres() sphere packing@endlink tool.
In addition, a number of level-set-specific tools, such as the
@vdblink::tools::LevelSetTracker level set tracker@endlink, throw
exceptions when invoked on grids that are not identified as level sets.
It is important, therefore, to set a grid&rsquo;s class appropriately.

When a vector-valued grid is transformed or resampled, it is often necessary
for the transform to be applied not just to voxel locations but also to
voxel values.
By default, grids are identified as &ldquo;world-space&rdquo;, meaning that
if the grid is vector-valued, its voxel values should be transformed.
Alternatively, voxel values of grids identified as
&ldquo;local-space&rdquo;, via
@vdblink::Grid::setIsInWorldSpace() setIsInWorldSpace@endlink, do not
undergo transformation.
A world-space grid&rsquo;s @vdblink::VecType vector type@endlink, specified
with @vdblink::Grid::setVectorType() setVectorType@endlink, may be invariant,
covariant or contravariant, which determines how transforms are applied
to the grid&rsquo;s voxel values (for details see, for example,
<A HREF="http://en.wikipedia.org/wiki/Covariance_and_contravariance_of_vectors">
<I>Covariance and contravariance of vectors</I></A>&nbsp;[Wikipedia]).
The @vdblink::tools::transformVectors() transformVectors@endlink tool can be
used to apply a transform to a grid&rsquo;s voxel values, and it handles all
of the supported vector types.

A grid can optionally be assigned @vdblink::Grid::setName() name@endlink and
@vdblink::Grid::setCreator() creator@endlink strings.
These are purely informational, though it might be desirable to name grids
so as to easily select which ones to read from files that contain multiple
grids.
In the absence of grid names, or at least of unique names, OpenVDB&rsquo;s
file I/O routines recognize an ordinal suffix:
&ldquo;<TT>[0]</TT>&rdquo; refers to the first unnamed grid,
&ldquo;<TT>[1]</TT>&rdquo; refers to the second, and so on, and
&ldquo;<TT>density[0]</TT>&rdquo; and &ldquo;<TT>density[1]</TT>&rdquo;
refer to the first and second grids named &ldquo;density&rdquo;.
Also of interest for file I/O is a grid&rsquo;s
&ldquo;@vdblink::Grid::setSaveFloatAsHalf() save float as half@endlink&rdquo;
setting, which allows it to be written more compactly using 16-bit
floating point values rather than full-precision values.
Finally, during file output certain statistics are computed and stored
as per-grid metadata.
These include the grid&rsquo;s index-space active voxel bounding box,
its active voxel count and its memory usage in bytes.
This information can also be
@vdblink::io::File::readAllGridMetadata() retrieved@endlink
efficiently from a file.


@section secToolUtils Utilities and Tools

OpenVDB provides utility functions and classes for the manipulation of grids
and the data they hold.
Tools such as those found in GridOperators.h compute vector quantities from
scalar data or vice-versa.
Other tools perform filtering (Filter.h and LevelSetFilter.h) and
interpolation (Interpolation.h) as well as sampling (GridTransformer.h),
compositing and constructive solid geometry (Composite.h), and other
transformations (ValueTransformer.h).
OpenVDB also supports advanced finite difference computations through
a variety of local support stencils (Stencils.h).


@section secIterator Iterators

OpenVDB provides efficient, often multithreaded, implementations of a large
variety of morphological, filtering and other algorithms that address common
data manipulation tasks on three-dimensional grids.   For more specialized
tasks, OpenVDB provides lower-level data accessors that enable fast
iteration over all or selected voxels and over the elements of a @c Tree.
These take several forms: iterator classes of various types, functor-based
@b visitor methods, and the
@vdblink::tree::ValueAccessor ValueAccessor@endlink,
an accelerator for indexed @ijk voxel lookups.

Iterator classes follow a fairly consistent naming scheme.  First, the
@b CIter and @b Iter suffixes denote @const and non-@const iterators, i.e.,
iterators that offer, respectively, read-only and read/write access to the
underlying tree or node.  Second, iterators over tile and voxel values are
denoted either @b On, @b Off or @b All, indicating that they visit only
active values, only inactive values, or both active and inactive values.
So, for example, @c Tree::ValueOnCIter is a read-only iterator over all
active values (both tile and voxel) of a tree, whereas
@c LeafNode::ValueAllIter is a read/write iterator over all values, both
active and inactive, of a single leaf node.

OpenVDB iterators are not STL-compatible in that one can always request
an iterator that points to the beginning of a collection of elements (nodes,
voxels, etc.), but one usually cannot request an iterator that points to the
end of the collection.  (This is because finding the end might require a
full tree traversal.)  Instead, all OpenVDB iterators implement a @c test()
method that returns @c true as long as the iterator is not exhausted and
@c false as soon as it is.  Typical usage is as follows:
@code
typedef openvdb::FloatGrid GridType;
GridType grid = ...;
for (GridType::ValueOnCIter iter = grid.cbeginValueOn(); iter.test(); ++iter) ...
@endcode
or more compactly
@code
for (GridType::ValueOnCIter iter = grid.cbeginValueOn(); iter; ++iter) ...
@endcode
Note that the naming scheme for methods that return "begin" iterators
closely mirrors that of the iterators themselves.  That is,
@c Grid::cbeginValueOn() returns a @const iterator to the first of a grid's
active values, whereas @c LeafNode::beginValueAll() returns a non-@const
iterator to the first of a leaf node's values, both active and inactive.
(Const overloads of @c begin*() methods are usually provided, so that if
the @c Grid is itself @const, @c Grid::begin*() will actually return a
@const iterator.  This makes it more convenient to use these methods in
templated code.)

Finally, note that modifying the tree or node over which one is iterating
typically does not invalidate the iterator, though it might first need
to be incremented to point to the next existing element (for example,
if one deletes a child node to which the iterator is currently pointing).

@subsection subsecTreeIter Tree Iterators
@anchor treeValueIterRef
@par Tree::ValueIter
Tree-level value iterators traverse an entire tree, visiting each value
(tile or voxel) exactly once.  (It is also possible to restrict the
traversal to minimum and maximum levels of the tree.)  In addition to the
methods common to all OpenVDB iterators, such as @c test() and @c next(),
a @c Tree::ValueIter provides methods that return the depth in the tree of
the node within which the iterator is pointing (the root node has depth 0)
and the @ijk axis-aligned bounding box of the tile or voxel to which it is
pointing, and methods to get and set both the value and the active state of
the tile or voxel.  See the
@vdblink::tree::TreeValueIteratorBase TreeValueIteratorBase @endlink
class for the complete list.

@anchor treeLeafIterRef
@par Tree::LeafIter
By convention in OpenVDB, voxels in the narrow band of a narrow-band
level set are stored only at the leaf level of a tree, so to facilitate the
implementation of level set algorithms that operate on narrow-band voxels,
OpenVDB provides an iterator that visits each @c LeafNode in a tree exactly
once.
See the @vdblink::tree::LeafIteratorBase LeafIteratorBase@endlink class
for details, and also the related
@vdblink::tree::LeafManager LeafManager@endlink acceleration structure.

@anchor treeNodeIterRef
@par Tree::NodeIter
A node iterator traverses a tree in depth-first order, starting from its
root, and visits each node exactly once.  (It is also possible to restrict
the traversal to minimum and maximum node depths&mdash;see the
@vdblink::tree::NodeIteratorBase NodeIteratorBase @endlink
class for details.)  Like the tree-level value iterator, the node iterator
provides methods that return the depth in the tree of the node to which the
iterator is pointing (the root node has depth 0) and the @ijk axis-aligned
bounding box of the voxels subsumed by the node and all of its children.
@par
Naturally, a node iterator also provides access to the node to which it is
pointing, but this is complicated somewhat by the fact that nodes of the
various types (@c RootNode, @c InternalNode and @c LeafNode) do not inherit
from a common base class.  For efficiency, OpenVDB generally avoids class
inheritance and virtual functions in favor of templates, allowing the
compiler to optimize away function calls.  In particular, each node type is
templated on the type of its children, so even two <TT>InternalNode</TT>s at
different levels of a tree have distinct types.  As a result, it is
necessary to know the type of the node to which a node iterator is pointing
in order to request access to that node.  See the
@ref sNodeIterator "Cookbook" for an example of how to do this.

@subsection subsecNodeIter Node Iterators

Less commonly used than tree-level iterators (but found in the
implementations of some of the narrow-band level set algorithms referred to
@ref treeLeafIterRef "above") are node-level iterators.  A node
<B>value iterator</B> visits the values (active, inactive or both) stored in
a single @c RootNode, @c InternalNode or @c LeafNode, whereas a node
<B>child iterator</B> visits the children of a single root or internal node.
(Recall that non-leaf nodes store either a tile value or a child node at
each grid position.)


@subsection subsecValueAccessor Value Accessor

When traversing a grid by @ijk index in a spatially coherent pattern,
such as when iterating over neighboring voxels, request a
@vdblink::tree::ValueAccessor ValueAccessor@endlink from the grid
(with @vdblink::Grid::getAccessor() Grid::getAccessor()@endlink)
and use the accessor's
@vdblink::tree::ValueAccessor::getValue() getValue()@endlink and
@vdblink::tree::ValueAccessor::setValue() setValue()@endlink methods, since
these will usually be significantly faster (a factor of three is typical)
than accessing voxels directly in the grid's tree.
The accessor records the sequence of nodes
visited during the most recent access; on the next access, rather than
traversing the tree from the root node down, it performs an inverted
traversal from the deepest recorded node up.  For neighboring voxels, the
traversal need only proceed as far as the voxels' common ancestor node,
which more often than not is the first node in the sequence.

Multiple accessors may be associated with a single grid.  In fact, for
multithreaded, read-only access to a grid, it is recommended that each
thread be assigned its own accessor.  A thread-safe, mutex-locked accessor
is provided (see @vdblink::tree::ValueAccessorRW ValueAccessorRW@endlink),
but the locking negates much of the performance benefit of inverted traversal;
and because it is the accessor object that is thread-safe, not the grid,
concurrent reads and writes are not safe unless all threads share a single
accessor.

All accessors associated with a grid must be cleared after any operation that
removes nodes from the grid's tree, such as pruning, CSG or compositing.
For those and other built-in operations, this is done automatically via
a callback mechanism, but developers must be careful to call
@vdblink::tree::Tree::clearAllAccessors() Tree::clearAllAccessors()@endlink
whenever deleting nodes directly.


@subsection subsecTraversal Tree Traversal

<I>To be written</I>

*/
