// COTD Entry submitted by Paul Nettle [midnight@FluidStudios.com]
// Corresponds with an Ask MidNight response (http://www.flipcode.com/askmid/)
// -----------------------------------------------------------------------------
// This defines a callback for traversal
// -----------------------------------------------------------------------------
class Octree;
typedef bool (*callback)(const Octree &o, void *data);
// -----------------------------------------------------------------------------
// This defines a point class (it's incomplete, but the data elements are there)
// -----------------------------------------------------------------------------
class Point
{
public:
double x, y, z; // Position
double n; // User's unique identifier
unsigned int code; // Used during octree generation
// Insert typical operators, such as *, +, -, etc.
};
// -----------------------------------------------------------------------------
// This defines a cubic bounding volume (center, radius)
// -----------------------------------------------------------------------------
typedef struct
{
Point center; // Center of a cubic bounding volume
double radius; // Radius of a cubic bounding volume
} Bounds;
// -----------------------------------------------------------------------------
// The octree class -- almost real code!
// -----------------------------------------------------------------------------
class Octree
{
public:
// Construction/Destruction
Octree();
virtual ~Octree();
// Accessors
inline const Point * const * points() const {return _points;}
inline const unsigned int pointCount() const {return _pointCount;}
// Implementation
virtual const bool build(Point **points,
const unsigned int count,
const unsigned int threshold,
const unsigned int maximumDepth,
const Bounds &bounds,
const unsigned int currentDepth = 0);
static const Bounds calcCubicBounds(const Point * const * points,
const unsigned int count);
virtual const bool traverse(callback proc, void *data) const;
protected:
Octree *_child[8];
unsigned int _pointCount;
Point **_points;
Point _center;
double _radius;
};
// -----------------------------------------------------------------------------
// Construction -- Just "nullify" the class
// -----------------------------------------------------------------------------
Octree::Octree()
: _pointCount(0), _points(NULL), _center(0,0,0,0), _radius(0.0)
{
memset(_child, 0, sizeof(_child));
}
// -----------------------------------------------------------------------------
// Destruction -- free up memory
// -----------------------------------------------------------------------------
Octree::~Octree()
{
delete[] _points;
}
// -----------------------------------------------------------------------------
// Build the octree
// -----------------------------------------------------------------------------
const bool Octree::build(Point **points,
const unsigned int count,
const unsigned int threshold,
const unsigned int maximumDepth,
const Bounds &bounds,
const unsigned int currentDepth)
{
// You know you're a leaf when...
//
// 1. The number of points is <= the threshold
// 2. We've recursed too deep into the tree
// (currentDepth >= maximumDepth)
//
// NOTE: We specifically use ">=" for the depth comparison so that we
// can set the maximumDepth depth to 0 if we want a tree with
// no depth.
if (count <= threshold || currentDepth >= maximumDepth)
{
// Just store the points in the node, making it a leaf
_pointCount = count;
_points = new Point *[count];
memcpy(_points, points, sizeof(Point *) * count);
return true;
}
// We'll need this (see comment further down in this source)
unsigned int childPointCounts[8];
// Classify each point to a child node
for (unsigned int i = 0; i < count; i++)
{
// Current point
Point &p = *points[i];
// Center of this node
const Point &c = bounds.center;
// Here, we need to know which child each point belongs to. To
// do this, we build an index into the _child[] array using the
// relative position of the point to the center of the current
// node
p.code = 0;
if (p.x > c.x) p.code |= 1;
if (p.y > c.y) p.code |= 2;
if (p.z > c.z) p.code |= 4;
// We'll need to keep track of how many points get stuck in each
// child so we'll just keep track of it here, since we have the
// information handy.
childPointCounts[p.code]++;
}
// Recursively call build() for each of the 8 children
for (i = 0; i < 8; i++)
{
// Don't bother going any further if there aren't any points for
// this child
if (!childPointCounts[i]) continue;
// Allocate the child
_child[i] = new Octree;
// Allocate a list of points that were coded JUST for this child
// only
Point **newList = new Point *[childPointCounts[i]];
// Go through the input list of points and copy over the points
// that were coded for this child
Point **ptr = newList;
for (unsigned int j = 0; j < count; j++)
{
if (points[j]->code == i)
{
*ptr = points[j];
ptr++;
}
}
// At this point, we have a list of points that will belong to
// this child node. We'll want to remove any point with a
// duplicate 'n' in them...
//
// [We won't need to reallocate the list, since it's temporary]
int newCount = 0;
for (j = 0; j < childPointCounts[i]; j++)
{
// Remove duplicates from newList
// ...
// Keep track of the new count in 'newCount'
}
// Generate a new bounding volume -- We do this with a touch of
// trickery...
//
// We use a table of offsets. These offsets determine where a
// node is, relative to it's parent. So, for example, if want to
// generate the bottom-left-rear (-x, -y, -z) child for a node,
// we use (-1, -1, -1).
//
// However, since the radius of a child is always half of its
// parent's, we use a table of 0.5, rather than 1.0.
//
// These values are stored the following table. Note that this
// won't compile because it assumes Points are structs, but you
// get the idea.
Point boundsOffsetTable[8] =
{
{-0.5, -0.5, -0.5},
{+0.5, -0.5, -0.5},
{-0.5, +0.5, -0.5},
{+0.5, +0.5, -0.5},
{-0.5, -0.5, +0.5},
{+0.5, -0.5, +0.5},
{-0.5, +0.5, +0.5},
{+0.5, +0.5, +0.5}
};
// Calculate our offset from the center of the parent's node to
// the center of the child's node
Point offset = boundsOffsetTable[i] * bounds.radius;
// Create a new Bounds, with the center offset and half the
// radius
Bounds newBounds;
newBounds.radius = bounds.radius * 0.5;
newBounds.center = bounds.center + offset;
// Recurse
_child[i]->build(newList, newCount, threshold, maximumDepth,
newBounds, currentDepth+1);
// Clean up
delete[] newList;
}
return true;
}
// -----------------------------------------------------------------------------
// Determine the [cubic] bounding volume for a set of points
// -----------------------------------------------------------------------------
const Bounds Octree::calcCubicBounds(const Point * const * points,
const unsigned int count)
{
// What we'll give to the caller
Bounds b;
// Determine min/max of the given set of points
Point min = *points[0];
Point max = *points[0];
for (unsigned int i = 1; i < count; i++)
{
const Point &p = *points[i];
if (p.x < min.x) min.x = p.x;
if (p.y < min.y) min.y = p.y;
if (p.z < min.z) min.z = p.z;
if (p.x > max.x) max.x = p.x;
if (p.y > max.y) max.y = p.y;
if (p.z > max.z) max.z = p.z;
}
// The radius of the volume (dimensions in each direction)
Point radius = max - min;
// Find the center of this space
b.center = min + radius * 0.5;
// We want a CUBIC space. By this, I mean we want a bounding cube, not
// just a bounding box. We already have the center, we just need a
// radius that contains the entire volume. To do this, we find the
// maxumum value of the radius' X/Y/Z components and use that
b.radius = radius.x;
if (b.radius < radius.y) b.radius = radius.y;
if (b.radius < radius.z) b.radius = radius.z;
// Done
return b;
}
// -----------------------------------------------------------------------------
// Generic tree traversal
// -----------------------------------------------------------------------------
const bool Octree::traverse(callback proc, void *data) const
{
// Call the callback for this node (if the callback returns false, then
// stop traversing.
if (!proc(*this, data)) return false;
// If I'm a node, recursively traverse my children
if (!_pointCount)
{
for (unsigned int i = 0; i < 8; i++)
{
// We store incomplete trees (i.e. we're not guaranteed
// that a node has all 8 children)
if (!_child[i]) continue;
if (!_child[i]->traverse(proc, data)) return false;
}
}
return true;
}
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