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Program: Visualization Toolkit
Module: vtkModifiedBSPTree.h
Copyright (c) Ken Martin, Will Schroeder, Bill Lorensen
All rights reserved.
See Copyright.txt or for details.
This software is distributed WITHOUT ANY WARRANTY; without even
PURPOSE. See the above copyright notice for more information.
This code is derived from an earlier work and is distributed
with permission from, and thanks to
Copyright (C) 1997-2000 John Biddiscombe
Rutherford Appleton Laboratory,
Chilton, Oxon, England
Copyright (C) 2000-2004 John Biddiscombe
Skipping Mouse Software Ltd,
Blewbury, England
Copyright (C) 2004-2009 John Biddiscombe
CSCS - Swiss National Supercomputing Centre
Galleria 2 - Via Cantonale
CH-6928 Manno, Switzerland
// .NAME vtkModifiedBSPTree - Generate axis aligned BBox tree for raycasting and other Locator based searches
// .SECTION Description
// vtkModifiedBSPTree creates an evenly balanced BSP tree using a top down
// implementation. Axis aligned split planes are found which evenly divide
// cells into two buckets. Generally a split plane will intersect some cells
// and these are usually stored in both child nodes of the current parent.
// (Or split into separate cells which we cannot consider in this case).
// Storing cells in multiple buckets creates problems associated with multiple
// tests against rays and increases the required storage as complex meshes
// will have many cells straddling a split plane (and further splits may
// cause multiple copies of these).
// During a discussion with Arno Formella in 1998 he suggested using
// a third child node to store objects which straddle split planes. I've not
// seen this published (Yes! - see below), but thought it worth trying. This
// implementation of the BSP tree creates a third child node for storing cells
// lying across split planes, the third cell may overlap the other two, but the
// two 'proper' nodes otherwise conform to usual BSP rules.
// The advantage of this implementation is cells only ever lie in one node
// and mailbox testing is avoided. All BBoxes are axis aligned and a ray cast
// uses an efficient search strategy based on near/far nodes and rejects
// all BBoxes using simple tests.
// For fast raytracing, 6 copies of cell lists are stored in each leaf node
// each list is in axis sorted order +/- x,y,z and cells are always tested
// in the direction of the ray dominant axis. Once an intersection is found
// any cell or BBox with a closest point further than the I-point can be
// instantly rejected and raytracing stops as soon as no nodes can be closer
// than the current best intersection point.
// The addition of the 'middle' node upsets the optimal balance of the tree,
// but is a minor overhead during the raytrace. Each child node is contracted
// such that it tightly fits all cells inside it, enabling further ray/box
// rejections.
// This class is intented for persons requiring many ray tests and is optimized
// for this purpose. As no cell ever lies in more than one leaf node, and parent
// nodes do not maintain cell lists, the memory overhead of the sorted cell
// lists is 6*num_cells*4 for 6 lists of ints, each num_cells in length.
// The memory requirement of the nodes themselves is usually of minor
// significance.
// Subdividision is controlled by MaxCellsPerNode - any node with more than
// this number will be subdivided providing a good split plane can be found and
// the max depth is not exceeded.
// The average cells per leaf will usually be around half the MaxCellsPerNode,
// though the middle node is usually sparsely populated and lowers the average
// slightly. The middle node will not be created when not needed.
// Subdividing down to very small cells per node is not generally suggested
// as then the 6 stored cell lists are effectively redundant.
// Values of MaxcellsPerNode of around 16->128 depending on dataset size will
// usually give good results.
// Cells are only sorted into 6 lists once - before tree creation, each node
// segments the lists and passes them down to the new child nodes whilst
// maintaining sorted order. This makes for an efficient subdivision strategy.
// NB. The following reference has been sent to me
// @Article{formella-1995-ray,
// author = "Arno Formella and Christian Gill",
// title = "{Ray Tracing: A Quantitative Analysis and a New
// Practical Algorithm}",
// journal = "{The Visual Computer}",
// year = "{1995}",
// month = dec,
// pages = "{465--476}",
// volume = "{11}",
// number = "{9}",
// publisher = "{Springer}",
// keywords = "{ray tracing, space subdivision, plane traversal,
// octree, clustering, benchmark scenes}",
// annote = "{We present a new method to accelerate the process of
// finding nearest ray--object intersections in ray
// tracing. The algorithm consumes an amount of memory
// more or less linear in the number of objects. The basic
// ideas can be characterized with a modified BSP--tree
// and plane traversal. Plane traversal is a fast linear
// time algorithm to find the closest intersection point
// in a list of bounding volumes hit by a ray. We use
// plane traversal at every node of the high outdegree
// BSP--tree. Our implementation is competitive to fast
// ray tracing programs. We present a benchmark suite
// which allows for an extensive comparison of ray tracing
// algorithms.}",
// }
// .SECTION Thanks
// John Biddiscombe for developing and contributing this class
// -------------
// Implement intersection heap for testing rays against transparent objects
// .SECTION Style
// --------------
// This class is currently maintained by J. Biddiscombe who has specially
// requested that the code style not be modified to the kitware standard.
// Please respect the contribution of this class by keeping the style
// as close as possible to the author's original.
#ifndef _vtkModifiedBSPTree_h
#define _vtkModifiedBSPTree_h
#include "vtkAbstractCellLocator.h"
#include "vtkSmartPointer.h" // required because it is nice
class Sorted_cell_extents_Lists;
class BSPNode;
class vtkGenericCell;
class vtkIdList;
class vtkIdListCollection;
class VTK_FILTERING_EXPORT vtkModifiedBSPTree : public vtkAbstractCellLocator {
// Description:
// Standard Type-Macro
void PrintSelf(ostream& os, vtkIndent indent);
// Description:
// Construct with maximum 32 cells per node. (average 16->31)
static vtkModifiedBSPTree *New();
using vtkAbstractCellLocator::IntersectWithLine;
using vtkAbstractCellLocator::FindClosestPoint;
using vtkAbstractCellLocator::FindClosestPointWithinRadius;
// Description:
// Free tree memory
void FreeSearchStructure();
// Description:
// Build Tree
void BuildLocator();
// Description:
// Generate BBox representation of Nth level
virtual void GenerateRepresentation(int level, vtkPolyData *pd);
// Description:
// Generate BBox representation of all leaf nodes
virtual void GenerateRepresentationLeafs(vtkPolyData *pd);
// Description:
// Return intersection point (if any) of finite line with cells contained
// in cell locator.
virtual int IntersectWithLine(
double p1[3], double p2[3], double tol, double& t, double x[3],
double pcoords[3], int &subId)
{ return this->Superclass::IntersectWithLine(p1, p2, tol, t, x, pcoords, subId); }
// Description:
// Return intersection point (if any) AND the cell which was intersected by
// the finite line. Uses fast tree-search BBox rejection tests.
virtual int IntersectWithLine(
double p1[3], double p2[3], double tol, double &t, double x[3],
double pcoords[3], int &subId, vtkIdType &cellId);
// Description:
// Return intersection point (if any) AND the cell which was intersected by
// the finite line. The cell is returned as a cell id and as a generic cell.
virtual int IntersectWithLine(
double p1[3], double p2[3], double tol, double &t, double x[3],
double pcoords[3], int &subId, vtkIdType &cellId, vtkGenericCell *cell);
// Description:
// Take the passed line segment and intersect it with the data set.
// This method assumes that the data set is a vtkPolyData that describes
// a closed surface, and the intersection points that are returned in
// 'points' alternate between entrance points and exit points.
// The return value of the function is 0 if no intersections were found,
// -1 if point 'a0' lies inside the closed surface, or +1 if point 'a0'
// lies outside the closed surface.
// Either 'points' or 'cellIds' can be set to NULL if you don't want
// to receive that information. This method is currently only implemented
// in vtkOBBTree
virtual int IntersectWithLine(
const double p1[3], const double p2[3],
vtkPoints *points, vtkIdList *cellIds)
{ return this->Superclass::IntersectWithLine(p1, p2, points, cellIds); }
// Description:
// Take the passed line segment and intersect it with the data set.
// The return value of the function is 0 if no intersections were found.
// For each intersection found, the vtkPoints and CellIds objects
// have the relevant information added in order of intersection increasing
// from ray start to end. If either vtkPoints or CellIds are NULL
// pointers, then no information is generated for that list.
virtual int IntersectWithLine(
const double p1[3], const double p2[3], const double tol,
vtkPoints *points, vtkIdList *cellIds);
// Description:
// Returns the Id of the cell containing the point,
// returns -1 if no cell found. This interface uses a tolerance of zero
virtual vtkIdType FindCell(double x[3])
{ return this->Superclass::FindCell(x); }
// Description:
// Test a point to find if it is inside a cell. Returns the cellId if inside
// or -1 if not.
virtual vtkIdType FindCell(double x[3], double tol2, vtkGenericCell *GenCell,
double pcoords[3], double *weights);
bool InsideCellBounds(double x[3], vtkIdType cell_ID);
// Description:
// After subdivision has completed, one may wish to query the tree to find
// which cells are in which leaf nodes. This function returns a list
// which holds a cell Id list for each leaf node.
vtkIdListCollection *GetLeafNodeCellInformation();
BSPNode *mRoot; // bounding box root node
int npn;
int nln;
int tot_depth;
// The main subdivision routine
void Subdivide(BSPNode *node, Sorted_cell_extents_Lists *lists, vtkDataSet *dataSet,
vtkIdType nCells, int depth, int maxlevel, vtkIdType maxCells, int &MaxDepth);
// We provide a function which does the cell/ray test so that
// it can be overriden by subclasses to perform special treatment
// (Example : Particles stored in tree, have no dimension, so we must
// override the cell test to return a value based on some particle size
virtual int IntersectCellInternal(vtkIdType cell_ID, const double p1[3], const double p2[3],
const double tol, double &t, double ipt[3], double pcoords[3], int &subId);
void BuildLocatorIfNeeded();
void ForceBuildLocator();
void BuildLocatorInternal();
vtkModifiedBSPTree(const vtkModifiedBSPTree&); // Not implemented.
void operator=(const vtkModifiedBSPTree&); // Not implemented.
// BSP Node
// A BSP Node is a BBox - axis aligned etc etc
class BSPNode {
// Constructor
BSPNode(void) {
mChild[0] = mChild[1] = mChild[2] = NULL;
for (int i=0; i<6; i++) sorted_cell_lists[i] = NULL;
for (int i=0; i<3; i++) { bounds[i*2] = VTK_LARGE_FLOAT; bounds[i*2+1] = -VTK_LARGE_FLOAT; }
// Destructor
~BSPNode(void) {
for (int i=0; i<3; i++) if (mChild[i]) delete mChild[i];
for (int i=0; i<6; i++) if (sorted_cell_lists[i]) delete []sorted_cell_lists[i];
// Set min box limits
void setMin(double minx, double miny, double minz) {
bounds[0] = minx; bounds[2] = miny; bounds[4] = minz;
// Set max box limits
void setMax(double maxx, double maxy, double maxz) {
bounds[1] = maxx; bounds[3] = maxy; bounds[5] = maxz;
bool Inside(double point[3]) const;
// BBox
double bounds[6];
// The child nodes of this one (if present - NULL otherwise)
BSPNode *mChild[3];
// The axis we subdivide this voxel along
int mAxis;
// Just for reference
int depth;
// the number of cells in this node
int num_cells;
// 6 lists, sorted after the 6 dominant axes
vtkIdType *sorted_cell_lists[6];
// Order nodes as near/mid far relative to ray
void Classify(const double origin[3], const double dir[3],
double &rDist, BSPNode *&Near, BSPNode *&Mid, BSPNode *&Far) const;
// Test ray against node BBox : clip t values to extremes
bool RayMinMaxT(const double origin[3], const double dir[3],
double &rTmin, double &rTmax) const;
friend class vtkModifiedBSPTree;
friend class vtkParticleBoxTree;
static bool VTK_FILTERING_EXPORT RayMinMaxT(
const double bounds[6], const double origin[3], const double dir[3], double &rTmin, double &rTmax);
static int VTK_FILTERING_EXPORT getDominantAxis(const double dir[3]);