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 // This file is part of Eigen, a lightweight C++ template library // for linear algebra. // // Copyright (C) 2009 Ilya Baran // // This Source Code Form is subject to the terms of the Mozilla // Public License v. 2.0. If a copy of the MPL was not distributed // with this file, You can obtain one at http://mozilla.org/MPL/2.0/. #ifndef EIGEN_BVH_MODULE_H #define EIGEN_BVH_MODULE_H #include #include #include #include #include namespace Eigen { /** * \defgroup BVH_Module BVH module * \brief This module provides generic bounding volume hierarchy algorithms * and reference tree implementations. * * * \code * #include * \endcode * * A bounding volume hierarchy (BVH) can accelerate many geometric queries. This module provides a generic implementation * of the two basic algorithms over a BVH: intersection of a query object against all objects in the hierarchy and minimization * of a function over the objects in the hierarchy. It also provides intersection and minimization over a cartesian product of * two BVH's. A BVH accelerates intersection by using the fact that if a query object does not intersect a volume, then it cannot * intersect any object contained in that volume. Similarly, a BVH accelerates minimization because the minimum of a function * over a volume is no greater than the minimum of a function over any object contained in it. * * Some sample queries that can be written in terms of intersection are: * - Determine all points where a ray intersects a triangle mesh * - Given a set of points, determine which are contained in a query sphere * - Given a set of spheres, determine which contain the query point * - Given a set of disks, determine if any is completely contained in a query rectangle (represent each 2D disk as a point \f$(x,y,r)\f$ * in 3D and represent the rectangle as a pyramid based on the original rectangle and shrinking in the \f$r\f$ direction) * - Given a set of points, count how many pairs are \f$d\pm\epsilon\f$ apart (done by looking at the cartesian product of the set * of points with itself) * * Some sample queries that can be written in terms of function minimization over a set of objects are: * - Find the intersection between a ray and a triangle mesh closest to the ray origin (function is infinite off the ray) * - Given a polyline and a query point, determine the closest point on the polyline to the query * - Find the diameter of a point cloud (done by looking at the cartesian product and using negative distance as the function) * - Determine how far two meshes are from colliding (this is also a cartesian product query) * * This implementation decouples the basic algorithms both from the type of hierarchy (and the types of the bounding volumes) and * from the particulars of the query. To enable abstraction from the BVH, the BVH is required to implement a generic mechanism * for traversal. To abstract from the query, the query is responsible for keeping track of results. * * To be used in the algorithms, a hierarchy must implement the following traversal mechanism (see KdBVH for a sample implementation): \code typedef Volume //the type of bounding volume typedef Object //the type of object in the hierarchy typedef Index //a reference to a node in the hierarchy--typically an int or a pointer typedef VolumeIterator //an iterator type over node children--returns Index typedef ObjectIterator //an iterator over object (leaf) children--returns const Object & Index getRootIndex() const //returns the index of the hierarchy root const Volume &getVolume(Index index) const //returns the bounding volume of the node at given index void getChildren(Index index, VolumeIterator &outVBegin, VolumeIterator &outVEnd, ObjectIterator &outOBegin, ObjectIterator &outOEnd) const //getChildren takes a node index and makes [outVBegin, outVEnd) range over its node children //and [outOBegin, outOEnd) range over its object children \endcode * * To use the hierarchy, call BVIntersect or BVMinimize, passing it a BVH (or two, for cartesian product) and a minimizer or intersector. * For an intersection query on a single BVH, the intersector encapsulates the query and must provide two functions: * \code bool intersectVolume(const Volume &volume) //returns true if the query intersects the volume bool intersectObject(const Object &object) //returns true if the intersection search should terminate immediately \endcode * The guarantee that BVIntersect provides is that intersectObject will be called on every object whose bounding volume * intersects the query (but possibly on other objects too) unless the search is terminated prematurely. It is the * responsibility of the intersectObject function to keep track of the results in whatever manner is appropriate. * The cartesian product intersection and the BVMinimize queries are similar--see their individual documentation. * * The following is a simple but complete example for how to use the BVH to accelerate the search for a closest red-blue point pair: * \include BVH_Example.cpp * Output: \verbinclude BVH_Example.out */ } //@{ #include "src/BVH/BVAlgorithms.h" #include "src/BVH/KdBVH.h" //@} #endif // EIGEN_BVH_MODULE_H