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* http://www.apache.org/licenses/LICENSE-2.0
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package org.apache.commons.math3.geometry.partitioning;
import java.util.ArrayList;
import java.util.List;
import org.apache.commons.math3.exception.MathIllegalStateException;
import org.apache.commons.math3.exception.MathInternalError;
import org.apache.commons.math3.exception.util.LocalizedFormats;
import org.apache.commons.math3.geometry.Point;
import org.apache.commons.math3.geometry.Space;
import org.apache.commons.math3.geometry.Vector;
import org.apache.commons.math3.util.FastMath;
/** This class represent a Binary Space Partition tree.
* BSP trees are an efficient way to represent space partitions and
* to associate attributes with each cell. Each node in a BSP tree
* represents a convex region which is partitioned in two convex
* sub-regions at each side of a cut hyperplane. The root tree
* contains the complete space.
* The main use of such partitions is to use a boolean attribute to
* define an inside/outside property, hence representing arbitrary
* polytopes (line segments in 1D, polygons in 2D and polyhedrons in
* 3D) and to operate on them.
* Another example would be to represent Voronoi tesselations, the
* attribute of each cell holding the defining point of the cell.
* The application-defined attributes are shared among copied
* instances and propagated to split parts. These attributes are not
* used by the BSP-tree algorithms themselves, so the application can
* use them for any purpose. Since the tree visiting method holds
* internal and leaf nodes differently, it is possible to use
* different classes for internal nodes attributes and leaf nodes
* attributes. This should be used with care, though, because if the
* tree is modified in any way after attributes have been set, some
* internal nodes may become leaf nodes and some leaf nodes may become
* internal nodes.
* One of the main sources for the development of this package was
* Bruce Naylor, John Amanatides and William Thibault paper Merging
* BSP Trees Yields Polyhedral Set Operations Proc. Siggraph '90,
* Computer Graphics 24(4), August 1990, pp 115-124, published by the
* Association for Computing Machinery (ACM).
* @param Type of the space.
* @since 3.0
*/
public class BSPTree {
/** Cut sub-hyperplane. */
private SubHyperplane cut;
/** Tree at the plus side of the cut hyperplane. */
private BSPTree plus;
/** Tree at the minus side of the cut hyperplane. */
private BSPTree minus;
/** Parent tree. */
private BSPTree parent;
/** Application-defined attribute. */
private Object attribute;
/** Build a tree having only one root cell representing the whole space.
*/
public BSPTree() {
cut = null;
plus = null;
minus = null;
parent = null;
attribute = null;
}
/** Build a tree having only one root cell representing the whole space.
* @param attribute attribute of the tree (may be null)
*/
public BSPTree(final Object attribute) {
cut = null;
plus = null;
minus = null;
parent = null;
this.attribute = attribute;
}
/** Build a BSPTree from its underlying elements.
* This method does not perform any verification on
* consistency of its arguments, it should therefore be used only
* when then caller knows what it is doing.
* This method is mainly useful to build trees
* bottom-up. Building trees top-down is realized with the help of
* method {@link #insertCut insertCut}.
* @param cut cut sub-hyperplane for the tree
* @param plus plus side sub-tree
* @param minus minus side sub-tree
* @param attribute attribute associated with the node (may be null)
* @see #insertCut
*/
public BSPTree(final SubHyperplane cut, final BSPTree plus, final BSPTree minus,
final Object attribute) {
this.cut = cut;
this.plus = plus;
this.minus = minus;
this.parent = null;
this.attribute = attribute;
plus.parent = this;
minus.parent = this;
}
/** Insert a cut sub-hyperplane in a node.
* The sub-tree starting at this node will be completely
* overwritten. The new cut sub-hyperplane will be built from the
* intersection of the provided hyperplane with the cell. If the
* hyperplane does intersect the cell, the cell will have two
* children cells with {@code null} attributes on each side of
* the inserted cut sub-hyperplane. If the hyperplane does not
* intersect the cell then no cut hyperplane will be
* inserted and the cell will be changed to a leaf cell. The
* attribute of the node is never changed.
* This method is mainly useful when called on leaf nodes
* (i.e. nodes for which {@link #getCut getCut} returns
* {@code null}), in this case it provides a way to build a
* tree top-down (whereas the {@link #BSPTree(SubHyperplane,
* BSPTree, BSPTree, Object) 4 arguments constructor} is devoted to
* build trees bottom-up).
* @param hyperplane hyperplane to insert, it will be chopped in
* order to fit in the cell defined by the parent nodes of the
* instance
* @return true if a cut sub-hyperplane has been inserted (i.e. if
* the cell now has two leaf child nodes)
* @see #BSPTree(SubHyperplane, BSPTree, BSPTree, Object)
*/
public boolean insertCut(final Hyperplane hyperplane) {
if (cut != null) {
plus.parent = null;
minus.parent = null;
}
final SubHyperplane chopped = fitToCell(hyperplane.wholeHyperplane());
if (chopped == null || chopped.isEmpty()) {
cut = null;
plus = null;
minus = null;
return false;
}
cut = chopped;
plus = new BSPTree();
plus.parent = this;
minus = new BSPTree();
minus.parent = this;
return true;
}
/** Copy the instance.
* The instance created is completely independent of the original
* one. A deep copy is used, none of the underlying objects are
* shared (except for the nodes attributes and immutable
* objects).
* @return a new tree, copy of the instance
*/
public BSPTree copySelf() {
if (cut == null) {
return new BSPTree(attribute);
}
return new BSPTree(cut.copySelf(), plus.copySelf(), minus.copySelf(),
attribute);
}
/** Get the cut sub-hyperplane.
* @return cut sub-hyperplane, null if this is a leaf tree
*/
public SubHyperplane getCut() {
return cut;
}
/** Get the tree on the plus side of the cut hyperplane.
* @return tree on the plus side of the cut hyperplane, null if this
* is a leaf tree
*/
public BSPTree getPlus() {
return plus;
}
/** Get the tree on the minus side of the cut hyperplane.
* @return tree on the minus side of the cut hyperplane, null if this
* is a leaf tree
*/
public BSPTree getMinus() {
return minus;
}
/** Get the parent node.
* @return parent node, null if the node has no parents
*/
public BSPTree getParent() {
return parent;
}
/** Associate an attribute with the instance.
* @param attribute attribute to associate with the node
* @see #getAttribute
*/
public void setAttribute(final Object attribute) {
this.attribute = attribute;
}
/** Get the attribute associated with the instance.
* @return attribute associated with the node or null if no
* attribute has been explicitly set using the {@link #setAttribute
* setAttribute} method
* @see #setAttribute
*/
public Object getAttribute() {
return attribute;
}
/** Visit the BSP tree nodes.
* @param visitor object visiting the tree nodes
*/
public void visit(final BSPTreeVisitor visitor) {
if (cut == null) {
visitor.visitLeafNode(this);
} else {
switch (visitor.visitOrder(this)) {
case PLUS_MINUS_SUB:
plus.visit(visitor);
minus.visit(visitor);
visitor.visitInternalNode(this);
break;
case PLUS_SUB_MINUS:
plus.visit(visitor);
visitor.visitInternalNode(this);
minus.visit(visitor);
break;
case MINUS_PLUS_SUB:
minus.visit(visitor);
plus.visit(visitor);
visitor.visitInternalNode(this);
break;
case MINUS_SUB_PLUS:
minus.visit(visitor);
visitor.visitInternalNode(this);
plus.visit(visitor);
break;
case SUB_PLUS_MINUS:
visitor.visitInternalNode(this);
plus.visit(visitor);
minus.visit(visitor);
break;
case SUB_MINUS_PLUS:
visitor.visitInternalNode(this);
minus.visit(visitor);
plus.visit(visitor);
break;
default:
throw new MathInternalError();
}
}
}
/** Fit a sub-hyperplane inside the cell defined by the instance.
* Fitting is done by chopping off the parts of the
* sub-hyperplane that lie outside of the cell using the
* cut-hyperplanes of the parent nodes of the instance.
* @param sub sub-hyperplane to fit
* @return a new sub-hyperplane, guaranteed to have no part outside
* of the instance cell
*/
private SubHyperplane fitToCell(final SubHyperplane sub) {
SubHyperplane s = sub;
for (BSPTree tree = this; tree.parent != null && s != null; tree = tree.parent) {
if (tree == tree.parent.plus) {
s = s.split(tree.parent.cut.getHyperplane()).getPlus();
} else {
s = s.split(tree.parent.cut.getHyperplane()).getMinus();
}
}
return s;
}
/** Get the cell to which a point belongs.
* If the returned cell is a leaf node the points belongs to the
* interior of the node, if the cell is an internal node the points
* belongs to the node cut sub-hyperplane.
* @param point point to check
* @return the tree cell to which the point belongs
* @deprecated as of 3.3, replaced with {@link #getCell(Point, double)}
*/
@Deprecated
public BSPTree getCell(final Vector point) {
return getCell((Point) point, 1.0e-10);
}
/** Get the cell to which a point belongs.
* If the returned cell is a leaf node the points belongs to the
* interior of the node, if the cell is an internal node the points
* belongs to the node cut sub-hyperplane.
* @param point point to check
* @param tolerance tolerance below which points close to a cut hyperplane
* are considered to belong to the hyperplane itself
* @return the tree cell to which the point belongs
*/
public BSPTree getCell(final Point point, final double tolerance) {
if (cut == null) {
return this;
}
// position of the point with respect to the cut hyperplane
final double offset = cut.getHyperplane().getOffset(point);
if (FastMath.abs(offset) < tolerance) {
return this;
} else if (offset <= 0) {
// point is on the minus side of the cut hyperplane
return minus.getCell(point, tolerance);
} else {
// point is on the plus side of the cut hyperplane
return plus.getCell(point, tolerance);
}
}
/** Get the cells whose cut sub-hyperplanes are close to the point.
* @param point point to check
* @param maxOffset offset below which a cut sub-hyperplane is considered
* close to the point (in absolute value)
* @return close cells (may be empty if all cut sub-hyperplanes are farther
* than maxOffset from the point)
*/
public List> getCloseCuts(final Point point, final double maxOffset) {
final List> close = new ArrayList>();
recurseCloseCuts(point, maxOffset, close);
return close;
}
/** Get the cells whose cut sub-hyperplanes are close to the point.
* @param point point to check
* @param maxOffset offset below which a cut sub-hyperplane is considered
* close to the point (in absolute value)
* @param close list to fill
*/
private void recurseCloseCuts(final Point point, final double maxOffset,
final List> close) {
if (cut != null) {
// position of the point with respect to the cut hyperplane
final double offset = cut.getHyperplane().getOffset(point);
if (offset < -maxOffset) {
// point is on the minus side of the cut hyperplane
minus.recurseCloseCuts(point, maxOffset, close);
} else if (offset > maxOffset) {
// point is on the plus side of the cut hyperplane
plus.recurseCloseCuts(point, maxOffset, close);
} else {
// point is close to the cut hyperplane
close.add(this);
minus.recurseCloseCuts(point, maxOffset, close);
plus.recurseCloseCuts(point, maxOffset, close);
}
}
}
/** Perform condensation on a tree.
* The condensation operation is not recursive, it must be called
* explicitly from leaves to root.
*/
private void condense() {
if ((cut != null) && (plus.cut == null) && (minus.cut == null) &&
(((plus.attribute == null) && (minus.attribute == null)) ||
((plus.attribute != null) && plus.attribute.equals(minus.attribute)))) {
attribute = (plus.attribute == null) ? minus.attribute : plus.attribute;
cut = null;
plus = null;
minus = null;
}
}
/** Merge a BSP tree with the instance.
* All trees are modified (parts of them are reused in the new
* tree), it is the responsibility of the caller to ensure a copy
* has been done before if any of the former tree should be
* preserved, no such copy is done here!
* The algorithm used here is directly derived from the one
* described in the Naylor, Amanatides and Thibault paper (section
* III, Binary Partitioning of a BSP Tree).
* @param tree other tree to merge with the instance (will be
* unusable after the operation, as well as the
* instance itself)
* @param leafMerger object implementing the final merging phase
* (this is where the semantic of the operation occurs, generally
* depending on the attribute of the leaf node)
* @return a new tree, result of instance <op>
* tree, this value can be ignored if parentTree is not null
* since all connections have already been established
*/
public BSPTree merge(final BSPTree tree, final LeafMerger leafMerger) {
return merge(tree, leafMerger, null, false);
}
/** Merge a BSP tree with the instance.
* @param tree other tree to merge with the instance (will be
* unusable after the operation, as well as the
* instance itself)
* @param leafMerger object implementing the final merging phase
* (this is where the semantic of the operation occurs, generally
* depending on the attribute of the leaf node)
* @param parentTree parent tree to connect to (may be null)
* @param isPlusChild if true and if parentTree is not null, the
* resulting tree should be the plus child of its parent, ignored if
* parentTree is null
* @return a new tree, result of instance <op>
* tree, this value can be ignored if parentTree is not null
* since all connections have already been established
*/
private BSPTree merge(final BSPTree tree, final LeafMerger leafMerger,
final BSPTree parentTree, final boolean isPlusChild) {
if (cut == null) {
// cell/tree operation
return leafMerger.merge(this, tree, parentTree, isPlusChild, true);
} else if (tree.cut == null) {
// tree/cell operation
return leafMerger.merge(tree, this, parentTree, isPlusChild, false);
} else {
// tree/tree operation
final BSPTree merged = tree.split(cut);
if (parentTree != null) {
merged.parent = parentTree;
if (isPlusChild) {
parentTree.plus = merged;
} else {
parentTree.minus = merged;
}
}
// merging phase
plus.merge(merged.plus, leafMerger, merged, true);
minus.merge(merged.minus, leafMerger, merged, false);
merged.condense();
if (merged.cut != null) {
merged.cut = merged.fitToCell(merged.cut.getHyperplane().wholeHyperplane());
}
return merged;
}
}
/** This interface gather the merging operations between a BSP tree
* leaf and another BSP tree.
* As explained in Bruce Naylor, John Amanatides and William
* Thibault paper Merging
* BSP Trees Yields Polyhedral Set Operations,
* the operations on {@link BSPTree BSP trees} can be expressed as a
* generic recursive merging operation where only the final part,
* when one of the operand is a leaf, is specific to the real
* operation semantics. For example, a tree representing a region
* using a boolean attribute to identify inside cells and outside
* cells would use four different objects to implement the final
* merging phase of the four set operations union, intersection,
* difference and symmetric difference (exclusive or).
* @param Type of the space.
*/
public interface LeafMerger {
/** Merge a leaf node and a tree node.
* This method is called at the end of a recursive merging
* resulting from a {@code tree1.merge(tree2, leafMerger)}
* call, when one of the sub-trees involved is a leaf (i.e. when
* its cut-hyperplane is null). This is the only place where the
* precise semantics of the operation are required. For all upper
* level nodes in the tree, the merging operation is only a
* generic partitioning algorithm.
* Since the final operation may be non-commutative, it is
* important to know if the leaf node comes from the instance tree
* ({@code tree1}) or the argument tree
* ({@code tree2}). The third argument of the method is
* devoted to this. It can be ignored for commutative
* operations.
* The {@link BSPTree#insertInTree BSPTree.insertInTree} method
* may be useful to implement this method.
* @param leaf leaf node (its cut hyperplane is guaranteed to be
* null)
* @param tree tree node (its cut hyperplane may be null or not)
* @param parentTree parent tree to connect to (may be null)
* @param isPlusChild if true and if parentTree is not null, the
* resulting tree should be the plus child of its parent, ignored if
* parentTree is null
* @param leafFromInstance if true, the leaf node comes from the
* instance tree ({@code tree1}) and the tree node comes from
* the argument tree ({@code tree2})
* @return the BSP tree resulting from the merging (may be one of
* the arguments)
*/
BSPTree merge(BSPTree leaf, BSPTree tree, BSPTree parentTree,
boolean isPlusChild, boolean leafFromInstance);
}
/** This interface handles the corner cases when an internal node cut sub-hyperplane vanishes.
*
* Such cases happens for example when a cut sub-hyperplane is inserted into
* another tree (during a merge operation), and is split in several parts,
* some of which becomes smaller than the tolerance. The corresponding node
* as then no cut sub-hyperplane anymore, but does have children. This interface
* specifies how to handle this situation.
* setting
*
* @param Type of the space.
* @since 3.4
*/
public interface VanishingCutHandler {
/** Fix a node with both vanished cut and children.
* @param node node to fix
* @return fixed node
*/
BSPTree fixNode(BSPTree node);
}
/** Split a BSP tree by an external sub-hyperplane.
* Split a tree in two halves, on each side of the
* sub-hyperplane. The instance is not modified.
* The tree returned is not upward-consistent: despite all of its
* sub-trees cut sub-hyperplanes (including its own cut
* sub-hyperplane) are bounded to the current cell, it is not
* attached to any parent tree yet. This tree is intended to be
* later inserted into an higher level tree.
* The algorithm used here is the one given in Naylor, Amanatides
* and Thibault paper (section III, Binary Partitioning of a BSP
* Tree).
* @param sub partitioning sub-hyperplane, must be already clipped
* to the convex region represented by the instance, will be used as
* the cut sub-hyperplane of the returned tree
* @return a tree having the specified sub-hyperplane as its cut
* sub-hyperplane, the two parts of the split instance as its two
* sub-trees and a null parent
*/
public BSPTree split(final SubHyperplane sub) {
if (cut == null) {
return new BSPTree(sub, copySelf(), new BSPTree(attribute), null);
}
final Hyperplane cHyperplane = cut.getHyperplane();
final Hyperplane sHyperplane = sub.getHyperplane();
final SubHyperplane.SplitSubHyperplane subParts = sub.split(cHyperplane);
switch (subParts.getSide()) {
case PLUS :
{ // the partitioning sub-hyperplane is entirely in the plus sub-tree
final BSPTree split = plus.split(sub);
if (cut.split(sHyperplane).getSide() == Side.PLUS) {
split.plus =
new BSPTree(cut.copySelf(), split.plus, minus.copySelf(), attribute);
split.plus.condense();
split.plus.parent = split;
} else {
split.minus =
new BSPTree(cut.copySelf(), split.minus, minus.copySelf(), attribute);
split.minus.condense();
split.minus.parent = split;
}
return split;
}
case MINUS :
{ // the partitioning sub-hyperplane is entirely in the minus sub-tree
final BSPTree split = minus.split(sub);
if (cut.split(sHyperplane).getSide() == Side.PLUS) {
split.plus =
new BSPTree(cut.copySelf(), plus.copySelf(), split.plus, attribute);
split.plus.condense();
split.plus.parent = split;
} else {
split.minus =
new BSPTree(cut.copySelf(), plus.copySelf(), split.minus, attribute);
split.minus.condense();
split.minus.parent = split;
}
return split;
}
case BOTH :
{
final SubHyperplane.SplitSubHyperplane cutParts = cut.split(sHyperplane);
final BSPTree split =
new BSPTree(sub, plus.split(subParts.getPlus()), minus.split(subParts.getMinus()),
null);
split.plus.cut = cutParts.getPlus();
split.minus.cut = cutParts.getMinus();
final BSPTree tmp = split.plus.minus;
split.plus.minus = split.minus.plus;
split.plus.minus.parent = split.plus;
split.minus.plus = tmp;
split.minus.plus.parent = split.minus;
split.plus.condense();
split.minus.condense();
return split;
}
default :
return cHyperplane.sameOrientationAs(sHyperplane) ?
new BSPTree(sub, plus.copySelf(), minus.copySelf(), attribute) :
new BSPTree(sub, minus.copySelf(), plus.copySelf(), attribute);
}
}
/** Insert the instance into another tree.
* The instance itself is modified so its former parent should
* not be used anymore.
* @param parentTree parent tree to connect to (may be null)
* @param isPlusChild if true and if parentTree is not null, the
* resulting tree should be the plus child of its parent, ignored if
* parentTree is null
* @see LeafMerger
* @deprecated as of 3.4, replaced with {@link #insertInTree(BSPTree, boolean, VanishingCutHandler)}
*/
@Deprecated
public void insertInTree(final BSPTree parentTree, final boolean isPlusChild) {
insertInTree(parentTree, isPlusChild, new VanishingCutHandler() {
/** {@inheritDoc} */
public BSPTree fixNode(BSPTree node) {
// the cut should not be null
throw new MathIllegalStateException(LocalizedFormats.NULL_NOT_ALLOWED);
}
});
}
/** Insert the instance into another tree.
* The instance itself is modified so its former parent should
* not be used anymore.
* @param parentTree parent tree to connect to (may be null)
* @param isPlusChild if true and if parentTree is not null, the
* resulting tree should be the plus child of its parent, ignored if
* parentTree is null
* @param vanishingHandler handler to use for handling very rare corner
* cases of vanishing cut sub-hyperplanes in internal nodes during merging
* @see LeafMerger
* @since 3.4
*/
public void insertInTree(final BSPTree parentTree, final boolean isPlusChild,
final VanishingCutHandler vanishingHandler) {
// set up parent/child links
parent = parentTree;
if (parentTree != null) {
if (isPlusChild) {
parentTree.plus = this;
} else {
parentTree.minus = this;
}
}
// make sure the inserted tree lies in the cell defined by its parent nodes
if (cut != null) {
// explore the parent nodes from here towards tree root
for (BSPTree tree = this; tree.parent != null; tree = tree.parent) {
// this is an hyperplane of some parent node
final Hyperplane hyperplane = tree.parent.cut.getHyperplane();
// chop off the parts of the inserted tree that extend
// on the wrong side of this parent hyperplane
if (tree == tree.parent.plus) {
cut = cut.split(hyperplane).getPlus();
plus.chopOffMinus(hyperplane, vanishingHandler);
minus.chopOffMinus(hyperplane, vanishingHandler);
} else {
cut = cut.split(hyperplane).getMinus();
plus.chopOffPlus(hyperplane, vanishingHandler);
minus.chopOffPlus(hyperplane, vanishingHandler);
}
if (cut == null) {
// the cut sub-hyperplane has vanished
final BSPTree fixed = vanishingHandler.fixNode(this);
cut = fixed.cut;
plus = fixed.plus;
minus = fixed.minus;
attribute = fixed.attribute;
if (cut == null) {
break;
}
}
}
// since we may have drop some parts of the inserted tree,
// perform a condensation pass to keep the tree structure simple
condense();
}
}
/** Prune a tree around a cell.
*
* This method can be used to extract a convex cell from a tree.
* The original cell may either be a leaf node or an internal node.
* If it is an internal node, it's subtree will be ignored (i.e. the
* extracted cell will be a leaf node in all cases). The original
* tree to which the original cell belongs is not touched at all,
* a new independent tree will be built.
*
* @param cellAttribute attribute to set for the leaf node
* corresponding to the initial instance cell
* @param otherLeafsAttributes attribute to set for the other leaf
* nodes
* @param internalAttributes attribute to set for the internal nodes
* @return a new tree (the original tree is left untouched) containing
* a single branch with the cell as a leaf node, and other leaf nodes
* as the remnants of the pruned branches
* @since 3.3
*/
public BSPTree pruneAroundConvexCell(final Object cellAttribute,
final Object otherLeafsAttributes,
final Object internalAttributes) {
// build the current cell leaf
BSPTree tree = new BSPTree(cellAttribute);
// build the pruned tree bottom-up
for (BSPTree current = this; current.parent != null; current = current.parent) {
final SubHyperplane parentCut = current.parent.cut.copySelf();
final BSPTree sibling = new BSPTree(otherLeafsAttributes);
if (current == current.parent.plus) {
tree = new BSPTree(parentCut, tree, sibling, internalAttributes);
} else {
tree = new BSPTree(parentCut, sibling, tree, internalAttributes);
}
}
return tree;
}
/** Chop off parts of the tree.
* The instance is modified in place, all the parts that are on
* the minus side of the chopping hyperplane are discarded, only the
* parts on the plus side remain.
* @param hyperplane chopping hyperplane
* @param vanishingHandler handler to use for handling very rare corner
* cases of vanishing cut sub-hyperplanes in internal nodes during merging
*/
private void chopOffMinus(final Hyperplane hyperplane, final VanishingCutHandler vanishingHandler) {
if (cut != null) {
cut = cut.split(hyperplane).getPlus();
plus.chopOffMinus(hyperplane, vanishingHandler);
minus.chopOffMinus(hyperplane, vanishingHandler);
if (cut == null) {
// the cut sub-hyperplane has vanished
final BSPTree fixed = vanishingHandler.fixNode(this);
cut = fixed.cut;
plus = fixed.plus;
minus = fixed.minus;
attribute = fixed.attribute;
}
}
}
/** Chop off parts of the tree.
* The instance is modified in place, all the parts that are on
* the plus side of the chopping hyperplane are discarded, only the
* parts on the minus side remain.
* @param hyperplane chopping hyperplane
* @param vanishingHandler handler to use for handling very rare corner
* cases of vanishing cut sub-hyperplanes in internal nodes during merging
*/
private void chopOffPlus(final Hyperplane hyperplane, final VanishingCutHandler vanishingHandler) {
if (cut != null) {
cut = cut.split(hyperplane).getMinus();
plus.chopOffPlus(hyperplane, vanishingHandler);
minus.chopOffPlus(hyperplane, vanishingHandler);
if (cut == null) {
// the cut sub-hyperplane has vanished
final BSPTree fixed = vanishingHandler.fixNode(this);
cut = fixed.cut;
plus = fixed.plus;
minus = fixed.minus;
attribute = fixed.attribute;
}
}
}
}