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* Licensed to the Apache Software Foundation (ASF) under one or more
* contributor license agreements. See the NOTICE file distributed with
* this work for additional information regarding copyright ownership.
* The ASF licenses this file to You under the Apache License, Version 2.0
* (the "License"); you may not use this file except in compliance with
* the License. You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
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* See the License for the specific language governing permissions and
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package org.apache.commons.math3.geometry.euclidean.threed;
import java.awt.geom.AffineTransform;
import java.util.Collection;
import org.apache.commons.math3.geometry.Point;
import org.apache.commons.math3.geometry.euclidean.oned.Euclidean1D;
import org.apache.commons.math3.geometry.euclidean.twod.Euclidean2D;
import org.apache.commons.math3.geometry.euclidean.twod.SubLine;
import org.apache.commons.math3.geometry.euclidean.twod.Vector2D;
import org.apache.commons.math3.geometry.partitioning.AbstractRegion;
import org.apache.commons.math3.geometry.partitioning.BSPTree;
import org.apache.commons.math3.geometry.partitioning.BSPTreeVisitor;
import org.apache.commons.math3.geometry.partitioning.BoundaryAttribute;
import org.apache.commons.math3.geometry.partitioning.Hyperplane;
import org.apache.commons.math3.geometry.partitioning.Region;
import org.apache.commons.math3.geometry.partitioning.RegionFactory;
import org.apache.commons.math3.geometry.partitioning.SubHyperplane;
import org.apache.commons.math3.geometry.partitioning.Transform;
import org.apache.commons.math3.util.FastMath;
/** This class represents a 3D region: a set of polyhedrons.
* @version $Id: PolyhedronsSet.java 1590254 2014-04-26 17:36:34Z luc $
* @since 3.0
*/
public class PolyhedronsSet extends AbstractRegion {
/** Default value for tolerance. */
private static final double DEFAULT_TOLERANCE = 1.0e-10;
/** Build a polyhedrons set representing the whole real line.
* @param tolerance tolerance below which points are considered identical
* @since 3.3
*/
public PolyhedronsSet(final double tolerance) {
super(tolerance);
}
/** Build a polyhedrons set from a BSP tree.
* The leaf nodes of the BSP tree must have a
* {@code Boolean} attribute representing the inside status of
* the corresponding cell (true for inside cells, false for outside
* cells). In order to avoid building too many small objects, it is
* recommended to use the predefined constants
* {@code Boolean.TRUE} and {@code Boolean.FALSE}
*
* This constructor is aimed at expert use, as building the tree may
* be a difficult taks. It is not intended for general use and for
* performances reasons does not check thoroughly its input, as this would
* require walking the full tree each time. Failing to provide a tree with
* the proper attributes, will therefore generate problems like
* {@link NullPointerException} or {@link ClassCastException} only later on.
* This limitation is known and explains why this constructor is for expert
* use only. The caller does have the responsibility to provided correct arguments.
*
* @param tree inside/outside BSP tree representing the region
* @param tolerance tolerance below which points are considered identical
* @since 3.3
*/
public PolyhedronsSet(final BSPTree tree, final double tolerance) {
super(tree, tolerance);
}
/** Build a polyhedrons set from a Boundary REPresentation (B-rep).
* The boundary is provided as a collection of {@link
* SubHyperplane sub-hyperplanes}. Each sub-hyperplane has the
* interior part of the region on its minus side and the exterior on
* its plus side.
* The boundary elements can be in any order, and can form
* several non-connected sets (like for example polyhedrons with holes
* or a set of disjoint polyhedrons considered as a whole). In
* fact, the elements do not even need to be connected together
* (their topological connections are not used here). However, if the
* boundary does not really separate an inside open from an outside
* open (open having here its topological meaning), then subsequent
* calls to the {@link Region#checkPoint(Point) checkPoint} method will
* not be meaningful anymore.
* If the boundary is empty, the region will represent the whole
* space.
* @param boundary collection of boundary elements, as a
* collection of {@link SubHyperplane SubHyperplane} objects
* @param tolerance tolerance below which points are considered identical
* @since 3.3
*/
public PolyhedronsSet(final Collection> boundary,
final double tolerance) {
super(boundary, tolerance);
}
/** Build a parallellepipedic box.
* @param xMin low bound along the x direction
* @param xMax high bound along the x direction
* @param yMin low bound along the y direction
* @param yMax high bound along the y direction
* @param zMin low bound along the z direction
* @param zMax high bound along the z direction
* @param tolerance tolerance below which points are considered identical
* @since 3.3
*/
public PolyhedronsSet(final double xMin, final double xMax,
final double yMin, final double yMax,
final double zMin, final double zMax,
final double tolerance) {
super(buildBoundary(xMin, xMax, yMin, yMax, zMin, zMax, tolerance), tolerance);
}
/** Build a polyhedrons set representing the whole real line.
* @deprecated as of 3.3, replaced with {@link #PolyhedronsSet(double)}
*/
@Deprecated
public PolyhedronsSet() {
this(DEFAULT_TOLERANCE);
}
/** Build a polyhedrons set from a BSP tree.
* The leaf nodes of the BSP tree must have a
* {@code Boolean} attribute representing the inside status of
* the corresponding cell (true for inside cells, false for outside
* cells). In order to avoid building too many small objects, it is
* recommended to use the predefined constants
* {@code Boolean.TRUE} and {@code Boolean.FALSE}
* @param tree inside/outside BSP tree representing the region
* @deprecated as of 3.3, replaced with {@link #PolyhedronsSet(BSPTree, double)}
*/
@Deprecated
public PolyhedronsSet(final BSPTree tree) {
this(tree, DEFAULT_TOLERANCE);
}
/** Build a polyhedrons set from a Boundary REPresentation (B-rep).
* The boundary is provided as a collection of {@link
* SubHyperplane sub-hyperplanes}. Each sub-hyperplane has the
* interior part of the region on its minus side and the exterior on
* its plus side.
* The boundary elements can be in any order, and can form
* several non-connected sets (like for example polyhedrons with holes
* or a set of disjoint polyhedrons considered as a whole). In
* fact, the elements do not even need to be connected together
* (their topological connections are not used here). However, if the
* boundary does not really separate an inside open from an outside
* open (open having here its topological meaning), then subsequent
* calls to the {@link Region#checkPoint(Point) checkPoint} method will
* not be meaningful anymore.
* If the boundary is empty, the region will represent the whole
* space.
* @param boundary collection of boundary elements, as a
* collection of {@link SubHyperplane SubHyperplane} objects
* @deprecated as of 3.3, replaced with {@link #PolyhedronsSet(Collection, double)}
*/
@Deprecated
public PolyhedronsSet(final Collection> boundary) {
this(boundary, DEFAULT_TOLERANCE);
}
/** Build a parallellepipedic box.
* @param xMin low bound along the x direction
* @param xMax high bound along the x direction
* @param yMin low bound along the y direction
* @param yMax high bound along the y direction
* @param zMin low bound along the z direction
* @param zMax high bound along the z direction
* @deprecated as of 3.3, replaced with {@link #PolyhedronsSet(double, double,
* double, double, double, double, double)}
*/
@Deprecated
public PolyhedronsSet(final double xMin, final double xMax,
final double yMin, final double yMax,
final double zMin, final double zMax) {
this(xMin, xMax, yMin, yMax, zMin, zMax, DEFAULT_TOLERANCE);
}
/** Build a parallellepipedic box boundary.
* @param xMin low bound along the x direction
* @param xMax high bound along the x direction
* @param yMin low bound along the y direction
* @param yMax high bound along the y direction
* @param zMin low bound along the z direction
* @param zMax high bound along the z direction
* @param tolerance tolerance below which points are considered identical
* @return boundary tree
* @since 3.3
*/
private static BSPTree buildBoundary(final double xMin, final double xMax,
final double yMin, final double yMax,
final double zMin, final double zMax,
final double tolerance) {
// FIX
// if ((xMin >= xMax - tolerance) || (yMin >= yMax - tolerance) || (zMin >= zMax - tolerance)) {
// // too thin box, build an empty polygons set
// return new BSPTree(Boolean.FALSE);
// }
final Plane pxMin = new Plane(new Vector3D(xMin, 0, 0), Vector3D.MINUS_I, tolerance);
final Plane pxMax = new Plane(new Vector3D(xMax, 0, 0), Vector3D.PLUS_I, tolerance);
final Plane pyMin = new Plane(new Vector3D(0, yMin, 0), Vector3D.MINUS_J, tolerance);
final Plane pyMax = new Plane(new Vector3D(0, yMax, 0), Vector3D.PLUS_J, tolerance);
final Plane pzMin = new Plane(new Vector3D(0, 0, zMin), Vector3D.MINUS_K, tolerance);
final Plane pzMax = new Plane(new Vector3D(0, 0, zMax), Vector3D.PLUS_K, tolerance);
@SuppressWarnings("unchecked")
final Region boundary =
new RegionFactory().buildConvex(pxMin, pxMax, pyMin, pyMax, pzMin, pzMax);
return boundary.getTree(false);
}
/** {@inheritDoc} */
@Override
public PolyhedronsSet buildNew(final BSPTree tree) {
return new PolyhedronsSet(tree, getTolerance());
}
/** {@inheritDoc} */
@Override
protected void computeGeometricalProperties() {
// compute the contribution of all boundary facets
getTree(true).visit(new FacetsContributionVisitor());
if (getSize() < 0) {
// the polyhedrons set as a finite outside
// surrounded by an infinite inside
setSize(Double.POSITIVE_INFINITY);
setBarycenter((Point) Vector3D.NaN);
} else {
// the polyhedrons set is finite, apply the remaining scaling factors
setSize(getSize() / 3.0);
setBarycenter((Point) new Vector3D(1.0 / (4 * getSize()), (Vector3D) getBarycenter()));
}
}
/** Visitor computing geometrical properties. */
private class FacetsContributionVisitor implements BSPTreeVisitor {
/** Simple constructor. */
public FacetsContributionVisitor() {
setSize(0);
setBarycenter((Point) new Vector3D(0, 0, 0));
}
/** {@inheritDoc} */
public Order visitOrder(final BSPTree node) {
return Order.MINUS_SUB_PLUS;
}
/** {@inheritDoc} */
public void visitInternalNode(final BSPTree node) {
@SuppressWarnings("unchecked")
final BoundaryAttribute attribute =
(BoundaryAttribute) node.getAttribute();
if (attribute.getPlusOutside() != null) {
addContribution(attribute.getPlusOutside(), false);
}
if (attribute.getPlusInside() != null) {
addContribution(attribute.getPlusInside(), true);
}
}
/** {@inheritDoc} */
public void visitLeafNode(final BSPTree node) {
}
/** Add he contribution of a boundary facet.
* @param facet boundary facet
* @param reversed if true, the facet has the inside on its plus side
*/
private void addContribution(final SubHyperplane facet, final boolean reversed) {
final Region polygon = ((SubPlane) facet).getRemainingRegion();
final double area = polygon.getSize();
if (Double.isInfinite(area)) {
setSize(Double.POSITIVE_INFINITY);
setBarycenter((Point) Vector3D.NaN);
} else {
final Plane plane = (Plane) facet.getHyperplane();
final Vector3D facetB = plane.toSpace(polygon.getBarycenter());
double scaled = area * facetB.dotProduct(plane.getNormal());
if (reversed) {
scaled = -scaled;
}
setSize(getSize() + scaled);
setBarycenter((Point) new Vector3D(1.0, (Vector3D) getBarycenter(), scaled, facetB));
}
}
}
/** Get the first sub-hyperplane crossed by a semi-infinite line.
* @param point start point of the part of the line considered
* @param line line to consider (contains point)
* @return the first sub-hyperplaned crossed by the line after the
* given point, or null if the line does not intersect any
* sub-hyperplaned
*/
public SubHyperplane firstIntersection(final Vector3D point, final Line line) {
return recurseFirstIntersection(getTree(true), point, line);
}
/** Get the first sub-hyperplane crossed by a semi-infinite line.
* @param node current node
* @param point start point of the part of the line considered
* @param line line to consider (contains point)
* @return the first sub-hyperplaned crossed by the line after the
* given point, or null if the line does not intersect any
* sub-hyperplaned
*/
private SubHyperplane recurseFirstIntersection(final BSPTree node,
final Vector3D point,
final Line line) {
final SubHyperplane cut = node.getCut();
if (cut == null) {
return null;
}
final BSPTree minus = node.getMinus();
final BSPTree plus = node.getPlus();
final Plane plane = (Plane) cut.getHyperplane();
// establish search order
final double offset = plane.getOffset((Point) point);
final boolean in = FastMath.abs(offset) < 1.0e-10;
final BSPTree near;
final BSPTree far;
if (offset < 0) {
near = minus;
far = plus;
} else {
near = plus;
far = minus;
}
if (in) {
// search in the cut hyperplane
final SubHyperplane facet = boundaryFacet(point, node);
if (facet != null) {
return facet;
}
}
// search in the near branch
final SubHyperplane crossed = recurseFirstIntersection(near, point, line);
if (crossed != null) {
return crossed;
}
if (!in) {
// search in the cut hyperplane
final Vector3D hit3D = plane.intersection(line);
if (hit3D != null) {
final SubHyperplane facet = boundaryFacet(hit3D, node);
if (facet != null) {
return facet;
}
}
}
// search in the far branch
return recurseFirstIntersection(far, point, line);
}
/** Check if a point belongs to the boundary part of a node.
* @param point point to check
* @param node node containing the boundary facet to check
* @return the boundary facet this points belongs to (or null if it
* does not belong to any boundary facet)
*/
private SubHyperplane boundaryFacet(final Vector3D point,
final BSPTree node) {
final Vector2D point2D = ((Plane) node.getCut().getHyperplane()).toSubSpace((Point) point);
@SuppressWarnings("unchecked")
final BoundaryAttribute attribute =
(BoundaryAttribute) node.getAttribute();
if ((attribute.getPlusOutside() != null) &&
(((SubPlane) attribute.getPlusOutside()).getRemainingRegion().checkPoint(point2D) == Location.INSIDE)) {
return attribute.getPlusOutside();
}
if ((attribute.getPlusInside() != null) &&
(((SubPlane) attribute.getPlusInside()).getRemainingRegion().checkPoint(point2D) == Location.INSIDE)) {
return attribute.getPlusInside();
}
return null;
}
/** Rotate the region around the specified point.
* The instance is not modified, a new instance is created.
* @param center rotation center
* @param rotation vectorial rotation operator
* @return a new instance representing the rotated region
*/
public PolyhedronsSet rotate(final Vector3D center, final Rotation rotation) {
return (PolyhedronsSet) applyTransform(new RotationTransform(center, rotation));
}
/** 3D rotation as a Transform. */
private static class RotationTransform implements Transform {
/** Center point of the rotation. */
private Vector3D center;
/** Vectorial rotation. */
private Rotation rotation;
/** Cached original hyperplane. */
private Plane cachedOriginal;
/** Cached 2D transform valid inside the cached original hyperplane. */
private Transform cachedTransform;
/** Build a rotation transform.
* @param center center point of the rotation
* @param rotation vectorial rotation
*/
public RotationTransform(final Vector3D center, final Rotation rotation) {
this.center = center;
this.rotation = rotation;
}
/** {@inheritDoc} */
public Vector3D apply(final Point point) {
final Vector3D delta = ((Vector3D) point).subtract(center);
return new Vector3D(1.0, center, 1.0, rotation.applyTo(delta));
}
/** {@inheritDoc} */
public Plane apply(final Hyperplane hyperplane) {
return ((Plane) hyperplane).rotate(center, rotation);
}
/** {@inheritDoc} */
public SubHyperplane apply(final SubHyperplane sub,
final Hyperplane original,
final Hyperplane transformed) {
if (original != cachedOriginal) {
// we have changed hyperplane, reset the in-hyperplane transform
final Plane oPlane = (Plane) original;
final Plane tPlane = (Plane) transformed;
final Vector3D p00 = oPlane.getOrigin();
final Vector3D p10 = oPlane.toSpace((Point) new Vector2D(1.0, 0.0));
final Vector3D p01 = oPlane.toSpace((Point) new Vector2D(0.0, 1.0));
final Vector2D tP00 = tPlane.toSubSpace((Point) apply(p00));
final Vector2D tP10 = tPlane.toSubSpace((Point) apply(p10));
final Vector2D tP01 = tPlane.toSubSpace((Point) apply(p01));
final AffineTransform at =
new AffineTransform(tP10.getX() - tP00.getX(), tP10.getY() - tP00.getY(),
tP01.getX() - tP00.getX(), tP01.getY() - tP00.getY(),
tP00.getX(), tP00.getY());
cachedOriginal = (Plane) original;
cachedTransform = org.apache.commons.math3.geometry.euclidean.twod.Line.getTransform(at);
}
return ((SubLine) sub).applyTransform(cachedTransform);
}
}
/** Translate the region by the specified amount.
* The instance is not modified, a new instance is created.
* @param translation translation to apply
* @return a new instance representing the translated region
*/
public PolyhedronsSet translate(final Vector3D translation) {
return (PolyhedronsSet) applyTransform(new TranslationTransform(translation));
}
/** 3D translation as a transform. */
private static class TranslationTransform implements Transform {
/** Translation vector. */
private Vector3D translation;
/** Cached original hyperplane. */
private Plane cachedOriginal;
/** Cached 2D transform valid inside the cached original hyperplane. */
private Transform cachedTransform;
/** Build a translation transform.
* @param translation translation vector
*/
public TranslationTransform(final Vector3D translation) {
this.translation = translation;
}
/** {@inheritDoc} */
public Vector3D apply(final Point point) {
return new Vector3D(1.0, (Vector3D) point, 1.0, translation);
}
/** {@inheritDoc} */
public Plane apply(final Hyperplane hyperplane) {
return ((Plane) hyperplane).translate(translation);
}
/** {@inheritDoc} */
public SubHyperplane apply(final SubHyperplane sub,
final Hyperplane original,
final Hyperplane transformed) {
if (original != cachedOriginal) {
// we have changed hyperplane, reset the in-hyperplane transform
final Plane oPlane = (Plane) original;
final Plane tPlane = (Plane) transformed;
final Vector2D shift = tPlane.toSubSpace((Point) apply(oPlane.getOrigin()));
final AffineTransform at =
AffineTransform.getTranslateInstance(shift.getX(), shift.getY());
cachedOriginal = (Plane) original;
cachedTransform =
org.apache.commons.math3.geometry.euclidean.twod.Line.getTransform(at);
}
return ((SubLine) sub).applyTransform(cachedTransform);
}
}
}