/**
* Copyright 2010-2023 JogAmp Community. All rights reserved.
*
* Redistribution and use in source and binary forms, with or without modification, are
* permitted provided that the following conditions are met:
*
* 1. Redistributions of source code must retain the above copyright notice, this list of
* conditions and the following disclaimer.
*
* 2. Redistributions in binary form must reproduce the above copyright notice, this list
* of conditions and the following disclaimer in the documentation and/or other materials
* provided with the distribution.
*
* THIS SOFTWARE IS PROVIDED BY JogAmp Community ``AS IS'' AND ANY EXPRESS OR IMPLIED
* WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND
* FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL JogAmp Community OR
* CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
* CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
* SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
* ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
* NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF
* ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*
* The views and conclusions contained in the software and documentation are those of the
* authors and should not be interpreted as representing official policies, either expressed
* or implied, of JogAmp Community.
*/
package com.jogamp.opengl.math.geom;
import com.jogamp.graph.geom.plane.AffineTransform;
import com.jogamp.opengl.math.FloatUtil;
import com.jogamp.opengl.math.Matrix4f;
import com.jogamp.opengl.math.Quaternion;
import com.jogamp.opengl.math.Ray;
import com.jogamp.opengl.math.Recti;
import com.jogamp.opengl.math.Vec3f;
import com.jogamp.opengl.util.PMVMatrix;
/**
* Axis Aligned Bounding Box. Defined by two 3D coordinates (low and high)
* The low being the the lower left corner of the box, and the high being the upper
* right corner of the box.
* <p>
* A few references for collision detection, intersections:
* <pre>
* http://www.realtimerendering.com/intersections.html
* http://www.codercorner.com/RayAABB.cpp
* http://www.siggraph.org/education/materials/HyperGraph/raytrace/rtinter0.htm
* http://realtimecollisiondetection.net/files/levine_swept_sat.txt
* </pre>
* </p>
*
*/
public class AABBox {
private static final boolean DEBUG = FloatUtil.DEBUG;
private final Vec3f low = new Vec3f();
private final Vec3f high = new Vec3f();
private final Vec3f center = new Vec3f();
/**
* Create an Axis Aligned bounding box (AABBox) with the
* inverse low/high, allowing the next {@link #resize(float, float, float)} command to hit.
* <p>
* The dimension, i.e. {@link #getWidth()} abd {@link #getHeight()} is {@link Float#isInfinite()} thereafter.
* </p>
* @see #reset()
*/
public AABBox() {
reset();
}
/**
* Create an AABBox copying all values from the given one
* @param src the box value to be used for the new instance
*/
public AABBox(final AABBox src) {
copy(src);
}
/**
* Create an AABBox specifying the coordinates
* of the low and high
* @param lx min x-coordinate
* @param ly min y-coordnate
* @param lz min z-coordinate
* @param hx max x-coordinate
* @param hy max y-coordinate
* @param hz max z-coordinate
*/
public AABBox(final float lx, final float ly, final float lz,
final float hx, final float hy, final float hz) {
setSize(lx, ly, lz, hx, hy, hz);
}
/**
* Create a AABBox defining the low and high
* @param low min xyz-coordinates
* @param high max xyz-coordinates
*/
public AABBox(final float[] low, final float[] high) {
setSize(low, high);
}
/**
* Resets this box to the inverse low/high, allowing the next {@link #resize(float, float, float)} command to hit.
* <p>
* The dimension, i.e. {@link #getWidth()} abd {@link #getHeight()} is {@link Float#isInfinite()} thereafter.
* </p>
* @return this AABBox for chaining
*/
public final AABBox reset() {
setLow(Float.MAX_VALUE,Float.MAX_VALUE,Float.MAX_VALUE);
setHigh(-1*Float.MAX_VALUE,-1*Float.MAX_VALUE,-1*Float.MAX_VALUE);
center.set( 0f, 0f, 0f);
return this;
}
/** Get the max xyz-coordinates
* @return max xyz coordinates
*/
public final Vec3f getHigh() {
return high;
}
private final void setHigh(final float hx, final float hy, final float hz) {
this.high.set(hx, hy, hz);
}
/** Get the min xyz-coordinates
* @return min xyz coordinates
*/
public final Vec3f getLow() {
return low;
}
private final void setLow(final float lx, final float ly, final float lz) {
this.low.set(lx, ly, lz);
}
private final void computeCenter() {
center.set(high).add(low).scale(1f/2f);
}
/**
* Copy given AABBox 'src' values to this AABBox.
*
* @param src source AABBox
* @return this AABBox for chaining
*/
public final AABBox copy(final AABBox src) {
low.set(src.low);
high.set(src.high);
center.set(src.center);
return this;
}
/**
* Set size of the AABBox specifying the coordinates
* of the low and high.
*
* @param low min xyz-coordinates
* @param high max xyz-coordinates
* @return this AABBox for chaining
*/
public final AABBox setSize(final float[] low, final float[] high) {
return setSize(low[0],low[1],low[2], high[0],high[1],high[2]);
}
/**
* Set size of the AABBox specifying the coordinates
* of the low and high.
*
* @param lx min x-coordinate
* @param ly min y-coordnate
* @param lz min z-coordinate
* @param hx max x-coordinate
* @param hy max y-coordinate
* @param hz max z-coordinate
* @return this AABBox for chaining
*/
public final AABBox setSize(final float lx, final float ly, final float lz,
final float hx, final float hy, final float hz) {
this.low.set(lx, ly, lz);
this.high.set(hx, hy, hz);
computeCenter();
return this;
}
/**
* Set size of the AABBox specifying the coordinates
* of the low and high.
*
* @param low min xyz-coordinates
* @param high max xyz-coordinates
* @return this AABBox for chaining
*/
public final AABBox setSize(final Vec3f low, final Vec3f high) {
this.low.set(low);
this.high.set(high);
computeCenter();
return this;
}
/**
* Resize the AABBox to encapsulate another AABox
* @param newBox AABBox to be encapsulated in
* @return this AABBox for chaining
*/
public final AABBox resize(final AABBox newBox) {
final Vec3f newLow = newBox.getLow();
final Vec3f newHigh = newBox.getHigh();
/** test low */
if (newLow.x() < low.x()) {
low.setX( newLow.x() );
}
if (newLow.y() < low.y()) {
low.setY( newLow.y() );
}
if (newLow.z() < low.z()) {
low.setZ( newLow.z() );
}
/** test high */
if (newHigh.x() > high.x()) {
high.setX( newHigh.x() );
}
if (newHigh.y() > high.y()) {
high.setY( newHigh.y() );
}
if (newHigh.z() > high.z()) {
high.setZ( newHigh.z() );
}
computeCenter();
return this;
}
/**
* Resize the AABBox to encapsulate another AABox, which will be <i>transformed</i> on the fly first.
* @param newBox AABBox to be encapsulated in
* @param t the {@link AffineTransform} applied on <i>newBox</i> on the fly
* @param tmpV3 temporary storage
* @return this AABBox for chaining
*/
public final AABBox resize(final AABBox newBox, final AffineTransform t, final Vec3f tmpV3) {
/** test low */
{
final Vec3f newBoxLow = newBox.getLow();
t.transform(newBoxLow, tmpV3);
if (tmpV3.x() < low.x())
low.setX( tmpV3.x() );
if (tmpV3.y() < low.y())
low.setY( tmpV3.y() );
if (tmpV3.z() < low.z())
low.setZ( tmpV3.z() );
}
/** test high */
{
final Vec3f newBoxHigh = newBox.getHigh();
t.transform(newBoxHigh, tmpV3);
if (tmpV3.x() > high.x())
high.setX( tmpV3.x() );
if (tmpV3.y() > high.y())
high.setY( tmpV3.y() );
if (tmpV3.z() > high.z())
high.setZ( tmpV3.z() );
}
computeCenter();
return this;
}
/**
* Resize the AABBox to encapsulate the passed
* xyz-coordinates.
* @param x x-axis coordinate value
* @param y y-axis coordinate value
* @param z z-axis coordinate value
* @return this AABBox for chaining
*/
public final AABBox resize(final float x, final float y, final float z) {
/** test low */
if (x < low.x()) {
low.setX( x );
}
if (y < low.y()) {
low.setY( y );
}
if (z < low.z()) {
low.setZ( z );
}
/** test high */
if (x > high.x()) {
high.setX( x );
}
if (y > high.y()) {
high.setY( y );
}
if (z > high.z()) {
high.setZ( z );
}
computeCenter();
return this;
}
/**
* Resize the AABBox to encapsulate the passed
* xyz-coordinates.
* @param xyz xyz-axis coordinate values
* @param offset of the array
* @return this AABBox for chaining
*/
public final AABBox resize(final float[] xyz, final int offset) {
return resize(xyz[0+offset], xyz[1+offset], xyz[2+offset]);
}
/**
* Resize the AABBox to encapsulate the passed
* xyz-coordinates.
* @param xyz xyz-axis coordinate values
* @return this AABBox for chaining
*/
public final AABBox resize(final float[] xyz) {
return resize(xyz[0], xyz[1], xyz[2]);
}
/**
* Resize the AABBox to encapsulate the passed
* xyz-coordinates.
* @param xyz xyz-axis coordinate values
* @return this AABBox for chaining
*/
public final AABBox resize(final Vec3f xyz) {
return resize(xyz.x(), xyz.y(), xyz.z());
}
/**
* Check if the x & y coordinates are bounded/contained
* by this AABBox
* @param x x-axis coordinate value
* @param y y-axis coordinate value
* @return true if x belong to (low.x, high.x) and
* y belong to (low.y, high.y)
*/
public final boolean contains(final float x, final float y) {
if(x<low.x() || x>high.x()){
return false;
}
if(y<low.y()|| y>high.y()){
return false;
}
return true;
}
/**
* Check if the xyz coordinates are bounded/contained
* by this AABBox.
* @param x x-axis coordinate value
* @param y y-axis coordinate value
* @param z z-axis coordinate value
* @return true if x belong to (low.x, high.x) and
* y belong to (low.y, high.y) and z belong to (low.z, high.z)
*/
public final boolean contains(final float x, final float y, final float z) {
if(x<low.x() || x>high.x()){
return false;
}
if(y<low.y()|| y>high.y()){
return false;
}
if(z<low.z() || z>high.z()){
return false;
}
return true;
}
/**
* Check if there is a common region between this AABBox and the passed
* 2D region irrespective of z range
* @param x lower left x-coord
* @param y lower left y-coord
* @param w width
* @param h hight
* @return true if this AABBox might have a common region with this 2D region
*/
public final boolean intersects2DRegion(final float x, final float y, final float w, final float h) {
if (w <= 0 || h <= 0) {
return false;
}
final float _w = getWidth();
final float _h = getHeight();
if (_w <= 0 || _h <= 0) {
return false;
}
final float x0 = getMinX();
final float y0 = getMinY();
return (x + w > x0 &&
y + h > y0 &&
x < x0 + _w &&
y < y0 + _h);
}
/**
* Check if {@link Ray} intersects this bounding box.
* <p>
* Versions uses the SAT[1], testing 6 axes.
* Original code for OBBs from MAGIC.
* Rewritten for AABBs and reorganized for early exits[2].
* </p>
* <pre>
* [1] SAT = Separating Axis Theorem
* [2] http://www.codercorner.com/RayAABB.cpp
* </pre>
* @param ray
* @return
*/
public final boolean intersectsRay(final Ray ray) {
// diff[XYZ] -> VectorUtil.subVec3(diff, ray.orig, center);
// ext[XYZ] -> extend VectorUtil.subVec3(ext, high, center);
final float dirX = ray.dir.x();
final float diffX = ray.orig.x() - center.x();
final float extX = high.x() - center.x();
if( Math.abs(diffX) > extX && diffX*dirX >= 0f ) return false;
final float dirY = ray.dir.y();
final float diffY = ray.orig.y() - center.y();
final float extY = high.y() - center.y();
if( Math.abs(diffY) > extY && diffY*dirY >= 0f ) return false;
final float dirZ = ray.dir.z();
final float diffZ = ray.orig.z() - center.z();
final float extZ = high.z() - center.z();
if( Math.abs(diffZ) > extZ && diffZ*dirZ >= 0f ) return false;
final float absDirY = Math.abs(dirY);
final float absDirZ = Math.abs(dirZ);
float f = dirY * diffZ - dirZ * diffY;
if( Math.abs(f) > extY*absDirZ + extZ*absDirY ) return false;
final float absDirX = Math.abs(dirX);
f = dirZ * diffX - dirX * diffZ;
if( Math.abs(f) > extX*absDirZ + extZ*absDirX ) return false;
f = dirX * diffY - dirY * diffX;
if( Math.abs(f) > extX*absDirY + extY*absDirX ) return false;
return true;
}
/**
* Return intersection of a {@link Ray} with this bounding box,
* or null if none exist.
* <p>
* <ul>
* <li>Original code by Andrew Woo, from "Graphics Gems", Academic Press, 1990 [2]</li>
* <li>Optimized code by Pierre Terdiman, 2000 (~20-30% faster on my Celeron 500)</li>
* <li>Epsilon value added by Klaus Hartmann.</li>
* </ul>
* </p>
* <p>
* Method is based on the requirements:
* <ul>
* <li>the integer representation of 0.0f is 0x00000000</li>
* <li>the sign bit of the float is the most significant one</li>
* </ul>
* </p>
* <p>
* Report bugs: p.terdiman@codercorner.com (original author)
* </p>
* <pre>
* [1] http://www.codercorner.com/RayAABB.cpp
* [2] http://tog.acm.org/resources/GraphicsGems/gems/RayBox.c
* </pre>
* @param result vec3
* @param ray
* @param epsilon
* @param assumeIntersection if true, method assumes an intersection, i.e. by pre-checking via {@link #intersectsRay(Ray)}.
* In this case method will not validate a possible non-intersection and just computes
* coordinates.
* @return float[3] result of intersection coordinates, or null if none exists
*/
public final Vec3f getRayIntersection(final Vec3f result, final Ray ray, final float epsilon,
final boolean assumeIntersection) {
final float[] maxT = { -1f, -1f, -1f };
final Vec3f origin = ray.orig;
final Vec3f dir = ray.dir;
boolean inside = true;
// Find candidate planes.
for(int i=0; i<3; i++) {
final float origin_i = origin.get(i);
final float dir_i = dir.get(i);
final float low_i = low.get(i);
final float high_i = high.get(i);
if(origin_i < low_i) {
result.set(i, low_i);
inside = false;
// Calculate T distances to candidate planes
if( 0 != Float.floatToIntBits(dir_i) ) {
maxT[i] = (low_i - origin_i) / dir_i;
}
} else if(origin_i > high_i) {
result.set(i, high_i);
inside = false;
// Calculate T distances to candidate planes
if( 0 != Float.floatToIntBits(dir_i) ) {
maxT[i] = (high_i - origin_i) / dir_i;
}
}
}
// Ray origin inside bounding box
if(inside) {
result.set(origin);
return result;
}
// Get largest of the maxT's for final choice of intersection
int whichPlane = 0;
if(maxT[1] > maxT[whichPlane]) { whichPlane = 1; }
if(maxT[2] > maxT[whichPlane]) { whichPlane = 2; }
if( !assumeIntersection ) {
// Check final candidate actually inside box
if( 0 != ( Float.floatToIntBits(maxT[whichPlane]) & 0x80000000 ) ) {
return null;
}
/** Use unrolled version below ..
for(int i=0; i<3; i++) {
if( i!=whichPlane ) {
result[i] = origin[i] + maxT[whichPlane] * dir[i];
if(result[i] < minB[i] - epsilon || result[i] > maxB[i] + epsilon) { return null; }
// if(result[i] < minB[i] || result[i] > maxB[i] ) { return null; }
}
} */
switch( whichPlane ) {
case 0:
result.setY( origin.y() + maxT[whichPlane] * dir.y() );
if(result.y() < low.y() - epsilon || result.y() > high.y() + epsilon) { return null; }
result.setZ( origin.z() + maxT[whichPlane] * dir.z() );
if(result.z() < low.z() - epsilon || result.z() > high.z() + epsilon) { return null; }
break;
case 1:
result.setX( origin.x() + maxT[whichPlane] * dir.x() );
if(result.x() < low.x() - epsilon || result.x() > high.x() + epsilon) { return null; }
result.setZ( origin.z() + maxT[whichPlane] * dir.z() );
if(result.z() < low.z() - epsilon || result.z() > high.z() + epsilon) { return null; }
break;
case 2:
result.setX( origin.x() + maxT[whichPlane] * dir.x() );
if(result.x() < low.x() - epsilon || result.x() > high.x() + epsilon) { return null; }
result.setY( origin.y() + maxT[whichPlane] * dir.y() );
if(result.y() < low.y() - epsilon || result.y() > high.y() + epsilon) { return null; }
break;
default:
throw new InternalError("XXX");
}
} else {
switch( whichPlane ) {
case 0:
result.setY( origin.y() + maxT[whichPlane] * dir.y() );
result.setZ( origin.z() + maxT[whichPlane] * dir.z() );
break;
case 1:
result.setX( origin.x() + maxT[whichPlane] * dir.x() );
result.setZ( origin.z() + maxT[whichPlane] * dir.z() );
break;
case 2:
result.setX( origin.x() + maxT[whichPlane] * dir.x() );
result.setY( origin.y() + maxT[whichPlane] * dir.y() );
break;
default:
throw new InternalError("XXX");
}
}
return result; // ray hits box
}
/**
* Get the size of this AABBox where the size is represented by the
* length of the vector between low and high.
* @return a float representing the size of the AABBox
*/
public final float getSize() {
return low.dist(high);
}
/**
* Get the Center of this AABBox
* @return the xyz-coordinates of the center of the AABBox
*/
public final Vec3f getCenter() {
return center;
}
/**
* Scale this AABBox by a constant around fixed center
* <p>
* high and low is recomputed by scaling its distance to fixed center.
* </p>
* @param size a constant float value
* @return this AABBox for chaining
* @see #scale2(float, float[])
*/
public final AABBox scale(final float size) {
final Vec3f tmp = new Vec3f();
tmp.set(high).sub(center).scale(size);
high.set(center).add(tmp);
tmp.set(low).sub(center).scale(size);
low.set(center).add(tmp);
return this;
}
/**
* Scale this AABBox by a constant, recomputing center
* <p>
* high and low is scaled and center recomputed.
* </p>
* @param size a constant float value
* @return this AABBox for chaining
* @see #scale(float, float[])
*/
public final AABBox scale2(final float size) {
high.scale(size);
low.scale(size);
computeCenter();
return this;
}
/**
* Translate this AABBox by a float[3] vector
* @param dx the translation x-component
* @param dy the translation y-component
* @param dz the translation z-component
* @param t the float[3] translation vector
* @return this AABBox for chaining
*/
public final AABBox translate(final float dx, final float dy, final float dz) {
low.add(dx, dy, dz);
high.add(dx, dy, dz);
computeCenter();
return this;
}
/**
* Translate this AABBox by a float[3] vector
* @param t the float[3] translation vector
* @return this AABBox for chaining
*/
public final AABBox translate(final Vec3f t) {
low.add(t);
high.add(t);
computeCenter();
return this;
}
/**
* Rotate this AABBox by a float[3] vector
* @param quat the {@link Quaternion} used for rotation
* @return this AABBox for chaining
*/
public final AABBox rotate(final Quaternion quat) {
quat.rotateVector(low, low);
quat.rotateVector(high, high);
computeCenter();
return this;
}
public final float getMinX() {
return low.x();
}
public final float getMinY() {
return low.y();
}
public final float getMinZ() {
return low.z();
}
public final float getMaxX() {
return high.x();
}
public final float getMaxY() {
return high.y();
}
public final float getMaxZ() {
return high.z();
}
public final float getWidth(){
return high.x() - low.x();
}
public final float getHeight() {
return high.y() - low.y();
}
public final float getDepth() {
return high.z() - low.z();
}
@Override
public final boolean equals(final Object obj) {
if( obj == this ) {
return true;
}
if( null == obj || !(obj instanceof AABBox) ) {
return false;
}
final AABBox other = (AABBox) obj;
return low.isEqual(other.low) && high.isEqual(other.high);
}
@Override
public final int hashCode() {
throw new InternalError("hashCode not designed");
}
/**
* Transform this box using the given {@link Matrix4f} into {@code out}
* @param mat transformation {@link Matrix4f}
* @param out the resulting {@link AABBox}
* @return the resulting {@link AABBox} for chaining
*/
public AABBox transform(final Matrix4f mat, final AABBox out) {
final Vec3f tmp = new Vec3f();
out.reset();
out.resize( mat.mulVec3f(low, tmp) );
out.resize( mat.mulVec3f(high, tmp) );
out.computeCenter();
return out;
}
/**
* Transform this box using the {@link PMVMatrix#getMvMat() modelview} of the given {@link PMVMatrix} into {@code out}
* @param pmv transformation {@link PMVMatrix}
* @param out the resulting {@link AABBox}
* @return the resulting {@link AABBox} for chaining
*/
public AABBox transformMv(final PMVMatrix pmv, final AABBox out) {
final Vec3f tmp = new Vec3f();
out.reset();
out.resize( pmv.mulMvMatVec3f(low, tmp) );
out.resize( pmv.mulMvMatVec3f(high, tmp) );
out.computeCenter();
return out;
}
/**
* Assume this bounding box as being in object space and
* compute the window bounding box.
* <p>
* If <code>useCenterZ</code> is <code>true</code>,
* only 4 {@link FloatUtil#mapObjToWin(float, float, float, float[], int[], float[], float[], float[]) mapObjToWinCoords}
* operations are made on points [1..4] using {@link #getCenter()}'s z-value.
* Otherwise 8 {@link FloatUtil#mapObjToWin(float, float, float, float[], int[], float[], float[], float[]) mapObjToWinCoords}
* operation on all 8 points are performed.
* </p>
* <pre>
* .z() ------ [4]
* | |
* | |
* .y() ------ [3]
* </pre>
* @param mat4PMv [projection] x [modelview] matrix, i.e. P x Mv
* @param viewport viewport rectangle
* @param useCenterZ
* @param vec3Tmp0 3 component vector for temp storage
* @param vec4Tmp1 4 component vector for temp storage
* @param vec4Tmp2 4 component vector for temp storage
* @return
*/
public AABBox mapToWindow(final AABBox result, final Matrix4f mat4PMv, final Recti viewport, final boolean useCenterZ) {
final Vec3f tmp = new Vec3f();
final Vec3f winPos = new Vec3f();
{
final float objZ = useCenterZ ? center.z() : getMinZ();
result.reset();
Matrix4f.mapObjToWin(tmp.set(getMinX(), getMinY(), objZ), mat4PMv, viewport, winPos);
result.resize(winPos);
Matrix4f.mapObjToWin(tmp.set(getMinX(), getMaxY(), objZ), mat4PMv, viewport, winPos);
result.resize(winPos);
Matrix4f.mapObjToWin(tmp.set(getMaxX(), getMaxY(), objZ), mat4PMv, viewport, winPos);
result.resize(winPos);
Matrix4f.mapObjToWin(tmp.set(getMaxX(), getMinY(), objZ), mat4PMv, viewport, winPos);
result.resize(winPos);
}
if( !useCenterZ ) {
final float objZ = getMaxZ();
Matrix4f.mapObjToWin(tmp.set(getMinX(), getMinY(), objZ), mat4PMv, viewport, winPos);
result.resize(winPos);
Matrix4f.mapObjToWin(tmp.set(getMinX(), getMaxY(), objZ), mat4PMv, viewport, winPos);
result.resize(winPos);
Matrix4f.mapObjToWin(tmp.set(getMaxX(), getMaxY(), objZ), mat4PMv, viewport, winPos);
result.resize(winPos);
Matrix4f.mapObjToWin(tmp.set(getMaxX(), getMinY(), objZ), mat4PMv, viewport, winPos);
result.resize(winPos);
}
if( DEBUG ) {
System.err.printf("AABBox.mapToWindow: view[%s], this %s -> %s%n", viewport, toString(), result.toString());
}
return result;
}
@Override
public final String toString() {
return "[dim "+getWidth()+" x "+getHeight()+" x "+getDepth()+
", box "+low+" .. "+high+", ctr "+center+"]";
}
}