/*
* Copyright (c) 2009-2012 jMonkeyEngine
* All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions are
* met:
*
* * Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
*
* * 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.
*
* * Neither the name of 'jMonkeyEngine' nor the names of its contributors
* may be used to endorse or promote products derived from this software
* without specific prior written permission.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
* "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 THE COPYRIGHT OWNER 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.
*/
package acousticfield3d.math;
import acousticfield3d.utils.BufferUtils;
import java.nio.FloatBuffer;
/**
* <code>BoundingSphere</code> defines a sphere that defines a container for a
* group of vertices of a particular piece of geometry. This sphere defines a
* radius and a center. <br>
* <br>
* A typical usage is to allow the class define the center and radius by calling
* either <code>containAABB</code> or <code>averagePoints</code>. A call to
* <code>computeFramePoint</code> in turn calls <code>containAABB</code>.
*
* @author Mark Powell
* @version $Id: BoundingSphere.java,v 1.59 2007/08/17 10:34:26 rherlitz Exp $
*/
public class BoundingSphere {
Vector3f center = new Vector3f();
float radius;
private static final float RADIUS_EPSILON = 1f + 0.00001f;
/**
* Default contstructor instantiates a new <code>BoundingSphere</code>
* object.
*/
public BoundingSphere() {
}
/**
* Constructor instantiates a new <code>BoundingSphere</code> object.
*
* @param r
* the radius of the sphere.
* @param c
* the center of the sphere.
*/
public BoundingSphere(float r, Vector3f c) {
this.center.set(c);
this.radius = r;
}
/**
* <code>getRadius</code> returns the radius of the bounding sphere.
*
* @return the radius of the bounding sphere.
*/
public float getRadius() {
return radius;
}
/**
* <code>setRadius</code> sets the radius of this bounding sphere.
*
* @param radius
* the new radius of the bounding sphere.
*/
public void setRadius(float radius) {
this.radius = radius;
}
/**
* <code>computeFromPoints</code> creates a new Bounding Sphere from a
given copyTo of points. It uses the <code>calcWelzl</code> method as
* default.
*
* @param points
* the points to contain.
*/
public void computeFromPoints(FloatBuffer points) {
calcWelzl(points);
}
/**
* Calculates a minimum bounding sphere for the copyTo of points. The algorithm
* was originally found in C++ at
* <p><a href="http://www.flipcode.com/cgi-bin/msg.cgi?showThread=COTD-SmallestEnclosingSpheres&forum=cotd&id=-1">
* http://www.flipcode.com/cgi-bin/msg.cgi?showThread=COTD-SmallestEnclosingSpheres&forum=cotd&id=-1</a><br><strong>broken link</strong></p>
* <p>and translated to java by Cep21</p>
*
* @param points
* The points to calculate the minimum bounds from.
*/
public void calcWelzl(FloatBuffer points) {
if (center == null) {
center = new Vector3f();
}
FloatBuffer buf = BufferUtils.createFloatBuffer(points.limit());
points.rewind();
buf.put(points);
buf.flip();
recurseMini(buf, buf.limit() / 3, 0, 0);
}
/**
* Used from calcWelzl. This function recurses to calculate a minimum
* bounding sphere a few points at a time.
*
* @param points
* The array of points to look through.
* @param p
* The size of the list to be used.
* @param b
* The number of points currently considering to include with the
* sphere.
* @param ap
* A variable simulating pointer arithmatic from C++, and offset
* in <code>points</code>.
*/
private void recurseMini(FloatBuffer points, int p, int b, int ap) {
//TempVars vars = TempVars.get();
Vector3f tempA = new Vector3f(); //vars.vect1;
Vector3f tempB = new Vector3f(); //vars.vect2;
Vector3f tempC = new Vector3f(); //vars.vect3;
Vector3f tempD = new Vector3f(); //vars.vect4;
switch (b) {
case 0:
this.radius = 0;
this.center.set(0, 0, 0);
break;
case 1:
this.radius = 1f - RADIUS_EPSILON;
BufferUtils.populateFromBuffer(center, points, ap - 1);
break;
case 2:
BufferUtils.populateFromBuffer(tempA, points, ap - 1);
BufferUtils.populateFromBuffer(tempB, points, ap - 2);
setSphere(tempA, tempB);
break;
case 3:
BufferUtils.populateFromBuffer(tempA, points, ap - 1);
BufferUtils.populateFromBuffer(tempB, points, ap - 2);
BufferUtils.populateFromBuffer(tempC, points, ap - 3);
setSphere(tempA, tempB, tempC);
break;
case 4:
BufferUtils.populateFromBuffer(tempA, points, ap - 1);
BufferUtils.populateFromBuffer(tempB, points, ap - 2);
BufferUtils.populateFromBuffer(tempC, points, ap - 3);
BufferUtils.populateFromBuffer(tempD, points, ap - 4);
setSphere(tempA, tempB, tempC, tempD);
//vars.release();
return;
}
for (int i = 0; i < p; i++) {
BufferUtils.populateFromBuffer(tempA, points, i + ap);
if (tempA.distanceSquared(center) - (radius * radius) > RADIUS_EPSILON - 1f) {
for (int j = i; j > 0; j--) {
BufferUtils.populateFromBuffer(tempB, points, j + ap);
BufferUtils.populateFromBuffer(tempC, points, j - 1 + ap);
BufferUtils.setInBuffer(tempC, points, j + ap);
BufferUtils.setInBuffer(tempB, points, j - 1 + ap);
}
recurseMini(points, i, b + 1, ap + 1);
}
}
//vars.release();
}
/**
* Calculates the minimum bounding sphere of 4 points. Used in welzl's
* algorithm.
*
* @param O
* The 1st point inside the sphere.
* @param A
* The 2nd point inside the sphere.
* @param B
* The 3rd point inside the sphere.
* @param C
* The 4th point inside the sphere.
* @see #calcWelzl(java.nio.FloatBuffer)
*/
private void setSphere(Vector3f O, Vector3f A, Vector3f B, Vector3f C) {
Vector3f a = A.subtract(O);
Vector3f b = B.subtract(O);
Vector3f c = C.subtract(O);
float Denominator = 2.0f * (a.x * (b.y * c.z - c.y * b.z) - b.x
* (a.y * c.z - c.y * a.z) + c.x * (a.y * b.z - b.y * a.z));
if (Denominator == 0) {
center.set(0, 0, 0);
radius = 0;
} else {
Vector3f o = a.cross(b).multLocal(c.lengthSquared()).addLocal(
c.cross(a).multLocal(b.lengthSquared())).addLocal(
b.cross(c).multLocal(a.lengthSquared())).divideLocal(
Denominator);
radius = o.length() * RADIUS_EPSILON;
O.add(o, center);
}
}
/**
* Calculates the minimum bounding sphere of 3 points. Used in welzl's
* algorithm.
*
* @param O
* The 1st point inside the sphere.
* @param A
* The 2nd point inside the sphere.
* @param B
* The 3rd point inside the sphere.
* @see #calcWelzl(java.nio.FloatBuffer)
*/
private void setSphere(Vector3f O, Vector3f A, Vector3f B) {
Vector3f a = A.subtract(O);
Vector3f b = B.subtract(O);
Vector3f acrossB = a.cross(b);
float Denominator = 2.0f * acrossB.dot(acrossB);
if (Denominator == 0) {
center.set(0, 0, 0);
radius = 0;
} else {
Vector3f o = acrossB.cross(a).multLocal(b.lengthSquared()).addLocal(b.cross(acrossB).multLocal(a.lengthSquared())).divideLocal(Denominator);
radius = o.length() * RADIUS_EPSILON;
O.add(o, center);
}
}
/**
* Calculates the minimum bounding sphere of 2 points. Used in welzl's
* algorithm.
*
* @param O
* The 1st point inside the sphere.
* @param A
* The 2nd point inside the sphere.
* @see #calcWelzl(java.nio.FloatBuffer)
*/
private void setSphere(Vector3f O, Vector3f A) {
radius = M.sqrt(((A.x - O.x) * (A.x - O.x) + (A.y - O.y)
* (A.y - O.y) + (A.z - O.z) * (A.z - O.z)) / 4f) + RADIUS_EPSILON - 1f;
center.interpolateLocal(O, A, .5f);
}
/**
* <code>averagePoints</code> selects the sphere center to be the average
* of the points and the sphere radius to be the smallest value to enclose
* all points.
*
* @param points
* the list of points to contain.
*/
public void averagePoints(Vector3f[] points) {
center = points[0];
for (int i = 1; i < points.length; i++) {
center.addLocal(points[i]);
}
float quantity = 1.0f / points.length;
center.multLocal(quantity);
float maxRadiusSqr = 0;
for (int i = 0; i < points.length; i++) {
Vector3f diff = points[i].subtract(center);
float radiusSqr = diff.lengthSquared();
if (radiusSqr > maxRadiusSqr) {
maxRadiusSqr = radiusSqr;
}
}
radius = (float) Math.sqrt(maxRadiusSqr) + RADIUS_EPSILON - 1f;
}
/**
* <code>transform</code> modifies the center of the sphere to reflect the
* change made via a rotation, translation and scale.
*
* @param trans
* the transform to apply
* @param store
* sphere to store result in
* @return BoundingVolume
* @return ref
*/
public BoundingSphere transform(Transform trans, BoundingSphere store) {
BoundingSphere sphere;
if (store == null ) {
sphere = new BoundingSphere(1, new Vector3f(0, 0, 0));
} else {
sphere = (BoundingSphere) store;
}
center.mult(trans.getScale(), sphere.center);
trans.getRotation().mult(sphere.center, sphere.center);
sphere.center.addLocal(trans.getTranslation());
sphere.radius = M.abs(getMaxAxis(trans.getScale()) * radius) + RADIUS_EPSILON - 1f;
return sphere;
}
public BoundingSphere transform(Matrix4f trans, BoundingSphere store) {
BoundingSphere sphere;
if (store == null ) {
sphere = new BoundingSphere(1, new Vector3f(0, 0, 0));
} else {
sphere = (BoundingSphere) store;
}
trans.mult(center, sphere.center);
Vector3f axes = new Vector3f(1, 1, 1);
trans.mult(axes, axes);
float ax = getMaxAxis(axes);
sphere.radius = M.abs(ax * radius) + RADIUS_EPSILON - 1f;
return sphere;
}
private float getMaxAxis(Vector3f scale) {
float x = M.abs(scale.x);
float y = M.abs(scale.y);
float z = M.abs(scale.z);
if (x >= y) {
if (x >= z) {
return x;
}
return z;
}
if (y >= z) {
return y;
}
return z;
}
/**
* <code>whichSide</code> takes a plane (typically provided by a view
* frustum) to determine which side this bound is on.
*
* @param plane
* the plane to check against.
* @return side
*/
public Plane.Side whichSide(Plane plane) {
float distance = plane.pseudoDistance(center);
if (distance <= -radius) {
return Plane.Side.Negative;
} else if (distance >= radius) {
return Plane.Side.Positive;
} else {
return Plane.Side.None;
}
}
/**
* <code>toString</code> returns the string representation of this object.
* The form is: "Radius: RRR.SSSS Center: <Vector>".
*
* @return the string representation of this.
*/
@Override
public String toString() {
return getClass().getSimpleName() + " [Radius: " + radius + " Center: "
+ center + "]";
}
/*
* (non-Javadoc)
*
* @see com.jme.bounding.BoundingVolume#intersectsSphere(com.jme.bounding.BoundingSphere)
*/
public boolean intersectsSphere(BoundingSphere bs) {
assert Vector3f.isValidVector(center) && Vector3f.isValidVector(bs.center);
TempVars vars = TempVars.get();
Vector3f diff = center.subtract(bs.center, vars.vect1);
float rsum = getRadius() + bs.getRadius();
boolean eq = (diff.dot(diff) <= rsum * rsum);
vars.release();
return eq;
}
/*
* (non-Javadoc)
*
* @see com.jme.bounding.BoundingVolume#intersectsBoundingBox(com.jme.bounding.BoundingBox)
*/
public boolean intersectsBoundingBox(BoundingBox bb) {
assert Vector3f.isValidVector(center) && Vector3f.isValidVector(bb.center);
if (M.abs(bb.center.x - center.x) < getRadius()
+ bb.xExtent
&& M.abs(bb.center.y - center.y) < getRadius()
+ bb.yExtent
&& M.abs(bb.center.z - center.z) < getRadius()
+ bb.zExtent) {
return true;
}
return false;
}
/*
* (non-Javadoc)
*
* @see com.jme.bounding.BoundingVolume#intersectsOrientedBoundingBox(com.jme.bounding.OrientedBoundingBox)
*/
// public boolean intersectsOrientedBoundingBox(OrientedBoundingBox obb) {
// return obb.intersectsSphere(this);
// }
/*
* (non-Javadoc)
*
* @see com.jme.bounding.BoundingVolume#intersects(com.jme.math.Ray)
*/
public boolean intersects(Ray ray) {
assert Vector3f.isValidVector(center);
TempVars vars = TempVars.get();
Vector3f diff = vars.vect1.set(ray.getOrigin()).subtractLocal(center);
float radiusSquared = getRadius() * getRadius();
float a = diff.dot(diff) - radiusSquared;
if (a <= 0.0) {
vars.release();
// in sphere
return true;
}
// outside sphere
float b = ray.getDirection().dot(diff);
vars.release();
if (b >= 0.0) {
return false;
}
return b * b >= a;
}
/*
* (non-Javadoc)
*
* @see com.jme.bounding.BoundingVolume#intersectsWhere(com.jme.math.Ray)
*/
private int collideWithRay(Ray ray) {
TempVars vars = TempVars.get();
Vector3f diff = vars.vect1.set(ray.getOrigin()).subtractLocal(
center);
float a = diff.dot(diff) - (getRadius() * getRadius());
float a1, discr, root;
if (a <= 0.0) {
// inside sphere
a1 = ray.direction.dot(diff);
discr = (a1 * a1) - a;
root = M.sqrt(discr);
float distance = root - a1;
Vector3f point = new Vector3f(ray.direction).multLocal(distance).addLocal(ray.origin);
/*
CollisionResult result = new CollisionResult(point, distance);
results.addCollision(result);
vars.release();*/
return 1;
}
a1 = ray.direction.dot(diff);
vars.release();
if (a1 >= 0.0) {
return 0;
}
discr = a1 * a1 - a;
if (discr < 0.0) {
return 0;
} else if (discr >= M.ZERO_TOLERANCE) {
root = M.sqrt(discr);
float dist = -a1 - root;
/*
Vector3f point = new Vector3f(ray.direction).multLocal(dist).addLocal(ray.origin);
results.addCollision(new CollisionResult(point, dist));
dist = -a1 + root;
point = new Vector3f(ray.direction).multLocal(dist).addLocal(ray.origin);
results.addCollision(new CollisionResult(point, dist));
*/
return 2;
} else {
float dist = -a1;
/*
Vector3f point = new Vector3f(ray.direction).multLocal(dist).addLocal(ray.origin);
results.addCollision(new CollisionResult(point, dist));*/
return 1;
}
}
public Vector3f intersectPoint(Ray ray) {
TempVars vars = TempVars.get();
Vector3f diff = vars.vect1.set(ray.getOrigin()).subtractLocal(
center);
float a = diff.dot(diff) - (getRadius() * getRadius());
float a1, discr, root;
if (a <= 0.0) {
// inside sphere
a1 = ray.direction.dot(diff);
discr = (a1 * a1) - a;
root = M.sqrt(discr);
float distance = root - a1;
Vector3f point = new Vector3f(ray.direction).multLocal(distance).addLocal(ray.origin);
return point;
}
a1 = ray.direction.dot(diff);
vars.release();
if (a1 >= 0.0) {
return null;
}
discr = a1 * a1 - a;
if (discr < 0.0) {
return null;
} else if (discr >= M.ZERO_TOLERANCE) {
root = M.sqrt(discr);
float dist = -a1 - root;
Vector3f point = new Vector3f(ray.direction).multLocal(dist).addLocal(ray.origin);
return point;
/*
dist = -a1 + root;
point = new Vector3f(ray.direction).multLocal(dist).addLocal(ray.origin);
*/
} else {
float dist = -a1;
Vector3f point = new Vector3f(ray.direction).multLocal(dist).addLocal(ray.origin);
return point;
}
}
public boolean contains(Vector3f point) {
return center.distanceSquared(point) < (getRadius() * getRadius());
}
public boolean intersects(Vector3f point) {
return center.distanceSquared(point) <= (getRadius() * getRadius());
}
public float distanceToEdge(Vector3f point) {
return center.distance(point) - radius;
}
public float getVolume() {
return 4 * M.ONE_THIRD * M.PI * radius * radius * radius;
}
}
