/*
* Copyright (c) 2009-2012 jMonkeyEngine
* All rights reserved.
*
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* modification, are permitted provided that the following conditions are
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*
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*
* * 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.
*
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* 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
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package com.jme3.bounding;
import com.jme3.math.FastMath;
import com.jme3.math.Plane;
import com.jme3.math.Vector3f;
import com.jme3.util.TempVars;
import static java.lang.Math.max;
import static java.lang.Math.min;
/**
* This class includes some utility methods for computing intersection
* between bounding volumes and triangles.
*
* @author Kirill
*/
public final class Intersection {
private Intersection() {
}
public static boolean intersect(BoundingSphere sphere, Vector3f center, float radius) {
assert Vector3f.isValidVector(center) && Vector3f.isValidVector(sphere.center);
TempVars vars = TempVars.get();
try {
Vector3f diff = center.subtract(sphere.center, vars.vect1);
float rsum = sphere.getRadius() + radius;
return (diff.dot(diff) <= rsum * rsum);
} finally {
vars.release();
}
}
public static boolean intersect(BoundingBox bbox, Vector3f center, float radius) {
assert Vector3f.isValidVector(center) && Vector3f.isValidVector(bbox.center);
// Arvo's algorithm
float distSqr = radius * radius;
float minX = bbox.center.x - bbox.xExtent;
float maxX = bbox.center.x + bbox.xExtent;
float minY = bbox.center.y - bbox.yExtent;
float maxY = bbox.center.y + bbox.yExtent;
float minZ = bbox.center.z - bbox.zExtent;
float maxZ = bbox.center.z + bbox.zExtent;
if (center.x < minX) distSqr -= FastMath.sqr(center.x - minX);
else if (center.x > maxX) distSqr -= FastMath.sqr(center.x - maxX);
if (center.y < minY) distSqr -= FastMath.sqr(center.y - minY);
else if (center.y > maxY) distSqr -= FastMath.sqr(center.y - maxY);
if (center.z < minZ) distSqr -= FastMath.sqr(center.z - minZ);
else if (center.z > maxZ) distSqr -= FastMath.sqr(center.z - maxZ);
return distSqr > 0;
}
private static final void findMinMax(float x0, float x1, float x2, Vector3f minMax) {
minMax.set(x0, x0, 0);
if (x1 < minMax.x) {
minMax.setX(x1);
}
if (x1 > minMax.y) {
minMax.setY(x1);
}
if (x2 < minMax.x) {
minMax.setX(x2);
}
if (x2 > minMax.y) {
minMax.setY(x2);
}
}
// private boolean axisTest(float a, float b, float fa, float fb, Vector3f v0, Vector3f v1, )
// private boolean axisTestX01(float a, float b, float fa, float fb,
// Vector3f center, Vector3f ext,
// Vector3f v1, Vector3f v2, Vector3f v3){
// float p0 = a * v0.y - b * v0.z;
// float p2 = a * v2.y - b * v2.z;
// if(p0 < p2){
// min = p0;
// max = p2;
// } else {
// min = p2;
// max = p0;
// }
// float rad = fa * boxhalfsize.y + fb * boxhalfsize.z;
// if(min > rad || max < -rad)
// return false;
// }
public static boolean intersect(BoundingBox bbox, Vector3f v1, Vector3f v2, Vector3f v3) {
// use separating axis theorem to test overlap between triangle and box
// need to test for overlap in these directions:
// 1) the {x,y,z}-directions (actually, since we use the AABB of the triangle
// we do not even need to test these)
// 2) normal of the triangle
// 3) crossproduct(edge from tri, {x,y,z}-directin)
// this gives 3x3=9 more tests
TempVars vars = TempVars.get();
Vector3f tmp0 = vars.vect1,
tmp1 = vars.vect2,
tmp2 = vars.vect3;
Vector3f e0 = vars.vect4,
e1 = vars.vect5,
e2 = vars.vect6;
Vector3f center = bbox.getCenter();
Vector3f extent = bbox.getExtent(null);
// float min,max,p0,p1,p2,rad,fex,fey,fez;
// float normal[3]
// This is the fastest branch on Sun
// move everything so that the boxcenter is in (0,0,0)
v1.subtract(center, tmp0);
v2.subtract(center, tmp1);
v3.subtract(center, tmp2);
// compute triangle edges
tmp1.subtract(tmp0, e0); // tri edge 0
tmp2.subtract(tmp1, e1); // tri edge 1
tmp0.subtract(tmp2, e2); // tri edge 2
// Bullet 3:
// test the 9 tests first (this was faster)
float min, max;
float p0, p1, p2, rad;
float fex = FastMath.abs(e0.x);
float fey = FastMath.abs(e0.y);
float fez = FastMath.abs(e0.z);
//AXISTEST_X01(e0[Z], e0[Y], fez, fey);
p0 = e0.z * tmp0.y - e0.y * tmp0.z;
p2 = e0.z * tmp2.y - e0.y * tmp2.z;
min = min(p0, p2);
max = max(p0, p2);
rad = fez * extent.y + fey * extent.z;
if (min > rad || max < -rad) {
vars.release();
return false;
}
// AXISTEST_Y02(e0[Z], e0[X], fez, fex);
p0 = -e0.z * tmp0.x + e0.x * tmp0.z;
p2 = -e0.z * tmp2.x + e0.x * tmp2.z;
min = min(p0, p2);
max = max(p0, p2);
rad = fez * extent.x + fex * extent.z;
if (min > rad || max < -rad) {
vars.release();
return false;
}
// AXISTEST_Z12(e0[Y], e0[X], fey, fex);
p1 = e0.y * tmp1.x - e0.x * tmp1.y;
p2 = e0.y * tmp2.x - e0.x * tmp2.y;
min = min(p1, p2);
max = max(p1, p2);
rad = fey * extent.x + fex * extent.y;
if (min > rad || max < -rad) {
vars.release();
return false;
}
fex = FastMath.abs(e1.x);
fey = FastMath.abs(e1.y);
fez = FastMath.abs(e1.z);
// AXISTEST_X01(e1[Z], e1[Y], fez, fey);
p0 = e1.z * tmp0.y - e1.y * tmp0.z;
p2 = e1.z * tmp2.y - e1.y * tmp2.z;
min = min(p0, p2);
max = max(p0, p2);
rad = fez * extent.y + fey * extent.z;
if (min > rad || max < -rad) {
vars.release();
return false;
}
// AXISTEST_Y02(e1[Z], e1[X], fez, fex);
p0 = -e1.z * tmp0.x + e1.x * tmp0.z;
p2 = -e1.z * tmp2.x + e1.x * tmp2.z;
min = min(p0, p2);
max = max(p0, p2);
rad = fez * extent.x + fex * extent.z;
if (min > rad || max < -rad) {
vars.release();
return false;
}
// AXISTEST_Z0(e1[Y], e1[X], fey, fex);
p0 = e1.y * tmp0.x - e1.x * tmp0.y;
p1 = e1.y * tmp1.x - e1.x * tmp1.y;
min = min(p0, p1);
max = max(p0, p1);
rad = fey * extent.x + fex * extent.y;
if (min > rad || max < -rad) {
vars.release();
return false;
}
//
fex = FastMath.abs(e2.x);
fey = FastMath.abs(e2.y);
fez = FastMath.abs(e2.z);
// AXISTEST_X2(e2[Z], e2[Y], fez, fey);
p0 = e2.z * tmp0.y - e2.y * tmp0.z;
p1 = e2.z * tmp1.y - e2.y * tmp1.z;
min = min(p0, p1);
max = max(p0, p1);
rad = fez * extent.y + fey * extent.z;
if (min > rad || max < -rad) {
vars.release();
return false;
}
// AXISTEST_Y1(e2[Z], e2[X], fez, fex);
p0 = -e2.z * tmp0.x + e2.x * tmp0.z;
p1 = -e2.z * tmp1.x + e2.x * tmp1.z;
min = min(p0, p1);
max = max(p0, p1);
rad = fez * extent.x + fex * extent.y;
if (min > rad || max < -rad) {
vars.release();
return false;
}
// AXISTEST_Z12(e2[Y], e2[X], fey, fex);
p1 = e2.y * tmp1.x - e2.x * tmp1.y;
p2 = e2.y * tmp2.x - e2.x * tmp2.y;
min = min(p1, p2);
max = max(p1, p2);
rad = fey * extent.x + fex * extent.y;
if (min > rad || max < -rad) {
vars.release();
return false;
}
// Bullet 1:
// first test overlap in the {x,y,z}-directions
// find min, max of the triangle each direction, and test for overlap in
// that direction -- this is equivalent to testing a minimal AABB around
// the triangle against the AABB
Vector3f minMax = vars.vect7;
// test in X-direction
findMinMax(tmp0.x, tmp1.x, tmp2.x, minMax);
if (minMax.x > extent.x || minMax.y < -extent.x) {
vars.release();
return false;
}
// test in Y-direction
findMinMax(tmp0.y, tmp1.y, tmp2.y, minMax);
if (minMax.x > extent.y || minMax.y < -extent.y) {
vars.release();
return false;
}
// test in Z-direction
findMinMax(tmp0.z, tmp1.z, tmp2.z, minMax);
if (minMax.x > extent.z || minMax.y < -extent.z) {
vars.release();
return false;
}
// // Bullet 2:
// // test if the box intersects the plane of the triangle
// // compute plane equation of triangle: normal * x + d = 0
// Vector3f normal = new Vector3f();
// e0.cross(e1, normal);
Plane p = vars.plane;
p.setPlanePoints(v1, v2, v3);
if (bbox.whichSide(p) == Plane.Side.Negative) {
vars.release();
return false;
}
//
// if(!planeBoxOverlap(normal,v0,boxhalfsize)) return false;
vars.release();
return true; /* box and triangle overlaps */
}
}