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OverlapTester.java
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OverlapTester.java
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class OverlapTester
{
static final int X=0;
static final int Y=1;
static final int Z=2;
private double[] crossProduct(double[] v1, double[] v2){
double[] dest = new double[3];
dest[0] = v1[1]*v2[2] - v1[2]*v2[1];
dest[1] = v1[2]*v2[0] - v1[0]*v2[2];
dest[2] = v1[0]*v2[1] - v1[1]*v2[0];
/*double magnitude = dest[0]*dest[0]+dest[1]*dest[1]+dest[2]*dest[2];
for(int i=0; i<3; i++) dest[i] = dest[i]/magnitude;*/
return dest;
}
private double dotProduct(double []v1,double []v2) {
return ( v1[0]*v2[0] + v1[1]*v2[1] + v1[2]*v2[2] );
}
private double[] sub(double[] v1, double[] v2) {
double[] dest = new double[3];
dest[0] = v1[0]-v2[0];
dest[1] = v1[1]-v2[1];
dest[2] = v1[2]-v2[2];
return dest;
}
private double[] minMax(double x0, double x1, double x2) {
double min=x0;
double max=x0;
if(x1<min) min=x1;
if(x1>max) max=x1;
if(x2<min) min=x2;
if(x2>max) max=x2;
return new double[] {min, max};
}
private boolean planeBoxOverlap(double[] normal, double[] vert, double[] maxbox) {
int q;
double[] vmin = new double[3];
double[] vmax = new double[3];
double v;
for(q=X;q<=Z;q++)
{
v=vert[q];
if(normal[q]>0.0f) {
vmin[q]=-maxbox[q] - v;
vmax[q]= maxbox[q] - v;
}
else {
vmin[q]= maxbox[q] - v;
vmax[q]=-maxbox[q] - v;
}
}
if(dotProduct(normal,vmin)>0.0f) return false;
if(dotProduct(normal,vmax)>=0.0f) return true;
return false;
}
/*======================== X-tests ========================*/
private boolean axisTestX01(double a,double b,double[] v0,double[] v2, double[] boxhalfsize) {
double p0 = a*v0[Y] - b*v0[Z];
double p2 = a*v2[Y] - b*v2[Z];
double min,max;
if(p0<p2) {
min=p0;
max=p2;
}
else {
min=p2;
max=p0;
}
double rad = Math.abs(a) * boxhalfsize[Y] + Math.abs(b) * boxhalfsize[Z];
if(min>rad || max< -rad) return false;
return true;
}
private boolean axisTestX2(double a,double b,double[] v0,double[] v1, double[] boxhalfsize) {
double p0 = a*v0[Y] - b*v0[Z];
double p1 = a*v1[Y] - b*v1[Z];
double min,max;
if(p0<p1) {
min=p0;
max=p1;
}
else {
min=p1;
max=p0;
}
double rad = Math.abs(a) * boxhalfsize[Y] + Math.abs(b) * boxhalfsize[Z];
if(min>rad || max< -rad) return false;
return true;
}
/*======================== Y-tests ========================*/
private boolean axisTestY02(double a,double b, double[] v0,double[] v2, double[] boxhalfsize) {
double p0 = -a*v0[X] + b*v0[Z];
double p2 = -a*v2[X] + b*v2[Z];
double min,max;
if(p0<p2) {
min=p0;
max=p2;
}
else {
min=p2;
max=p0;
}
double rad = Math.abs(a) * boxhalfsize[X] + Math.abs(b) * boxhalfsize[Z];
if(min>rad || max< -rad) return false;
return true;
}
private boolean axisTestY1(double a,double b, double[] v0,double[] v1, double[] boxhalfsize) {
double p0 = -a*v0[X] + b*v0[Z];
double p1 = -a*v1[X] + b*v1[Z];
double min,max;
if(p0<p1) {
min=p0;
max=p1;
}
else {
min=p1;
max=p0;
}
double rad = Math.abs(a) * boxhalfsize[X] + Math.abs(b) * boxhalfsize[Z];
if(min>rad || max<-rad) return false;
return true;
}
/*======================== Z-tests ========================*/
private boolean axisTestZ12(double a,double b,double[] v1, double[] v2, double[] boxhalfsize) {
double p1 = a*v1[X] - b*v1[Y];
double p2 = a*v2[X] - b*v2[Y];
double min,max;
if(p2<p1) {
min=p2;
max=p1;
}
else {
min=p1;
max=p2;
}
double rad = Math.abs(a) * boxhalfsize[X] + Math.abs(b) * boxhalfsize[Y];
if(min>rad || max<-rad) return false;
return true;
}
private boolean axisTestZ0(double a,double b,double[] v0, double[] v1, double[] boxhalfsize) {
double p0 = a*v0[X] - b*v0[Y];
double p1 = a*v1[X] - b*v1[Y];
double min,max;
if(p0<p1) {
min=p0;
max=p1;
}
else {
min=p1;
max=p0;
}
double rad = Math.abs(a) * boxhalfsize[X] + Math.abs(b) * boxhalfsize[Y];
if(min>rad || max<-rad) return false;
return true;
}
public boolean triBoxOverlap(double[] boxcenter,double[] boxhalfsize,double[][] triverts) {
/*using separating axis theorem to test overlap between triangle and box, we
need to test for overlap in these directions:
1) the {x,y,z}-directions (axes perpendicular to faces of box)
2) normal of the triangle
3) crossproduct(edge from tri, {x,y,z}-direction i.e. the axes perpendicular to box faces)
this gives 3x3=9 more tests
so 13 axis in total*/
// double axis[3];
double min,max,rad;
double[] normal,v0,v1,v2,e0,e1,e2,range;
// move everything so that the boxcenter is in (0,0,0)
v0 = sub(triverts[0],boxcenter);
v1 = sub(triverts[1],boxcenter);
v2 = sub(triverts[2],boxcenter);
// compute triangle edges
e0 = sub(v1,v0); // tri edge 0
e1 = sub(v2,v1); // tri edge 1
e2 = sub(v0,v2); // tri edge 2
// Bullet 3:
// test the 9 tests first
if(!axisTestX01(e0[Z], e0[Y], v0, v2, boxhalfsize)) return false;
if(!axisTestY02(e0[Z], e0[X], v0, v2, boxhalfsize)) return false;
if(!axisTestZ12(e0[Y], e0[X], v1, v2, boxhalfsize)) return false;
if(!axisTestX01(e1[Z], e1[Y], v0, v2, boxhalfsize)) return false;
if(!axisTestY02(e1[Z], e1[X], v0, v2, boxhalfsize)) return false;
if(!axisTestZ0(e1[Y], e1[X], v0, v1, boxhalfsize)) return false;
if(!axisTestX2(e2[Z], e2[Y], v0, v1, boxhalfsize)) return false;
if(!axisTestY1(e2[Z], e2[X], v0, v1, boxhalfsize)) return false;
if(!axisTestZ12(e2[Y], e2[X], v1, v2, boxhalfsize)) 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 */
// test in X-direction
range = minMax(v0[X],v1[X],v2[X]);
min=range[0];
max=range[1];
if(min>boxhalfsize[X] || max< -boxhalfsize[X]) return false;
// test in Y-direction
range = minMax(v0[Y],v1[Y],v2[Y]);
min=range[0];
max=range[1];
if(min>boxhalfsize[Y] || max< -boxhalfsize[Y]) return false;
// test in Z-direction
range = minMax(v0[Z],v1[Z],v2[Z]);
min=range[0];
max=range[1];
if(min>boxhalfsize[Z] || max< -boxhalfsize[Z]) return false;
/* Bullet 2:
test if the box intersects the plane of the triangle
compute plane equation of triangle: normal*x+d=0 */
normal = crossProduct(e0,e1);
if(!planeBoxOverlap(normal,v0,boxhalfsize)) return false;
return true; // box and triangle overlaps
}
//driver program to test our code
public static void main (String[] args) throws java.lang.Exception
{
double[] center = {0.5,0.5,0.5};
double[] extent = {0.5,0.5,0.5};
double[][] vertices = new double[3][3];
vertices[0][0]=0.3;
vertices[0][1]=0.2;
vertices[0][2]=0.1;
vertices[1][0]=2.5;
vertices[1][1]=1.3;
vertices[1][2]=3.2;
vertices[2][0]=-2.1;
vertices[2][1]=-1.5;
vertices[2][2]=-2.3;
OverlapTester obj = new OverlapTester();
if(obj.triBoxOverlap(center,extent,vertices)) System.out.println("overlaps");
else System.out.println("does not overlap");
}
}