//AABBtriangle.h
#pragma once
/********************************************************/
/* AABB-triangle overlap test code */
/* Function: int triBoxOverlap(float boxcenter[3], float boxhalfsize[3], float triverts[3][3]); */
/********************************************************/
#include <math.h>
#include <stdio.h>
#define X 0
#define Y 1
#define Z 2
#define CROSS(dest,v1,v2) 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];
#define DOT(v1,v2) v1[0]*v2[0]+v1[1]*v2[1]+v1[2]*v2[2]
#define SUB(dest,v1,v2) dest[0] = v1[0] - v2[0];dest[1] = v1[1] - v2[1]; dest[2] = v1[2] - v2[2];
#define FINDMINMAX(x0,x1,x2,min,max) min = max = x0; if (x1 < min) min = x1; if (x1 > max) max = x1; if (x2 < min) min = x2; if (x2 > max) max = x2;
int planeBoxOverlap(float normal[3], float d, float maxbox[3]);
/*======================== X-tests ========================*/
#define AXISTEST_X01(a, b, fa, fb) p0 = a*v0[Y] - b*v0[Z];p2 = a*v2[Y] - b*v2[Z]; if (p0<p2) { min = p0; max = p2; } else { min = p2; max = p0; } rad = fa * boxhalfsize[Y] + fb * boxhalfsize[Z]; if (min>rad || max<-rad) return 0;
#define AXISTEST_X2(a, b, fa, fb) p0 = a*v0[Y] - b*v0[Z]; p1 = a*v1[Y] - b*v1[Z]; if (p0<p1) { min = p0; max = p1; }else { min = p1; max = p0; } rad = fa * boxhalfsize[Y] + fb * boxhalfsize[Z]; if (min>rad || max<-rad) return 0;
/*======================== Y-tests ========================*/
#define AXISTEST_Y02(a, b, fa, fb) p0 = -a*v0[X] + b*v0[Z]; p2 = -a*v2[X] + b*v2[Z];if (p0<p2) { min = p0; max = p2; }else { min = p2; max = p0; } rad = fa * boxhalfsize[X] + fb * boxhalfsize[Z]; if (min>rad || max<-rad) return 0;
#define AXISTEST_Y1(a, b, fa, fb) p0 = -a*v0[X] + b*v0[Z]; p1 = -a*v1[X] + b*v1[Z];if (p0<p1) { min = p0; max = p1; }else { min = p1; max = p0; } rad = fa * boxhalfsize[X] + fb * boxhalfsize[Z]; if (min>rad || max<-rad) return 0;
/*======================== Z-tests ========================*/
#define AXISTEST_Z12(a, b, fa, fb) p1 = a*v1[X] - b*v1[Y]; p2 = a*v2[X] - b*v2[Y]; if (p2<p1) { min = p2; max = p1; }else { min = p1; max = p2; }rad = fa * boxhalfsize[X] + fb * boxhalfsize[Y]; if (min>rad || max<-rad) return 0;
#define AXISTEST_Z0(a, b, fa, fb) p0 = a*v0[X] - b*v0[Y]; p1 = a*v1[X] - b*v1[Y]; if (p0<p1) { min = p0; max = p1; }else { min = p1; max = p0; }rad = fa * boxhalfsize[X] + fb * boxhalfsize[Y]; if (min>rad || max<-rad) return 0;
int triBoxOverlap(float boxcenter[3], float boxhalfsize[3], float triverts[3][3]);
//AABBtriangle.cpp
#include"AABBtriangle.h"
int planeBoxOverlap(float normal[3], float d, float maxbox[3])
{
int q;
float vmin[3], vmax[3];
for (q = X; q <= Z; q++)
{
if (normal[q] > 0.0f)
{
vmin[q] = -maxbox[q];
vmax[q] = maxbox[q];
}
else
{
vmin[q] = maxbox[q];
vmax[q] = -maxbox[q];
}
}
if (DOT(normal, vmin) + d > 0.0f) return 0;
if (DOT(normal, vmax) + d >= 0.0f) return 1;
return 0;
}
int triBoxOverlap(float boxcenter[3], float boxhalfsize[3], float triverts[3][3])
{
/* 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 */
float v0[3], v1[3], v2[3];
float axis[3];
float min, max, d, p0, p1, p2, rad, fex, fey, fez;
float normal[3], e0[3], e1[3], e2[3];
/* This is the fastest branch on Sun */
/* move everything so that the boxcenter is in (0,0,0) */
SUB(v0,triverts[0],boxcenter);
SUB(v1, triverts[1], boxcenter);
SUB(v2, triverts[2], boxcenter);
/* compute triangle edges */
SUB(e0, v1, v0); /* tri edge 0 */
SUB(e1, v2, v1); /* tri edge 1 */
SUB(e2, v0, v2); /* tri edge 2 */
/* Bullet 3: */
/* test the 9 tests first (this was faster) */
fex = fabs(e0[X]);
fey = fabs(e0[Y]);
fez = fabs(e0[Z]);
AXISTEST_X01(e0[Z], e0[Y], fez, fey);
AXISTEST_Y02(e0[Z], e0[X], fez, fex);
AXISTEST_Z12(e0[Y], e0[X], fey, fex);
fex = fabs(e1[X]);
fey = fabs(e1[Y]);
fez = fabs(e1[Z]);
AXISTEST_X01(e1[Z], e1[Y], fez, fey);
AXISTEST_Y02(e1[Z], e1[X], fez, fex);
AXISTEST_Z0(e1[Y], e1[X], fey, fex);
fex = fabs(e2[X]);
fey = fabs(e2[Y]);
fez = fabs(e2[Z]);
AXISTEST_X2(e2[Z], e2[Y], fez, fey);
AXISTEST_Y1(e2[Z], e2[X], fez, fex);
AXISTEST_Z12(e2[Y], e2[X], fey, fex);
/* 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 */
FINDMINMAX(v0[X],v1[X],v2[X],min,max);
if (min>boxhalfsize[X] || max<-boxhalfsize[X]) return 0;
/* test in Y-direction */
FINDMINMAX(v0[Y], v1[Y], v2[Y], min, max);
if (min>boxhalfsize[Y] || max<-boxhalfsize[Y]) return 0;
/* test in Z-direction */
FINDMINMAX(v0[Z], v1[Z], v2[Z], min, max);
if (min>boxhalfsize[Z] || max<-boxhalfsize[Z]) return 0;
/* Bullet 2: */
/* test if the box intersects the plane of the triangle */
/* compute plane equation of triangle: normal*x+d=0 */
CROSS(normal, e0, e1);
d = -DOT(normal, v0); /* plane eq: normal.x+d=0 */
if (!planeBoxOverlap(normal, d, boxhalfsize)) return 0;
return 1; /* box and triangle overlaps */
}