3D Geometry code and good references
which I think is defined as a Euclidean shortest path problem in 3D
space which apparently is hard, really hard. Triangle box overlap algorithm
http://www.cs.lth.se/home/Tomas_Akenine_Moller/code/tribox3.txt
My search led to to some terms:
* visibility graphs
* Continuous Dijkstra
* AABB
* ERIT
* BSP Tree
* Piano Movers
* Spider and Fly
* Geodesic and some good sites.
http://www.cs.lth.se/home/Tomas_Akenine_Moller/code/
HIs book "Real time Rendering"
http://books.google.com/books?id=mOKEfBTw4x0C&printsec=frontcover&dq=Fast+3D+...
chapter 13 (a 3rd edition is out)
http://www.realtimerendering.com/intersections.html site for his book.
/********************************************************/
/* AABB-triangle overlap test code */
/* by Tomas Akenine-Möller */
/* Function: int triBoxOverlap(float boxcenter[3], */
/* float boxhalfsize[3],float triverts[3][3]); */
/* History: */
/* 2001-03-05: released the code in its first version */
/* 2001-06-18: changed the order of the tests, faster */
/* */
/* Acknowledgement: Many thanks to Pierre Terdiman for */
/* suggestions and discussions on how to optimize code. */
/* Thanks to David Hunt for finding a ">="-bug! */
/********************************************************/
#include
#include
#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(x1max) max=x1;\
if(x2max) max=x2;
int planeBoxOverlap(float normal[3], float vert[3], float maxbox[3]) // -NJMP-
{
int q;
float vmin[3],vmax[3],v;
for(q=X;q
{
v=vert[q]; // -NJMP-
if(normal[q]>0.0f)
{
vmin[q]=-maxbox[q] - v; // -NJMP-
vmax[q]= maxbox[q] - v; // -NJMP-
}
else
{
vmin[q]= maxbox[q] - v; // -NJMP-
vmax[q]=-maxbox[q] - v; // -NJMP-
}
}
if(DOT(normal,vmin)>0.0f) return 0; // -NJMP-
if(DOT(normal,vmax)>=0.0f) return 1; // -NJMP-
return 0;
}
/*======================== X-tests ========================*/
#define AXISTEST_X01(a, b, fa, fb) \
p0 = a*v0[Y] - b*v0[Z]; \
p2 = a*v2[Y] - b*v2[Z]; \
if(p0rad || max
#define AXISTEST_X2(a, b, fa, fb) \
p0 = a*v0[Y] - b*v0[Z]; \
p1 = a*v1[Y] - b*v1[Z]; \
if(p0rad || max
/*======================== Y-tests ========================*/
#define AXISTEST_Y02(a, b, fa, fb) \
p0 = -a*v0[X] + b*v0[Z]; \
p2 = -a*v2[X] + b*v2[Z]; \
if(p0rad || max
#define AXISTEST_Y1(a, b, fa, fb) \
p0 = -a*v0[X] + b*v0[Z]; \
p1 = -a*v1[X] + b*v1[Z]; \
if(p0rad || max
/*======================== Z-tests ========================*/
#define AXISTEST_Z12(a, b, fa, fb) \
p1 = a*v1[X] - b*v1[Y]; \
p2 = a*v2[X] - b*v2[Y]; \
if(p2rad || max
#define AXISTEST_Z0(a, b, fa, fb) \
p0 = a*v0[X] - b*v0[Y]; \
p1 = a*v1[X] - b*v1[Y]; \
if(p0rad || max
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,p0,p1,p2,rad,fex,fey,fez; // -NJMP- "d" local variable removed
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 = fabsf(e0[X]);
fey = fabsf(e0[Y]);
fez = fabsf(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 = fabsf(e1[X]);
fey = fabsf(e1[Y]);
fez = fabsf(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 = fabsf(e2[X]);
fey = fabsf(e2[Y]);
fez = fabsf(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
/* test in Y-direction */
FINDMINMAX(v0[Y],v1[Y],v2[Y],min,max);
if(min>boxhalfsize[Y] || max
/* test in Z-direction */
FINDMINMAX(v0[Z],v1[Z],v2[Z],min,max);
if(min>boxhalfsize[Z] || max
/* 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);
// -NJMP- (line removed here)
if(!planeBoxOverlap(normal,v0,boxhalfsize)) return 0; // -NJMP-
return 1; /* box and triangle overlaps */
}
