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#ifndef lint
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static const char RCSid[] = "$Id: sphere.c,v 2.5 2004/03/30 16:13:00 schorsch Exp $";
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#endif
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/*
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* sphere.c - routines for creating octrees for spheres.
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*
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* 7/28/85
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*/
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#include "standard.h"
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#include "octree.h"
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#include "object.h"
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#include "otypes.h"
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#define ROOT3 1.732050808
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/*
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* Regrettably, the algorithm for determining a cube's location
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* with respect to a sphere is not simple. First, a quick test is
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* made to determine if the sphere and the bounding sphere of the cube
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* are disjoint. This of course means no intersection. Failing this,
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* we determine if the cube lies inside the sphere. The cube is
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* entirely inside if the bounding sphere on the cube is
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* contained within our sphere. This means no intersection. Otherwise,
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* if the cube radius is smaller than the sphere's and the cube center is
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* inside the sphere, we assume intersection. If these tests fail,
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* we proceed as follows.
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* The sphere center is located in relation to the 6 cube faces,
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* and one of four things is done depending on the number of
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* planes the center lies between:
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*
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* 0: The sphere is closest to a cube corner, find the
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* distance to that corner.
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*
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* 1: The sphere is closest to a cube edge, find this
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* distance.
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*
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* 2: The sphere is closest to a cube face, find the distance.
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*
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* 3: The sphere has its center inside the cube.
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*
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* In cases 0-2, if the closest part of the cube is within
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* the radius distance from the sphere center, we have intersection.
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* If it is not, the cube must be outside the sphere.
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* In case 3, there must be intersection, and no further
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* tests are necessary.
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*/
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int
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o_sphere( /* determine if sphere intersects cube */
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OBJREC *o,
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CUBE *cu
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)
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{
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FVECT v1;
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double d1, d2;
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RREAL *fa;
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int i;
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#define cent fa
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#define rad fa[3]
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/* get arguments */
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if (o->oargs.nfargs != 4)
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objerror(o, USER, "bad # arguments");
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fa = o->oargs.farg;
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if (rad < -FTINY) {
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objerror(o, WARNING, "negative radius");
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o->otype = o->otype == OBJ_SPHERE ?
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OBJ_BUBBLE : OBJ_SPHERE;
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rad = -rad;
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} else if (rad <= FTINY) {
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objerror(o, WARNING, "zero radius");
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return(O_MISS);
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}
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d1 = ROOT3/2.0 * cu->cusize; /* bounding radius for cube */
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d2 = cu->cusize * 0.5; /* get distance between centers */
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for (i = 0; i < 3; i++)
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v1[i] = cu->cuorg[i] + d2 - cent[i];
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d2 = DOT(v1,v1);
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if (d2 > (rad+d1+FTINY)*(rad+d1+FTINY)) /* quick test */
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return(O_MISS); /* cube outside */
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/* check sphere interior */
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if (d1 < rad) {
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if (d2 < (rad-d1-FTINY)*(rad-d1-FTINY))
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return(O_MISS); /* cube inside sphere */
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if (d2 < (rad+FTINY)*(rad+FTINY))
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return(O_HIT); /* cube center inside */
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}
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/* find closest distance */
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for (i = 0; i < 3; i++)
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if (cent[i] < cu->cuorg[i])
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v1[i] = cu->cuorg[i] - cent[i];
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else if (cent[i] > cu->cuorg[i] + cu->cusize)
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v1[i] = cent[i] - (cu->cuorg[i] + cu->cusize);
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else
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v1[i] = 0;
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/* final intersection check */
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if (DOT(v1,v1) <= (rad+FTINY)*(rad+FTINY))
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return(O_HIT);
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else
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return(O_MISS);
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}
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