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#ifndef lint |
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static const char RCSid[] = "$Id: sphere.c,v 2.4 2004/03/27 12:41:45 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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|
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#include "standard.h" |
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|
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#include "octree.h" |
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|
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#include "object.h" |
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|
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#include "otypes.h" |
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|
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#define ROOT3 1.732050808 |
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|
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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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|
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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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register 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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register RREAL *fa; |
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register 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, USER, "zero radius"); |
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|
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d1 = ROOT3/2.0 * cu->cusize; /* bounding radius for cube */ |
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|
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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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|
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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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|
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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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} |
