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#ifndef lint |
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static const char RCSid[] = "$Id: sphere.c,v 2.5 2003/03/12 04:59:05 greg Exp $"; |
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#endif |
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/* |
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* sphere.c - compute ray intersection with spheres. |
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*/ |
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|
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#include "copyright.h" |
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|
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#include "ray.h" |
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|
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#include "otypes.h" |
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|
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|
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o_sphere(so, r) /* compute intersection with sphere */ |
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OBJREC *so; |
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register RAY *r; |
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{ |
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double a, b, c; /* coefficients for quadratic equation */ |
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double root[2]; /* quadratic roots */ |
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int nroots; |
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double t; |
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register RREAL *ap; |
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register int i; |
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|
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if (so->oargs.nfargs != 4) |
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objerror(so, USER, "bad # arguments"); |
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ap = so->oargs.farg; |
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if (ap[3] < -FTINY) { |
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objerror(so, WARNING, "negative radius"); |
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so->otype = so->otype == OBJ_SPHERE ? |
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OBJ_BUBBLE : OBJ_SPHERE; |
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ap[3] = -ap[3]; |
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} else if (ap[3] <= FTINY) |
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objerror(so, USER, "zero radius"); |
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|
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/* |
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* We compute the intersection by substituting into |
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* the surface equation for the sphere. The resulting |
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* quadratic equation in t is then solved for the |
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* smallest positive root, which is our point of |
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* intersection. |
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* Since the ray is normalized, a should always be |
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* one. We compute it here to prevent instability in the |
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* intersection calculation. |
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*/ |
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/* compute quadratic coefficients */ |
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a = b = c = 0.0; |
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for (i = 0; i < 3; i++) { |
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a += r->rdir[i]*r->rdir[i]; |
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t = r->rorg[i] - ap[i]; |
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b += 2.0*r->rdir[i]*t; |
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c += t*t; |
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} |
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c -= ap[3] * ap[3]; |
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|
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nroots = quadratic(root, a, b, c); /* solve quadratic */ |
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|
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for (i = 0; i < nroots; i++) /* get smallest positive */ |
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if ((t = root[i]) > FTINY) |
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break; |
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if (i >= nroots) |
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return(0); /* no positive root */ |
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|
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if (t >= r->rot) |
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return(0); /* other is closer */ |
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|
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r->ro = so; |
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r->rot = t; |
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/* compute normal */ |
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a = ap[3]; |
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if (so->otype == OBJ_BUBBLE) |
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a = -a; /* reverse */ |
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for (i = 0; i < 3; i++) { |
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r->rop[i] = r->rorg[i] + r->rdir[i]*t; |
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r->ron[i] = (r->rop[i] - ap[i]) / a; |
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} |
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r->rod = -DOT(r->rdir, r->ron); |
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r->rox = NULL; |
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r->pert[0] = r->pert[1] = r->pert[2] = 0.0; |
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r->uv[0] = r->uv[1] = 0.0; |
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|
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return(1); /* hit */ |
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} |
