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#ifndef lint
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static const char RCSid[] = "$Id: sphere.c,v 2.9 2021/01/31 18:08:04 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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#include "copyright.h"
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#include "ray.h"
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#include "otypes.h"
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#include "rtotypes.h"
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int
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o_sphere( /* compute intersection with sphere */
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OBJREC *so,
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RAY *r
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)
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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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RREAL *ap;
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int i;
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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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* 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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nroots = quadratic(root, a, b, c); /* solve quadratic */
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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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if (rayreject(so, r, t, 0))
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return(0); /* previous hit better */
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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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return(1); /* hit */
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}
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