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RadiancePmap/o_cone.c
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o_cone.c
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#ifndef lint
static const char RCSid[] = "$Id: o_cone.c,v 2.10 2021/01/31 18:08:04 greg Exp $";
#endif
/*
* o_cone.c - routine to determine ray intersection with cones.
*/
#include "copyright.h"
#include "ray.h"
#include "otypes.h"
#include "rtotypes.h"
#include "cone.h"
int
o_cone( /* intersect ray with cone */
OBJREC *o,
RAY *r
)
{
FVECT rox, rdx;
double a, b, c;
double root[2];
int nroots, rn;
CONE *co;
int i;
/* get cone structure */
co = getcone(o, 1);
if (co == NULL)
objerror(o, INTERNAL, "unexpected illegal");
/*
* To intersect a ray with a cone, we transform the
* ray into the cone's normalized space. This greatly
* simplifies the computation.
* For a cone or cup, normalization results in the
* equation:
*
* x*x + y*y - z*z == 0
*
* For a cylinder or tube, the normalized equation is:
*
* x*x + y*y - r*r == 0
*
* A normalized ring obeys the following set of equations:
*
* z == 0 &&
* x*x + y*y >= r0*r0 &&
* x*x + y*y <= r1*r1
*/
/* transform ray */
multp3(rox, r->rorg, co->tm);
multv3(rdx, r->rdir, co->tm);
/* compute intersection */
if (o->otype == OBJ_CONE || o->otype == OBJ_CUP) {
a = rdx[0]*rdx[0] + rdx[1]*rdx[1] - rdx[2]*rdx[2];
b = 2.0*(rdx[0]*rox[0] + rdx[1]*rox[1] - rdx[2]*rox[2]);
c = rox[0]*rox[0] + rox[1]*rox[1] - rox[2]*rox[2];
} else if (o->otype == OBJ_CYLINDER || o->otype == OBJ_TUBE) {
a = rdx[0]*rdx[0] + rdx[1]*rdx[1];
b = 2.0*(rdx[0]*rox[0] + rdx[1]*rox[1]);
c = rox[0]*rox[0] + rox[1]*rox[1] - CO_R0(co)*CO_R0(co);
} else { /* OBJ_RING */
if ((rdx[2] <= FTINY) & (rdx[2] >= -FTINY))
return(0); /* parallel */
root[0] = -rox[2]/rdx[2];
if (rayreject(o, r, root[0]))
return(0); /* have better */
b = root[0]*rdx[0] + rox[0];
c = root[0]*rdx[1] + rox[1];
a = b*b + c*c;
if (a < CO_R0(co)*CO_R0(co) || a > CO_R1(co)*CO_R1(co))
return(0); /* outside radii */
r->ro = o;
r->rot = root[0];
VSUM(r->rop, r->rorg, r->rdir, r->rot);
VCOPY(r->ron, co->ad);
r->rod = -rdx[2];
r->rox = NULL;
return(1); /* good */
}
/* roots for cone, cup, cyl., tube */
nroots = quadratic(root, a, b, c);
for (rn = 0; rn < nroots; rn++) { /* check real roots */
if (root[rn] <= FTINY)
continue; /* too small */
if (root[rn] > r->rot + FTINY)
break; /* too big */
/* check endpoints */
VSUM(rox, r->rorg, r->rdir, root[rn]);
VSUB(rdx, rox, CO_P0(co));
b = DOT(rdx, co->ad);
if (b < 0.0)
continue; /* before p0 */
if (b > co->al)
continue; /* after p1 */
if (rayreject(o, r, root[rn]))
break; /* previous hit better */
r->ro = o;
r->rot = root[rn];
VCOPY(r->rop, rox);
/* get normal */
if (o->otype == OBJ_CYLINDER)
a = CO_R0(co);
else if (o->otype == OBJ_TUBE)
a = -CO_R0(co);
else { /* OBJ_CONE || OBJ_CUP */
c = CO_R1(co) - CO_R0(co);
a = CO_R0(co) + b*c/co->al;
if (o->otype == OBJ_CUP) {
c = -c;
a = -a;
}
}
for (i = 0; i < 3; i++)
r->ron[i] = (rdx[i] - b*co->ad[i])/a;
if (o->otype == OBJ_CONE || o->otype == OBJ_CUP)
for (i = 0; i < 3; i++)
r->ron[i] = (co->al*r->ron[i] - c*co->ad[i])
/ co->sl;
a = DOT(r->ron, r->ron);
if (a > 1.+FTINY || a < 1.-FTINY) {
c = 1./(.5 + .5*a); /* avoid numerical error */
r->ron[0] *= c; r->ron[1] *= c; r->ron[2] *= c;
}
r->rod = -DOT(r->rdir, r->ron);
r->pert[0] = r->pert[1] = r->pert[2] = 0.0;
r->uv[0] = r->uv[1] = 0.0;
r->rox = NULL;
return(1); /* good */
}
return(0);
}
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