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#ifndef lint |
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static const char RCSid[] = "$Id: o_cone.c,v 2.11 2021/12/16 21:37:21 greg Exp $"; |
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#endif |
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/* |
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* o_cone.c - routine to determine ray intersection with cones. |
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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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#include "otypes.h" |
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#include "rtotypes.h" |
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#include "cone.h" |
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|
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|
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int |
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o_cone( /* intersect ray with cone */ |
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OBJREC *o, |
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RAY *r |
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) |
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{ |
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FVECT rox, rdx; |
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double a, b, c; |
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double root[2]; |
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int nroots, rn; |
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CONE *co; |
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int i; |
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|
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/* get cone structure */ |
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co = getcone(o, 1); |
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if (co == NULL) |
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objerror(o, INTERNAL, "unexpected illegal"); |
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|
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/* |
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* To intersect a ray with a cone, we transform the |
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* ray into the cone's normalized space. This greatly |
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* simplifies the computation. |
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* For a cone or cup, normalization results in the |
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* equation: |
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* |
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* x*x + y*y - z*z == 0 |
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* |
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* For a cylinder or tube, the normalized equation is: |
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* |
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* x*x + y*y - r*r == 0 |
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* |
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* A normalized ring obeys the following set of equations: |
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* |
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* z == 0 && |
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* x*x + y*y >= r0*r0 && |
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* x*x + y*y <= r1*r1 |
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*/ |
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|
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/* transform ray */ |
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multp3(rox, r->rorg, co->tm); |
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multv3(rdx, r->rdir, co->tm); |
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/* compute intersection */ |
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|
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if (o->otype == OBJ_CONE || o->otype == OBJ_CUP) { |
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|
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a = rdx[0]*rdx[0] + rdx[1]*rdx[1] - rdx[2]*rdx[2]; |
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b = 2.0*(rdx[0]*rox[0] + rdx[1]*rox[1] - rdx[2]*rox[2]); |
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c = rox[0]*rox[0] + rox[1]*rox[1] - rox[2]*rox[2]; |
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|
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} else if (o->otype == OBJ_CYLINDER || o->otype == OBJ_TUBE) { |
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|
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a = rdx[0]*rdx[0] + rdx[1]*rdx[1]; |
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b = 2.0*(rdx[0]*rox[0] + rdx[1]*rox[1]); |
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c = rox[0]*rox[0] + rox[1]*rox[1] - CO_R0(co)*CO_R0(co); |
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|
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} else { /* OBJ_RING */ |
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|
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if ((rdx[2] <= FTINY) & (rdx[2] >= -FTINY)) |
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return(0); /* parallel */ |
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root[0] = -rox[2]/rdx[2]; |
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if (rayreject(o, r, root[0], -rdx[2])) |
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return(0); /* have better */ |
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b = root[0]*rdx[0] + rox[0]; |
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c = root[0]*rdx[1] + rox[1]; |
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a = b*b + c*c; |
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if (a < CO_R0(co)*CO_R0(co) || a > CO_R1(co)*CO_R1(co)) |
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return(0); /* outside radii */ |
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r->ro = o; |
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r->rot = root[0]; |
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VSUM(r->rop, r->rorg, r->rdir, r->rot); |
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VCOPY(r->ron, co->ad); |
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r->rod = -rdx[2]; |
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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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r->rox = NULL; |
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return(1); /* good */ |
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} |
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/* roots for cone, cup, cyl., tube */ |
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nroots = quadratic(root, a, b, c); |
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|
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for (rn = 0; rn < nroots; rn++) { /* check real roots */ |
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if (root[rn] <= FTINY) |
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continue; /* too small */ |
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if (root[rn] > r->rot + FTINY) |
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break; /* too big */ |
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/* check endpoints */ |
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VSUM(rox, r->rorg, r->rdir, root[rn]); |
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VSUB(rdx, rox, CO_P0(co)); |
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b = DOT(rdx, co->ad); |
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if (b < 0.0) |
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continue; /* before p0 */ |
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if (b > co->al) |
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continue; /* after p1 */ |
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if (rayreject(o, r, root[rn], 0)) |
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break; /* previous hit better */ |
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r->ro = o; |
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r->rot = root[rn]; |
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VCOPY(r->rop, rox); |
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/* get normal */ |
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if (o->otype == OBJ_CYLINDER) |
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a = CO_R0(co); |
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else if (o->otype == OBJ_TUBE) |
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a = -CO_R0(co); |
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else { /* OBJ_CONE || OBJ_CUP */ |
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c = CO_R1(co) - CO_R0(co); |
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a = CO_R0(co) + b*c/co->al; |
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if (o->otype == OBJ_CUP) { |
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c = -c; |
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a = -a; |
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} |
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} |
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for (i = 0; i < 3; i++) |
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r->ron[i] = (rdx[i] - b*co->ad[i])/a; |
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if (o->otype == OBJ_CONE || o->otype == OBJ_CUP) |
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for (i = 0; i < 3; i++) |
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r->ron[i] = (co->al*r->ron[i] - c*co->ad[i]) |
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/ co->sl; |
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a = DOT(r->ron, r->ron); |
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if (a > 1.+FTINY || a < 1.-FTINY) { |
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c = 1./(.5 + .5*a); /* avoid numerical error */ |
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r->ron[0] *= c; r->ron[1] *= c; r->ron[2] *= c; |
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} |
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r->rod = -DOT(r->rdir, r->ron); |
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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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r->rox = NULL; |
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return(1); /* good */ |
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} |
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return(0); |
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} |
