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/* Copyright (c) 1998 Silicon Graphics, Inc. */ |
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|
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#ifndef lint |
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static char SCCSid[] = "$SunId$ SGI"; |
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#endif |
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|
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/* |
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* sm_geom.c |
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*/ |
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|
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#include "standard.h" |
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#include "sm_geom.h" |
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|
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tri_centroid(v0,v1,v2,c) |
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FVECT v0,v1,v2,c; |
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{ |
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/* Average three triangle vertices to give centroid: return in c */ |
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c[0] = (v0[0] + v1[0] + v2[0])/3.0; |
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c[1] = (v0[1] + v1[1] + v2[1])/3.0; |
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c[2] = (v0[2] + v1[2] + v2[2])/3.0; |
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} |
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|
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|
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int |
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vec3_equal(v1,v2) |
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FVECT v1,v2; |
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{ |
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return(EQUAL(v1[0],v2[0]) && EQUAL(v1[1],v2[1])&& EQUAL(v1[2],v2[2])); |
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} |
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#if 0 |
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extern FVECT Norm[500]; |
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extern int Ncnt; |
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#endif |
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|
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int |
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convex_angle(v0,v1,v2) |
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FVECT v0,v1,v2; |
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{ |
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FVECT cp,cp01,cp12,v10,v02; |
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double dp; |
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|
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/* test sign of (v0Xv1)X(v1Xv2). v1 */ |
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VCROSS(cp01,v0,v1); |
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VCROSS(cp12,v1,v2); |
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VCROSS(cp,cp01,cp12); |
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|
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dp = DOT(cp,v1); |
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#if 0 |
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VCOPY(Norm[Ncnt++],cp01); |
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VCOPY(Norm[Ncnt++],cp12); |
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VCOPY(Norm[Ncnt++],cp); |
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#endif |
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if(ZERO(dp) || dp < 0.0) |
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return(FALSE); |
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return(TRUE); |
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} |
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|
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/* calculates the normal of a face contour using Newell's formula. e |
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|
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a = SUMi (yi - yi+1)(zi + zi+1); |
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b = SUMi (zi - zi+1)(xi + xi+1) |
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c = SUMi (xi - xi+1)(yi + yi+1) |
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*/ |
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double |
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tri_normal(v0,v1,v2,n,norm) |
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FVECT v0,v1,v2,n; |
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int norm; |
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{ |
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double mag; |
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|
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n[0] = (v0[2] + v1[2]) * (v0[1] - v1[1]) + |
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(v1[2] + v2[2]) * (v1[1] - v2[1]) + |
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(v2[2] + v0[2]) * (v2[1] - v0[1]); |
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|
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n[1] = (v0[2] - v1[2]) * (v0[0] + v1[0]) + |
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(v1[2] - v2[2]) * (v1[0] + v2[0]) + |
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(v2[2] - v0[2]) * (v2[0] + v0[0]); |
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|
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n[2] = (v0[1] + v1[1]) * (v0[0] - v1[0]) + |
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(v1[1] + v2[1]) * (v1[0] - v2[0]) + |
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(v2[1] + v0[1]) * (v2[0] - v0[0]); |
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|
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if(!norm) |
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return(0); |
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|
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mag = normalize(n); |
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|
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return(mag); |
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} |
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|
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|
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tri_plane_equation(v0,v1,v2,peqptr,norm) |
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FVECT v0,v1,v2; |
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FPEQ *peqptr; |
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int norm; |
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{ |
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tri_normal(v0,v1,v2,FP_N(*peqptr),norm); |
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|
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FP_D(*peqptr) = -(DOT(FP_N(*peqptr),v0)); |
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} |
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|
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/* From quad_edge-code */ |
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int |
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point_in_circle_thru_origin(p,p0,p1) |
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FVECT p; |
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FVECT p0,p1; |
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{ |
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|
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double dp0,dp1; |
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double dp,det; |
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|
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dp0 = DOT_VEC2(p0,p0); |
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dp1 = DOT_VEC2(p1,p1); |
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dp = DOT_VEC2(p,p); |
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|
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det = -dp0*CROSS_VEC2(p1,p) + dp1*CROSS_VEC2(p0,p) - dp*CROSS_VEC2(p0,p1); |
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|
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return (det > (1e-10)); |
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} |
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|
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|
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double |
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point_on_sphere(ps,p,c) |
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FVECT ps,p,c; |
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{ |
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double d; |
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VSUB(ps,p,c); |
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d= normalize(ps); |
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return(d); |
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} |
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|
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|
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/* returns TRUE if ray from origin in direction v intersects plane defined |
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* by normal plane_n, and plane_d. If plane is not parallel- returns |
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* intersection point if r != NULL. If tptr!= NULL returns value of |
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* t, if parallel, returns t=FHUGE |
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*/ |
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int |
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intersect_vector_plane(v,peq,tptr,r) |
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FVECT v; |
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FPEQ peq; |
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double *tptr; |
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FVECT r; |
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{ |
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double t,d; |
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int hit; |
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/* |
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Plane is Ax + By + Cz +D = 0: |
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plane[0] = A,plane[1] = B,plane[2] = C,plane[3] = D |
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*/ |
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|
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/* line is l = p1 + (p2-p1)t, p1=origin */ |
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|
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/* Solve for t: */ |
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d = -(DOT(FP_N(peq),v)); |
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if(ZERO(d)) |
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{ |
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t = FHUGE; |
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hit = 0; |
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} |
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else |
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{ |
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t = FP_D(peq)/d; |
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if(t < 0 ) |
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hit = 0; |
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else |
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hit = 1; |
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if(r) |
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{ |
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r[0] = v[0]*t; |
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r[1] = v[1]*t; |
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r[2] = v[2]*t; |
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} |
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} |
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if(tptr) |
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*tptr = t; |
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return(hit); |
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} |
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|
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int |
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intersect_ray_plane(orig,dir,peq,pd,r) |
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FVECT orig,dir; |
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FPEQ peq; |
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double *pd; |
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FVECT r; |
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{ |
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double t,d; |
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int hit; |
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/* |
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Plane is Ax + By + Cz +D = 0: |
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plane[0] = A,plane[1] = B,plane[2] = C,plane[3] = D |
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*/ |
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/* A(orig[0] + dxt) + B(orig[1] + dyt) + C(orig[2] + dzt) + pd = 0 |
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t = -(DOT(plane_n,orig)+ plane_d)/(DOT(plane_n,d)) |
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line is l = p1 + (p2-p1)t |
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*/ |
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/* Solve for t: */ |
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d = DOT(FP_N(peq),dir); |
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if(ZERO(d)) |
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return(0); |
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t = -(DOT(FP_N(peq),orig) + FP_D(peq))/d; |
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|
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if(t < 0) |
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hit = 0; |
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else |
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hit = 1; |
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|
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if(r) |
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VSUM(r,orig,dir,t); |
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|
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if(pd) |
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*pd = t; |
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return(hit); |
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} |
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|
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|
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int |
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intersect_ray_oplane(orig,dir,n,pd,r) |
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FVECT orig,dir; |
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FVECT n; |
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double *pd; |
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FVECT r; |
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{ |
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double t,d; |
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int hit; |
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/* |
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Plane is Ax + By + Cz +D = 0: |
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plane[0] = A,plane[1] = B,plane[2] = C,plane[3] = D |
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*/ |
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/* A(orig[0] + dxt) + B(orig[1] + dyt) + C(orig[2] + dzt) + pd = 0 |
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t = -(DOT(plane_n,orig)+ plane_d)/(DOT(plane_n,d)) |
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line is l = p1 + (p2-p1)t |
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*/ |
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/* Solve for t: */ |
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d= DOT(n,dir); |
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if(ZERO(d)) |
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return(0); |
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t = -(DOT(n,orig))/d; |
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if(t < 0) |
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hit = 0; |
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else |
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hit = 1; |
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|
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if(r) |
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VSUM(r,orig,dir,t); |
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|
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if(pd) |
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*pd = t; |
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return(hit); |
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} |
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|
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/* Assumption: know crosses plane:dont need to check for 'on' case */ |
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intersect_edge_coord_plane(v0,v1,w,r) |
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FVECT v0,v1; |
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int w; |
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FVECT r; |
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{ |
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FVECT dv; |
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int wnext; |
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double t; |
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|
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VSUB(dv,v1,v0); |
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t = -v0[w]/dv[w]; |
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r[w] = 0.0; |
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wnext = (w+1)%3; |
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r[wnext] = v0[wnext] + dv[wnext]*t; |
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wnext = (w+2)%3; |
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r[wnext] = v0[wnext] + dv[wnext]*t; |
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} |
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|
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int |
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intersect_edge_plane(e0,e1,peq,pd,r) |
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FVECT e0,e1; |
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FPEQ peq; |
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double *pd; |
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FVECT r; |
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{ |
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double t; |
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int hit; |
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FVECT d; |
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/* |
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Plane is Ax + By + Cz +D = 0: |
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plane[0] = A,plane[1] = B,plane[2] = C,plane[3] = D |
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*/ |
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/* A(orig[0] + dxt) + B(orig[1] + dyt) + C(orig[2] + dzt) + pd = 0 |
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t = -(DOT(plane_n,orig)+ plane_d)/(DOT(plane_n,d)) |
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line is l = p1 + (p2-p1)t |
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*/ |
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/* Solve for t: */ |
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VSUB(d,e1,e0); |
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t = -(DOT(FP_N(peq),e0) + FP_D(peq))/(DOT(FP_N(peq),d)); |
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if(t < 0) |
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hit = 0; |
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else |
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hit = 1; |
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|
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VSUM(r,e0,d,t); |
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|
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if(pd) |
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*pd = t; |
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return(hit); |
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} |
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|
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|
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int |
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point_in_cone(p,p0,p1,p2) |
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FVECT p; |
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FVECT p0,p1,p2; |
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{ |
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FVECT np,x_axis,y_axis; |
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double d1,d2; |
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FPEQ peq; |
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|
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/* Find the equation of the circle defined by the intersection |
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of the cone with the plane defined by p1,p2,p3- project p into |
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that plane and do an in-circle test in the plane |
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*/ |
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|
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/* find the equation of the plane defined by p0-p2 */ |
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tri_plane_equation(p0,p1,p2,&peq,FALSE); |
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|
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/* define a coordinate system on the plane: the x axis is in |
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the direction of np2-np1, and the y axis is calculated from |
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n cross x-axis |
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*/ |
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/* Project p onto the plane */ |
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/* NOTE: check this: does sideness check?*/ |
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if(!intersect_vector_plane(p,peq,NULL,np)) |
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return(FALSE); |
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|
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/* create coordinate system on plane: p1-p0 defines the x_axis*/ |
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VSUB(x_axis,p1,p0); |
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normalize(x_axis); |
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/* The y axis is */ |
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VCROSS(y_axis,FP_N(peq),x_axis); |
336 |
normalize(y_axis); |
337 |
|
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VSUB(p1,p1,p0); |
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VSUB(p2,p2,p0); |
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VSUB(np,np,p0); |
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|
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p1[0] = DOT(p1,x_axis); |
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p1[1] = 0; |
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|
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d1 = DOT(p2,x_axis); |
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d2 = DOT(p2,y_axis); |
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p2[0] = d1; |
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p2[1] = d2; |
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|
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d1 = DOT(np,x_axis); |
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d2 = DOT(np,y_axis); |
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np[0] = d1; |
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np[1] = d2; |
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|
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/* perform the in-circle test in the new coordinate system */ |
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return(point_in_circle_thru_origin(np,p1,p2)); |
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} |
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|
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int |
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point_set_in_stri(v0,v1,v2,p,n,nset,sides) |
361 |
FVECT v0,v1,v2,p; |
362 |
FVECT n[3]; |
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int *nset; |
364 |
int sides[3]; |
365 |
|
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{ |
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double d; |
368 |
/* Find the normal to the triangle ORIGIN:v0:v1 */ |
369 |
if(!NTH_BIT(*nset,0)) |
370 |
{ |
371 |
VCROSS(n[0],v0,v1); |
372 |
SET_NTH_BIT(*nset,0); |
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} |
374 |
/* Test the point for sidedness */ |
375 |
d = DOT(n[0],p); |
376 |
|
377 |
if(d > 0.0) |
378 |
{ |
379 |
sides[0] = GT_OUT; |
380 |
sides[1] = sides[2] = GT_INVALID; |
381 |
return(FALSE); |
382 |
} |
383 |
else |
384 |
sides[0] = GT_INTERIOR; |
385 |
|
386 |
/* Test next edge */ |
387 |
if(!NTH_BIT(*nset,1)) |
388 |
{ |
389 |
VCROSS(n[1],v1,v2); |
390 |
SET_NTH_BIT(*nset,1); |
391 |
} |
392 |
/* Test the point for sidedness */ |
393 |
d = DOT(n[1],p); |
394 |
if(d > 0.0) |
395 |
{ |
396 |
sides[1] = GT_OUT; |
397 |
sides[2] = GT_INVALID; |
398 |
return(FALSE); |
399 |
} |
400 |
else |
401 |
sides[1] = GT_INTERIOR; |
402 |
/* Test next edge */ |
403 |
if(!NTH_BIT(*nset,2)) |
404 |
{ |
405 |
VCROSS(n[2],v2,v0); |
406 |
SET_NTH_BIT(*nset,2); |
407 |
} |
408 |
/* Test the point for sidedness */ |
409 |
d = DOT(n[2],p); |
410 |
if(d > 0.0) |
411 |
{ |
412 |
sides[2] = GT_OUT; |
413 |
return(FALSE); |
414 |
} |
415 |
else |
416 |
sides[2] = GT_INTERIOR; |
417 |
/* Must be interior to the pyramid */ |
418 |
return(GT_INTERIOR); |
419 |
} |
420 |
|
421 |
|
422 |
|
423 |
|
424 |
int |
425 |
point_in_stri(v0,v1,v2,p) |
426 |
FVECT v0,v1,v2,p; |
427 |
{ |
428 |
double d; |
429 |
FVECT n; |
430 |
|
431 |
VCROSS(n,v0,v1); |
432 |
/* Test the point for sidedness */ |
433 |
d = DOT(n,p); |
434 |
if(d > 0.0) |
435 |
return(FALSE); |
436 |
|
437 |
/* Test next edge */ |
438 |
VCROSS(n,v1,v2); |
439 |
/* Test the point for sidedness */ |
440 |
d = DOT(n,p); |
441 |
if(d > 0.0) |
442 |
return(FALSE); |
443 |
|
444 |
/* Test next edge */ |
445 |
VCROSS(n,v2,v0); |
446 |
/* Test the point for sidedness */ |
447 |
d = DOT(n,p); |
448 |
if(d > 0.0) |
449 |
return(FALSE); |
450 |
/* Must be interior to the pyramid */ |
451 |
return(GT_INTERIOR); |
452 |
} |
453 |
|
454 |
int |
455 |
vertices_in_stri(t0,t1,t2,p0,p1,p2,nset,n,avg,pt_sides) |
456 |
FVECT t0,t1,t2,p0,p1,p2; |
457 |
int *nset; |
458 |
FVECT n[3]; |
459 |
FVECT avg; |
460 |
int pt_sides[3][3]; |
461 |
|
462 |
{ |
463 |
int below_plane[3],test; |
464 |
|
465 |
SUM_3VEC3(avg,t0,t1,t2); |
466 |
*nset = 0; |
467 |
/* Test vertex v[i] against triangle j*/ |
468 |
/* Check if v[i] lies below plane defined by avg of 3 vectors |
469 |
defining triangle |
470 |
*/ |
471 |
|
472 |
/* test point 0 */ |
473 |
if(DOT(avg,p0) < 0.0) |
474 |
below_plane[0] = 1; |
475 |
else |
476 |
below_plane[0] = 0; |
477 |
/* Test if b[i] lies in or on triangle a */ |
478 |
test = point_set_in_stri(t0,t1,t2,p0,n,nset,pt_sides[0]); |
479 |
/* If pts[i] is interior: done */ |
480 |
if(!below_plane[0]) |
481 |
{ |
482 |
if(test == GT_INTERIOR) |
483 |
return(TRUE); |
484 |
} |
485 |
/* Now test point 1*/ |
486 |
|
487 |
if(DOT(avg,p1) < 0.0) |
488 |
below_plane[1] = 1; |
489 |
else |
490 |
below_plane[1]=0; |
491 |
/* Test if b[i] lies in or on triangle a */ |
492 |
test = point_set_in_stri(t0,t1,t2,p1,n,nset,pt_sides[1]); |
493 |
/* If pts[i] is interior: done */ |
494 |
if(!below_plane[1]) |
495 |
{ |
496 |
if(test == GT_INTERIOR) |
497 |
return(TRUE); |
498 |
} |
499 |
|
500 |
/* Now test point 2 */ |
501 |
if(DOT(avg,p2) < 0.0) |
502 |
below_plane[2] = 1; |
503 |
else |
504 |
below_plane[2] = 0; |
505 |
/* Test if b[i] lies in or on triangle a */ |
506 |
test = point_set_in_stri(t0,t1,t2,p2,n,nset,pt_sides[2]); |
507 |
|
508 |
/* If pts[i] is interior: done */ |
509 |
if(!below_plane[2]) |
510 |
{ |
511 |
if(test == GT_INTERIOR) |
512 |
return(TRUE); |
513 |
} |
514 |
|
515 |
/* If all three points below separating plane: trivial reject */ |
516 |
if(below_plane[0] && below_plane[1] && below_plane[2]) |
517 |
return(FALSE); |
518 |
/* Now check vertices in a against triangle b */ |
519 |
return(FALSE); |
520 |
} |
521 |
|
522 |
|
523 |
set_sidedness_tests(t0,t1,t2,p0,p1,p2,test,sides,nset,n) |
524 |
FVECT t0,t1,t2,p0,p1,p2; |
525 |
int test[3]; |
526 |
int sides[3][3]; |
527 |
int nset; |
528 |
FVECT n[3]; |
529 |
{ |
530 |
int t; |
531 |
double d; |
532 |
|
533 |
|
534 |
/* p=0 */ |
535 |
test[0] = 0; |
536 |
if(sides[0][0] == GT_INVALID) |
537 |
{ |
538 |
if(!NTH_BIT(nset,0)) |
539 |
VCROSS(n[0],t0,t1); |
540 |
/* Test the point for sidedness */ |
541 |
d = DOT(n[0],p0); |
542 |
if(d >= 0.0) |
543 |
SET_NTH_BIT(test[0],0); |
544 |
} |
545 |
else |
546 |
if(sides[0][0] != GT_INTERIOR) |
547 |
SET_NTH_BIT(test[0],0); |
548 |
|
549 |
if(sides[0][1] == GT_INVALID) |
550 |
{ |
551 |
if(!NTH_BIT(nset,1)) |
552 |
VCROSS(n[1],t1,t2); |
553 |
/* Test the point for sidedness */ |
554 |
d = DOT(n[1],p0); |
555 |
if(d >= 0.0) |
556 |
SET_NTH_BIT(test[0],1); |
557 |
} |
558 |
else |
559 |
if(sides[0][1] != GT_INTERIOR) |
560 |
SET_NTH_BIT(test[0],1); |
561 |
|
562 |
if(sides[0][2] == GT_INVALID) |
563 |
{ |
564 |
if(!NTH_BIT(nset,2)) |
565 |
VCROSS(n[2],t2,t0); |
566 |
/* Test the point for sidedness */ |
567 |
d = DOT(n[2],p0); |
568 |
if(d >= 0.0) |
569 |
SET_NTH_BIT(test[0],2); |
570 |
} |
571 |
else |
572 |
if(sides[0][2] != GT_INTERIOR) |
573 |
SET_NTH_BIT(test[0],2); |
574 |
|
575 |
/* p=1 */ |
576 |
test[1] = 0; |
577 |
/* t=0*/ |
578 |
if(sides[1][0] == GT_INVALID) |
579 |
{ |
580 |
if(!NTH_BIT(nset,0)) |
581 |
VCROSS(n[0],t0,t1); |
582 |
/* Test the point for sidedness */ |
583 |
d = DOT(n[0],p1); |
584 |
if(d >= 0.0) |
585 |
SET_NTH_BIT(test[1],0); |
586 |
} |
587 |
else |
588 |
if(sides[1][0] != GT_INTERIOR) |
589 |
SET_NTH_BIT(test[1],0); |
590 |
|
591 |
/* t=1 */ |
592 |
if(sides[1][1] == GT_INVALID) |
593 |
{ |
594 |
if(!NTH_BIT(nset,1)) |
595 |
VCROSS(n[1],t1,t2); |
596 |
/* Test the point for sidedness */ |
597 |
d = DOT(n[1],p1); |
598 |
if(d >= 0.0) |
599 |
SET_NTH_BIT(test[1],1); |
600 |
} |
601 |
else |
602 |
if(sides[1][1] != GT_INTERIOR) |
603 |
SET_NTH_BIT(test[1],1); |
604 |
|
605 |
/* t=2 */ |
606 |
if(sides[1][2] == GT_INVALID) |
607 |
{ |
608 |
if(!NTH_BIT(nset,2)) |
609 |
VCROSS(n[2],t2,t0); |
610 |
/* Test the point for sidedness */ |
611 |
d = DOT(n[2],p1); |
612 |
if(d >= 0.0) |
613 |
SET_NTH_BIT(test[1],2); |
614 |
} |
615 |
else |
616 |
if(sides[1][2] != GT_INTERIOR) |
617 |
SET_NTH_BIT(test[1],2); |
618 |
|
619 |
/* p=2 */ |
620 |
test[2] = 0; |
621 |
/* t = 0 */ |
622 |
if(sides[2][0] == GT_INVALID) |
623 |
{ |
624 |
if(!NTH_BIT(nset,0)) |
625 |
VCROSS(n[0],t0,t1); |
626 |
/* Test the point for sidedness */ |
627 |
d = DOT(n[0],p2); |
628 |
if(d >= 0.0) |
629 |
SET_NTH_BIT(test[2],0); |
630 |
} |
631 |
else |
632 |
if(sides[2][0] != GT_INTERIOR) |
633 |
SET_NTH_BIT(test[2],0); |
634 |
/* t=1 */ |
635 |
if(sides[2][1] == GT_INVALID) |
636 |
{ |
637 |
if(!NTH_BIT(nset,1)) |
638 |
VCROSS(n[1],t1,t2); |
639 |
/* Test the point for sidedness */ |
640 |
d = DOT(n[1],p2); |
641 |
if(d >= 0.0) |
642 |
SET_NTH_BIT(test[2],1); |
643 |
} |
644 |
else |
645 |
if(sides[2][1] != GT_INTERIOR) |
646 |
SET_NTH_BIT(test[2],1); |
647 |
/* t=2 */ |
648 |
if(sides[2][2] == GT_INVALID) |
649 |
{ |
650 |
if(!NTH_BIT(nset,2)) |
651 |
VCROSS(n[2],t2,t0); |
652 |
/* Test the point for sidedness */ |
653 |
d = DOT(n[2],p2); |
654 |
if(d >= 0.0) |
655 |
SET_NTH_BIT(test[2],2); |
656 |
} |
657 |
else |
658 |
if(sides[2][2] != GT_INTERIOR) |
659 |
SET_NTH_BIT(test[2],2); |
660 |
} |
661 |
|
662 |
|
663 |
int |
664 |
stri_intersect(a1,a2,a3,b1,b2,b3) |
665 |
FVECT a1,a2,a3,b1,b2,b3; |
666 |
{ |
667 |
int which,test,n_set[2]; |
668 |
int sides[2][3][3],i,j,inext,jnext; |
669 |
int tests[2][3]; |
670 |
FVECT n[2][3],p,avg[2],t1,t2,t3; |
671 |
|
672 |
#ifdef DEBUG |
673 |
tri_normal(b1,b2,b3,p,FALSE); |
674 |
if(DOT(p,b1) > 0) |
675 |
{ |
676 |
VCOPY(t3,b1); |
677 |
VCOPY(t2,b2); |
678 |
VCOPY(t1,b3); |
679 |
} |
680 |
else |
681 |
#endif |
682 |
{ |
683 |
VCOPY(t1,b1); |
684 |
VCOPY(t2,b2); |
685 |
VCOPY(t3,b3); |
686 |
} |
687 |
|
688 |
/* Test the vertices of triangle a against the pyramid formed by triangle |
689 |
b and the origin. If any vertex of a is interior to triangle b, or |
690 |
if all 3 vertices of a are ON the edges of b,return TRUE. Remember |
691 |
the results of the edge normal and sidedness tests for later. |
692 |
*/ |
693 |
if(vertices_in_stri(a1,a2,a3,t1,t2,t3,&(n_set[0]),n[0],avg[0],sides[1])) |
694 |
return(TRUE); |
695 |
|
696 |
if(vertices_in_stri(t1,t2,t3,a1,a2,a3,&(n_set[1]),n[1],avg[1],sides[0])) |
697 |
return(TRUE); |
698 |
|
699 |
|
700 |
set_sidedness_tests(t1,t2,t3,a1,a2,a3,tests[0],sides[0],n_set[1],n[1]); |
701 |
if(tests[0][0]&tests[0][1]&tests[0][2]) |
702 |
return(FALSE); |
703 |
|
704 |
set_sidedness_tests(a1,a2,a3,t1,t2,t3,tests[1],sides[1],n_set[0],n[0]); |
705 |
if(tests[1][0]&tests[1][1]&tests[1][2]) |
706 |
return(FALSE); |
707 |
|
708 |
for(j=0; j < 3;j++) |
709 |
{ |
710 |
jnext = (j+1)%3; |
711 |
/* IF edge b doesnt cross any great circles of a, punt */ |
712 |
if(tests[1][j] & tests[1][jnext]) |
713 |
continue; |
714 |
for(i=0;i<3;i++) |
715 |
{ |
716 |
inext = (i+1)%3; |
717 |
/* IF edge a doesnt cross any great circles of b, punt */ |
718 |
if(tests[0][i] & tests[0][inext]) |
719 |
continue; |
720 |
/* Now find the great circles that cross and test */ |
721 |
if((NTH_BIT(tests[0][i],j)^(NTH_BIT(tests[0][inext],j))) |
722 |
&& (NTH_BIT(tests[1][j],i)^NTH_BIT(tests[1][jnext],i))) |
723 |
{ |
724 |
VCROSS(p,n[0][i],n[1][j]); |
725 |
|
726 |
/* If zero cp= done */ |
727 |
if(ZERO_VEC3(p)) |
728 |
continue; |
729 |
/* check above both planes */ |
730 |
if(DOT(avg[0],p) < 0 || DOT(avg[1],p) < 0) |
731 |
{ |
732 |
NEGATE_VEC3(p); |
733 |
if(DOT(avg[0],p) < 0 || DOT(avg[1],p) < 0) |
734 |
continue; |
735 |
} |
736 |
return(TRUE); |
737 |
} |
738 |
} |
739 |
} |
740 |
return(FALSE); |
741 |
} |
742 |
|
743 |
int |
744 |
ray_intersect_tri(orig,dir,v0,v1,v2,pt) |
745 |
FVECT orig,dir; |
746 |
FVECT v0,v1,v2; |
747 |
FVECT pt; |
748 |
{ |
749 |
FVECT p0,p1,p2,p; |
750 |
FPEQ peq; |
751 |
int type; |
752 |
|
753 |
VSUB(p0,v0,orig); |
754 |
VSUB(p1,v1,orig); |
755 |
VSUB(p2,v2,orig); |
756 |
|
757 |
if(point_in_stri(p0,p1,p2,dir)) |
758 |
{ |
759 |
/* Intersect the ray with the triangle plane */ |
760 |
tri_plane_equation(v0,v1,v2,&peq,FALSE); |
761 |
return(intersect_ray_plane(orig,dir,peq,NULL,pt)); |
762 |
} |
763 |
return(FALSE); |
764 |
} |
765 |
|
766 |
|
767 |
calculate_view_frustum(vp,hv,vv,horiz,vert,near,far,fnear,ffar) |
768 |
FVECT vp,hv,vv; |
769 |
double horiz,vert,near,far; |
770 |
FVECT fnear[4],ffar[4]; |
771 |
{ |
772 |
double height,width; |
773 |
FVECT t,nhv,nvv,ndv; |
774 |
double w2,h2; |
775 |
/* Calculate the x and y dimensions of the near face */ |
776 |
/* hv and vv are the horizontal and vertical vectors in the |
777 |
view frame-the magnitude is the dimension of the front frustum |
778 |
face at z =1 |
779 |
*/ |
780 |
VCOPY(nhv,hv); |
781 |
VCOPY(nvv,vv); |
782 |
w2 = normalize(nhv); |
783 |
h2 = normalize(nvv); |
784 |
/* Use similar triangles to calculate the dimensions at z=near */ |
785 |
width = near*0.5*w2; |
786 |
height = near*0.5*h2; |
787 |
|
788 |
VCROSS(ndv,nvv,nhv); |
789 |
/* Calculate the world space points corresponding to the 4 corners |
790 |
of the front face of the view frustum |
791 |
*/ |
792 |
fnear[0][0] = width*nhv[0] + height*nvv[0] + near*ndv[0] + vp[0] ; |
793 |
fnear[0][1] = width*nhv[1] + height*nvv[1] + near*ndv[1] + vp[1]; |
794 |
fnear[0][2] = width*nhv[2] + height*nvv[2] + near*ndv[2] + vp[2]; |
795 |
fnear[1][0] = -width*nhv[0] + height*nvv[0] + near*ndv[0] + vp[0]; |
796 |
fnear[1][1] = -width*nhv[1] + height*nvv[1] + near*ndv[1] + vp[1]; |
797 |
fnear[1][2] = -width*nhv[2] + height*nvv[2] + near*ndv[2] + vp[2]; |
798 |
fnear[2][0] = -width*nhv[0] - height*nvv[0] + near*ndv[0] + vp[0]; |
799 |
fnear[2][1] = -width*nhv[1] - height*nvv[1] + near*ndv[1] + vp[1]; |
800 |
fnear[2][2] = -width*nhv[2] - height*nvv[2] + near*ndv[2] + vp[2]; |
801 |
fnear[3][0] = width*nhv[0] - height*nvv[0] + near*ndv[0] + vp[0]; |
802 |
fnear[3][1] = width*nhv[1] - height*nvv[1] + near*ndv[1] + vp[1]; |
803 |
fnear[3][2] = width*nhv[2] - height*nvv[2] + near*ndv[2] + vp[2]; |
804 |
|
805 |
/* Now do the far face */ |
806 |
width = far*0.5*w2; |
807 |
height = far*0.5*h2; |
808 |
ffar[0][0] = width*nhv[0] + height*nvv[0] + far*ndv[0] + vp[0] ; |
809 |
ffar[0][1] = width*nhv[1] + height*nvv[1] + far*ndv[1] + vp[1] ; |
810 |
ffar[0][2] = width*nhv[2] + height*nvv[2] + far*ndv[2] + vp[2] ; |
811 |
ffar[1][0] = -width*nhv[0] + height*nvv[0] + far*ndv[0] + vp[0] ; |
812 |
ffar[1][1] = -width*nhv[1] + height*nvv[1] + far*ndv[1] + vp[1] ; |
813 |
ffar[1][2] = -width*nhv[2] + height*nvv[2] + far*ndv[2] + vp[2] ; |
814 |
ffar[2][0] = -width*nhv[0] - height*nvv[0] + far*ndv[0] + vp[0] ; |
815 |
ffar[2][1] = -width*nhv[1] - height*nvv[1] + far*ndv[1] + vp[1] ; |
816 |
ffar[2][2] = -width*nhv[2] - height*nvv[2] + far*ndv[2] + vp[2] ; |
817 |
ffar[3][0] = width*nhv[0] - height*nvv[0] + far*ndv[0] + vp[0] ; |
818 |
ffar[3][1] = width*nhv[1] - height*nvv[1] + far*ndv[1] + vp[1] ; |
819 |
ffar[3][2] = width*nhv[2] - height*nvv[2] + far*ndv[2] + vp[2] ; |
820 |
} |
821 |
|
822 |
int |
823 |
max_index(v,r) |
824 |
FVECT v; |
825 |
double *r; |
826 |
{ |
827 |
double p[3]; |
828 |
int i; |
829 |
|
830 |
p[0] = fabs(v[0]); |
831 |
p[1] = fabs(v[1]); |
832 |
p[2] = fabs(v[2]); |
833 |
i = (p[0]>=p[1])?((p[0]>=p[2])?0:2):((p[1]>=p[2])?1:2); |
834 |
if(r) |
835 |
*r = p[i]; |
836 |
return(i); |
837 |
} |
838 |
|
839 |
int |
840 |
closest_point_in_tri(p0,p1,p2,p,p0id,p1id,p2id) |
841 |
FVECT p0,p1,p2,p; |
842 |
int p0id,p1id,p2id; |
843 |
{ |
844 |
double d,d1; |
845 |
int i; |
846 |
|
847 |
d = DIST_SQ(p,p0); |
848 |
d1 = DIST_SQ(p,p1); |
849 |
if(d < d1) |
850 |
{ |
851 |
d1 = DIST_SQ(p,p2); |
852 |
i = (d1 < d)?p2id:p0id; |
853 |
} |
854 |
else |
855 |
{ |
856 |
d = DIST_SQ(p,p2); |
857 |
i = (d < d1)? p2id:p1id; |
858 |
} |
859 |
return(i); |
860 |
} |
861 |
|
862 |
|
863 |
int |
864 |
sedge_intersect(a0,a1,b0,b1) |
865 |
FVECT a0,a1,b0,b1; |
866 |
{ |
867 |
FVECT na,nb,avga,avgb,p; |
868 |
double d; |
869 |
int sb0,sb1,sa0,sa1; |
870 |
|
871 |
/* First test if edge b straddles great circle of a */ |
872 |
VCROSS(na,a0,a1); |
873 |
d = DOT(na,b0); |
874 |
sb0 = ZERO(d)?0:(d<0)? -1: 1; |
875 |
d = DOT(na,b1); |
876 |
sb1 = ZERO(d)?0:(d<0)? -1: 1; |
877 |
/* edge b entirely on one side of great circle a: edges cannot intersect*/ |
878 |
if(sb0*sb1 > 0) |
879 |
return(FALSE); |
880 |
/* test if edge a straddles great circle of b */ |
881 |
VCROSS(nb,b0,b1); |
882 |
d = DOT(nb,a0); |
883 |
sa0 = ZERO(d)?0:(d<0)? -1: 1; |
884 |
d = DOT(nb,a1); |
885 |
sa1 = ZERO(d)?0:(d<0)? -1: 1; |
886 |
/* edge a entirely on one side of great circle b: edges cannot intersect*/ |
887 |
if(sa0*sa1 > 0) |
888 |
return(FALSE); |
889 |
|
890 |
/* Find one of intersection points of the great circles */ |
891 |
VCROSS(p,na,nb); |
892 |
/* If they lie on same great circle: call an intersection */ |
893 |
if(ZERO_VEC3(p)) |
894 |
return(TRUE); |
895 |
|
896 |
VADD(avga,a0,a1); |
897 |
VADD(avgb,b0,b1); |
898 |
if(DOT(avga,p) < 0 || DOT(avgb,p) < 0) |
899 |
{ |
900 |
NEGATE_VEC3(p); |
901 |
if(DOT(avga,p) < 0 || DOT(avgb,p) < 0) |
902 |
return(FALSE); |
903 |
} |
904 |
if((!sb0 || !sb1) && (!sa0 || !sa1)) |
905 |
return(FALSE); |
906 |
return(TRUE); |
907 |
} |
908 |
|
909 |
|
910 |
/* Find the normalized barycentric coordinates of p relative to |
911 |
* triangle v0,v1,v2. Return result in coord |
912 |
*/ |
913 |
bary2d(x1,y1,x2,y2,x3,y3,px,py,coord) |
914 |
double x1,y1,x2,y2,x3,y3; |
915 |
double px,py; |
916 |
double coord[3]; |
917 |
{ |
918 |
double a; |
919 |
|
920 |
a = (x2 - x1) * (y3 - y1) - (x3 - x1) * (y2 - y1); |
921 |
coord[0] = ((x2 - px) * (y3 - py) - (x3 - px) * (y2 - py)) / a; |
922 |
coord[1] = ((x3 - px) * (y1 - py) - (x1 - px) * (y3 - py)) / a; |
923 |
coord[2] = ((x1 - px) * (y2 - py) - (x2 - px) * (y1 - py)) / a; |
924 |
|
925 |
} |
926 |
|
927 |
|
928 |
|
929 |
|
930 |
bary_parent(coord,i) |
931 |
BCOORD coord[3]; |
932 |
int i; |
933 |
{ |
934 |
switch(i) { |
935 |
case 0: |
936 |
/* update bary for child */ |
937 |
coord[0] = (coord[0] >> 1) + MAXBCOORD4; |
938 |
coord[1] >>= 1; |
939 |
coord[2] >>= 1; |
940 |
break; |
941 |
case 1: |
942 |
coord[0] >>= 1; |
943 |
coord[1] = (coord[1] >> 1) + MAXBCOORD4; |
944 |
coord[2] >>= 1; |
945 |
break; |
946 |
|
947 |
case 2: |
948 |
coord[0] >>= 1; |
949 |
coord[1] >>= 1; |
950 |
coord[2] = (coord[2] >> 1) + MAXBCOORD4; |
951 |
break; |
952 |
|
953 |
case 3: |
954 |
coord[0] = MAXBCOORD4 - (coord[0] >> 1); |
955 |
coord[1] = MAXBCOORD4 - (coord[1] >> 1); |
956 |
coord[2] = MAXBCOORD4 - (coord[2] >> 1); |
957 |
break; |
958 |
#ifdef DEBUG |
959 |
default: |
960 |
eputs("bary_parent():Invalid child\n"); |
961 |
break; |
962 |
#endif |
963 |
} |
964 |
} |
965 |
|
966 |
bary_from_child(coord,child,next) |
967 |
BCOORD coord[3]; |
968 |
int child,next; |
969 |
{ |
970 |
#ifdef DEBUG |
971 |
if(child <0 || child > 3) |
972 |
{ |
973 |
eputs("bary_from_child():Invalid child\n"); |
974 |
return; |
975 |
} |
976 |
if(next <0 || next > 3) |
977 |
{ |
978 |
eputs("bary_from_child():Invalid next\n"); |
979 |
return; |
980 |
} |
981 |
#endif |
982 |
if(next == child) |
983 |
return; |
984 |
|
985 |
switch(child){ |
986 |
case 0: |
987 |
coord[0] = 0; |
988 |
coord[1] = MAXBCOORD2 - coord[1]; |
989 |
coord[2] = MAXBCOORD2 - coord[2]; |
990 |
break; |
991 |
case 1: |
992 |
coord[0] = MAXBCOORD2 - coord[0]; |
993 |
coord[1] = 0; |
994 |
coord[2] = MAXBCOORD2 - coord[2]; |
995 |
break; |
996 |
case 2: |
997 |
coord[0] = MAXBCOORD2 - coord[0]; |
998 |
coord[1] = MAXBCOORD2 - coord[1]; |
999 |
coord[2] = 0; |
1000 |
break; |
1001 |
case 3: |
1002 |
switch(next){ |
1003 |
case 0: |
1004 |
coord[0] = 0; |
1005 |
coord[1] = MAXBCOORD2 - coord[1]; |
1006 |
coord[2] = MAXBCOORD2 - coord[2]; |
1007 |
break; |
1008 |
case 1: |
1009 |
coord[0] = MAXBCOORD2 - coord[0]; |
1010 |
coord[1] = 0; |
1011 |
coord[2] = MAXBCOORD2 - coord[2]; |
1012 |
break; |
1013 |
case 2: |
1014 |
coord[0] = MAXBCOORD2 - coord[0]; |
1015 |
coord[1] = MAXBCOORD2 - coord[1]; |
1016 |
coord[2] = 0; |
1017 |
break; |
1018 |
} |
1019 |
break; |
1020 |
} |
1021 |
} |
1022 |
|
1023 |
int |
1024 |
bary_child(coord) |
1025 |
BCOORD coord[3]; |
1026 |
{ |
1027 |
int i; |
1028 |
|
1029 |
if(coord[0] > MAXBCOORD4) |
1030 |
{ |
1031 |
/* update bary for child */ |
1032 |
coord[0] = (coord[0]<< 1) - MAXBCOORD2; |
1033 |
coord[1] <<= 1; |
1034 |
coord[2] <<= 1; |
1035 |
return(0); |
1036 |
} |
1037 |
else |
1038 |
if(coord[1] > MAXBCOORD4) |
1039 |
{ |
1040 |
coord[0] <<= 1; |
1041 |
coord[1] = (coord[1] << 1) - MAXBCOORD2; |
1042 |
coord[2] <<= 1; |
1043 |
return(1); |
1044 |
} |
1045 |
else |
1046 |
if(coord[2] > MAXBCOORD4) |
1047 |
{ |
1048 |
coord[0] <<= 1; |
1049 |
coord[1] <<= 1; |
1050 |
coord[2] = (coord[2] << 1) - MAXBCOORD2; |
1051 |
return(2); |
1052 |
} |
1053 |
else |
1054 |
{ |
1055 |
coord[0] = MAXBCOORD2 - (coord[0] << 1); |
1056 |
coord[1] = MAXBCOORD2 - (coord[1] << 1); |
1057 |
coord[2] = MAXBCOORD2 - (coord[2] << 1); |
1058 |
return(3); |
1059 |
} |
1060 |
} |
1061 |
|
1062 |
int |
1063 |
bary_nth_child(coord,i) |
1064 |
BCOORD coord[3]; |
1065 |
int i; |
1066 |
{ |
1067 |
|
1068 |
switch(i){ |
1069 |
case 0: |
1070 |
/* update bary for child */ |
1071 |
coord[0] = (coord[0]<< 1) - MAXBCOORD2; |
1072 |
coord[1] <<= 1; |
1073 |
coord[2] <<= 1; |
1074 |
break; |
1075 |
case 1: |
1076 |
coord[0] <<= 1; |
1077 |
coord[1] = (coord[1] << 1) - MAXBCOORD2; |
1078 |
coord[2] <<= 1; |
1079 |
break; |
1080 |
case 2: |
1081 |
coord[0] <<= 1; |
1082 |
coord[1] <<= 1; |
1083 |
coord[2] = (coord[2] << 1) - MAXBCOORD2; |
1084 |
break; |
1085 |
case 3: |
1086 |
coord[0] = MAXBCOORD2 - (coord[0] << 1); |
1087 |
coord[1] = MAXBCOORD2 - (coord[1] << 1); |
1088 |
coord[2] = MAXBCOORD2 - (coord[2] << 1); |
1089 |
break; |
1090 |
} |
1091 |
} |
1092 |
|
1093 |
|
1094 |
|