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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; |
16 |
{ |
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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])); |
29 |
} |
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|
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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 cp01,cp12,cp; |
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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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if(DOT(cp,v1) < 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 |
54 |
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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|
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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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|
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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,n,nd,norm) |
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FVECT v0,v1,v2,n; |
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double *nd; |
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int norm; |
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{ |
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tri_normal(v0,v1,v2,n,norm); |
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|
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*nd = -(DOT(n,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 > 0); |
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} |
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|
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|
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|
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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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VSUB(ps,p,c); |
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normalize(ps); |
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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,plane_n,plane_d,tptr,r) |
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FVECT v,plane_n; |
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double plane_d; |
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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(plane_n,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 = plane_d/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,plane_n,plane_d,pd,r) |
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FVECT orig,dir; |
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FVECT plane_n; |
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double plane_d; |
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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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/* |
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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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t = -(DOT(plane_n,orig) + plane_d)/(DOT(plane_n,dir)); |
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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_edge_plane(e0,e1,plane_n,plane_d,pd,r) |
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FVECT e0,e1; |
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FVECT plane_n; |
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double plane_d; |
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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(plane_n,e0) + plane_d)/(DOT(plane_n,d)); |
225 |
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 n; |
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FVECT np,x_axis,y_axis; |
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double d1,d2,d; |
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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 p1-p3 */ |
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tri_plane_equation(p0,p1,p2,n,&d,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,n,d,NULL,np)) |
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return(FALSE); |
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|
264 |
/* create coordinate system on plane: p2-p1 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,n,x_axis); |
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normalize(y_axis); |
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|
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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] = VLEN(p1); |
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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) |
294 |
FVECT v0,v1,v2,p; |
295 |
FVECT n[3]; |
296 |
int *nset; |
297 |
int sides[3]; |
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|
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{ |
300 |
double d; |
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/* Find the normal to the triangle ORIGIN:v0:v1 */ |
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if(!NTH_BIT(*nset,0)) |
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{ |
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VCROSS(n[0],v1,v0); |
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SET_NTH_BIT(*nset,0); |
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} |
307 |
/* Test the point for sidedness */ |
308 |
d = DOT(n[0],p); |
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|
310 |
if(d > 0.0) |
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{ |
312 |
sides[0] = GT_OUT; |
313 |
sides[1] = sides[2] = GT_INVALID; |
314 |
return(FALSE); |
315 |
} |
316 |
else |
317 |
sides[0] = GT_INTERIOR; |
318 |
|
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/* Test next edge */ |
320 |
if(!NTH_BIT(*nset,1)) |
321 |
{ |
322 |
VCROSS(n[1],v2,v1); |
323 |
SET_NTH_BIT(*nset,1); |
324 |
} |
325 |
/* Test the point for sidedness */ |
326 |
d = DOT(n[1],p); |
327 |
if(d > 0.0) |
328 |
{ |
329 |
sides[1] = GT_OUT; |
330 |
sides[2] = GT_INVALID; |
331 |
return(FALSE); |
332 |
} |
333 |
else |
334 |
sides[1] = GT_INTERIOR; |
335 |
/* Test next edge */ |
336 |
if(!NTH_BIT(*nset,2)) |
337 |
{ |
338 |
VCROSS(n[2],v0,v2); |
339 |
SET_NTH_BIT(*nset,2); |
340 |
} |
341 |
/* Test the point for sidedness */ |
342 |
d = DOT(n[2],p); |
343 |
if(d > 0.0) |
344 |
{ |
345 |
sides[2] = GT_OUT; |
346 |
return(FALSE); |
347 |
} |
348 |
else |
349 |
sides[2] = GT_INTERIOR; |
350 |
/* Must be interior to the pyramid */ |
351 |
return(GT_INTERIOR); |
352 |
} |
353 |
|
354 |
|
355 |
|
356 |
|
357 |
int |
358 |
point_in_stri(v0,v1,v2,p) |
359 |
FVECT v0,v1,v2,p; |
360 |
{ |
361 |
double d; |
362 |
FVECT n; |
363 |
|
364 |
VCROSS(n,v1,v0); |
365 |
/* Test the point for sidedness */ |
366 |
d = DOT(n,p); |
367 |
if(d > 0.0) |
368 |
return(FALSE); |
369 |
|
370 |
/* Test next edge */ |
371 |
VCROSS(n,v2,v1); |
372 |
/* Test the point for sidedness */ |
373 |
d = DOT(n,p); |
374 |
if(d > 0.0) |
375 |
return(FALSE); |
376 |
|
377 |
/* Test next edge */ |
378 |
VCROSS(n,v0,v2); |
379 |
/* Test the point for sidedness */ |
380 |
d = DOT(n,p); |
381 |
if(d > 0.0) |
382 |
return(FALSE); |
383 |
/* Must be interior to the pyramid */ |
384 |
return(GT_INTERIOR); |
385 |
} |
386 |
|
387 |
int |
388 |
vertices_in_stri(t0,t1,t2,p0,p1,p2,nset,n,avg,pt_sides) |
389 |
FVECT t0,t1,t2,p0,p1,p2; |
390 |
int *nset; |
391 |
FVECT n[3]; |
392 |
FVECT avg; |
393 |
int pt_sides[3][3]; |
394 |
|
395 |
{ |
396 |
int below_plane[3],test; |
397 |
|
398 |
SUM_3VEC3(avg,t0,t1,t2); |
399 |
*nset = 0; |
400 |
/* Test vertex v[i] against triangle j*/ |
401 |
/* Check if v[i] lies below plane defined by avg of 3 vectors |
402 |
defining triangle |
403 |
*/ |
404 |
|
405 |
/* test point 0 */ |
406 |
if(DOT(avg,p0) < 0.0) |
407 |
below_plane[0] = 1; |
408 |
else |
409 |
below_plane[0] = 0; |
410 |
/* Test if b[i] lies in or on triangle a */ |
411 |
test = point_set_in_stri(t0,t1,t2,p0,n,nset,pt_sides[0]); |
412 |
/* If pts[i] is interior: done */ |
413 |
if(!below_plane[0]) |
414 |
{ |
415 |
if(test == GT_INTERIOR) |
416 |
return(TRUE); |
417 |
} |
418 |
/* Now test point 1*/ |
419 |
|
420 |
if(DOT(avg,p1) < 0.0) |
421 |
below_plane[1] = 1; |
422 |
else |
423 |
below_plane[1]=0; |
424 |
/* Test if b[i] lies in or on triangle a */ |
425 |
test = point_set_in_stri(t0,t1,t2,p1,n,nset,pt_sides[1]); |
426 |
/* If pts[i] is interior: done */ |
427 |
if(!below_plane[1]) |
428 |
{ |
429 |
if(test == GT_INTERIOR) |
430 |
return(TRUE); |
431 |
} |
432 |
|
433 |
/* Now test point 2 */ |
434 |
if(DOT(avg,p2) < 0.0) |
435 |
below_plane[2] = 1; |
436 |
else |
437 |
below_plane[2] = 0; |
438 |
/* Test if b[i] lies in or on triangle a */ |
439 |
test = point_set_in_stri(t0,t1,t2,p2,n,nset,pt_sides[2]); |
440 |
|
441 |
/* If pts[i] is interior: done */ |
442 |
if(!below_plane[2]) |
443 |
{ |
444 |
if(test == GT_INTERIOR) |
445 |
return(TRUE); |
446 |
} |
447 |
|
448 |
/* If all three points below separating plane: trivial reject */ |
449 |
if(below_plane[0] && below_plane[1] && below_plane[2]) |
450 |
return(FALSE); |
451 |
/* Now check vertices in a against triangle b */ |
452 |
return(FALSE); |
453 |
} |
454 |
|
455 |
|
456 |
set_sidedness_tests(t0,t1,t2,p0,p1,p2,test,sides,nset,n) |
457 |
FVECT t0,t1,t2,p0,p1,p2; |
458 |
int test[3]; |
459 |
int sides[3][3]; |
460 |
int nset; |
461 |
FVECT n[3]; |
462 |
{ |
463 |
int t; |
464 |
double d; |
465 |
|
466 |
|
467 |
/* p=0 */ |
468 |
test[0] = 0; |
469 |
if(sides[0][0] == GT_INVALID) |
470 |
{ |
471 |
if(!NTH_BIT(nset,0)) |
472 |
VCROSS(n[0],t1,t0); |
473 |
/* Test the point for sidedness */ |
474 |
d = DOT(n[0],p0); |
475 |
if(d >= 0.0) |
476 |
SET_NTH_BIT(test[0],0); |
477 |
} |
478 |
else |
479 |
if(sides[0][0] != GT_INTERIOR) |
480 |
SET_NTH_BIT(test[0],0); |
481 |
|
482 |
if(sides[0][1] == GT_INVALID) |
483 |
{ |
484 |
if(!NTH_BIT(nset,1)) |
485 |
VCROSS(n[1],t2,t1); |
486 |
/* Test the point for sidedness */ |
487 |
d = DOT(n[1],p0); |
488 |
if(d >= 0.0) |
489 |
SET_NTH_BIT(test[0],1); |
490 |
} |
491 |
else |
492 |
if(sides[0][1] != GT_INTERIOR) |
493 |
SET_NTH_BIT(test[0],1); |
494 |
|
495 |
if(sides[0][2] == GT_INVALID) |
496 |
{ |
497 |
if(!NTH_BIT(nset,2)) |
498 |
VCROSS(n[2],t0,t2); |
499 |
/* Test the point for sidedness */ |
500 |
d = DOT(n[2],p0); |
501 |
if(d >= 0.0) |
502 |
SET_NTH_BIT(test[0],2); |
503 |
} |
504 |
else |
505 |
if(sides[0][2] != GT_INTERIOR) |
506 |
SET_NTH_BIT(test[0],2); |
507 |
|
508 |
/* p=1 */ |
509 |
test[1] = 0; |
510 |
/* t=0*/ |
511 |
if(sides[1][0] == GT_INVALID) |
512 |
{ |
513 |
if(!NTH_BIT(nset,0)) |
514 |
VCROSS(n[0],t1,t0); |
515 |
/* Test the point for sidedness */ |
516 |
d = DOT(n[0],p1); |
517 |
if(d >= 0.0) |
518 |
SET_NTH_BIT(test[1],0); |
519 |
} |
520 |
else |
521 |
if(sides[1][0] != GT_INTERIOR) |
522 |
SET_NTH_BIT(test[1],0); |
523 |
|
524 |
/* t=1 */ |
525 |
if(sides[1][1] == GT_INVALID) |
526 |
{ |
527 |
if(!NTH_BIT(nset,1)) |
528 |
VCROSS(n[1],t2,t1); |
529 |
/* Test the point for sidedness */ |
530 |
d = DOT(n[1],p1); |
531 |
if(d >= 0.0) |
532 |
SET_NTH_BIT(test[1],1); |
533 |
} |
534 |
else |
535 |
if(sides[1][1] != GT_INTERIOR) |
536 |
SET_NTH_BIT(test[1],1); |
537 |
|
538 |
/* t=2 */ |
539 |
if(sides[1][2] == GT_INVALID) |
540 |
{ |
541 |
if(!NTH_BIT(nset,2)) |
542 |
VCROSS(n[2],t0,t2); |
543 |
/* Test the point for sidedness */ |
544 |
d = DOT(n[2],p1); |
545 |
if(d >= 0.0) |
546 |
SET_NTH_BIT(test[1],2); |
547 |
} |
548 |
else |
549 |
if(sides[1][2] != GT_INTERIOR) |
550 |
SET_NTH_BIT(test[1],2); |
551 |
|
552 |
/* p=2 */ |
553 |
test[2] = 0; |
554 |
/* t = 0 */ |
555 |
if(sides[2][0] == GT_INVALID) |
556 |
{ |
557 |
if(!NTH_BIT(nset,0)) |
558 |
VCROSS(n[0],t1,t0); |
559 |
/* Test the point for sidedness */ |
560 |
d = DOT(n[0],p2); |
561 |
if(d >= 0.0) |
562 |
SET_NTH_BIT(test[2],0); |
563 |
} |
564 |
else |
565 |
if(sides[2][0] != GT_INTERIOR) |
566 |
SET_NTH_BIT(test[2],0); |
567 |
/* t=1 */ |
568 |
if(sides[2][1] == GT_INVALID) |
569 |
{ |
570 |
if(!NTH_BIT(nset,1)) |
571 |
VCROSS(n[1],t2,t1); |
572 |
/* Test the point for sidedness */ |
573 |
d = DOT(n[1],p2); |
574 |
if(d >= 0.0) |
575 |
SET_NTH_BIT(test[2],1); |
576 |
} |
577 |
else |
578 |
if(sides[2][1] != GT_INTERIOR) |
579 |
SET_NTH_BIT(test[2],1); |
580 |
/* t=2 */ |
581 |
if(sides[2][2] == GT_INVALID) |
582 |
{ |
583 |
if(!NTH_BIT(nset,2)) |
584 |
VCROSS(n[2],t0,t2); |
585 |
/* Test the point for sidedness */ |
586 |
d = DOT(n[2],p2); |
587 |
if(d >= 0.0) |
588 |
SET_NTH_BIT(test[2],2); |
589 |
} |
590 |
else |
591 |
if(sides[2][2] != GT_INTERIOR) |
592 |
SET_NTH_BIT(test[2],2); |
593 |
} |
594 |
|
595 |
|
596 |
int |
597 |
stri_intersect(a1,a2,a3,b1,b2,b3) |
598 |
FVECT a1,a2,a3,b1,b2,b3; |
599 |
{ |
600 |
int which,test,n_set[2]; |
601 |
int sides[2][3][3],i,j,inext,jnext; |
602 |
int tests[2][3]; |
603 |
FVECT n[2][3],p,avg[2]; |
604 |
|
605 |
/* Test the vertices of triangle a against the pyramid formed by triangle |
606 |
b and the origin. If any vertex of a is interior to triangle b, or |
607 |
if all 3 vertices of a are ON the edges of b,return TRUE. Remember |
608 |
the results of the edge normal and sidedness tests for later. |
609 |
*/ |
610 |
if(vertices_in_stri(a1,a2,a3,b1,b2,b3,&(n_set[0]),n[0],avg[0],sides[1])) |
611 |
return(TRUE); |
612 |
|
613 |
if(vertices_in_stri(b1,b2,b3,a1,a2,a3,&(n_set[1]),n[1],avg[1],sides[0])) |
614 |
return(TRUE); |
615 |
|
616 |
|
617 |
set_sidedness_tests(b1,b2,b3,a1,a2,a3,tests[0],sides[0],n_set[1],n[1]); |
618 |
if(tests[0][0]&tests[0][1]&tests[0][2]) |
619 |
return(FALSE); |
620 |
|
621 |
set_sidedness_tests(a1,a2,a3,b1,b2,b3,tests[1],sides[1],n_set[0],n[0]); |
622 |
if(tests[1][0]&tests[1][1]&tests[1][2]) |
623 |
return(FALSE); |
624 |
|
625 |
for(j=0; j < 3;j++) |
626 |
{ |
627 |
jnext = (j+1)%3; |
628 |
/* IF edge b doesnt cross any great circles of a, punt */ |
629 |
if(tests[1][j] & tests[1][jnext]) |
630 |
continue; |
631 |
for(i=0;i<3;i++) |
632 |
{ |
633 |
inext = (i+1)%3; |
634 |
/* IF edge a doesnt cross any great circles of b, punt */ |
635 |
if(tests[0][i] & tests[0][inext]) |
636 |
continue; |
637 |
/* Now find the great circles that cross and test */ |
638 |
if((NTH_BIT(tests[0][i],j)^(NTH_BIT(tests[0][inext],j))) |
639 |
&& (NTH_BIT(tests[1][j],i)^NTH_BIT(tests[1][jnext],i))) |
640 |
{ |
641 |
VCROSS(p,n[0][i],n[1][j]); |
642 |
|
643 |
/* If zero cp= done */ |
644 |
if(ZERO_VEC3(p)) |
645 |
continue; |
646 |
/* check above both planes */ |
647 |
if(DOT(avg[0],p) < 0 || DOT(avg[1],p) < 0) |
648 |
{ |
649 |
NEGATE_VEC3(p); |
650 |
if(DOT(avg[0],p) < 0 || DOT(avg[1],p) < 0) |
651 |
continue; |
652 |
} |
653 |
return(TRUE); |
654 |
} |
655 |
} |
656 |
} |
657 |
return(FALSE); |
658 |
} |
659 |
|
660 |
int |
661 |
ray_intersect_tri(orig,dir,v0,v1,v2,pt) |
662 |
FVECT orig,dir; |
663 |
FVECT v0,v1,v2; |
664 |
FVECT pt; |
665 |
{ |
666 |
FVECT p0,p1,p2,p,n; |
667 |
double pd; |
668 |
int type; |
669 |
|
670 |
VSUB(p0,v0,orig); |
671 |
VSUB(p1,v1,orig); |
672 |
VSUB(p2,v2,orig); |
673 |
|
674 |
if(point_in_stri(p0,p1,p2,dir)) |
675 |
{ |
676 |
/* Intersect the ray with the triangle plane */ |
677 |
tri_plane_equation(v0,v1,v2,n,&pd,FALSE); |
678 |
return(intersect_ray_plane(orig,dir,n,pd,NULL,pt)); |
679 |
} |
680 |
return(FALSE); |
681 |
} |
682 |
|
683 |
|
684 |
calculate_view_frustum(vp,hv,vv,horiz,vert,near,far,fnear,ffar) |
685 |
FVECT vp,hv,vv; |
686 |
double horiz,vert,near,far; |
687 |
FVECT fnear[4],ffar[4]; |
688 |
{ |
689 |
double height,width; |
690 |
FVECT t,nhv,nvv,ndv; |
691 |
double w2,h2; |
692 |
/* Calculate the x and y dimensions of the near face */ |
693 |
/* hv and vv are the horizontal and vertical vectors in the |
694 |
view frame-the magnitude is the dimension of the front frustum |
695 |
face at z =1 |
696 |
*/ |
697 |
VCOPY(nhv,hv); |
698 |
VCOPY(nvv,vv); |
699 |
w2 = normalize(nhv); |
700 |
h2 = normalize(nvv); |
701 |
/* Use similar triangles to calculate the dimensions at z=near */ |
702 |
width = near*0.5*w2; |
703 |
height = near*0.5*h2; |
704 |
|
705 |
VCROSS(ndv,nvv,nhv); |
706 |
/* Calculate the world space points corresponding to the 4 corners |
707 |
of the front face of the view frustum |
708 |
*/ |
709 |
fnear[0][0] = width*nhv[0] + height*nvv[0] + near*ndv[0] + vp[0] ; |
710 |
fnear[0][1] = width*nhv[1] + height*nvv[1] + near*ndv[1] + vp[1]; |
711 |
fnear[0][2] = width*nhv[2] + height*nvv[2] + near*ndv[2] + vp[2]; |
712 |
fnear[1][0] = -width*nhv[0] + height*nvv[0] + near*ndv[0] + vp[0]; |
713 |
fnear[1][1] = -width*nhv[1] + height*nvv[1] + near*ndv[1] + vp[1]; |
714 |
fnear[1][2] = -width*nhv[2] + height*nvv[2] + near*ndv[2] + vp[2]; |
715 |
fnear[2][0] = -width*nhv[0] - height*nvv[0] + near*ndv[0] + vp[0]; |
716 |
fnear[2][1] = -width*nhv[1] - height*nvv[1] + near*ndv[1] + vp[1]; |
717 |
fnear[2][2] = -width*nhv[2] - height*nvv[2] + near*ndv[2] + vp[2]; |
718 |
fnear[3][0] = width*nhv[0] - height*nvv[0] + near*ndv[0] + vp[0]; |
719 |
fnear[3][1] = width*nhv[1] - height*nvv[1] + near*ndv[1] + vp[1]; |
720 |
fnear[3][2] = width*nhv[2] - height*nvv[2] + near*ndv[2] + vp[2]; |
721 |
|
722 |
/* Now do the far face */ |
723 |
width = far*0.5*w2; |
724 |
height = far*0.5*h2; |
725 |
ffar[0][0] = width*nhv[0] + height*nvv[0] + far*ndv[0] + vp[0] ; |
726 |
ffar[0][1] = width*nhv[1] + height*nvv[1] + far*ndv[1] + vp[1] ; |
727 |
ffar[0][2] = width*nhv[2] + height*nvv[2] + far*ndv[2] + vp[2] ; |
728 |
ffar[1][0] = -width*nhv[0] + height*nvv[0] + far*ndv[0] + vp[0] ; |
729 |
ffar[1][1] = -width*nhv[1] + height*nvv[1] + far*ndv[1] + vp[1] ; |
730 |
ffar[1][2] = -width*nhv[2] + height*nvv[2] + far*ndv[2] + vp[2] ; |
731 |
ffar[2][0] = -width*nhv[0] - height*nvv[0] + far*ndv[0] + vp[0] ; |
732 |
ffar[2][1] = -width*nhv[1] - height*nvv[1] + far*ndv[1] + vp[1] ; |
733 |
ffar[2][2] = -width*nhv[2] - height*nvv[2] + far*ndv[2] + vp[2] ; |
734 |
ffar[3][0] = width*nhv[0] - height*nvv[0] + far*ndv[0] + vp[0] ; |
735 |
ffar[3][1] = width*nhv[1] - height*nvv[1] + far*ndv[1] + vp[1] ; |
736 |
ffar[3][2] = width*nhv[2] - height*nvv[2] + far*ndv[2] + vp[2] ; |
737 |
} |
738 |
|
739 |
int |
740 |
max_index(v,r) |
741 |
FVECT v; |
742 |
double *r; |
743 |
{ |
744 |
double p[3]; |
745 |
int i; |
746 |
|
747 |
p[0] = fabs(v[0]); |
748 |
p[1] = fabs(v[1]); |
749 |
p[2] = fabs(v[2]); |
750 |
i = (p[0]>=p[1])?((p[0]>=p[2])?0:2):((p[1]>=p[2])?1:2); |
751 |
if(r) |
752 |
*r = p[i]; |
753 |
return(i); |
754 |
} |
755 |
|
756 |
int |
757 |
closest_point_in_tri(p0,p1,p2,p,p0id,p1id,p2id) |
758 |
FVECT p0,p1,p2,p; |
759 |
int p0id,p1id,p2id; |
760 |
{ |
761 |
double d,d1; |
762 |
int i; |
763 |
|
764 |
d = DIST_SQ(p,p0); |
765 |
d1 = DIST_SQ(p,p1); |
766 |
if(d < d1) |
767 |
{ |
768 |
d1 = DIST_SQ(p,p2); |
769 |
i = (d1 < d)?p2id:p0id; |
770 |
} |
771 |
else |
772 |
{ |
773 |
d = DIST_SQ(p,p2); |
774 |
i = (d < d1)? p2id:p1id; |
775 |
} |
776 |
return(i); |
777 |
} |
778 |
|
779 |
|
780 |
int |
781 |
sedge_intersect(a0,a1,b0,b1) |
782 |
FVECT a0,a1,b0,b1; |
783 |
{ |
784 |
FVECT na,nb,avga,avgb,p; |
785 |
double d; |
786 |
int sb0,sb1,sa0,sa1; |
787 |
|
788 |
/* First test if edge b straddles great circle of a */ |
789 |
VCROSS(na,a0,a1); |
790 |
d = DOT(na,b0); |
791 |
sb0 = ZERO(d)?0:(d<0)? -1: 1; |
792 |
d = DOT(na,b1); |
793 |
sb1 = ZERO(d)?0:(d<0)? -1: 1; |
794 |
/* edge b entirely on one side of great circle a: edges cannot intersect*/ |
795 |
if(sb0*sb1 > 0) |
796 |
return(FALSE); |
797 |
/* test if edge a straddles great circle of b */ |
798 |
VCROSS(nb,b0,b1); |
799 |
d = DOT(nb,a0); |
800 |
sa0 = ZERO(d)?0:(d<0)? -1: 1; |
801 |
d = DOT(nb,a1); |
802 |
sa1 = ZERO(d)?0:(d<0)? -1: 1; |
803 |
/* edge a entirely on one side of great circle b: edges cannot intersect*/ |
804 |
if(sa0*sa1 > 0) |
805 |
return(FALSE); |
806 |
|
807 |
/* Find one of intersection points of the great circles */ |
808 |
VCROSS(p,na,nb); |
809 |
/* If they lie on same great circle: call an intersection */ |
810 |
if(ZERO_VEC3(p)) |
811 |
return(TRUE); |
812 |
|
813 |
VADD(avga,a0,a1); |
814 |
VADD(avgb,b0,b1); |
815 |
if(DOT(avga,p) < 0 || DOT(avgb,p) < 0) |
816 |
{ |
817 |
NEGATE_VEC3(p); |
818 |
if(DOT(avga,p) < 0 || DOT(avgb,p) < 0) |
819 |
return(FALSE); |
820 |
} |
821 |
if((!sb0 || !sb1) && (!sa0 || !sa1)) |
822 |
return(FALSE); |
823 |
return(TRUE); |
824 |
} |
825 |
|
826 |
|
827 |
|
828 |
/* Find the normalized barycentric coordinates of p relative to |
829 |
* triangle v0,v1,v2. Return result in coord |
830 |
*/ |
831 |
bary2d(x1,y1,x2,y2,x3,y3,px,py,coord) |
832 |
double x1,y1,x2,y2,x3,y3; |
833 |
double px,py; |
834 |
double coord[3]; |
835 |
{ |
836 |
double a; |
837 |
|
838 |
a = (x2 - x1) * (y3 - y1) - (x3 - x1) * (y2 - y1); |
839 |
coord[0] = ((x2 - px) * (y3 - py) - (x3 - px) * (y2 - py)) / a; |
840 |
coord[1] = ((x3 - px) * (y1 - py) - (x1 - px) * (y3 - py)) / a; |
841 |
coord[2] = ((x1 - px) * (y2 - py) - (x2 - px) * (y1 - py)) / a; |
842 |
|
843 |
} |
844 |
|
845 |
bary_ith_child(coord,i) |
846 |
double coord[3]; |
847 |
int i; |
848 |
{ |
849 |
|
850 |
switch(i){ |
851 |
case 0: |
852 |
/* update bary for child */ |
853 |
coord[0] = 2.0*coord[0]- 1.0; |
854 |
coord[1] *= 2.0; |
855 |
coord[2] *= 2.0; |
856 |
break; |
857 |
case 1: |
858 |
coord[0] *= 2.0; |
859 |
coord[1] = 2.0*coord[1]- 1.0; |
860 |
coord[2] *= 2.0; |
861 |
break; |
862 |
case 2: |
863 |
coord[0] *= 2.0; |
864 |
coord[1] *= 2.0; |
865 |
coord[2] = 2.0*coord[2]- 1.0; |
866 |
break; |
867 |
case 3: |
868 |
coord[0] = 1.0 - 2.0*coord[0]; |
869 |
coord[1] = 1.0 - 2.0*coord[1]; |
870 |
coord[2] = 1.0 - 2.0*coord[2]; |
871 |
break; |
872 |
#ifdef DEBUG |
873 |
default: |
874 |
eputs("bary_ith_child():Invalid child\n"); |
875 |
break; |
876 |
#endif |
877 |
} |
878 |
} |
879 |
|
880 |
|
881 |
int |
882 |
bary_child(coord) |
883 |
double coord[3]; |
884 |
{ |
885 |
int i; |
886 |
|
887 |
if(coord[0] > 0.5) |
888 |
{ |
889 |
/* update bary for child */ |
890 |
coord[0] = 2.0*coord[0]- 1.0; |
891 |
coord[1] *= 2.0; |
892 |
coord[2] *= 2.0; |
893 |
return(0); |
894 |
} |
895 |
else |
896 |
if(coord[1] > 0.5) |
897 |
{ |
898 |
coord[0] *= 2.0; |
899 |
coord[1] = 2.0*coord[1]- 1.0; |
900 |
coord[2] *= 2.0; |
901 |
return(1); |
902 |
} |
903 |
else |
904 |
if(coord[2] > 0.5) |
905 |
{ |
906 |
coord[0] *= 2.0; |
907 |
coord[1] *= 2.0; |
908 |
coord[2] = 2.0*coord[2]- 1.0; |
909 |
return(2); |
910 |
} |
911 |
else |
912 |
{ |
913 |
coord[0] = 1.0 - 2.0*coord[0]; |
914 |
coord[1] = 1.0 - 2.0*coord[1]; |
915 |
coord[2] = 1.0 - 2.0*coord[2]; |
916 |
return(3); |
917 |
} |
918 |
} |
919 |
|
920 |
/* Coord was the ith child of the parent: set the coordinate |
921 |
relative to the parent |
922 |
*/ |
923 |
bary_parent(coord,i) |
924 |
double coord[3]; |
925 |
int i; |
926 |
{ |
927 |
|
928 |
switch(i) { |
929 |
case 0: |
930 |
/* update bary for child */ |
931 |
coord[0] = coord[0]*0.5 + 0.5; |
932 |
coord[1] *= 0.5; |
933 |
coord[2] *= 0.5; |
934 |
break; |
935 |
case 1: |
936 |
coord[0] *= 0.5; |
937 |
coord[1] = coord[1]*0.5 + 0.5; |
938 |
coord[2] *= 0.5; |
939 |
break; |
940 |
|
941 |
case 2: |
942 |
coord[0] *= 0.5; |
943 |
coord[1] *= 0.5; |
944 |
coord[2] = coord[2]*0.5 + 0.5; |
945 |
break; |
946 |
|
947 |
case 3: |
948 |
coord[0] = 0.5 - 0.5*coord[0]; |
949 |
coord[1] = 0.5 - 0.5*coord[1]; |
950 |
coord[2] = 0.5 - 0.5*coord[2]; |
951 |
break; |
952 |
#ifdef DEBUG |
953 |
default: |
954 |
eputs("bary_parent():Invalid child\n"); |
955 |
break; |
956 |
#endif |
957 |
} |
958 |
} |
959 |
|
960 |
bary_from_child(coord,child,next) |
961 |
double coord[3]; |
962 |
int child,next; |
963 |
{ |
964 |
#ifdef DEBUG |
965 |
if(child <0 || child > 3) |
966 |
{ |
967 |
eputs("bary_from_child():Invalid child\n"); |
968 |
return; |
969 |
} |
970 |
if(next <0 || next > 3) |
971 |
{ |
972 |
eputs("bary_from_child():Invalid next\n"); |
973 |
return; |
974 |
} |
975 |
#endif |
976 |
if(next == child) |
977 |
return; |
978 |
|
979 |
switch(child){ |
980 |
case 0: |
981 |
switch(next){ |
982 |
case 1: |
983 |
coord[0] += 1.0; |
984 |
coord[1] -= 1.0; |
985 |
break; |
986 |
case 2: |
987 |
coord[0] += 1.0; |
988 |
coord[2] -= 1.0; |
989 |
break; |
990 |
case 3: |
991 |
coord[0] *= -1.0; |
992 |
coord[1] = 1 - coord[1]; |
993 |
coord[2] = 1 - coord[2]; |
994 |
break; |
995 |
|
996 |
} |
997 |
break; |
998 |
case 1: |
999 |
switch(next){ |
1000 |
case 0: |
1001 |
coord[0] -= 1.0; |
1002 |
coord[1] += 1.0; |
1003 |
break; |
1004 |
case 2: |
1005 |
coord[1] += 1.0; |
1006 |
coord[2] -= 1.0; |
1007 |
break; |
1008 |
case 3: |
1009 |
coord[0] = 1 - coord[0]; |
1010 |
coord[1] *= -1.0; |
1011 |
coord[2] = 1 - coord[2]; |
1012 |
break; |
1013 |
} |
1014 |
break; |
1015 |
case 2: |
1016 |
switch(next){ |
1017 |
case 0: |
1018 |
coord[0] -= 1.0; |
1019 |
coord[2] += 1.0; |
1020 |
break; |
1021 |
case 1: |
1022 |
coord[1] -= 1.0; |
1023 |
coord[2] += 1.0; |
1024 |
break; |
1025 |
case 3: |
1026 |
coord[0] = 1 - coord[0]; |
1027 |
coord[1] = 1 - coord[1]; |
1028 |
coord[2] *= -1.0; |
1029 |
break; |
1030 |
} |
1031 |
break; |
1032 |
case 3: |
1033 |
switch(next){ |
1034 |
case 0: |
1035 |
coord[0] *= -1.0; |
1036 |
coord[1] = 1 - coord[1]; |
1037 |
coord[2] = 1 - coord[2]; |
1038 |
break; |
1039 |
case 1: |
1040 |
coord[0] = 1 - coord[0]; |
1041 |
coord[1] *= -1.0; |
1042 |
coord[2] = 1 - coord[2]; |
1043 |
break; |
1044 |
case 2: |
1045 |
coord[0] = 1 - coord[0]; |
1046 |
coord[1] = 1 - coord[1]; |
1047 |
coord[2] *= -1.0; |
1048 |
break; |
1049 |
} |
1050 |
break; |
1051 |
} |
1052 |
} |
1053 |
|
1054 |
|
1055 |
baryi_parent(coord,i) |
1056 |
BCOORD coord[3]; |
1057 |
int i; |
1058 |
{ |
1059 |
|
1060 |
switch(i) { |
1061 |
case 0: |
1062 |
/* update bary for child */ |
1063 |
coord[0] = (coord[0] >> 1) + MAXBCOORD2; |
1064 |
coord[1] >>= 1; |
1065 |
coord[2] >>= 1; |
1066 |
break; |
1067 |
case 1: |
1068 |
coord[0] >>= 1; |
1069 |
coord[1] = (coord[1] >> 1) + MAXBCOORD2; |
1070 |
coord[2] >>= 1; |
1071 |
break; |
1072 |
|
1073 |
case 2: |
1074 |
coord[0] >>= 1; |
1075 |
coord[1] >>= 1; |
1076 |
coord[2] = (coord[2] >> 1) + MAXBCOORD2; |
1077 |
break; |
1078 |
|
1079 |
case 3: |
1080 |
coord[0] = MAXBCOORD2 - (coord[0] >> 1); |
1081 |
coord[1] = MAXBCOORD2 - (coord[1] >> 1); |
1082 |
coord[2] = MAXBCOORD2 - (coord[2] >> 1); |
1083 |
break; |
1084 |
#ifdef DEBUG |
1085 |
default: |
1086 |
eputs("baryi_parent():Invalid child\n"); |
1087 |
break; |
1088 |
#endif |
1089 |
} |
1090 |
} |
1091 |
|
1092 |
baryi_from_child(coord,child,next) |
1093 |
BCOORD coord[3]; |
1094 |
int child,next; |
1095 |
{ |
1096 |
#ifdef DEBUG |
1097 |
if(child <0 || child > 3) |
1098 |
{ |
1099 |
eputs("baryi_from_child():Invalid child\n"); |
1100 |
return; |
1101 |
} |
1102 |
if(next <0 || next > 3) |
1103 |
{ |
1104 |
eputs("baryi_from_child():Invalid next\n"); |
1105 |
return; |
1106 |
} |
1107 |
#endif |
1108 |
if(next == child) |
1109 |
return; |
1110 |
|
1111 |
switch(child){ |
1112 |
case 0: |
1113 |
coord[0] = 0; |
1114 |
coord[1] = MAXBCOORD - coord[1]; |
1115 |
coord[2] = MAXBCOORD - coord[2]; |
1116 |
break; |
1117 |
case 1: |
1118 |
coord[0] = MAXBCOORD - coord[0]; |
1119 |
coord[1] = 0; |
1120 |
coord[2] = MAXBCOORD - coord[2]; |
1121 |
break; |
1122 |
case 2: |
1123 |
coord[0] = MAXBCOORD - coord[0]; |
1124 |
coord[1] = MAXBCOORD - coord[1]; |
1125 |
coord[2] = 0; |
1126 |
break; |
1127 |
case 3: |
1128 |
switch(next){ |
1129 |
case 0: |
1130 |
coord[0] = 0; |
1131 |
coord[1] = MAXBCOORD - coord[1]; |
1132 |
coord[2] = MAXBCOORD - coord[2]; |
1133 |
break; |
1134 |
case 1: |
1135 |
coord[0] = MAXBCOORD - coord[0]; |
1136 |
coord[1] = 0; |
1137 |
coord[2] = MAXBCOORD - coord[2]; |
1138 |
break; |
1139 |
case 2: |
1140 |
coord[0] = MAXBCOORD - coord[0]; |
1141 |
coord[1] = MAXBCOORD - coord[1]; |
1142 |
coord[2] = 0; |
1143 |
break; |
1144 |
} |
1145 |
break; |
1146 |
} |
1147 |
} |
1148 |
|
1149 |
int |
1150 |
baryi_child(coord) |
1151 |
BCOORD coord[3]; |
1152 |
{ |
1153 |
int i; |
1154 |
|
1155 |
if(coord[0] > MAXBCOORD2) |
1156 |
{ |
1157 |
/* update bary for child */ |
1158 |
coord[0] = (coord[0]<< 1) - MAXBCOORD; |
1159 |
coord[1] <<= 1; |
1160 |
coord[2] <<= 1; |
1161 |
return(0); |
1162 |
} |
1163 |
else |
1164 |
if(coord[1] > MAXBCOORD2) |
1165 |
{ |
1166 |
coord[0] <<= 1; |
1167 |
coord[1] = (coord[1] << 1) - MAXBCOORD; |
1168 |
coord[2] <<= 1; |
1169 |
return(1); |
1170 |
} |
1171 |
else |
1172 |
if(coord[2] > MAXBCOORD2) |
1173 |
{ |
1174 |
coord[0] <<= 1; |
1175 |
coord[1] <<= 1; |
1176 |
coord[2] = (coord[2] << 1) - MAXBCOORD; |
1177 |
return(2); |
1178 |
} |
1179 |
else |
1180 |
{ |
1181 |
coord[0] = MAXBCOORD - (coord[0] << 1); |
1182 |
coord[1] = MAXBCOORD - (coord[1] << 1); |
1183 |
coord[2] = MAXBCOORD - (coord[2] << 1); |
1184 |
return(3); |
1185 |
} |
1186 |
} |
1187 |
|
1188 |
/* convert barycentric coordinate b in [-eps,1+eps] to [0,MAXLONG], |
1189 |
dir unbounded to [-MAXLONG,MAXLONG] |
1190 |
*/ |
1191 |
bary_dtol(b,db,bi,dbi,t) |
1192 |
double b[3],db[3][3]; |
1193 |
BCOORD bi[3]; |
1194 |
BDIR dbi[3][3]; |
1195 |
TINT t[3]; |
1196 |
{ |
1197 |
int i,id,j; |
1198 |
double d; |
1199 |
|
1200 |
for(i=0; i < 2;i++) |
1201 |
{ |
1202 |
if(b[i] <= 0.0) |
1203 |
{ |
1204 |
bi[i]= 0; |
1205 |
} |
1206 |
else |
1207 |
if(b[i] >= 1.0) |
1208 |
{ |
1209 |
bi[i]= MAXBCOORD; |
1210 |
} |
1211 |
else |
1212 |
bi[i] = (BCOORD)(b[i]*MAXBCOORD); |
1213 |
} |
1214 |
bi[2] = MAXBCOORD - bi[0] - bi[1]; |
1215 |
|
1216 |
if(bi[2] < 0) |
1217 |
{ |
1218 |
bi[2] = 0; |
1219 |
bi[1] = MAXBCOORD - bi[0]; |
1220 |
} |
1221 |
for(j=0; j< 3; j++) |
1222 |
{ |
1223 |
if(t[j]==0) |
1224 |
continue; |
1225 |
if(t[j] == HUGET) |
1226 |
max_index(db[j],&d); |
1227 |
for(i=0; i< 3; i++) |
1228 |
if(t[j] != HUGET) |
1229 |
dbi[j][i] = (BDIR)(db[j][i]*MAXBDIR); |
1230 |
else |
1231 |
dbi[j][i] = (BDIR)(db[j][i]/d*MAXBDIR); |
1232 |
} |
1233 |
} |
1234 |
|
1235 |
|
1236 |
|
1237 |
|
1238 |
|
1239 |
|
1240 |
|
1241 |
|
1242 |
|