| 1 |
/* Copyright (c) 1998 Silicon Graphics, Inc. */ |
| 2 |
|
| 3 |
#ifndef lint |
| 4 |
static char SCCSid[] = "$SunId$ SGI"; |
| 5 |
#endif |
| 6 |
|
| 7 |
/* |
| 8 |
* sm_geom.c |
| 9 |
*/ |
| 10 |
|
| 11 |
#include "standard.h" |
| 12 |
#include "sm_geom.h" |
| 13 |
|
| 14 |
tri_centroid(v0,v1,v2,c) |
| 15 |
FVECT v0,v1,v2,c; |
| 16 |
{ |
| 17 |
/* Average three triangle vertices to give centroid: return in c */ |
| 18 |
c[0] = (v0[0] + v1[0] + v2[0])/3.0; |
| 19 |
c[1] = (v0[1] + v1[1] + v2[1])/3.0; |
| 20 |
c[2] = (v0[2] + v1[2] + v2[2])/3.0; |
| 21 |
} |
| 22 |
|
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|
| 24 |
int |
| 25 |
vec3_equal(v1,v2) |
| 26 |
FVECT v1,v2; |
| 27 |
{ |
| 28 |
return(EQUAL(v1[0],v2[0]) && EQUAL(v1[1],v2[1])&& EQUAL(v1[2],v2[2])); |
| 29 |
} |
| 30 |
#if 0 |
| 31 |
extern FVECT Norm[500]; |
| 32 |
extern int Ncnt; |
| 33 |
#endif |
| 34 |
|
| 35 |
int |
| 36 |
convex_angle(v0,v1,v2) |
| 37 |
FVECT v0,v1,v2; |
| 38 |
{ |
| 39 |
double dp,dp1; |
| 40 |
int test,test1; |
| 41 |
FVECT nv0,nv1,nv2; |
| 42 |
FVECT cp01,cp12,cp; |
| 43 |
|
| 44 |
/* test sign of (v0Xv1)X(v1Xv2). v1 */ |
| 45 |
/* un-Simplified: */ |
| 46 |
VCOPY(nv0,v0); |
| 47 |
normalize(nv0); |
| 48 |
VCOPY(nv1,v1); |
| 49 |
normalize(nv1); |
| 50 |
VCOPY(nv2,v2); |
| 51 |
normalize(nv2); |
| 52 |
|
| 53 |
VCROSS(cp01,nv0,nv1); |
| 54 |
VCROSS(cp12,nv1,nv2); |
| 55 |
VCROSS(cp,cp01,cp12); |
| 56 |
normalize(cp); |
| 57 |
dp1 = DOT(cp,nv1); |
| 58 |
if(dp1 <= 1e-8 || dp1 >= (1-1e-8)) /* Test if on other side,or colinear*/ |
| 59 |
test1 = FALSE; |
| 60 |
else |
| 61 |
test1 = TRUE; |
| 62 |
|
| 63 |
dp = nv0[2]*nv1[0]*nv2[1] - nv0[2]*nv1[1]*nv2[0] - nv0[0]*nv1[2]*nv2[1] |
| 64 |
+ nv0[0]*nv1[1]*nv2[2] + nv0[1]*nv1[2]*nv2[0] - nv0[1]*nv1[0]*nv2[2]; |
| 65 |
|
| 66 |
if(dp <= 1e-8 || dp1 >= (1-1e-8)) |
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test = FALSE; |
| 68 |
else |
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test = TRUE; |
| 70 |
|
| 71 |
if(test != test1) |
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fprintf(stderr,"test %f simplified %f\n",dp1,dp); |
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return(test1); |
| 74 |
} |
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|
| 76 |
/* calculates the normal of a face contour using Newell's formula. e |
| 77 |
|
| 78 |
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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*/ |
| 82 |
double |
| 83 |
tri_normal(v0,v1,v2,n,norm) |
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FVECT v0,v1,v2,n; |
| 85 |
int norm; |
| 86 |
{ |
| 87 |
double mag; |
| 88 |
|
| 89 |
n[0] = (v0[2] + v1[2]) * (v0[1] - v1[1]) + |
| 90 |
(v1[2] + v2[2]) * (v1[1] - v2[1]) + |
| 91 |
(v2[2] + v0[2]) * (v2[1] - v0[1]); |
| 92 |
|
| 93 |
n[1] = (v0[2] - v1[2]) * (v0[0] + v1[0]) + |
| 94 |
(v1[2] - v2[2]) * (v1[0] + v2[0]) + |
| 95 |
(v2[2] - v0[2]) * (v2[0] + v0[0]); |
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|
| 97 |
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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|
| 101 |
if(!norm) |
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return(0); |
| 103 |
|
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mag = normalize(n); |
| 105 |
|
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return(mag); |
| 107 |
} |
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|
| 109 |
|
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tri_plane_equation(v0,v1,v2,peqptr,norm) |
| 111 |
FVECT v0,v1,v2; |
| 112 |
FPEQ *peqptr; |
| 113 |
int norm; |
| 114 |
{ |
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tri_normal(v0,v1,v2,FP_N(*peqptr),norm); |
| 116 |
|
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FP_D(*peqptr) = -(DOT(FP_N(*peqptr),v0)); |
| 118 |
} |
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|
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|
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/* returns TRUE if ray from origin in direction v intersects plane defined |
| 122 |
* by normal plane_n, and plane_d. If plane is not parallel- returns |
| 123 |
* intersection point if r != NULL. If tptr!= NULL returns value of |
| 124 |
* t, if parallel, returns t=FHUGE |
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*/ |
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int |
| 127 |
intersect_vector_plane(v,peq,tptr,r) |
| 128 |
FVECT v; |
| 129 |
FPEQ peq; |
| 130 |
double *tptr; |
| 131 |
FVECT r; |
| 132 |
{ |
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double t,d; |
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int hit; |
| 135 |
/* |
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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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|
| 140 |
/* 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)); |
| 144 |
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; |
| 152 |
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; |
| 171 |
FPEQ peq; |
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double *pd; |
| 173 |
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); |
| 187 |
if(ZERO(d)) |
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return(0); |
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t = -(DOT(FP_N(peq),orig) + FP_D(peq))/d; |
| 190 |
|
| 191 |
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); |
| 198 |
|
| 199 |
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 |
| 206 |
intersect_ray_oplane(orig,dir,n,pd,r) |
| 207 |
FVECT orig,dir; |
| 208 |
FVECT n; |
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double *pd; |
| 210 |
FVECT r; |
| 211 |
{ |
| 212 |
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; |
| 247 |
int wnext; |
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double t; |
| 249 |
|
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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; |
| 255 |
wnext = (w+2)%3; |
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r[wnext] = v0[wnext] + dv[wnext]*t; |
| 257 |
} |
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|
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int |
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intersect_edge_plane(e0,e1,peq,pd,r) |
| 261 |
FVECT e0,e1; |
| 262 |
FPEQ peq; |
| 263 |
double *pd; |
| 264 |
FVECT r; |
| 265 |
{ |
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double t; |
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int hit; |
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FVECT d; |
| 269 |
/* |
| 270 |
Plane is Ax + By + Cz +D = 0: |
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plane[0] = A,plane[1] = B,plane[2] = C,plane[3] = D |
| 272 |
*/ |
| 273 |
/* A(orig[0] + dxt) + B(orig[1] + dyt) + C(orig[2] + dzt) + pd = 0 |
| 274 |
t = -(DOT(plane_n,orig)+ plane_d)/(DOT(plane_n,d)) |
| 275 |
line is l = p1 + (p2-p1)t |
| 276 |
*/ |
| 277 |
/* Solve for t: */ |
| 278 |
VSUB(d,e1,e0); |
| 279 |
t = -(DOT(FP_N(peq),e0) + FP_D(peq))/(DOT(FP_N(peq),d)); |
| 280 |
if(t < 0) |
| 281 |
hit = 0; |
| 282 |
else |
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hit = 1; |
| 284 |
|
| 285 |
VSUM(r,e0,d,t); |
| 286 |
|
| 287 |
if(pd) |
| 288 |
*pd = t; |
| 289 |
return(hit); |
| 290 |
} |
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|
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int |
| 293 |
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]; |
| 298 |
|
| 299 |
{ |
| 300 |
double d; |
| 301 |
/* Find the normal to the triangle ORIGIN:v0:v1 */ |
| 302 |
if(!NTH_BIT(*nset,0)) |
| 303 |
{ |
| 304 |
VCROSS(n[0],v0,v1); |
| 305 |
SET_NTH_BIT(*nset,0); |
| 306 |
} |
| 307 |
/* Test the point for sidedness */ |
| 308 |
d = DOT(n[0],p); |
| 309 |
|
| 310 |
if(d > 0.0) |
| 311 |
{ |
| 312 |
sides[0] = GT_OUT; |
| 313 |
sides[1] = sides[2] = GT_INVALID; |
| 314 |
return(FALSE); |
| 315 |
} |
| 316 |
else |
| 317 |
sides[0] = GT_INTERIOR; |
| 318 |
|
| 319 |
/* Test next edge */ |
| 320 |
if(!NTH_BIT(*nset,1)) |
| 321 |
{ |
| 322 |
VCROSS(n[1],v1,v2); |
| 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],v2,v0); |
| 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 |
set_sidedness_tests(t0,t1,t2,p0,p1,p2,test,sides,nset,n) |
| 357 |
FVECT t0,t1,t2,p0,p1,p2; |
| 358 |
int test[3]; |
| 359 |
int sides[3][3]; |
| 360 |
int nset; |
| 361 |
FVECT n[3]; |
| 362 |
{ |
| 363 |
int t; |
| 364 |
double d; |
| 365 |
|
| 366 |
|
| 367 |
/* p=0 */ |
| 368 |
test[0] = 0; |
| 369 |
if(sides[0][0] == GT_INVALID) |
| 370 |
{ |
| 371 |
if(!NTH_BIT(nset,0)) |
| 372 |
VCROSS(n[0],t0,t1); |
| 373 |
/* Test the point for sidedness */ |
| 374 |
d = DOT(n[0],p0); |
| 375 |
if(d >= 0.0) |
| 376 |
SET_NTH_BIT(test[0],0); |
| 377 |
} |
| 378 |
else |
| 379 |
if(sides[0][0] != GT_INTERIOR) |
| 380 |
SET_NTH_BIT(test[0],0); |
| 381 |
|
| 382 |
if(sides[0][1] == GT_INVALID) |
| 383 |
{ |
| 384 |
if(!NTH_BIT(nset,1)) |
| 385 |
VCROSS(n[1],t1,t2); |
| 386 |
/* Test the point for sidedness */ |
| 387 |
d = DOT(n[1],p0); |
| 388 |
if(d >= 0.0) |
| 389 |
SET_NTH_BIT(test[0],1); |
| 390 |
} |
| 391 |
else |
| 392 |
if(sides[0][1] != GT_INTERIOR) |
| 393 |
SET_NTH_BIT(test[0],1); |
| 394 |
|
| 395 |
if(sides[0][2] == GT_INVALID) |
| 396 |
{ |
| 397 |
if(!NTH_BIT(nset,2)) |
| 398 |
VCROSS(n[2],t2,t0); |
| 399 |
/* Test the point for sidedness */ |
| 400 |
d = DOT(n[2],p0); |
| 401 |
if(d >= 0.0) |
| 402 |
SET_NTH_BIT(test[0],2); |
| 403 |
} |
| 404 |
else |
| 405 |
if(sides[0][2] != GT_INTERIOR) |
| 406 |
SET_NTH_BIT(test[0],2); |
| 407 |
|
| 408 |
/* p=1 */ |
| 409 |
test[1] = 0; |
| 410 |
/* t=0*/ |
| 411 |
if(sides[1][0] == GT_INVALID) |
| 412 |
{ |
| 413 |
if(!NTH_BIT(nset,0)) |
| 414 |
VCROSS(n[0],t0,t1); |
| 415 |
/* Test the point for sidedness */ |
| 416 |
d = DOT(n[0],p1); |
| 417 |
if(d >= 0.0) |
| 418 |
SET_NTH_BIT(test[1],0); |
| 419 |
} |
| 420 |
else |
| 421 |
if(sides[1][0] != GT_INTERIOR) |
| 422 |
SET_NTH_BIT(test[1],0); |
| 423 |
|
| 424 |
/* t=1 */ |
| 425 |
if(sides[1][1] == GT_INVALID) |
| 426 |
{ |
| 427 |
if(!NTH_BIT(nset,1)) |
| 428 |
VCROSS(n[1],t1,t2); |
| 429 |
/* Test the point for sidedness */ |
| 430 |
d = DOT(n[1],p1); |
| 431 |
if(d >= 0.0) |
| 432 |
SET_NTH_BIT(test[1],1); |
| 433 |
} |
| 434 |
else |
| 435 |
if(sides[1][1] != GT_INTERIOR) |
| 436 |
SET_NTH_BIT(test[1],1); |
| 437 |
|
| 438 |
/* t=2 */ |
| 439 |
if(sides[1][2] == GT_INVALID) |
| 440 |
{ |
| 441 |
if(!NTH_BIT(nset,2)) |
| 442 |
VCROSS(n[2],t2,t0); |
| 443 |
/* Test the point for sidedness */ |
| 444 |
d = DOT(n[2],p1); |
| 445 |
if(d >= 0.0) |
| 446 |
SET_NTH_BIT(test[1],2); |
| 447 |
} |
| 448 |
else |
| 449 |
if(sides[1][2] != GT_INTERIOR) |
| 450 |
SET_NTH_BIT(test[1],2); |
| 451 |
|
| 452 |
/* p=2 */ |
| 453 |
test[2] = 0; |
| 454 |
/* t = 0 */ |
| 455 |
if(sides[2][0] == GT_INVALID) |
| 456 |
{ |
| 457 |
if(!NTH_BIT(nset,0)) |
| 458 |
VCROSS(n[0],t0,t1); |
| 459 |
/* Test the point for sidedness */ |
| 460 |
d = DOT(n[0],p2); |
| 461 |
if(d >= 0.0) |
| 462 |
SET_NTH_BIT(test[2],0); |
| 463 |
} |
| 464 |
else |
| 465 |
if(sides[2][0] != GT_INTERIOR) |
| 466 |
SET_NTH_BIT(test[2],0); |
| 467 |
/* t=1 */ |
| 468 |
if(sides[2][1] == GT_INVALID) |
| 469 |
{ |
| 470 |
if(!NTH_BIT(nset,1)) |
| 471 |
VCROSS(n[1],t1,t2); |
| 472 |
/* Test the point for sidedness */ |
| 473 |
d = DOT(n[1],p2); |
| 474 |
if(d >= 0.0) |
| 475 |
SET_NTH_BIT(test[2],1); |
| 476 |
} |
| 477 |
else |
| 478 |
if(sides[2][1] != GT_INTERIOR) |
| 479 |
SET_NTH_BIT(test[2],1); |
| 480 |
/* t=2 */ |
| 481 |
if(sides[2][2] == GT_INVALID) |
| 482 |
{ |
| 483 |
if(!NTH_BIT(nset,2)) |
| 484 |
VCROSS(n[2],t2,t0); |
| 485 |
/* Test the point for sidedness */ |
| 486 |
d = DOT(n[2],p2); |
| 487 |
if(d >= 0.0) |
| 488 |
SET_NTH_BIT(test[2],2); |
| 489 |
} |
| 490 |
else |
| 491 |
if(sides[2][2] != GT_INTERIOR) |
| 492 |
SET_NTH_BIT(test[2],2); |
| 493 |
} |
| 494 |
|
| 495 |
double |
| 496 |
point_on_sphere(ps,p,c) |
| 497 |
FVECT ps,p,c; |
| 498 |
{ |
| 499 |
double d; |
| 500 |
VSUB(ps,p,c); |
| 501 |
d= normalize(ps); |
| 502 |
return(d); |
| 503 |
} |
| 504 |
|
| 505 |
int |
| 506 |
point_in_stri(v0,v1,v2,p) |
| 507 |
FVECT v0,v1,v2,p; |
| 508 |
{ |
| 509 |
double d; |
| 510 |
FVECT n; |
| 511 |
|
| 512 |
VCROSS(n,v0,v1); |
| 513 |
/* Test the point for sidedness */ |
| 514 |
d = DOT(n,p); |
| 515 |
if(d > 0.0) |
| 516 |
return(FALSE); |
| 517 |
|
| 518 |
/* Test next edge */ |
| 519 |
VCROSS(n,v1,v2); |
| 520 |
/* Test the point for sidedness */ |
| 521 |
d = DOT(n,p); |
| 522 |
if(d > 0.0) |
| 523 |
return(FALSE); |
| 524 |
|
| 525 |
/* Test next edge */ |
| 526 |
VCROSS(n,v2,v0); |
| 527 |
/* Test the point for sidedness */ |
| 528 |
d = DOT(n,p); |
| 529 |
if(d > 0.0) |
| 530 |
return(FALSE); |
| 531 |
/* Must be interior to the pyramid */ |
| 532 |
return(GT_INTERIOR); |
| 533 |
} |
| 534 |
|
| 535 |
|
| 536 |
int |
| 537 |
ray_intersect_tri(orig,dir,v0,v1,v2,pt) |
| 538 |
FVECT orig,dir; |
| 539 |
FVECT v0,v1,v2; |
| 540 |
FVECT pt; |
| 541 |
{ |
| 542 |
FVECT p0,p1,p2,p; |
| 543 |
FPEQ peq; |
| 544 |
int type; |
| 545 |
|
| 546 |
VSUB(p0,v0,orig); |
| 547 |
VSUB(p1,v1,orig); |
| 548 |
VSUB(p2,v2,orig); |
| 549 |
|
| 550 |
if(point_in_stri(p0,p1,p2,dir)) |
| 551 |
{ |
| 552 |
/* Intersect the ray with the triangle plane */ |
| 553 |
tri_plane_equation(v0,v1,v2,&peq,FALSE); |
| 554 |
return(intersect_ray_plane(orig,dir,peq,NULL,pt)); |
| 555 |
} |
| 556 |
return(FALSE); |
| 557 |
} |
| 558 |
|
| 559 |
|
| 560 |
calculate_view_frustum(vp,hv,vv,horiz,vert,near,far,fnear,ffar) |
| 561 |
FVECT vp,hv,vv; |
| 562 |
double horiz,vert,near,far; |
| 563 |
FVECT fnear[4],ffar[4]; |
| 564 |
{ |
| 565 |
double height,width; |
| 566 |
FVECT t,nhv,nvv,ndv; |
| 567 |
double w2,h2; |
| 568 |
/* Calculate the x and y dimensions of the near face */ |
| 569 |
/* hv and vv are the horizontal and vertical vectors in the |
| 570 |
view frame-the magnitude is the dimension of the front frustum |
| 571 |
face at z =1 |
| 572 |
*/ |
| 573 |
VCOPY(nhv,hv); |
| 574 |
VCOPY(nvv,vv); |
| 575 |
w2 = normalize(nhv); |
| 576 |
h2 = normalize(nvv); |
| 577 |
/* Use similar triangles to calculate the dimensions at z=near */ |
| 578 |
width = near*0.5*w2; |
| 579 |
height = near*0.5*h2; |
| 580 |
|
| 581 |
VCROSS(ndv,nvv,nhv); |
| 582 |
/* Calculate the world space points corresponding to the 4 corners |
| 583 |
of the front face of the view frustum |
| 584 |
*/ |
| 585 |
fnear[0][0] = width*nhv[0] + height*nvv[0] + near*ndv[0] + vp[0] ; |
| 586 |
fnear[0][1] = width*nhv[1] + height*nvv[1] + near*ndv[1] + vp[1]; |
| 587 |
fnear[0][2] = width*nhv[2] + height*nvv[2] + near*ndv[2] + vp[2]; |
| 588 |
fnear[1][0] = -width*nhv[0] + height*nvv[0] + near*ndv[0] + vp[0]; |
| 589 |
fnear[1][1] = -width*nhv[1] + height*nvv[1] + near*ndv[1] + vp[1]; |
| 590 |
fnear[1][2] = -width*nhv[2] + height*nvv[2] + near*ndv[2] + vp[2]; |
| 591 |
fnear[2][0] = -width*nhv[0] - height*nvv[0] + near*ndv[0] + vp[0]; |
| 592 |
fnear[2][1] = -width*nhv[1] - height*nvv[1] + near*ndv[1] + vp[1]; |
| 593 |
fnear[2][2] = -width*nhv[2] - height*nvv[2] + near*ndv[2] + vp[2]; |
| 594 |
fnear[3][0] = width*nhv[0] - height*nvv[0] + near*ndv[0] + vp[0]; |
| 595 |
fnear[3][1] = width*nhv[1] - height*nvv[1] + near*ndv[1] + vp[1]; |
| 596 |
fnear[3][2] = width*nhv[2] - height*nvv[2] + near*ndv[2] + vp[2]; |
| 597 |
|
| 598 |
/* Now do the far face */ |
| 599 |
width = far*0.5*w2; |
| 600 |
height = far*0.5*h2; |
| 601 |
ffar[0][0] = width*nhv[0] + height*nvv[0] + far*ndv[0] + vp[0] ; |
| 602 |
ffar[0][1] = width*nhv[1] + height*nvv[1] + far*ndv[1] + vp[1] ; |
| 603 |
ffar[0][2] = width*nhv[2] + height*nvv[2] + far*ndv[2] + vp[2] ; |
| 604 |
ffar[1][0] = -width*nhv[0] + height*nvv[0] + far*ndv[0] + vp[0] ; |
| 605 |
ffar[1][1] = -width*nhv[1] + height*nvv[1] + far*ndv[1] + vp[1] ; |
| 606 |
ffar[1][2] = -width*nhv[2] + height*nvv[2] + far*ndv[2] + vp[2] ; |
| 607 |
ffar[2][0] = -width*nhv[0] - height*nvv[0] + far*ndv[0] + vp[0] ; |
| 608 |
ffar[2][1] = -width*nhv[1] - height*nvv[1] + far*ndv[1] + vp[1] ; |
| 609 |
ffar[2][2] = -width*nhv[2] - height*nvv[2] + far*ndv[2] + vp[2] ; |
| 610 |
ffar[3][0] = width*nhv[0] - height*nvv[0] + far*ndv[0] + vp[0] ; |
| 611 |
ffar[3][1] = width*nhv[1] - height*nvv[1] + far*ndv[1] + vp[1] ; |
| 612 |
ffar[3][2] = width*nhv[2] - height*nvv[2] + far*ndv[2] + vp[2] ; |
| 613 |
} |
| 614 |
|
| 615 |
int |
| 616 |
max_index(v,r) |
| 617 |
FVECT v; |
| 618 |
double *r; |
| 619 |
{ |
| 620 |
double p[3]; |
| 621 |
int i; |
| 622 |
|
| 623 |
p[0] = fabs(v[0]); |
| 624 |
p[1] = fabs(v[1]); |
| 625 |
p[2] = fabs(v[2]); |
| 626 |
i = (p[0]>=p[1])?((p[0]>=p[2])?0:2):((p[1]>=p[2])?1:2); |
| 627 |
if(r) |
| 628 |
*r = p[i]; |
| 629 |
return(i); |
| 630 |
} |
| 631 |
|
| 632 |
int |
| 633 |
closest_point_in_tri(p0,p1,p2,p,p0id,p1id,p2id) |
| 634 |
FVECT p0,p1,p2,p; |
| 635 |
int p0id,p1id,p2id; |
| 636 |
{ |
| 637 |
double d,d1; |
| 638 |
int i; |
| 639 |
|
| 640 |
d = DIST_SQ(p,p0); |
| 641 |
d1 = DIST_SQ(p,p1); |
| 642 |
if(d < d1) |
| 643 |
{ |
| 644 |
d1 = DIST_SQ(p,p2); |
| 645 |
i = (d1 < d)?p2id:p0id; |
| 646 |
} |
| 647 |
else |
| 648 |
{ |
| 649 |
d = DIST_SQ(p,p2); |
| 650 |
i = (d < d1)? p2id:p1id; |
| 651 |
} |
| 652 |
return(i); |
| 653 |
} |
| 654 |
|
| 655 |
/* Find the normalized barycentric coordinates of p relative to |
| 656 |
* triangle v0,v1,v2. Return result in coord |
| 657 |
*/ |
| 658 |
bary2d(x1,y1,x2,y2,x3,y3,px,py,coord) |
| 659 |
double x1,y1,x2,y2,x3,y3; |
| 660 |
double px,py; |
| 661 |
double coord[3]; |
| 662 |
{ |
| 663 |
double a; |
| 664 |
|
| 665 |
a = (x2 - x1) * (y3 - y1) - (x3 - x1) * (y2 - y1); |
| 666 |
coord[0] = ((x2 - px) * (y3 - py) - (x3 - px) * (y2 - py)) / a; |
| 667 |
coord[1] = ((x3 - px) * (y1 - py) - (x1 - px) * (y3 - py)) / a; |
| 668 |
coord[2] = ((x1 - px) * (y2 - py) - (x2 - px) * (y1 - py)) / a; |
| 669 |
|
| 670 |
} |
| 671 |
|
| 672 |
|
| 673 |
|
| 674 |
|
| 675 |
bary_parent(coord,i) |
| 676 |
BCOORD coord[3]; |
| 677 |
int i; |
| 678 |
{ |
| 679 |
switch(i) { |
| 680 |
case 0: |
| 681 |
/* update bary for child */ |
| 682 |
coord[0] = (coord[0] >> 1) + MAXBCOORD4; |
| 683 |
coord[1] >>= 1; |
| 684 |
coord[2] >>= 1; |
| 685 |
break; |
| 686 |
case 1: |
| 687 |
coord[0] >>= 1; |
| 688 |
coord[1] = (coord[1] >> 1) + MAXBCOORD4; |
| 689 |
coord[2] >>= 1; |
| 690 |
break; |
| 691 |
|
| 692 |
case 2: |
| 693 |
coord[0] >>= 1; |
| 694 |
coord[1] >>= 1; |
| 695 |
coord[2] = (coord[2] >> 1) + MAXBCOORD4; |
| 696 |
break; |
| 697 |
|
| 698 |
case 3: |
| 699 |
coord[0] = MAXBCOORD4 - (coord[0] >> 1); |
| 700 |
coord[1] = MAXBCOORD4 - (coord[1] >> 1); |
| 701 |
coord[2] = MAXBCOORD4 - (coord[2] >> 1); |
| 702 |
break; |
| 703 |
#ifdef DEBUG |
| 704 |
default: |
| 705 |
eputs("bary_parent():Invalid child\n"); |
| 706 |
break; |
| 707 |
#endif |
| 708 |
} |
| 709 |
} |
| 710 |
|
| 711 |
bary_from_child(coord,child,next) |
| 712 |
BCOORD coord[3]; |
| 713 |
int child,next; |
| 714 |
{ |
| 715 |
#ifdef DEBUG |
| 716 |
if(child <0 || child > 3) |
| 717 |
{ |
| 718 |
eputs("bary_from_child():Invalid child\n"); |
| 719 |
return; |
| 720 |
} |
| 721 |
if(next <0 || next > 3) |
| 722 |
{ |
| 723 |
eputs("bary_from_child():Invalid next\n"); |
| 724 |
return; |
| 725 |
} |
| 726 |
#endif |
| 727 |
if(next == child) |
| 728 |
return; |
| 729 |
|
| 730 |
switch(child){ |
| 731 |
case 0: |
| 732 |
coord[0] = 0; |
| 733 |
coord[1] = MAXBCOORD2 - coord[1]; |
| 734 |
coord[2] = MAXBCOORD2 - coord[2]; |
| 735 |
break; |
| 736 |
case 1: |
| 737 |
coord[0] = MAXBCOORD2 - coord[0]; |
| 738 |
coord[1] = 0; |
| 739 |
coord[2] = MAXBCOORD2 - coord[2]; |
| 740 |
break; |
| 741 |
case 2: |
| 742 |
coord[0] = MAXBCOORD2 - coord[0]; |
| 743 |
coord[1] = MAXBCOORD2 - coord[1]; |
| 744 |
coord[2] = 0; |
| 745 |
break; |
| 746 |
case 3: |
| 747 |
switch(next){ |
| 748 |
case 0: |
| 749 |
coord[0] = 0; |
| 750 |
coord[1] = MAXBCOORD2 - coord[1]; |
| 751 |
coord[2] = MAXBCOORD2 - coord[2]; |
| 752 |
break; |
| 753 |
case 1: |
| 754 |
coord[0] = MAXBCOORD2 - coord[0]; |
| 755 |
coord[1] = 0; |
| 756 |
coord[2] = MAXBCOORD2 - coord[2]; |
| 757 |
break; |
| 758 |
case 2: |
| 759 |
coord[0] = MAXBCOORD2 - coord[0]; |
| 760 |
coord[1] = MAXBCOORD2 - coord[1]; |
| 761 |
coord[2] = 0; |
| 762 |
break; |
| 763 |
} |
| 764 |
break; |
| 765 |
} |
| 766 |
} |
| 767 |
|
| 768 |
int |
| 769 |
bary_child(coord) |
| 770 |
BCOORD coord[3]; |
| 771 |
{ |
| 772 |
int i; |
| 773 |
|
| 774 |
if(coord[0] > MAXBCOORD4) |
| 775 |
{ |
| 776 |
/* update bary for child */ |
| 777 |
coord[0] = (coord[0]<< 1) - MAXBCOORD2; |
| 778 |
coord[1] <<= 1; |
| 779 |
coord[2] <<= 1; |
| 780 |
return(0); |
| 781 |
} |
| 782 |
else |
| 783 |
if(coord[1] > MAXBCOORD4) |
| 784 |
{ |
| 785 |
coord[0] <<= 1; |
| 786 |
coord[1] = (coord[1] << 1) - MAXBCOORD2; |
| 787 |
coord[2] <<= 1; |
| 788 |
return(1); |
| 789 |
} |
| 790 |
else |
| 791 |
if(coord[2] > MAXBCOORD4) |
| 792 |
{ |
| 793 |
coord[0] <<= 1; |
| 794 |
coord[1] <<= 1; |
| 795 |
coord[2] = (coord[2] << 1) - MAXBCOORD2; |
| 796 |
return(2); |
| 797 |
} |
| 798 |
else |
| 799 |
{ |
| 800 |
coord[0] = MAXBCOORD2 - (coord[0] << 1); |
| 801 |
coord[1] = MAXBCOORD2 - (coord[1] << 1); |
| 802 |
coord[2] = MAXBCOORD2 - (coord[2] << 1); |
| 803 |
return(3); |
| 804 |
} |
| 805 |
} |
| 806 |
|
| 807 |
int |
| 808 |
bary_nth_child(coord,i) |
| 809 |
BCOORD coord[3]; |
| 810 |
int i; |
| 811 |
{ |
| 812 |
|
| 813 |
switch(i){ |
| 814 |
case 0: |
| 815 |
/* update bary for child */ |
| 816 |
coord[0] = (coord[0]<< 1) - MAXBCOORD2; |
| 817 |
coord[1] <<= 1; |
| 818 |
coord[2] <<= 1; |
| 819 |
break; |
| 820 |
case 1: |
| 821 |
coord[0] <<= 1; |
| 822 |
coord[1] = (coord[1] << 1) - MAXBCOORD2; |
| 823 |
coord[2] <<= 1; |
| 824 |
break; |
| 825 |
case 2: |
| 826 |
coord[0] <<= 1; |
| 827 |
coord[1] <<= 1; |
| 828 |
coord[2] = (coord[2] << 1) - MAXBCOORD2; |
| 829 |
break; |
| 830 |
case 3: |
| 831 |
coord[0] = MAXBCOORD2 - (coord[0] << 1); |
| 832 |
coord[1] = MAXBCOORD2 - (coord[1] << 1); |
| 833 |
coord[2] = MAXBCOORD2 - (coord[2] << 1); |
| 834 |
break; |
| 835 |
} |
| 836 |
} |
| 837 |
|
| 838 |
|
| 839 |
|
