| 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) |
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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 |
} |
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|
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|
| 24 |
int |
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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 |
|
| 31 |
|
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int |
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convex_angle(v0,v1,v2) |
| 34 |
FVECT v0,v1,v2; |
| 35 |
{ |
| 36 |
FVECT cp01,cp12,cp; |
| 37 |
|
| 38 |
/* test sign of (v0Xv1)X(v1Xv2). v1 */ |
| 39 |
VCROSS(cp01,v0,v1); |
| 40 |
VCROSS(cp12,v1,v2); |
| 41 |
VCROSS(cp,cp01,cp12); |
| 42 |
if(DOT(cp,v1) < 0.0) |
| 43 |
return(FALSE); |
| 44 |
return(TRUE); |
| 45 |
} |
| 46 |
|
| 47 |
/* calculates the normal of a face contour using Newell's formula. e |
| 48 |
|
| 49 |
a = SUMi (yi - yi+1)(zi + zi+1) |
| 50 |
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) |
| 55 |
FVECT v0,v1,v2,n; |
| 56 |
int norm; |
| 57 |
{ |
| 58 |
double mag; |
| 59 |
|
| 60 |
n[0] = (v0[2] + v1[2]) * (v0[1] - v1[1]) + |
| 61 |
(v1[2] + v2[2]) * (v1[1] - v2[1]) + |
| 62 |
(v2[2] + v0[2]) * (v2[1] - v0[1]); |
| 63 |
|
| 64 |
n[1] = (v0[2] - v1[2]) * (v0[0] + v1[0]) + |
| 65 |
(v1[2] - v2[2]) * (v1[0] + v2[0]) + |
| 66 |
(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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|
| 73 |
if(!norm) |
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return(0); |
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|
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|
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mag = normalize(n); |
| 78 |
|
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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; |
| 85 |
double *nd; |
| 86 |
int norm; |
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{ |
| 88 |
tri_normal(v0,v1,v2,n,norm); |
| 89 |
|
| 90 |
*nd = -(DOT(n,v0)); |
| 91 |
} |
| 92 |
|
| 93 |
/* From quad_edge-code */ |
| 94 |
int |
| 95 |
point_in_circle_thru_origin(p,p0,p1) |
| 96 |
FVECT p; |
| 97 |
FVECT p0,p1; |
| 98 |
{ |
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|
| 100 |
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) |
| 129 |
FVECT v,plane_n; |
| 130 |
double plane_d; |
| 131 |
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 */ |
| 142 |
|
| 143 |
/* Solve for t: */ |
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d = -(DOT(plane_n,v)); |
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if(ZERO(d)) |
| 146 |
{ |
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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; |
| 172 |
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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|
| 197 |
if(pd) |
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*pd = t; |
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return(hit); |
| 200 |
} |
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|
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|
| 203 |
int |
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intersect_edge_plane(e0,e1,plane_n,plane_d,pd,r) |
| 205 |
FVECT e0,e1; |
| 206 |
FVECT plane_n; |
| 207 |
double plane_d; |
| 208 |
double *pd; |
| 209 |
FVECT r; |
| 210 |
{ |
| 211 |
double t; |
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int hit; |
| 213 |
FVECT d; |
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/* |
| 215 |
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 |
| 257 |
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?*/ |
| 261 |
if(!intersect_vector_plane(p,n,d,NULL,np)) |
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return(FALSE); |
| 263 |
|
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/* 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); |
| 270 |
|
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VSUB(p1,p1,p0); |
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VSUB(p2,p2,p0); |
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VSUB(np,np,p0); |
| 274 |
|
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p1[0] = VLEN(p1); |
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p1[1] = 0; |
| 277 |
|
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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; |
| 281 |
p2[1] = d2; |
| 282 |
|
| 283 |
d1 = DOT(np,x_axis); |
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d2 = DOT(np,y_axis); |
| 285 |
np[0] = d1; |
| 286 |
np[1] = d2; |
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|
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/* perform the in-circle test in the new coordinate system */ |
| 289 |
return(point_in_circle_thru_origin(np,p1,p2)); |
| 290 |
} |
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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]; |
| 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],v1,v0); |
| 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],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 |
|
| 740 |
|
| 741 |
|
| 742 |
int |
| 743 |
sedge_intersect(a0,a1,b0,b1) |
| 744 |
FVECT a0,a1,b0,b1; |
| 745 |
{ |
| 746 |
FVECT na,nb,avga,avgb,p; |
| 747 |
double d; |
| 748 |
int sb0,sb1,sa0,sa1; |
| 749 |
|
| 750 |
/* First test if edge b straddles great circle of a */ |
| 751 |
VCROSS(na,a0,a1); |
| 752 |
d = DOT(na,b0); |
| 753 |
sb0 = ZERO(d)?0:(d<0)? -1: 1; |
| 754 |
d = DOT(na,b1); |
| 755 |
sb1 = ZERO(d)?0:(d<0)? -1: 1; |
| 756 |
/* edge b entirely on one side of great circle a: edges cannot intersect*/ |
| 757 |
if(sb0*sb1 > 0) |
| 758 |
return(FALSE); |
| 759 |
/* test if edge a straddles great circle of b */ |
| 760 |
VCROSS(nb,b0,b1); |
| 761 |
d = DOT(nb,a0); |
| 762 |
sa0 = ZERO(d)?0:(d<0)? -1: 1; |
| 763 |
d = DOT(nb,a1); |
| 764 |
sa1 = ZERO(d)?0:(d<0)? -1: 1; |
| 765 |
/* edge a entirely on one side of great circle b: edges cannot intersect*/ |
| 766 |
if(sa0*sa1 > 0) |
| 767 |
return(FALSE); |
| 768 |
|
| 769 |
/* Find one of intersection points of the great circles */ |
| 770 |
VCROSS(p,na,nb); |
| 771 |
/* If they lie on same great circle: call an intersection */ |
| 772 |
if(ZERO_VEC3(p)) |
| 773 |
return(TRUE); |
| 774 |
|
| 775 |
VADD(avga,a0,a1); |
| 776 |
VADD(avgb,b0,b1); |
| 777 |
if(DOT(avga,p) < 0 || DOT(avgb,p) < 0) |
| 778 |
{ |
| 779 |
NEGATE_VEC3(p); |
| 780 |
if(DOT(avga,p) < 0 || DOT(avgb,p) < 0) |
| 781 |
return(FALSE); |
| 782 |
} |
| 783 |
if((!sb0 || !sb1) && (!sa0 || !sa1)) |
| 784 |
return(FALSE); |
| 785 |
return(TRUE); |
| 786 |
} |
| 787 |
|
| 788 |
|
| 789 |
|
| 790 |
/* Find the normalized barycentric coordinates of p relative to |
| 791 |
* triangle v0,v1,v2. Return result in coord |
| 792 |
*/ |
| 793 |
bary2d(x1,y1,x2,y2,x3,y3,px,py,coord) |
| 794 |
double x1,y1,x2,y2,x3,y3; |
| 795 |
double px,py; |
| 796 |
double coord[3]; |
| 797 |
{ |
| 798 |
double a; |
| 799 |
|
| 800 |
a = (x2 - x1) * (y3 - y1) - (x3 - x1) * (y2 - y1); |
| 801 |
coord[0] = ((x2 - px) * (y3 - py) - (x3 - px) * (y2 - py)) / a; |
| 802 |
coord[1] = ((x3 - px) * (y1 - py) - (x1 - px) * (y3 - py)) / a; |
| 803 |
coord[2] = 1.0 - coord[0] - coord[1]; |
| 804 |
|
| 805 |
} |
| 806 |
|
| 807 |
bary_ith_child(coord,i) |
| 808 |
double coord[3]; |
| 809 |
int i; |
| 810 |
{ |
| 811 |
|
| 812 |
switch(i){ |
| 813 |
case 0: |
| 814 |
/* update bary for child */ |
| 815 |
coord[0] = 2.0*coord[0]- 1.0; |
| 816 |
coord[1] *= 2.0; |
| 817 |
coord[2] *= 2.0; |
| 818 |
break; |
| 819 |
case 1: |
| 820 |
coord[0] *= 2.0; |
| 821 |
coord[1] = 2.0*coord[1]- 1.0; |
| 822 |
coord[2] *= 2.0; |
| 823 |
break; |
| 824 |
case 2: |
| 825 |
coord[0] *= 2.0; |
| 826 |
coord[1] *= 2.0; |
| 827 |
coord[2] = 2.0*coord[2]- 1.0; |
| 828 |
break; |
| 829 |
case 3: |
| 830 |
coord[0] = 1.0 - 2.0*coord[0]; |
| 831 |
coord[1] = 1.0 - 2.0*coord[1]; |
| 832 |
coord[2] = 1.0 - 2.0*coord[2]; |
| 833 |
break; |
| 834 |
#ifdef DEBUG |
| 835 |
default: |
| 836 |
eputs("bary_ith_child():Invalid child\n"); |
| 837 |
break; |
| 838 |
#endif |
| 839 |
} |
| 840 |
} |
| 841 |
|
| 842 |
|
| 843 |
int |
| 844 |
bary_child(coord) |
| 845 |
double coord[3]; |
| 846 |
{ |
| 847 |
int i; |
| 848 |
|
| 849 |
if(coord[0] > 0.5) |
| 850 |
{ |
| 851 |
/* update bary for child */ |
| 852 |
coord[0] = 2.0*coord[0]- 1.0; |
| 853 |
coord[1] *= 2.0; |
| 854 |
coord[2] *= 2.0; |
| 855 |
return(0); |
| 856 |
} |
| 857 |
else |
| 858 |
if(coord[1] > 0.5) |
| 859 |
{ |
| 860 |
coord[0] *= 2.0; |
| 861 |
coord[1] = 2.0*coord[1]- 1.0; |
| 862 |
coord[2] *= 2.0; |
| 863 |
return(1); |
| 864 |
} |
| 865 |
else |
| 866 |
if(coord[2] > 0.5) |
| 867 |
{ |
| 868 |
coord[0] *= 2.0; |
| 869 |
coord[1] *= 2.0; |
| 870 |
coord[2] = 2.0*coord[2]- 1.0; |
| 871 |
return(2); |
| 872 |
} |
| 873 |
else |
| 874 |
{ |
| 875 |
coord[0] = 1.0 - 2.0*coord[0]; |
| 876 |
coord[1] = 1.0 - 2.0*coord[1]; |
| 877 |
coord[2] = 1.0 - 2.0*coord[2]; |
| 878 |
return(3); |
| 879 |
} |
| 880 |
} |
| 881 |
|
| 882 |
/* Coord was the ith child of the parent: set the coordinate |
| 883 |
relative to the parent |
| 884 |
*/ |
| 885 |
bary_parent(coord,i) |
| 886 |
double coord[3]; |
| 887 |
int i; |
| 888 |
{ |
| 889 |
|
| 890 |
switch(i) { |
| 891 |
case 0: |
| 892 |
/* update bary for child */ |
| 893 |
coord[0] = coord[0]*0.5 + 0.5; |
| 894 |
coord[1] *= 0.5; |
| 895 |
coord[2] *= 0.5; |
| 896 |
break; |
| 897 |
case 1: |
| 898 |
coord[0] *= 0.5; |
| 899 |
coord[1] = coord[1]*0.5 + 0.5; |
| 900 |
coord[2] *= 0.5; |
| 901 |
break; |
| 902 |
|
| 903 |
case 2: |
| 904 |
coord[0] *= 0.5; |
| 905 |
coord[1] *= 0.5; |
| 906 |
coord[2] = coord[2]*0.5 + 0.5; |
| 907 |
break; |
| 908 |
|
| 909 |
case 3: |
| 910 |
coord[0] = 0.5 - 0.5*coord[0]; |
| 911 |
coord[1] = 0.5 - 0.5*coord[1]; |
| 912 |
coord[2] = 0.5 - 0.5*coord[2]; |
| 913 |
break; |
| 914 |
#ifdef DEBUG |
| 915 |
default: |
| 916 |
eputs("bary_parent():Invalid child\n"); |
| 917 |
break; |
| 918 |
#endif |
| 919 |
} |
| 920 |
} |
| 921 |
|
| 922 |
bary_from_child(coord,child,next) |
| 923 |
double coord[3]; |
| 924 |
int child,next; |
| 925 |
{ |
| 926 |
#ifdef DEBUG |
| 927 |
if(child <0 || child > 3) |
| 928 |
{ |
| 929 |
eputs("bary_from_child():Invalid child\n"); |
| 930 |
return; |
| 931 |
} |
| 932 |
if(next <0 || next > 3) |
| 933 |
{ |
| 934 |
eputs("bary_from_child():Invalid next\n"); |
| 935 |
return; |
| 936 |
} |
| 937 |
#endif |
| 938 |
if(next == child) |
| 939 |
return; |
| 940 |
|
| 941 |
switch(child){ |
| 942 |
case 0: |
| 943 |
switch(next){ |
| 944 |
case 1: |
| 945 |
coord[0] += 1.0; |
| 946 |
coord[1] -= 1.0; |
| 947 |
break; |
| 948 |
case 2: |
| 949 |
coord[0] += 1.0; |
| 950 |
coord[2] -= 1.0; |
| 951 |
break; |
| 952 |
case 3: |
| 953 |
coord[0] *= -1.0; |
| 954 |
coord[1] = 1 - coord[1]; |
| 955 |
coord[2] = 1 - coord[2]; |
| 956 |
break; |
| 957 |
|
| 958 |
} |
| 959 |
break; |
| 960 |
case 1: |
| 961 |
switch(next){ |
| 962 |
case 0: |
| 963 |
coord[0] -= 1.0; |
| 964 |
coord[1] += 1.0; |
| 965 |
break; |
| 966 |
case 2: |
| 967 |
coord[1] += 1.0; |
| 968 |
coord[2] -= 1.0; |
| 969 |
break; |
| 970 |
case 3: |
| 971 |
coord[0] = 1 - coord[0]; |
| 972 |
coord[1] *= -1.0; |
| 973 |
coord[2] = 1 - coord[2]; |
| 974 |
break; |
| 975 |
} |
| 976 |
break; |
| 977 |
case 2: |
| 978 |
switch(next){ |
| 979 |
case 0: |
| 980 |
coord[0] -= 1.0; |
| 981 |
coord[2] += 1.0; |
| 982 |
break; |
| 983 |
case 1: |
| 984 |
coord[1] -= 1.0; |
| 985 |
coord[2] += 1.0; |
| 986 |
break; |
| 987 |
case 3: |
| 988 |
coord[0] = 1 - coord[0]; |
| 989 |
coord[1] = 1 - coord[1]; |
| 990 |
coord[2] *= -1.0; |
| 991 |
break; |
| 992 |
} |
| 993 |
break; |
| 994 |
case 3: |
| 995 |
switch(next){ |
| 996 |
case 0: |
| 997 |
coord[0] *= -1.0; |
| 998 |
coord[1] = 1 - coord[1]; |
| 999 |
coord[2] = 1 - coord[2]; |
| 1000 |
break; |
| 1001 |
case 1: |
| 1002 |
coord[0] = 1 - coord[0]; |
| 1003 |
coord[1] *= -1.0; |
| 1004 |
coord[2] = 1 - coord[2]; |
| 1005 |
break; |
| 1006 |
case 2: |
| 1007 |
coord[0] = 1 - coord[0]; |
| 1008 |
coord[1] = 1 - coord[1]; |
| 1009 |
coord[2] *= -1.0; |
| 1010 |
break; |
| 1011 |
} |
| 1012 |
break; |
| 1013 |
} |
| 1014 |
} |
| 1015 |
|
| 1016 |
int |
| 1017 |
max_index(v) |
| 1018 |
FVECT v; |
| 1019 |
{ |
| 1020 |
double a,b,c; |
| 1021 |
int i; |
| 1022 |
|
| 1023 |
a = fabs(v[0]); |
| 1024 |
b = fabs(v[1]); |
| 1025 |
c = fabs(v[2]); |
| 1026 |
i = (a>=b)?((a>=c)?0:2):((b>=c)?1:2); |
| 1027 |
return(i); |
| 1028 |
} |
| 1029 |
|
| 1030 |
int |
| 1031 |
closest_point_in_tri(p0,p1,p2,p,p0id,p1id,p2id) |
| 1032 |
FVECT p0,p1,p2,p; |
| 1033 |
int p0id,p1id,p2id; |
| 1034 |
{ |
| 1035 |
double d,d1; |
| 1036 |
int i; |
| 1037 |
|
| 1038 |
d = DIST_SQ(p,p0); |
| 1039 |
d1 = DIST_SQ(p,p1); |
| 1040 |
if(d < d1) |
| 1041 |
{ |
| 1042 |
d1 = DIST_SQ(p,p2); |
| 1043 |
i = (d1 < d)?p2id:p0id; |
| 1044 |
} |
| 1045 |
else |
| 1046 |
{ |
| 1047 |
d = DIST_SQ(p,p2); |
| 1048 |
i = (d < d1)? p2id:p1id; |
| 1049 |
} |
| 1050 |
return(i); |
| 1051 |
} |
| 1052 |
|
| 1053 |
|
| 1054 |
|
| 1055 |
|
| 1056 |
|
| 1057 |
|
| 1058 |
|
