| 1 |
/* Copyright (c) 1998 Silicon Graphics, Inc. */ |
| 2 |
|
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#ifndef lint |
| 4 |
static char SCCSid[] = "$SunId$ SGI"; |
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#endif |
| 6 |
|
| 7 |
/* |
| 8 |
* sm_geom.c |
| 9 |
*/ |
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|
| 11 |
#include "standard.h" |
| 12 |
#include "sm_geom.h" |
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|
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tri_centroid(v0,v1,v2,c) |
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FVECT v0,v1,v2,c; |
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{ |
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/* Average three triangle vertices to give centroid: return in c */ |
| 18 |
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; |
| 27 |
{ |
| 28 |
return(EQUAL(v1[0],v2[0]) && EQUAL(v1[1],v2[1])&& EQUAL(v1[2],v2[2])); |
| 29 |
} |
| 30 |
|
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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; |
| 35 |
{ |
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FVECT cp01,cp12,cp; |
| 37 |
|
| 38 |
/* test sign of (v0Xv1)X(v1Xv2). v1 */ |
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VCROSS(cp01,v0,v1); |
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VCROSS(cp12,v1,v2); |
| 41 |
VCROSS(cp,cp01,cp12); |
| 42 |
if(DOT(cp,v1) < 0) |
| 43 |
return(FALSE); |
| 44 |
return(TRUE); |
| 45 |
} |
| 46 |
|
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/* calculates the normal of a face contour using Newell's formula. e |
| 48 |
|
| 49 |
a = SUMi (yi - yi+1)(zi + zi+1) |
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b = SUMi (zi - zi+1)(xi + xi+1) |
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c = SUMi (xi - xi+1)(yi + yi+1) |
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*/ |
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double |
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tri_normal(v0,v1,v2,n,norm) |
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FVECT v0,v1,v2,n; |
| 56 |
char norm; |
| 57 |
{ |
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double mag; |
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|
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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 |
|
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n[1] = (v0[2] - v1[2]) * (v0[0] + v1[0]) + |
| 65 |
(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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char 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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int |
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point_relative_to_plane(p,n,nd) |
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FVECT p,n; |
| 96 |
double nd; |
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{ |
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double d; |
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|
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d = p[0]*n[0] + p[1]*n[1] + p[2]*n[2] + nd; |
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if(d < 0) |
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return(-1); |
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if(ZERO(d)) |
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return(0); |
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else |
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return(1); |
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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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int |
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intersect_vector_plane(v,plane_n,plane_d,pd,r) |
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FVECT v,plane_n; |
| 141 |
double plane_d; |
| 142 |
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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|
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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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t = plane_d/-(DOT(plane_n,v)); |
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if(t >0 || ZERO(t)) |
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hit = 1; |
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else |
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hit = 0; |
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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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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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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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/* Solve for t: */ |
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t = -(DOT(plane_n,orig) + plane_d)/(DOT(plane_n,dir)); |
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if(ZERO(t) || t >0) |
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hit = 1; |
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else |
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hit = 0; |
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|
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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 |
| 201 |
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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if(!intersect_vector_plane(p,n,d,NULL,np)) |
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return(FALSE); |
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|
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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); |
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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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test_point_against_spherical_tri(v0,v1,v2,p,n,nset,which,sides) |
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FVECT v0,v1,v2,p; |
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FVECT n[3]; |
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char *nset; |
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char *which; |
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char sides[3]; |
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|
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{ |
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float d; |
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|
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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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} |
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/* Test the point for sidedness */ |
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d = DOT(n[0],p); |
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|
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if(ZERO(d)) |
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sides[0] = GT_EDGE; |
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else |
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if(d > 0) |
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{ |
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sides[0] = GT_OUT; |
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sides[1] = sides[2] = GT_INVALID; |
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return(FALSE); |
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} |
| 282 |
else |
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sides[0] = GT_INTERIOR; |
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|
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/* Test next edge */ |
| 286 |
if(!NTH_BIT(*nset,1)) |
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{ |
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VCROSS(n[1],v2,v1); |
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SET_NTH_BIT(*nset,1); |
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} |
| 291 |
/* Test the point for sidedness */ |
| 292 |
d = DOT(n[1],p); |
| 293 |
if(ZERO(d)) |
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{ |
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sides[1] = GT_EDGE; |
| 296 |
/* If on plane 0-and on plane 1: lies on edge */ |
| 297 |
if(sides[0] == GT_EDGE) |
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{ |
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*which = 1; |
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sides[2] = GT_INVALID; |
| 301 |
return(GT_EDGE); |
| 302 |
} |
| 303 |
} |
| 304 |
else if(d > 0) |
| 305 |
{ |
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sides[1] = GT_OUT; |
| 307 |
sides[2] = GT_INVALID; |
| 308 |
return(FALSE); |
| 309 |
} |
| 310 |
else |
| 311 |
sides[1] = GT_INTERIOR; |
| 312 |
/* Test next edge */ |
| 313 |
if(!NTH_BIT(*nset,2)) |
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{ |
| 315 |
|
| 316 |
VCROSS(n[2],v0,v2); |
| 317 |
SET_NTH_BIT(*nset,2); |
| 318 |
} |
| 319 |
/* Test the point for sidedness */ |
| 320 |
d = DOT(n[2],p); |
| 321 |
if(ZERO(d)) |
| 322 |
{ |
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sides[2] = GT_EDGE; |
| 324 |
|
| 325 |
/* If on plane 0 and 2: lies on edge 0*/ |
| 326 |
if(sides[0] == GT_EDGE) |
| 327 |
{ |
| 328 |
*which = 0; |
| 329 |
return(GT_EDGE); |
| 330 |
} |
| 331 |
/* If on plane 1 and 2: lies on edge 2*/ |
| 332 |
if(sides[1] == GT_EDGE) |
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{ |
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*which = 2; |
| 335 |
return(GT_EDGE); |
| 336 |
} |
| 337 |
/* otherwise: on face 2 */ |
| 338 |
else |
| 339 |
{ |
| 340 |
*which = 2; |
| 341 |
return(GT_FACE); |
| 342 |
} |
| 343 |
} |
| 344 |
else if(d > 0) |
| 345 |
{ |
| 346 |
sides[2] = GT_OUT; |
| 347 |
return(FALSE); |
| 348 |
} |
| 349 |
/* If on edge */ |
| 350 |
else |
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sides[2] = GT_INTERIOR; |
| 352 |
|
| 353 |
/* If on plane 0 only: on face 0 */ |
| 354 |
if(sides[0] == GT_EDGE) |
| 355 |
{ |
| 356 |
*which = 0; |
| 357 |
return(GT_FACE); |
| 358 |
} |
| 359 |
/* If on plane 1 only: on face 1 */ |
| 360 |
if(sides[1] == GT_EDGE) |
| 361 |
{ |
| 362 |
*which = 1; |
| 363 |
return(GT_FACE); |
| 364 |
} |
| 365 |
/* Must be interior to the pyramid */ |
| 366 |
return(GT_INTERIOR); |
| 367 |
} |
| 368 |
|
| 369 |
|
| 370 |
|
| 371 |
|
| 372 |
int |
| 373 |
test_single_point_against_spherical_tri(v0,v1,v2,p,which) |
| 374 |
FVECT v0,v1,v2,p; |
| 375 |
char *which; |
| 376 |
{ |
| 377 |
float d; |
| 378 |
FVECT n; |
| 379 |
char sides[3]; |
| 380 |
|
| 381 |
/* First test if point coincides with any of the vertices */ |
| 382 |
if(EQUAL_VEC3(p,v0)) |
| 383 |
{ |
| 384 |
*which = 0; |
| 385 |
return(GT_VERTEX); |
| 386 |
} |
| 387 |
if(EQUAL_VEC3(p,v1)) |
| 388 |
{ |
| 389 |
*which = 1; |
| 390 |
return(GT_VERTEX); |
| 391 |
} |
| 392 |
if(EQUAL_VEC3(p,v2)) |
| 393 |
{ |
| 394 |
*which = 2; |
| 395 |
return(GT_VERTEX); |
| 396 |
} |
| 397 |
VCROSS(n,v1,v0); |
| 398 |
/* Test the point for sidedness */ |
| 399 |
d = DOT(n,p); |
| 400 |
if(ZERO(d)) |
| 401 |
sides[0] = GT_EDGE; |
| 402 |
else |
| 403 |
if(d > 0) |
| 404 |
return(FALSE); |
| 405 |
else |
| 406 |
sides[0] = GT_INTERIOR; |
| 407 |
/* Test next edge */ |
| 408 |
VCROSS(n,v2,v1); |
| 409 |
/* Test the point for sidedness */ |
| 410 |
d = DOT(n,p); |
| 411 |
if(ZERO(d)) |
| 412 |
{ |
| 413 |
sides[1] = GT_EDGE; |
| 414 |
/* If on plane 0-and on plane 1: lies on edge */ |
| 415 |
if(sides[0] == GT_EDGE) |
| 416 |
{ |
| 417 |
*which = 1; |
| 418 |
return(GT_VERTEX); |
| 419 |
} |
| 420 |
} |
| 421 |
else if(d > 0) |
| 422 |
return(FALSE); |
| 423 |
else |
| 424 |
sides[1] = GT_INTERIOR; |
| 425 |
|
| 426 |
/* Test next edge */ |
| 427 |
VCROSS(n,v0,v2); |
| 428 |
/* Test the point for sidedness */ |
| 429 |
d = DOT(n,p); |
| 430 |
if(ZERO(d)) |
| 431 |
{ |
| 432 |
sides[2] = GT_EDGE; |
| 433 |
|
| 434 |
/* If on plane 0 and 2: lies on edge 0*/ |
| 435 |
if(sides[0] == GT_EDGE) |
| 436 |
{ |
| 437 |
*which = 0; |
| 438 |
return(GT_VERTEX); |
| 439 |
} |
| 440 |
/* If on plane 1 and 2: lies on edge 2*/ |
| 441 |
if(sides[1] == GT_EDGE) |
| 442 |
{ |
| 443 |
*which = 2; |
| 444 |
return(GT_VERTEX); |
| 445 |
} |
| 446 |
/* otherwise: on face 2 */ |
| 447 |
else |
| 448 |
{ |
| 449 |
return(GT_FACE); |
| 450 |
} |
| 451 |
} |
| 452 |
else if(d > 0) |
| 453 |
return(FALSE); |
| 454 |
/* Must be interior to the pyramid */ |
| 455 |
return(GT_FACE); |
| 456 |
} |
| 457 |
|
| 458 |
int |
| 459 |
test_vertices_for_tri_inclusion(t0,t1,t2,p0,p1,p2,nset,n,avg,pt_sides) |
| 460 |
FVECT t0,t1,t2,p0,p1,p2; |
| 461 |
char *nset; |
| 462 |
FVECT n[3]; |
| 463 |
FVECT avg; |
| 464 |
char pt_sides[3][3]; |
| 465 |
|
| 466 |
{ |
| 467 |
char below_plane[3],on_edge,test; |
| 468 |
char which; |
| 469 |
|
| 470 |
SUM_3VEC3(avg,t0,t1,t2); |
| 471 |
on_edge = 0; |
| 472 |
*nset = 0; |
| 473 |
/* Test vertex v[i] against triangle j*/ |
| 474 |
/* Check if v[i] lies below plane defined by avg of 3 vectors |
| 475 |
defining triangle |
| 476 |
*/ |
| 477 |
|
| 478 |
/* test point 0 */ |
| 479 |
if(DOT(avg,p0) < 0) |
| 480 |
below_plane[0] = 1; |
| 481 |
else |
| 482 |
below_plane[0]=0; |
| 483 |
/* Test if b[i] lies in or on triangle a */ |
| 484 |
test = test_point_against_spherical_tri(t0,t1,t2,p0, |
| 485 |
n,nset,&which,pt_sides[0]); |
| 486 |
/* If pts[i] is interior: done */ |
| 487 |
if(!below_plane[0]) |
| 488 |
{ |
| 489 |
if(test == GT_INTERIOR) |
| 490 |
return(TRUE); |
| 491 |
/* Remember if b[i] fell on one of the 3 defining planes */ |
| 492 |
if(test) |
| 493 |
on_edge++; |
| 494 |
} |
| 495 |
/* Now test point 1*/ |
| 496 |
|
| 497 |
if(DOT(avg,p1) < 0) |
| 498 |
below_plane[1] = 1; |
| 499 |
else |
| 500 |
below_plane[1]=0; |
| 501 |
/* Test if b[i] lies in or on triangle a */ |
| 502 |
test = test_point_against_spherical_tri(t0,t1,t2,p1, |
| 503 |
n,nset,&which,pt_sides[1]); |
| 504 |
/* If pts[i] is interior: done */ |
| 505 |
if(!below_plane[1]) |
| 506 |
{ |
| 507 |
if(test == GT_INTERIOR) |
| 508 |
return(TRUE); |
| 509 |
/* Remember if b[i] fell on one of the 3 defining planes */ |
| 510 |
if(test) |
| 511 |
on_edge++; |
| 512 |
} |
| 513 |
|
| 514 |
/* Now test point 2 */ |
| 515 |
if(DOT(avg,p2) < 0) |
| 516 |
below_plane[2] = 1; |
| 517 |
else |
| 518 |
below_plane[2]=0; |
| 519 |
/* Test if b[i] lies in or on triangle a */ |
| 520 |
test = test_point_against_spherical_tri(t0,t1,t2,p2, |
| 521 |
n,nset,&which,pt_sides[2]); |
| 522 |
|
| 523 |
/* If pts[i] is interior: done */ |
| 524 |
if(!below_plane[2]) |
| 525 |
{ |
| 526 |
if(test == GT_INTERIOR) |
| 527 |
return(TRUE); |
| 528 |
/* Remember if b[i] fell on one of the 3 defining planes */ |
| 529 |
if(test) |
| 530 |
on_edge++; |
| 531 |
} |
| 532 |
|
| 533 |
/* If all three points below separating plane: trivial reject */ |
| 534 |
if(below_plane[0] && below_plane[1] && below_plane[2]) |
| 535 |
return(FALSE); |
| 536 |
/* Accept if all points lie on a triangle vertex/edge edge- accept*/ |
| 537 |
if(on_edge == 3) |
| 538 |
return(TRUE); |
| 539 |
/* Now check vertices in a against triangle b */ |
| 540 |
return(FALSE); |
| 541 |
} |
| 542 |
|
| 543 |
|
| 544 |
set_sidedness_tests(t0,t1,t2,p0,p1,p2,test,sides,nset,n) |
| 545 |
FVECT t0,t1,t2,p0,p1,p2; |
| 546 |
char test[3]; |
| 547 |
char sides[3][3]; |
| 548 |
char nset; |
| 549 |
FVECT n[3]; |
| 550 |
{ |
| 551 |
char t; |
| 552 |
double d; |
| 553 |
|
| 554 |
|
| 555 |
/* p=0 */ |
| 556 |
test[0] = 0; |
| 557 |
if(sides[0][0] == GT_INVALID) |
| 558 |
{ |
| 559 |
if(!NTH_BIT(nset,0)) |
| 560 |
VCROSS(n[0],t1,t0); |
| 561 |
/* Test the point for sidedness */ |
| 562 |
d = DOT(n[0],p0); |
| 563 |
if(d >= 0) |
| 564 |
SET_NTH_BIT(test[0],0); |
| 565 |
} |
| 566 |
else |
| 567 |
if(sides[0][0] != GT_INTERIOR) |
| 568 |
SET_NTH_BIT(test[0],0); |
| 569 |
|
| 570 |
if(sides[0][1] == GT_INVALID) |
| 571 |
{ |
| 572 |
if(!NTH_BIT(nset,1)) |
| 573 |
VCROSS(n[1],t2,t1); |
| 574 |
/* Test the point for sidedness */ |
| 575 |
d = DOT(n[1],p0); |
| 576 |
if(d >= 0) |
| 577 |
SET_NTH_BIT(test[0],1); |
| 578 |
} |
| 579 |
else |
| 580 |
if(sides[0][1] != GT_INTERIOR) |
| 581 |
SET_NTH_BIT(test[0],1); |
| 582 |
|
| 583 |
if(sides[0][2] == GT_INVALID) |
| 584 |
{ |
| 585 |
if(!NTH_BIT(nset,2)) |
| 586 |
VCROSS(n[2],t0,t2); |
| 587 |
/* Test the point for sidedness */ |
| 588 |
d = DOT(n[2],p0); |
| 589 |
if(d >= 0) |
| 590 |
SET_NTH_BIT(test[0],2); |
| 591 |
} |
| 592 |
else |
| 593 |
if(sides[0][2] != GT_INTERIOR) |
| 594 |
SET_NTH_BIT(test[0],2); |
| 595 |
|
| 596 |
/* p=1 */ |
| 597 |
test[1] = 0; |
| 598 |
/* t=0*/ |
| 599 |
if(sides[1][0] == GT_INVALID) |
| 600 |
{ |
| 601 |
if(!NTH_BIT(nset,0)) |
| 602 |
VCROSS(n[0],t1,t0); |
| 603 |
/* Test the point for sidedness */ |
| 604 |
d = DOT(n[0],p1); |
| 605 |
if(d >= 0) |
| 606 |
SET_NTH_BIT(test[1],0); |
| 607 |
} |
| 608 |
else |
| 609 |
if(sides[1][0] != GT_INTERIOR) |
| 610 |
SET_NTH_BIT(test[1],0); |
| 611 |
|
| 612 |
/* t=1 */ |
| 613 |
if(sides[1][1] == GT_INVALID) |
| 614 |
{ |
| 615 |
if(!NTH_BIT(nset,1)) |
| 616 |
VCROSS(n[1],t2,t1); |
| 617 |
/* Test the point for sidedness */ |
| 618 |
d = DOT(n[1],p1); |
| 619 |
if(d >= 0) |
| 620 |
SET_NTH_BIT(test[1],1); |
| 621 |
} |
| 622 |
else |
| 623 |
if(sides[1][1] != GT_INTERIOR) |
| 624 |
SET_NTH_BIT(test[1],1); |
| 625 |
|
| 626 |
/* t=2 */ |
| 627 |
if(sides[1][2] == GT_INVALID) |
| 628 |
{ |
| 629 |
if(!NTH_BIT(nset,2)) |
| 630 |
VCROSS(n[2],t0,t2); |
| 631 |
/* Test the point for sidedness */ |
| 632 |
d = DOT(n[2],p1); |
| 633 |
if(d >= 0) |
| 634 |
SET_NTH_BIT(test[1],2); |
| 635 |
} |
| 636 |
else |
| 637 |
if(sides[1][2] != GT_INTERIOR) |
| 638 |
SET_NTH_BIT(test[1],2); |
| 639 |
|
| 640 |
/* p=2 */ |
| 641 |
test[2] = 0; |
| 642 |
/* t = 0 */ |
| 643 |
if(sides[2][0] == GT_INVALID) |
| 644 |
{ |
| 645 |
if(!NTH_BIT(nset,0)) |
| 646 |
VCROSS(n[0],t1,t0); |
| 647 |
/* Test the point for sidedness */ |
| 648 |
d = DOT(n[0],p2); |
| 649 |
if(d >= 0) |
| 650 |
SET_NTH_BIT(test[2],0); |
| 651 |
} |
| 652 |
else |
| 653 |
if(sides[2][0] != GT_INTERIOR) |
| 654 |
SET_NTH_BIT(test[2],0); |
| 655 |
/* t=1 */ |
| 656 |
if(sides[2][1] == GT_INVALID) |
| 657 |
{ |
| 658 |
if(!NTH_BIT(nset,1)) |
| 659 |
VCROSS(n[1],t2,t1); |
| 660 |
/* Test the point for sidedness */ |
| 661 |
d = DOT(n[1],p2); |
| 662 |
if(d >= 0) |
| 663 |
SET_NTH_BIT(test[2],1); |
| 664 |
} |
| 665 |
else |
| 666 |
if(sides[2][1] != GT_INTERIOR) |
| 667 |
SET_NTH_BIT(test[2],1); |
| 668 |
/* t=2 */ |
| 669 |
if(sides[2][2] == GT_INVALID) |
| 670 |
{ |
| 671 |
if(!NTH_BIT(nset,2)) |
| 672 |
VCROSS(n[2],t0,t2); |
| 673 |
/* Test the point for sidedness */ |
| 674 |
d = DOT(n[2],p2); |
| 675 |
if(d >= 0) |
| 676 |
SET_NTH_BIT(test[2],2); |
| 677 |
} |
| 678 |
else |
| 679 |
if(sides[2][2] != GT_INTERIOR) |
| 680 |
SET_NTH_BIT(test[2],2); |
| 681 |
} |
| 682 |
|
| 683 |
|
| 684 |
int |
| 685 |
spherical_tri_intersect(a1,a2,a3,b1,b2,b3) |
| 686 |
FVECT a1,a2,a3,b1,b2,b3; |
| 687 |
{ |
| 688 |
char which,test,n_set[2]; |
| 689 |
char sides[2][3][3],i,j,inext,jnext; |
| 690 |
char tests[2][3]; |
| 691 |
FVECT n[2][3],p,avg[2]; |
| 692 |
|
| 693 |
/* Test the vertices of triangle a against the pyramid formed by triangle |
| 694 |
b and the origin. If any vertex of a is interior to triangle b, or |
| 695 |
if all 3 vertices of a are ON the edges of b,return TRUE. Remember |
| 696 |
the results of the edge normal and sidedness tests for later. |
| 697 |
*/ |
| 698 |
if(test_vertices_for_tri_inclusion(a1,a2,a3,b1,b2,b3, |
| 699 |
&(n_set[0]),n[0],avg[0],sides[1])) |
| 700 |
return(TRUE); |
| 701 |
|
| 702 |
if(test_vertices_for_tri_inclusion(b1,b2,b3,a1,a2,a3, |
| 703 |
&(n_set[1]),n[1],avg[1],sides[0])) |
| 704 |
return(TRUE); |
| 705 |
|
| 706 |
|
| 707 |
set_sidedness_tests(b1,b2,b3,a1,a2,a3,tests[0],sides[0],n_set[1],n[1]); |
| 708 |
if(tests[0][0]&tests[0][1]&tests[0][2]) |
| 709 |
return(FALSE); |
| 710 |
|
| 711 |
set_sidedness_tests(a1,a2,a3,b1,b2,b3,tests[1],sides[1],n_set[0],n[0]); |
| 712 |
if(tests[1][0]&tests[1][1]&tests[1][2]) |
| 713 |
return(FALSE); |
| 714 |
|
| 715 |
for(j=0; j < 3;j++) |
| 716 |
{ |
| 717 |
jnext = (j+1)%3; |
| 718 |
/* IF edge b doesnt cross any great circles of a, punt */ |
| 719 |
if(tests[1][j] & tests[1][jnext]) |
| 720 |
continue; |
| 721 |
for(i=0;i<3;i++) |
| 722 |
{ |
| 723 |
inext = (i+1)%3; |
| 724 |
/* IF edge a doesnt cross any great circles of b, punt */ |
| 725 |
if(tests[0][i] & tests[0][inext]) |
| 726 |
continue; |
| 727 |
/* Now find the great circles that cross and test */ |
| 728 |
if((NTH_BIT(tests[0][i],j)^(NTH_BIT(tests[0][inext],j))) |
| 729 |
&& (NTH_BIT(tests[1][j],i)^NTH_BIT(tests[1][jnext],i))) |
| 730 |
{ |
| 731 |
VCROSS(p,n[0][i],n[1][j]); |
| 732 |
|
| 733 |
/* If zero cp= done */ |
| 734 |
if(ZERO_VEC3(p)) |
| 735 |
continue; |
| 736 |
/* check above both planes */ |
| 737 |
if(DOT(avg[0],p) < 0 || DOT(avg[1],p) < 0) |
| 738 |
{ |
| 739 |
NEGATE_VEC3(p); |
| 740 |
if(DOT(avg[0],p) < 0 || DOT(avg[1],p) < 0) |
| 741 |
continue; |
| 742 |
} |
| 743 |
return(TRUE); |
| 744 |
} |
| 745 |
} |
| 746 |
} |
| 747 |
return(FALSE); |
| 748 |
} |
| 749 |
|
| 750 |
int |
| 751 |
ray_intersect_tri(orig,dir,v0,v1,v2,pt,wptr) |
| 752 |
FVECT orig,dir; |
| 753 |
FVECT v0,v1,v2; |
| 754 |
FVECT pt; |
| 755 |
char *wptr; |
| 756 |
{ |
| 757 |
FVECT p0,p1,p2,p,n; |
| 758 |
char type,which; |
| 759 |
double pd; |
| 760 |
|
| 761 |
point_on_sphere(p0,v0,orig); |
| 762 |
point_on_sphere(p1,v1,orig); |
| 763 |
point_on_sphere(p2,v2,orig); |
| 764 |
type = test_single_point_against_spherical_tri(p0,p1,p2,dir,&which); |
| 765 |
|
| 766 |
if(type) |
| 767 |
{ |
| 768 |
/* Intersect the ray with the triangle plane */ |
| 769 |
tri_plane_equation(v0,v1,v2,n,&pd,FALSE); |
| 770 |
intersect_ray_plane(orig,dir,n,pd,NULL,pt); |
| 771 |
} |
| 772 |
if(wptr) |
| 773 |
*wptr = which; |
| 774 |
|
| 775 |
return(type); |
| 776 |
} |
| 777 |
|
| 778 |
|
| 779 |
calculate_view_frustum(vp,hv,vv,horiz,vert,near,far,fnear,ffar) |
| 780 |
FVECT vp,hv,vv; |
| 781 |
double horiz,vert,near,far; |
| 782 |
FVECT fnear[4],ffar[4]; |
| 783 |
{ |
| 784 |
double height,width; |
| 785 |
FVECT t,nhv,nvv,ndv; |
| 786 |
double w2,h2; |
| 787 |
/* Calculate the x and y dimensions of the near face */ |
| 788 |
/* hv and vv are the horizontal and vertical vectors in the |
| 789 |
view frame-the magnitude is the dimension of the front frustum |
| 790 |
face at z =1 |
| 791 |
*/ |
| 792 |
VCOPY(nhv,hv); |
| 793 |
VCOPY(nvv,vv); |
| 794 |
w2 = normalize(nhv); |
| 795 |
h2 = normalize(nvv); |
| 796 |
/* Use similar triangles to calculate the dimensions at z=near */ |
| 797 |
width = near*0.5*w2; |
| 798 |
height = near*0.5*h2; |
| 799 |
|
| 800 |
VCROSS(ndv,nvv,nhv); |
| 801 |
/* Calculate the world space points corresponding to the 4 corners |
| 802 |
of the front face of the view frustum |
| 803 |
*/ |
| 804 |
fnear[0][0] = width*nhv[0] + height*nvv[0] + near*ndv[0] + vp[0] ; |
| 805 |
fnear[0][1] = width*nhv[1] + height*nvv[1] + near*ndv[1] + vp[1]; |
| 806 |
fnear[0][2] = width*nhv[2] + height*nvv[2] + near*ndv[2] + vp[2]; |
| 807 |
fnear[1][0] = -width*nhv[0] + height*nvv[0] + near*ndv[0] + vp[0]; |
| 808 |
fnear[1][1] = -width*nhv[1] + height*nvv[1] + near*ndv[1] + vp[1]; |
| 809 |
fnear[1][2] = -width*nhv[2] + height*nvv[2] + near*ndv[2] + vp[2]; |
| 810 |
fnear[2][0] = -width*nhv[0] - height*nvv[0] + near*ndv[0] + vp[0]; |
| 811 |
fnear[2][1] = -width*nhv[1] - height*nvv[1] + near*ndv[1] + vp[1]; |
| 812 |
fnear[2][2] = -width*nhv[2] - height*nvv[2] + near*ndv[2] + vp[2]; |
| 813 |
fnear[3][0] = width*nhv[0] - height*nvv[0] + near*ndv[0] + vp[0]; |
| 814 |
fnear[3][1] = width*nhv[1] - height*nvv[1] + near*ndv[1] + vp[1]; |
| 815 |
fnear[3][2] = width*nhv[2] - height*nvv[2] + near*ndv[2] + vp[2]; |
| 816 |
|
| 817 |
/* Now do the far face */ |
| 818 |
width = far*0.5*w2; |
| 819 |
height = far*0.5*h2; |
| 820 |
ffar[0][0] = width*nhv[0] + height*nvv[0] + far*ndv[0] + vp[0] ; |
| 821 |
ffar[0][1] = width*nhv[1] + height*nvv[1] + far*ndv[1] + vp[1] ; |
| 822 |
ffar[0][2] = width*nhv[2] + height*nvv[2] + far*ndv[2] + vp[2] ; |
| 823 |
ffar[1][0] = -width*nhv[0] + height*nvv[0] + far*ndv[0] + vp[0] ; |
| 824 |
ffar[1][1] = -width*nhv[1] + height*nvv[1] + far*ndv[1] + vp[1] ; |
| 825 |
ffar[1][2] = -width*nhv[2] + height*nvv[2] + far*ndv[2] + vp[2] ; |
| 826 |
ffar[2][0] = -width*nhv[0] - height*nvv[0] + far*ndv[0] + vp[0] ; |
| 827 |
ffar[2][1] = -width*nhv[1] - height*nvv[1] + far*ndv[1] + vp[1] ; |
| 828 |
ffar[2][2] = -width*nhv[2] - height*nvv[2] + far*ndv[2] + vp[2] ; |
| 829 |
ffar[3][0] = width*nhv[0] - height*nvv[0] + far*ndv[0] + vp[0] ; |
| 830 |
ffar[3][1] = width*nhv[1] - height*nvv[1] + far*ndv[1] + vp[1] ; |
| 831 |
ffar[3][2] = width*nhv[2] - height*nvv[2] + far*ndv[2] + vp[2] ; |
| 832 |
} |
| 833 |
|
| 834 |
|
| 835 |
|
| 836 |
|
| 837 |
int |
| 838 |
spherical_polygon_edge_intersect(a0,a1,b0,b1) |
| 839 |
FVECT a0,a1,b0,b1; |
| 840 |
{ |
| 841 |
FVECT na,nb,avga,avgb,p; |
| 842 |
double d; |
| 843 |
int sb0,sb1,sa0,sa1; |
| 844 |
|
| 845 |
/* First test if edge b straddles great circle of a */ |
| 846 |
VCROSS(na,a0,a1); |
| 847 |
d = DOT(na,b0); |
| 848 |
sb0 = ZERO(d)?0:(d<0)? -1: 1; |
| 849 |
d = DOT(na,b1); |
| 850 |
sb1 = ZERO(d)?0:(d<0)? -1: 1; |
| 851 |
/* edge b entirely on one side of great circle a: edges cannot intersect*/ |
| 852 |
if(sb0*sb1 > 0) |
| 853 |
return(FALSE); |
| 854 |
/* test if edge a straddles great circle of b */ |
| 855 |
VCROSS(nb,b0,b1); |
| 856 |
d = DOT(nb,a0); |
| 857 |
sa0 = ZERO(d)?0:(d<0)? -1: 1; |
| 858 |
d = DOT(nb,a1); |
| 859 |
sa1 = ZERO(d)?0:(d<0)? -1: 1; |
| 860 |
/* edge a entirely on one side of great circle b: edges cannot intersect*/ |
| 861 |
if(sa0*sa1 > 0) |
| 862 |
return(FALSE); |
| 863 |
|
| 864 |
/* Find one of intersection points of the great circles */ |
| 865 |
VCROSS(p,na,nb); |
| 866 |
/* If they lie on same great circle: call an intersection */ |
| 867 |
if(ZERO_VEC3(p)) |
| 868 |
return(TRUE); |
| 869 |
|
| 870 |
VADD(avga,a0,a1); |
| 871 |
VADD(avgb,b0,b1); |
| 872 |
if(DOT(avga,p) < 0 || DOT(avgb,p) < 0) |
| 873 |
{ |
| 874 |
NEGATE_VEC3(p); |
| 875 |
if(DOT(avga,p) < 0 || DOT(avgb,p) < 0) |
| 876 |
return(FALSE); |
| 877 |
} |
| 878 |
if((!sb0 || !sb1) && (!sa0 || !sa1)) |
| 879 |
return(FALSE); |
| 880 |
return(TRUE); |
| 881 |
} |
| 882 |
|
