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#ifndef lint
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static const char RCSid[] = "$Id: sm_geom.c,v 3.13 2003/02/22 02:07:25 greg Exp $";
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#endif
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/*
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* sm_geom.c
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* some geometric utility routines
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*/
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#include "standard.h"
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#include "sm_geom.h"
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/*
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* int
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* pt_in_cone(p,a,b,c)
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* : test if point p lies in cone defined by a,b,c and origin
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* double p[3]; : point to test
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* double a[3],b[3],c[3]; : points forming triangle
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*
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* Assumes apex at origin, a,b,c are unit vectors defining the
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* triangle which the cone circumscribes. Assumes p is also normalized
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* Test is implemented as:
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* r = (b-a)X(c-a)
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* in = (p.r) > (a.r)
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* The center of the cone is r, and corresponds to the triangle normal.
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* p.r is the proportional to the cosine of the angle between p and the
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* the cone center ray, and a.r to the radius of the cone. If the cosine
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* of the angle for p is greater than that for a, the angle between p
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* and r is smaller, and p lies in the cone.
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*/
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int
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pt_in_cone(p,a,b,c)
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double p[3],a[3],b[3],c[3];
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{
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double r[3];
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double pr,ar;
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double ab[3],ac[3];
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#ifdef DEBUG
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#if DEBUG > 1
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{
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double l;
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VSUB(ab,b,a);
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normalize(ab);
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VSUB(ac,c,a);
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normalize(ac);
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VCROSS(r,ab,ac);
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l = normalize(r);
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/* l = sin@ between ab,ac - if 0 vectors are colinear */
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if( l <= COLINEAR_EPS)
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{
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eputs("pt in cone: null triangle:returning FALSE\n");
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return(FALSE);
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}
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}
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#endif
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#endif
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VSUB(ab,b,a);
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VSUB(ac,c,a);
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VCROSS(r,ab,ac);
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pr = DOT(p,r);
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ar = DOT(a,r);
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/* Need to check for equality for degeneracy of 4 points on circle */
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if( pr > ar *( 1.0 + EQUALITY_EPS))
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return(TRUE);
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else
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return(FALSE);
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}
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/*
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* tri_centroid(v0,v1,v2,c)
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* : Average triangle vertices to give centroid: return in c
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*FVECT v0,v1,v2,c; : triangle vertices(v0,v1,v2) and vector to hold result(c)
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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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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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* double
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* tri_normal(v0,v1,v2,n,norm) : Calculates the normal of a face contour using
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* Newell's formula.
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* FVECT v0,v1,v2,n; : Triangle vertices(v0,v1,v2) and vector for result(n)
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* int norm; : If true result is normalized
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*
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* Triangle normal is calculated using the following:
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* A = SUMi (yi - yi+1)(zi + zi+1);
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* B = SUMi (zi - zi+1)(xi + xi+1)
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* C = SUMi (xi - xi+1)(yi + yi+1)
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*/
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double
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tri_normal(v0,v1,v2,n,norm)
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FVECT v0,v1,v2,n;
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int norm;
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{
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double mag;
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n[0] = (v0[2] + v1[2]) * (v0[1] - v1[1]) +
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(v1[2] + v2[2]) * (v1[1] - v2[1]) +
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(v2[2] + v0[2]) * (v2[1] - v0[1]);
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n[1] = (v0[2] - v1[2]) * (v0[0] + v1[0]) +
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(v1[2] - v2[2]) * (v1[0] + v2[0]) +
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(v2[2] - v0[2]) * (v2[0] + v0[0]);
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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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if(!norm)
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return(0);
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mag = normalize(n);
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return(mag);
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}
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/*
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* tri_plane_equation(v0,v1,v2,peqptr,norm)
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* : Calculates the plane equation (A,B,C,D) for triangle
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* v0,v1,v2 ( Ax + By + Cz = D)
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* FVECT v0,v1,v2; : Triangle vertices
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* FPEQ *peqptr; : ptr to structure to hold result
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* int norm; : if TRUE, return unit normal
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*/
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tri_plane_equation(v0,v1,v2,peqptr,norm)
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FVECT v0,v1,v2;
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FPEQ *peqptr;
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int norm;
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{
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tri_normal(v0,v1,v2,FP_N(*peqptr),norm);
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FP_D(*peqptr) = -(DOT(FP_N(*peqptr),v0));
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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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* : Intersects ray (orig,dir) with plane (peq). Returns TRUE
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* if intersection occurs. If r!=NULL, sets with resulting i
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* intersection point, and pd is set with parametric value of the
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* intersection.
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* FVECT orig,dir; : vectors defining the ray
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* FPEQ peq; : plane equation
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* double *pd; : holds resulting parametric intersection point
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* FVECT r; : holds resulting intersection point
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*
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* Plane is Ax + By + Cz +D = 0:
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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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*/
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int
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intersect_ray_plane(orig,dir,peq,pd,r)
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FVECT orig,dir;
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FPEQ peq;
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double *pd;
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FVECT r;
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{
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double t,d;
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int hit;
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d = DOT(FP_N(peq),dir);
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if(ZERO(d))
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return(0);
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t = -(DOT(FP_N(peq),orig) + FP_D(peq))/d;
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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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VSUM(r,orig,dir,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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* double
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* point_on_sphere(ps,p,c) : normalize p relative to sphere with center c
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* FVECT ps,p,c; : ps Holds result vector,p is the original point,
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* and c is the sphere center
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*/
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double
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point_on_sphere(ps,p,c)
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FVECT ps,p,c;
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{
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double d;
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VSUB(ps,p,c);
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d = normalize(ps);
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return(d);
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}
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/*
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* int
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* point_in_stri(v0,v1,v2,p) : Return TRUE if p is in pyramid defined by
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* tri v0,v1,v2 and origin
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* FVECT v0,v1,v2,p; :Triangle vertices(v0,v1,v2) and point in question(p)
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*
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* Tests orientation of p relative to each edge (v0v1,v1v2,v2v0), if it is
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* inside of all 3 edges, returns TRUE, else FALSE.
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*/
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int
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point_in_stri(v0,v1,v2,p)
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FVECT v0,v1,v2,p;
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{
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double d;
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FVECT n;
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VCROSS(n,v0,v1);
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/* Test the point for sidedness */
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d = DOT(n,p);
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if(d > 0.0)
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return(FALSE);
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/* Test next edge */
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VCROSS(n,v1,v2);
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/* Test the point for sidedness */
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d = DOT(n,p);
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if(d > 0.0)
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return(FALSE);
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/* Test next edge */
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VCROSS(n,v2,v0);
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/* Test the point for sidedness */
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d = DOT(n,p);
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if(d > 0.0)
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return(FALSE);
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/* Must be interior to the pyramid */
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return(TRUE);
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}
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/*
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* int
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* ray_intersect_tri(orig,dir,v0,v1,v2,pt)
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* : test if ray orig-dir intersects triangle v0v1v2, result in pt
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* FVECT orig,dir; : Vectors defining ray origin and direction
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* FVECT v0,v1,v2; : Triangle vertices
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* FVECT pt; : Intersection point (if any)
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*/
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int
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ray_intersect_tri(orig,dir,v0,v1,v2,pt)
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FVECT orig,dir;
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FVECT v0,v1,v2;
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FVECT pt;
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{
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FVECT p0,p1,p2,p;
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FPEQ peq;
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int type;
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VSUB(p0,v0,orig);
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VSUB(p1,v1,orig);
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VSUB(p2,v2,orig);
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if(point_in_stri(p0,p1,p2,dir))
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{
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/* Intersect the ray with the triangle plane */
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tri_plane_equation(v0,v1,v2,&peq,FALSE);
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return(intersect_ray_plane(orig,dir,peq,NULL,pt));
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}
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return(FALSE);
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}
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/*
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* calculate_view_frustum(vp,hv,vv,horiz,vert,near,far,fnear,ffar)
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* : Calculate vertices defining front and rear clip rectangles of
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* view frustum defined by vp,hv,vv,horiz,vert,near, and far and
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* return in fnear and ffar.
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* FVECT vp,hv,vv; : Viewpoint(vp),hv and vv are the horizontal and
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* vertical vectors in the view frame-magnitude is
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* the dimension of the front frustum face at z =1
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* double horiz,vert,near,far; : View angle horizontal and vertical(horiz,vert)
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* and distance to the near,far clipping planes
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* FVECT fnear[4],ffar[4]; : holds results
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*
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*/
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calculate_view_frustum(vp,hv,vv,horiz,vert,near,far,fnear,ffar)
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FVECT vp,hv,vv;
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double horiz,vert,near,far;
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FVECT fnear[4],ffar[4];
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{
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double height,width;
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FVECT t,nhv,nvv,ndv;
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double w2,h2;
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/* Calculate the x and y dimensions of the near face */
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VCOPY(nhv,hv);
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VCOPY(nvv,vv);
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w2 = normalize(nhv);
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h2 = normalize(nvv);
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/* Use similar triangles to calculate the dimensions at z=near */
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width = near*0.5*w2;
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height = near*0.5*h2;
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VCROSS(ndv,nvv,nhv);
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/* Calculate the world space points corresponding to the 4 corners
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of the front face of the view frustum
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*/
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fnear[0][0] = width*nhv[0] + height*nvv[0] + near*ndv[0] + vp[0] ;
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fnear[0][1] = width*nhv[1] + height*nvv[1] + near*ndv[1] + vp[1];
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fnear[0][2] = width*nhv[2] + height*nvv[2] + near*ndv[2] + vp[2];
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fnear[1][0] = -width*nhv[0] + height*nvv[0] + near*ndv[0] + vp[0];
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fnear[1][1] = -width*nhv[1] + height*nvv[1] + near*ndv[1] + vp[1];
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fnear[1][2] = -width*nhv[2] + height*nvv[2] + near*ndv[2] + vp[2];
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fnear[2][0] = -width*nhv[0] - height*nvv[0] + near*ndv[0] + vp[0];
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fnear[2][1] = -width*nhv[1] - height*nvv[1] + near*ndv[1] + vp[1];
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fnear[2][2] = -width*nhv[2] - height*nvv[2] + near*ndv[2] + vp[2];
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fnear[3][0] = width*nhv[0] - height*nvv[0] + near*ndv[0] + vp[0];
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fnear[3][1] = width*nhv[1] - height*nvv[1] + near*ndv[1] + vp[1];
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fnear[3][2] = width*nhv[2] - height*nvv[2] + near*ndv[2] + vp[2];
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/* Now do the far face */
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width = far*0.5*w2;
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height = far*0.5*h2;
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ffar[0][0] = width*nhv[0] + height*nvv[0] + far*ndv[0] + vp[0] ;
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ffar[0][1] = width*nhv[1] + height*nvv[1] + far*ndv[1] + vp[1] ;
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ffar[0][2] = width*nhv[2] + height*nvv[2] + far*ndv[2] + vp[2] ;
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ffar[1][0] = -width*nhv[0] + height*nvv[0] + far*ndv[0] + vp[0] ;
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ffar[1][1] = -width*nhv[1] + height*nvv[1] + far*ndv[1] + vp[1] ;
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ffar[1][2] = -width*nhv[2] + height*nvv[2] + far*ndv[2] + vp[2] ;
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ffar[2][0] = -width*nhv[0] - height*nvv[0] + far*ndv[0] + vp[0] ;
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ffar[2][1] = -width*nhv[1] - height*nvv[1] + far*ndv[1] + vp[1] ;
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ffar[2][2] = -width*nhv[2] - height*nvv[2] + far*ndv[2] + vp[2] ;
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ffar[3][0] = width*nhv[0] - height*nvv[0] + far*ndv[0] + vp[0] ;
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ffar[3][1] = width*nhv[1] - height*nvv[1] + far*ndv[1] + vp[1] ;
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ffar[3][2] = width*nhv[2] - height*nvv[2] + far*ndv[2] + vp[2] ;
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}
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/*
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* bary2d(x1,y1,x2,y2,x3,y3,px,py,coord)
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* : Find the normalized barycentric coordinates of p relative to
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* triangle v0,v1,v2. Return result in coord
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* double x1,y1,x2,y2,x3,y3; : defines triangle vertices 1,2,3
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* double px,py; : coordinates of pt
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* double coord[3]; : result
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*/
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bary2d(x1,y1,x2,y2,x3,y3,px,py,coord)
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double x1,y1,x2,y2,x3,y3;
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double px,py;
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double coord[3];
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{
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double a;
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a = (x2 - x1) * (y3 - y1) - (x3 - x1) * (y2 - y1);
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coord[0] = ((x2 - px) * (y3 - py) - (x3 - px) * (y2 - py)) / a;
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coord[1] = ((x3 - px) * (y1 - py) - (x1 - px) * (y3 - py)) / a;
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coord[2] = ((x1 - px) * (y2 - py) - (x2 - px) * (y1 - py)) / a;
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}
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