}
point3 pvec(point3 s1,point3 s2,point3 s3){
returnxmult(subt(s1,s2),subt(s2,s3));
}
double distance(point3 p1,point3 p2){
returnsqrt((p1.x-p2.x)*(p1.x-p2.x)(p1.y-p2.y)*(p1.y-p2.y)(p1.z-p2.z)*(p1.z-p2.z));
}
double vlen(point3 p){
returnsqrt(p.x*p.xp.y*p.yp.z*p.z);
}
int dots_inline(point3 p1,point3 p2,point3p3){
returnvlen(xmult(subt(p1,p2),subt(p2,p3)))<eps;
}
int dots_onplane(point3 a,point3 b,point3c,point3 d){
returnzero(dmult(pvec(a,b,c),subt(d,a)));
}
int dot_online_in(point3 p,line3 l){
returnzero(vlen(xmult(subt(p,l.a),subt(p,l.b))))&&(l.a.x-p.x)*(l.b.x-p.x)<eps&&
(l.a.y-p.y)*(l.b.y-p.y)<eps&&(l.a.z-p.z)*(l.b.z-p.z)<eps;
}
int dot_online_in(point3 p,point3 l1,point3l2){
returnzero(vlen(xmult(subt(p,l1),subt(p,l2))))&&(l1.x-p.x)*(l2.x-p.x)<eps&&
(l1.y-p.y)*(l2.y-p.y)<eps&&(l1.z-p.z)*(l2.z-p.z)<eps;
}
int dot_online_ex(point3 p,line3 l){
returndot_online_in(p,l)&&(!zero(p.x-l.a.x)||!zero(p.y-l.a.y)||!zero(p.z-l.a.z))&&
(!zero(p.x-l.b.x)||!zero(p.y-l.b.y)||!zero(p.z-l.b.z));
}
int dot_online_ex(point3 p,point3 l1,point3l2){
returndot_online_in(p,l1,l2)&&(!zero(p.x-l1.x)||!zero(p.y-l1.y)||!zero(p.z-l1.z))&&
(!zero(p.x-l2.x)||!zero(p.y-l2.y)||!zero(p.z-l2.z));
}
int dot_inplane_in(point3 p,plane3 s){
returnzero(vlen(xmult(subt(s.a,s.b),subt(s.a,s.c)))-vlen(xmult(subt(p,s.a),subt(p,s.b)))-
vlen(xmult(subt(p,s.b),subt(p,s.c)))-vlen(xmult(subt(p,s.c),subt(p,s.a))));
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