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realroot_doc 0.1.1
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realroot_doc 0.1.1
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#include <fatarcs.hpp>
Definition at line 119 of file fatarcs.hpp.
| typedef polynomial< coeff_t ,with<Bernstein> > bernstein_t |
Definition at line 126 of file fatarcs.hpp.
Definition at line 125 of file fatarcs.hpp.
| typedef C coeff_t |
Definition at line 122 of file fatarcs.hpp.
| typedef polynomial< coeff_t ,with<MonomialTensor> > monom_t |
Definition at line 127 of file fatarcs.hpp.
Definition at line 124 of file fatarcs.hpp.
Definition at line 123 of file fatarcs.hpp.
| arc_rep | ( | ) | [inline] |
Definition at line 137 of file fatarcs.hpp.
Definition at line 143 of file fatarcs.hpp.
References matrat(), mmx::size(), and v_minus().
| seq_t arc_eq | ( | ) | [inline] |
Definition at line 173 of file fatarcs.hpp.
References dot(), matrat(), v_minus(), and vec().
Referenced by circ_is(), and arc_rep< C >::offset().
{
vec_t cvec=matrat(v_minus(pts[0],pts[1]),v_minus(pts[2],pts[1]));
coeff_t eh2=cvec[1];
coeff_t ehx=dot(cvec, vec(pts[2][1]-pts[0][1],(coeff_t)(-1)*pts[0][0]-pts[2][0]));
coeff_t ehy=dot(cvec, vec(pts[0][0]-pts[2][0],(coeff_t)(-1)*pts[0][1]-pts[2][1]));
coeff_t ehc=dot(cvec, vec(pts[0][1]*pts[2][0]-pts[0][0]*pts[2][1],
pts[0][0]*pts[2][0]+pts[0][1]*pts[2][1]));
seq_t eh; eh<<eh2<<ehx<<ehy<<ehc;
return(eh);
}; /*coeff vector of monom rep: eh2*(x^2+y^2)+ehx*x+ehy*y+ehc=0*/
| vec_t critpt | ( | int | var | ) | [inline] |
Definition at line 191 of file fatarcs.hpp.
References mmx::eval(), is_unit1(), mmx::rep(), seq2b(), and vec().
Referenced by extpts().
{
vec_t pt;
Seq<coeff_t> coeffx,coeffy,wvec;
pt=vec(coeff_t(-1),coeff_t(-1));
coeffx<<pts[0][0]<< midc()[0]*weight()<< pts[2][0];
coeffy<<pts[0][1]<< midc()[1]*weight()<<pts[2][1];
wvec<<coeff_t(1)<< weight()<<coeff_t(1);
coeff_t t, cx,cy,w;
if (var==0 && (coeffx[2]-coeffx[0])!=0)
{
t=(coeffx[0]-coeffx[1])/(coeffx[2]-coeffx[0]);
}
else if (var==1 && (coeffy[2]-coeffy[0])!=0)
{
t=(coeffy[0]-coeffy[1])/(coeffy[2]-coeffy[0]);
};
if(is_unit1(t)){
tensor::eval(cx,seq2b(coeffx).rep(),t);
tensor::eval(cy,seq2b(coeffy).rep(),t);
tensor::eval(w,seq2b(wvec).rep(),t);
pt=vec( cx/w , cy/w );
}
// std::cout <<pt<<std::endl;
return(pt);
}; /*tang. pt in var*/
| vec_t midc | ( | ) | [inline] |
Definition at line 157 of file fatarcs.hpp.
References dot(), rotl(), mmx::sign(), mmx::sqrt(), v_div(), v_minus(), v_mul(), and v_plus().
Referenced by box_rep< C >::max_eval().
{
vec_t pp=v_minus(pts[0],pts[2]); pp=rotl(pp);
vec_t m=v_mul(coeff_t( sign(dot(pp, v_minus(pts[1],pts[2]) ))),pp);
coeff_t w=weight();
vec_t d;
if( (coeff_t(1)-w*w) > coeff_t(0) && w!=coeff_t(0) ){
d=v_plus(v_div(v_plus(pts[0],pts[2]),coeff_t(2)),v_div(v_mul(coeff_t(sqrt( coeff_t(1)-w*w )),m),(coeff_t(2)*w))); }
else {
d=v_div(v_plus(pts[0],pts[2]),coeff_t(2)); };
return(d);
};/*middle control point in bb rep.*/
Definition at line 221 of file fatarcs.hpp.
References arc_rep< C >::arc_eq(), is_arc(), is_unit1(), rotl(), Seq< C, R >::size(), solve2(), mmx::sqrt(), v_div(), v_length(), v_minus(), v_mul(), v_plus(), and vec().
Referenced by extpts().
{
vec_t newp[3];
Seq<coeff_t> mo, ehrat;
int i;unsigned j;
vec_t pp=rotl(v_minus(pts[0],pts[2]));
coeff_t l=v_length(pp);
coeff_t w=weight();
for( i=0; i<3; i++){newp[i]=vec_t(); };
arc_rep<coeff_t> ncirc(newp);
if( l!=coeff_t(0) ){
if( w==coeff_t(1)){ for( i=0; i<3; i++){ newp[i]=v_plus(pts[i],v_mul(r/l,pp)); } }//case of a quarter of a circle
else if (
//( coeff_t(1)-w*w )>coeff_t(0) &&
( r + l/(coeff_t(2)*sqrt( coeff_t(1)-w*w ) )) > coeff_t(0)
&& v_length( v_minus(pts[1],v_plus(pts[0],pts[2])) )!=coeff_t(0) )
{
newp[0]=v_plus(pts[0],v_mul(coeff_t(2)*r/l,
rotl( v_minus(v_minus(v_mul((coeff_t(1)+w),pts[1]),v_mul((w+ coeff_t(0.5)),pts[0])),
v_div(pts[2],coeff_t(2))
)
)
)
);
newp[1]=v_plus(pts[1],
v_mul(r/v_length(v_minus(pts[1],v_div(v_plus(pts[0],pts[2]),coeff_t(2)))),
v_minus(v_minus(pts[1],v_div(pts[0],coeff_t(2))),v_div(pts[2],coeff_t(2)))
)
);
newp[2]=v_minus(pts[2],
v_mul(coeff_t(2)*r/l,
rotl(v_minus(v_minus(v_mul((coeff_t(1)+w),pts[1]),v_mul((w+(coeff_t)(0.5)),pts[2])),
v_div(pts[0],coeff_t(2))
)
)
)
);
};
//std::cout <<"newp0: "<<newp[0]<<" "<<newp[1]<<" "<<newp[2]<<std::endl;
ncirc=arc_rep<coeff_t>(newp);
if(is_arc(ncirc)){
Seq<vec_t> isp;
ehrat=ncirc.arc_eq();
mo=solve2(ehrat[0],ehrat[2],ehrat[3]);
for( j=0; j<2; j++){if(is_unit1(mo[j])){isp<<vec(coeff_t(0),mo[j]);};};
mo=solve2(ehrat[0],ehrat[2],ehrat[0]+ehrat[1]+ehrat[3]);
for( j=0; j<2; j++){if(is_unit1(mo[j])){isp<<vec(coeff_t(1),mo[j]);};};
mo=solve2(ehrat[0],ehrat[1],ehrat[3]);
for( j=0; j<2; j++){if(is_unit1(mo[j])){isp<<vec(mo[j],coeff_t(0));};};
mo=solve2(ehrat[0],ehrat[1],ehrat[0]+ehrat[2]+ehrat[3]);
for( j=0; j<2; j++){if(is_unit1(mo[j])){isp<<vec(mo[j],coeff_t(1));};};
if (isp.size()==0){newp[0]=vec_t(); }else{
newp[0]=isp[0];
for( j=1; j<isp.size(); j++)
{if(v_length(v_minus(isp[j],pts[0]))<v_length(v_minus(newp[0],pts[0]))){newp[0]=isp[j];};};
};
if (isp.size()==0){newp[2]=vec_t(); }else{
newp[2]=isp[0];
for( j=1; j<isp.size(); j++)
{if(v_length(v_minus(isp[j],pts[2]))<v_length(v_minus(newp[2],pts[2]))){newp[2]=isp[j];};};
};
ncirc=arc_rep<coeff_t>(newp);
// std::cout <<"newp1: "<<newp[0]<<" "<<newp[1]<<" "<<newp[2]<<std::endl;
/*if (is_arc(ncirc)){
if( matrat(v_minus(newp[1],newp[0]),v_minus(newp[2],newp[0]))[1]>coeff_t(0) )
{ vec_t u=newp[0]; newp[0]=newp[2]; newp[2]=u;}};*/
};
};
return( ncirc );
} /*offset arc computation(with precise endpoints) - OR OUTSIDE!!!*/
| coeff_t weight | ( | ) | [inline] |
Definition at line 131 of file fatarcs.hpp.
Referenced by extpts(), is_arc(), is_infatarc(), and box_rep< C >::max_eval().
