OptInterval bounds_local(const SBasisOf<double> &sb, const OptInterval &i, int order) {
#else
OptInterval bounds_local(const SBasis &sb, const OptInterval &i, int order) {
#endif
    double t0=i->min(), t1=i->max(), lo=0., hi=0.;
    for(int j = sb.size()-1; j>=order; j--) {
        double a=sb[j][0];
        double b=sb[j][1];

        double t = 0;
        if (lo<0) t = ((b-a)/lo+1)*0.5;
        if (lo>=0 || t<t0 || t>t1) {
            lo = std::min(a*(1-t0)+b*t0+lo*t0*(1-t0),a*(1-t1)+b*t1+lo*t1*(1-t1));
        }else{
            lo = lerp(t, a+lo*t, b);
        }

        if (hi>0) t = ((b-a)/hi+1)*0.5;
        if (hi<=0 || t<t0 || t>t1) {
            hi = std::max(a*(1-t0)+b*t0+hi*t0*(1-t0),a*(1-t1)+b*t1+hi*t1*(1-t1));
        }else{
            hi = lerp(t, a+hi*t, b);
        }
    }
    Interval res = Interval(lo,hi);
    if (order>0) res*=pow(.25,order);
    return res;
}
Ejemplo n.º 2
0
//TODO: this would work only for C1 pw<d2<sb>> input. Split the input at corners to work with pwd2sb...
//TODO: for more general purpose, return a path...
void toPoly(D2<SBasis> const &f, std::list<Point> &p, double tol, bool include_first=true){
    D2<SBasis> df = derivative(f);
    D2<SBasis> d2f = derivative(df);
    double t=0;
    if ( include_first ){ p.push_back( f.at0() );}
    while (t<1){
        Point v = unit_vector(df.valueAt(t));
        //OptInterval bounds = bounds_local(df[X]*v[Y]-df[Y]*v[X], Interval(t,1));
        OptInterval bounds = bounds_local(d2f[X]*v[Y]-d2f[Y]*v[X], Interval(t,1));
        if (bounds) {
            double bds_max = (-bounds->min()>bounds->max() ? -bounds->min() : bounds->max());
            double dt;
            //if (bds_max<tol) dt = 1;
            //else            dt = tol/bds_max;
            if (bds_max<tol/4) dt = 1;
            else              dt = 2*std::sqrt( tol / bds_max );
            t+=dt*5;
            if (t>1) t = 1;
        }else{
            t = 1;
        }
        p.push_back( f.valueAt(t) );
    }
    return;
}
void subdiv_sbasis(SBasis const & s,
                   std::vector<double> & roots,
                   double left, double right) {
    OptInterval bs = bounds_fast(s);
    if(!bs || bs->min() > 0 || bs->max() < 0)
        return; // no roots here
    if(s.tailError(1) < 1e-7) {
        double t = s[0][0] / (s[0][0] - s[0][1]);
        roots.push_back(left*(1-t) + t*right);
        return;
    }
    double middle = (left + right)/2;
    subdiv_sbasis(compose(s, Linear(0, 0.5)), roots, left, middle);
    subdiv_sbasis(compose(s, Linear(0.5, 1.)), roots, middle, right);
}
Ejemplo n.º 4
0
double goal_function(Piecewise<D2<SBasis> >const &A, 
                     Piecewise<D2<SBasis> >const&B) {
    if(goal_function_type) {
        OptInterval bnds = bounds_fast(dot(derivative(A), rot90(derivative(B))));
        //double h_dist = bnds.dimensions().length();
//0 is in the rect!, TODO:gain factor ~2 for free.
// njh: not really, the benefit is actually rather small.
        double h_dist = 0;
        if(bnds)
            h_dist = bnds->extent();
        return h_dist ;
    } else {
        Rect bnds = *bounds_fast(A - B);
        return max(bnds.min().length(), bnds.max().length());
    }  
}
Ejemplo n.º 5
0
static 
std::vector<double>
solve_lambda0(double a0,double a1,double c0,double c1,
             int insist_on_speeds_signs){

    SBasis p(3, Linear());
    p[0] = Linear( a1*c0*c0+c1, a1*a0*(a0+ 2*c0) +a1*c0*c0 +c1 -1  );
    p[1] = Linear( -a1*a0*(a0+2*c0), -a1*a0*(3*a0+2*c0) );
    p[2] = Linear( a1*a0*a0 );

    OptInterval domain = find_bounds_for_lambda0(a0,a1,c0,c1,insist_on_speeds_signs);
    if ( !domain ) 
        return std::vector<double>();
    p = compose(p,Linear(domain->min(),domain->max()));
    std::vector<double>rts = roots(p);
    for (unsigned i=0; i<rts.size(); i++){
        rts[i] = domain->min() + rts[i] * domain->extent();
    }
    return rts;
}
Ejemplo n.º 6
0
Geom::Piecewise<Geom::D2<Geom::SBasis> >
LPERecursiveSkeleton::doEffect_pwd2 (Geom::Piecewise<Geom::D2<Geom::SBasis> > const & pwd2_in)
{
    using namespace Geom;

    Piecewise<D2<SBasis> > output;
    std::vector<Piecewise<D2<SBasis> > > pre_output;

    double prop_scale = 1.0;

    D2<Piecewise<SBasis> > patternd2 = make_cuts_independent(pwd2_in);
    Piecewise<SBasis> x0 = false /*vertical_pattern.get_value()*/ ? Piecewise<SBasis>(patternd2[1]) : Piecewise<SBasis>(patternd2[0]);
    Piecewise<SBasis> y0 = false /*vertical_pattern.get_value()*/ ? Piecewise<SBasis>(patternd2[0]) : Piecewise<SBasis>(patternd2[1]);
    OptInterval pattBndsX = bounds_exact(x0);
    OptInterval pattBndsY = bounds_exact(y0);

    if ( !pattBndsX || !pattBndsY) {
        return pwd2_in;
    }

    x0 -= pattBndsX->min();
    y0 -= pattBndsY->middle();

    double xspace  = 0;//spacing;
    double noffset = 0;//normal_offset;
    double toffset = 0;//tang_offset;
    if (false /*prop_units.get_value()*/){
        xspace  *= pattBndsX->extent();
        noffset *= pattBndsY->extent();
        toffset *= pattBndsX->extent();
    }

    y0+=noffset;

    output = pwd2_in;

    for (int i = 0; i < iterations; ++i) {
        std::vector<Piecewise<D2<SBasis> > > skeleton = split_at_discontinuities(output);

        output.clear();
        for (unsigned idx = 0; idx < skeleton.size(); idx++){
            Piecewise<D2<SBasis> > path_i = skeleton[idx];
            Piecewise<SBasis> x = x0;
            Piecewise<SBasis> y = y0;
            Piecewise<D2<SBasis> > uskeleton = arc_length_parametrization(path_i,2,.1);
            uskeleton = remove_short_cuts(uskeleton,.01);
            Piecewise<D2<SBasis> > n = rot90(derivative(uskeleton));
            n = force_continuity(remove_short_cuts(n,.1));

            double scaling = 1;
            scaling = (uskeleton.domain().extent() - toffset)/pattBndsX->extent();

            // TODO investigate why pattWidth is not being used:
            double pattWidth = pattBndsX->extent() * scaling;

            if (scaling != 1.0) {
                x*=scaling;
            }

            if ( true /*scale_y_rel.get_value()*/ ) {
                y*=(scaling*prop_scale);
            } else {
                if (prop_scale != 1.0) y *= prop_scale;
            }
            x += toffset;

            output.concat(compose(uskeleton,x)+y*compose(n,x));
        }
    }

    return output;
}