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; }
//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); }
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()); } }
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; }
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; }