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#include <2geom/d2.h>
#include <2geom/sbasis.h>
#include <2geom/bezier-to-sbasis.h>
#include <2geom/sbasis-math.h>
#include <2geom/sbasis-geometric.h>
#include <toys/path-cairo.h>
#include <toys/toy-framework-2.h>
#include <vector>
using std::vector;
using namespace Geom;
Piecewise<SBasis>
arcLengthSb2(Piecewise<D2<SBasis> > const &M, double /*tol*/){
Piecewise<D2<SBasis> > dM = derivative(M);
Piecewise<SBasis> length = integral(dot(dM, unitVector(dM)));
length-=length.segs.front().at0();
return length;
}
class ArcBez: public Toy {
PointSetHandle bez_handle;
public:
ArcBez() {
for(int i = 0; i < 6; i++)
bez_handle.push_back(uniform()*400, uniform()*400);
handles.push_back(&bez_handle);
}
void draw(cairo_t *cr, std::ostringstream *notify, int width, int height, bool save, std::ostringstream *timing_stream) override {
cairo_set_source_rgba (cr, 0., 0., 0, 1);
cairo_set_line_width (cr, 1);
D2<SBasis> B = bez_handle.asBezier();
cairo_d2_sb(cr, B);
cairo_stroke(cr);
cairo_set_source_rgba (cr, 0.25, 0.5, 0, 0.8);
double tol = 0.01;
bool time_operations = true;
if(time_operations) {
std::string units_string("us");
Timer tm;
tm.ask_for_timeslice();
tm.start();
Piecewise<SBasis> als = arcLengthSb(B, tol);
Timer::Time als_time = tm.lap();
*timing_stream << "arcLengthSb based "
<< ", time = " << als_time
<< units_string << std::endl;
tm.start();
Piecewise<SBasis> als2 = arcLengthSb2(Piecewise<D2<SBasis> >(B), 0.01);
Timer::Time als2_time = tm.lap();
*timing_stream << "arcLengthSb2 based "
<< ", time = " << als2_time
<< units_string << std::endl;
double abs_error = 0;
double integrating_arc_length = 0;
tm.start();
length_integrating(B, integrating_arc_length, abs_error, 1e-10);
Timer::Time li_time = tm.lap();
*timing_stream << "gsl integrating "
<< ", time = " << li_time
<< units_string << std::endl;
}
Piecewise<SBasis> als = arcLengthSb(B, tol);
Piecewise<SBasis> als2 = arcLengthSb2(Piecewise<D2<SBasis> >(B), 0.01);
cairo_d2_pw_sb(cr, D2<Piecewise<SBasis> >(Piecewise<SBasis>(SBasis(Linear(0, width))) , Piecewise<SBasis>(Linear(height-5)) - Piecewise<SBasis>(als)) );
double abs_error = 0;
double integrating_arc_length = 0;
length_integrating(B, integrating_arc_length, abs_error, 1e-10);
*notify << "arc length = " << integrating_arc_length << "; abs error = " << abs_error << std::endl;
double als_arc_length = als.segs.back().at1();
*notify << "arc length = " << als_arc_length << "; error = " << als_arc_length - integrating_arc_length << std::endl;
double als_arc_length2 = als2.segs.back().at1();
*notify << "arc length2 = " << als_arc_length2 << "; error = " << als_arc_length2 - integrating_arc_length << std::endl;
{
double err = fabs(als_arc_length - integrating_arc_length);
double scale = 10./err;
Piecewise<D2<SBasis> > dM = derivative(Piecewise<D2<SBasis> >(B));
Piecewise<SBasis> ddM = dot(dM,dM);
Piecewise<SBasis> dMlength = sqrt(ddM,tol,3);
double plot_width = (width - 200);
Point org(100,height - 200);
cairo_move_to(cr, org);
for(double t = 0; t < 1; t += 0.01) {
cairo_line_to(cr, org + Point(t*plot_width, scale*(sqrt(ddM.valueAt(t)) - dMlength.valueAt(t))));
}
cairo_move_to(cr, org);
cairo_line_to(cr, org+Point(plot_width, 0));
cairo_stroke(cr);
draw_number(cr, org, scale);
}
Toy::draw(cr, notify, width, height, save,timing_stream);
}
};
int main(int argc, char **argv) {
init(argc, argv, new ArcBez());
return 0;
}
/*
Local Variables:
mode:c++
c-file-style:"stroustrup"
c-file-offsets:((innamespace . 0)(inline-open . 0)(case-label . +))
indent-tabs-mode:nil
fill-column:99
End:
*/
// vim: filetype=cpp:expandtab:shiftwidth=4:tabstop=8:softtabstop=4:fileencoding=utf-8:textwidth=99 :
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