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/**
* elliptics via 5 point w-pi basis. (njh)
* Affine, endpoint, tangent, exact circle
* full circle. Convex containment implies small circle.
* Also represents lumpy polar type curves
*/
#include <2geom/d2.h>
#include <2geom/sbasis.h>
#include <2geom/sbasis-math.h>
#include <2geom/bezier-to-sbasis.h>
#include <toys/path-cairo.h>
#include <toys/toy-framework-2.h>
using std::vector;
using namespace Geom;
const double w = 1./3;
const double cwp = cos(w*M_PI);
const double swp = sin(w*M_PI);
/*double phi(double t, double w) { return sin(w*t) - w*sin(t); }
double phih(double t, double w) { return sin(w*t) + w*sin(t); }
double b4(double t, double w) {return phi(t/2,w)*phih(t/2,w)/(swp*swp);}
double b3(double t, double w) {return cwp*phi(t,w)/(2*swp) - cwp*cwp*b4(t,w); }
double b2(double t, double w) {return 2*w*w*sin(t/2)*sin(t/2);}
double b1(double t, double w) {return b3(2*M_PI - t, w);}
double b0(double t, double w) {return b4(2*M_PI - t, w);}*/
class arc_basis{
public:
Piecewise<SBasis> basis[5];
double w;
Piecewise<SBasis> phi(Piecewise<SBasis> const &d, double w) {
return sin(d*w) - sin(d)*w;
}
Piecewise<SBasis> phih(Piecewise<SBasis> const &d, double w) {
return sin(d*w) + sin(d)*w;
}
Piecewise<SBasis> b4(Piecewise<SBasis> const &d, double w) {
return phi(d*.5,w)/(swp*swp)*phih(d*.5,w);
}
Piecewise<SBasis> b3(Piecewise<SBasis> const &d, double w) {
return phi(d,w)*(cwp/(2*swp)) - b4(d,w)*(cwp*cwp);
}
Piecewise<SBasis> b2(Piecewise<SBasis> const &d, double w) {
return sin(d*.5)*(2*w*w)*sin(d*.5);
}
Piecewise<SBasis> b1(Piecewise<SBasis> const &d, double w) {
return b3(reverse(d), w);
}
Piecewise<SBasis> b0(Piecewise<SBasis> const &d, double w) {
return b4(reverse(d), w);
}
arc_basis(double w) {
Piecewise<SBasis> dom(Linear(0, 2*M_PI));
basis[0] = b4(dom, w);
basis[1] = b3(dom, w);
basis[2] = b2(dom, w);
basis[3] = b1(dom, w);
basis[4] = b0(dom, w);
}
};
class Conic4: public Toy {
PointSetHandle psh;
public:
Conic4 () {
double sc = 30;
Geom::Point c(6*sc, 6*sc);
psh.push_back(sc*Geom::Point(0,0)+c);
psh.push_back(sc*Geom::Point(tan(w*M_PI)/w, 0)+c);
psh.push_back(sc*Geom::Point(0, 1/(w*w))+c);
psh.push_back(sc*Geom::Point(-tan(w*M_PI)/w, 0)+c);
psh.push_back(sc*Geom::Point(0,0)+c);
handles.push_back(&psh);
}
void draw(cairo_t *cr, std::ostringstream *notify, int width, int height, bool save, std::ostringstream *timer_stream) override {
std::vector<Geom::Point> e_h = psh.pts;
for(int i = 0; i < 5; i++) {
Geom::Point p = e_h[i];
if(i)
cairo_line_to(cr, p);
else
cairo_move_to(cr, p);
}
cairo_set_source_rgba (cr, 0., 0., 0, 1);
cairo_set_line_width (cr, 1);
cairo_stroke(cr);
arc_basis ab(1./3);
D2<Piecewise<SBasis> > B;
for(unsigned dim = 0; dim < 2; dim++)
for(unsigned i = 0; i < 5; i++)
B[dim] += ab.basis[i]*e_h[i][dim];
cairo_d2_pw_sb(cr, B);
cairo_set_source_rgba (cr, 1., 0.5, 0, 1);
cairo_set_line_width (cr, 1);
cairo_stroke(cr);
Toy::draw(cr, notify, width, height, save,timer_stream);
}
};
int main(int argc, char **argv) {
init(argc, argv, new Conic4());
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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