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#include <2geom/basic-intersection.h>
#include <2geom/d2.h>
#include <2geom/sbasis.h>
#include <2geom/sbasis-2d.h>
#include <2geom/bezier-to-sbasis.h>
#include <toys/path-cairo.h>
#include <toys/toy-framework-2.h>
using std::vector;
using namespace Geom;
/*
jfb: I think the evolute goes to infinity at inflection points, in which case you cannot "join" the pieces by hand.
jfb: for the evolute toy, you could not only cut at inflection points, but event remove the domains where cross(dda,da)<c*|da|^3, where c is a small constant, as these points will be off screen anyway.
*/
class Evolution: public Toy {
PointSetHandle psh;
void draw(cairo_t *cr, std::ostringstream *notify, int width, int height, bool save, std::ostringstream *timer_stream) override {
cairo_set_line_width (cr, 0.5);
cairo_set_source_rgba (cr, 0., 0., 0, 1);
D2<SBasis> A(psh.asBezier());
D2<SBasis> dA = derivative(A);
D2<SBasis> ddA = derivative(dA);
SBasis crs = cross(ddA, dA);
cairo_d2_sb(cr, D2<SBasis>(Linear(0,1000), crs*(500./bounds_exact(crs)->extent())));
vector<double> rts = roots(crs);
for(double rt : rts) {
draw_handle(cr, A(rt));
}
cairo_d2_sb(cr, A);
cairo_stroke(cr);
Interval r(0, 1);
if(!rts.empty())
r.setMax(rts[0]);
//if(rts[0] == 0)
//rts.erase(rts.begin(), rts.begin()+1);
A = portion(A, r.min(), r.max());
dA = portion(dA, r.min(), r.max());
ddA = portion(ddA, r.min(), r.max());
crs = portion(crs, r.min(), r.max());
cairo_stroke(cr);
Piecewise<SBasis> s = divide(dA[0]*dot(dA,dA), crs, 100, 1);
D2<Piecewise<SBasis> > ev4(Piecewise<SBasis>(A[0]) + divide(-dA[1]*dot(dA,dA), crs, 100, 1),
Piecewise<SBasis>(A[1]) + divide(dA[0]*dot(dA,dA), crs, 100, 1));
cairo_d2_pw_sb(cr, ev4);
cairo_stroke(cr);
if(1) {
std::cout << "bnd" << *bounds_exact(dot(ev4, ev4)) << std::endl;
cairo_d2_pw_sb(cr, D2<Piecewise<SBasis> >(Piecewise<SBasis>(SBasis(Linear(0,1000))), dot(ev4, ev4)*1000));
cairo_stroke(cr);
vector<double> rts = roots(dot(ev4, ev4)-1);
for(double rt : rts) {
std::cout << rt << std::endl;
draw_handle(cr, ev4(rt));
}
}
cairo_set_source_rgba (cr, 1., 0., 1, 1);
Toy::draw(cr, notify, width, height, save,timer_stream);
}
public:
Evolution (unsigned bez_ord) {
handles.push_back(&psh);
for(unsigned i = 0; i < bez_ord; i++)
psh.push_back(uniform()*400, uniform()*400);
}
};
int main(int argc, char **argv) {
unsigned bez_ord=5;
if(argc > 1)
sscanf(argv[1], "%d", &bez_ord);
init(argc, argv, new Evolution(bez_ord));
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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