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#include <2geom/d2.h>
#include <2geom/sbasis.h>
#include <2geom/bezier-to-sbasis.h>
#include <2geom/path.h>
#include <toys/path-cairo.h>
#include <toys/toy-framework-2.h>
#define ZROOTS_TEST 0
#if ZROOTS_TEST
#include <2geom/zroots.c>
#endif
#include <vector>
using std::vector;
using namespace Geom;
//#define HAVE_GSL
template <typename T>
void shift(T &a, T &b, T const &c) {
a = b;
b = c;
}
template <typename T>
void shift(T &a, T &b, T &c, T const &d) {
a = b;
b = c;
c = d;
}
extern unsigned total_steps, total_subs;
class MatchCurve: public Toy {
public:
double timer_precision;
double units;
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, 1);
cairo_set_source_rgb(cr, 0,0,0);
std::vector<Geom::Point> trans;
trans.resize(psh.size());
for(unsigned i = 0; i < psh.size(); i++) {
trans[i] = psh.pts[i] - Geom::Point(0, 3*width/4);
}
std::vector<double> solutions;
D2<SBasis> test_sb = psh.asBezier();
D2<SBasis> B = psh.asBezier();
Geom::Path pb;
pb.append(B);
pb.close(false);
cairo_path(cr, pb);
cairo_stroke(cr);
D2<SBasis> m;
D2<SBasis> dB = derivative(B);
D2<SBasis> ddB = derivative(dB);
D2<SBasis> dddB = derivative(ddB);
Geom::Point pt = B(0);
Geom::Point tang = dB(0);
Geom::Point dtang = ddB(0);
Geom::Point ddtang = dddB(0);
for(int dim = 0; dim < 2; dim++) {
m[dim] = Linear(pt[dim],pt[dim]+tang[dim]);
m[dim] += Linear(0, 1)*Linear(0, 1*dtang[dim])/2;
m[dim] += Linear(0, 1)*Linear(0, 1)*Linear(0, ddtang[dim])/6;
}
double lo = 0, hi = 1;
double eps = 5;
while(hi - lo > 0.0001) {
double mid = (hi + lo)/2;
//double Bmid = (Bhi + Blo)/2;
m = truncate(compose(B, Linear(0, mid)), 2);
// perform golden section search
double best_f = 0, best_x = 1;
for(int n = 2; n < 4; n++) {
Geom::Point m_pt = m(double(n)/6);
double x0 = 0, x3 = 1.; // just a guess!
const double R = 0.61803399;
const double C = 1 - R;
double x1 = C*x0 + R*x3;
double x2 = C*x1 + R*x3;
double f1 = Geom::distance(m_pt, B(x1));
double f2 = Geom::distance(m_pt, B(x2));
while(fabs(x3 - x0) > 1e-3*(fabs(x1) + fabs(x2))) {
if(f2 < f1) {
shift(x0, x1, x2, R*x1 + C*x3);
shift(f1, f2, Geom::distance(m_pt, B(x2)));
} else {
shift(x3, x2, x1, R*x2 + C*x0);
shift(f2, f1, Geom::distance(m_pt, B(x2)));
}
std::cout << x0 << ","
<< x1 << ","
<< x2 << ","
<< x3 << ","
<< std::endl;
}
if(f2 < f1) {
f1 = f2;
x1 = x2;
}
if(f1 > best_f) {
best_f = f1;
best_x = x1;
}
}
std::cout << mid << ":" << best_x << "->" << best_f << std::endl;
//draw_cross(cr, point_at(B, x1));
if(best_f > eps) {
hi = mid;
} else {
lo = mid;
}
}
std::cout << std::endl;
//draw_cross(cr, point_at(B, hi));
draw_circ(cr, m(hi));
{
Geom::Path pb;
pb.append(m);
pb.close(false);
cairo_path(cr, pb);
}
cairo_stroke(cr);
Toy::draw(cr, notify, width, height, save,timer_stream);
}
MatchCurve() : timer_precision(0.1), units(1e6) // microseconds
{
handles.push_back(&psh);
for(int i = 0; i < 6; i++)
psh.push_back(uniform()*400, uniform()*400);
}
};
int main(int argc, char **argv) {
init(argc, argv, new MatchCurve());
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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