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#include <2geom/d2.h>
#include <2geom/sbasis.h>
#include <2geom/bezier-to-sbasis.h>
#include <toys/path-cairo.h>
#include <toys/toy-framework-2.h>
#include <time.h>
using std::vector;
using namespace Geom;
using namespace std;
static void plot(cairo_t* cr, SBasis const &B,double vscale=1,double a=0,double b=1){
D2<SBasis> plot;
plot[0]=SBasis(Linear(150+a*300,150+b*300));
plot[1]=B*-vscale;
plot[1]+=450;
cairo_d2_sb(cr, plot);
cairo_stroke(cr);
}
static void plot(cairo_t* cr, Piecewise<SBasis> const &f,double vscale=1){
for (unsigned i=0;i<f.size();i++){
plot(cr,f.segs[i],vscale,f.cuts[i],f.cuts[i+1]);
draw_cross(cr,Geom::Point(f.cuts[i]*300 + 150, f.segs[i][0][0]*(-vscale) + 450));
}
}
static SBasis my_inverse(SBasis f, int order){
double a0 = f[0][0];
if(a0 != 0) {
f -= a0;
}
double a1 = f[0][1];
if(a1 == 0)
THROW_NOTINVERTIBLE();
//assert(a1 != 0);// not invertible.
if(a1 != 1) {
f /= a1;
}
SBasis g=SBasis(order, Linear());
g[0] = Linear(0,1);
double df0=derivative(f)(0);
double df1=derivative(f)(1);
SBasis r = Linear(0,1)-g(f);
for(int i=1; i<order; i++){
//std::cout<<"i: "<<i<<std::endl;
r=Linear(0,1)-g(f);
//std::cout<<"t-gof="<<r<<std::endl;
r.normalize();
if (r.size()==0) return(g);
double a=r[i][0]/std::pow(df0,i);
double b=r[i][1]/std::pow(df1,i);
g[i] = Linear(a,b);
}
return(g);
}
static Piecewise<SBasis> pw_inverse(SBasis const &f, int order,double tol=.1,int depth=0){
SBasis g=SBasis(Linear(0,1)),r;
Piecewise<SBasis> res,res1,res2;
//std::cout<<"depth: "<<depth<<std::endl;
g=my_inverse(f,order);
r=g(f);
//std::cout<<"error: "<<g.tail_error(1)<<std::endl;
if (g.tailError(1)<tol){
res.segs.push_back(g);
res.cuts.push_back(f[0][0]);
res.cuts.push_back(f[0][1]);
}else if (depth<200){
SBasis ff;
ff=f(Linear(0,.5));
res=pw_inverse(ff,order,tol,depth+1);
for (unsigned i=0;i<res.size();i++){
res.segs[i]*=.5;
}
ff=f(Linear(.5,1));
res1=pw_inverse(ff,order,tol,depth+1);
for (unsigned i=0;i<res1.size();i++){
res1.segs[i]*=.5;
res1.segs[i]+=.5;
}
res.concat(res1);
}
return(res);
}
class InverseTester: public Toy {
int size;
PointSetHandle hand;
void draw(cairo_t *cr, std::ostringstream *notify, int width, int height, bool save, std::ostringstream *timer_stream) override {
for (int i=0;i<size;i++){
hand.pts[i ][0]=150+15*(i-size);
hand.pts[i+size][0]=450+15*(i+1);
cairo_move_to(cr, Geom::Point(hand.pts[i ][0],150));
cairo_line_to(cr, Geom::Point(hand.pts[i ][0],450));
cairo_move_to(cr, Geom::Point(hand.pts[i+size][0],150));
cairo_line_to(cr, Geom::Point(hand.pts[i+size][0],450));
}
cairo_move_to(cr, Geom::Point(0,300));
cairo_line_to(cr, Geom::Point(600,300));
cairo_set_line_width (cr, 1);
cairo_set_source_rgba (cr, 0.2, 0.2, 0.2, 1);
cairo_stroke(cr);
SBasis f(size, Linear());//=SBasis(Linear(0,.5));
for (int i=0;i<size;i++){
f[i] = Linear(-(hand.pts[i ][1]-300)*std::pow(4.,i)/150,
-(hand.pts[i+size][1]-300)*std::pow(4.,i)/150 );
}
plot(cr,Linear(0,1),300);
f.normalize();
cairo_set_line_width (cr, 2);
cairo_set_source_rgba (cr, 0., 0., 0.8, 1);
plot(cr,f,300);
*notify<<"Use hand.pts to set the coefficients of the (blue) s-basis."<<std::endl;
*notify<<" (keep it monotonic!)"<<std::endl;
*notify<<"red=flipped inverse; should be the same as the blue one."<<std::endl;
try {
Piecewise<SBasis> g=pw_inverse(f,3);
cairo_set_line_width (cr, 1);
cairo_set_source_rgba (cr, 0.8, 0., 0., 1);
plot(cr,g,300);
Piecewise<SBasis> h=compose(g,f);
cairo_set_line_width (cr, 1);
cairo_set_source_rgba (cr, 0., 0.8, 0., 1);
plot(cr,h,300);
*notify<<g.size()<<" segments.";
} catch(NotInvertible) {
*notify << "function not invertible!" << std::endl;
}
Toy::draw(cr, notify, width, height, save,timer_stream);
}
public:
InverseTester() {
size=4;
if(hand.pts.empty()) {
for(int i = 0; i < 2*size; i++)
hand.pts.emplace_back(0,150+150+uniform()*300*0);
}
hand.pts[0][1]=300;
hand.pts[size][1]=150;
handles.push_back(&hand);
}
};
int main(int argc, char **argv) {
init(argc, argv, new InverseTester);
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:encoding = utf-8:textwidth = 99 :
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