path: root/src/toys/minsb2d-solver.cpp

#include <2geom/sbasis.h>
#include <2geom/sbasis-math.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;


//see a sb2d as an sb of u with coef in sbasis of v.
void
u_coef(SBasis2d f, unsigned deg, SBasis &a, SBasis &b) {
    a = SBasis(f.vs, Linear());
    b = SBasis(f.vs, Linear());
    for (unsigned v=0; v<f.vs; v++){
        a[v] = Linear(f.index(deg,v)[0], f.index(deg,v)[2]);
        b[v] = Linear(f.index(deg,v)[1], f.index(deg,v)[3]);
    }
}
void
v_coef(SBasis2d f, unsigned deg, SBasis &a, SBasis &b) {
    a = SBasis(f.us, Linear());
    b = SBasis(f.us, Linear());
    for (unsigned u=0; u<f.us; u++){
        a[u] = Linear(f.index(deg,u)[0], f.index(deg,u)[1]);
        b[u] = Linear(f.index(deg,u)[2], f.index(deg,u)[3]);
    }
}



//TODO: implement sb2d algebra!!
SBasis2d y_x2(){
    SBasis2d result(Linear2d(0,-1,1,0));    
    result.push_back(Linear2d(1,1,1,1));
    result.us = 2;
    result.vs = 1;
    return result;
}

SBasis2d x2_plus_y2_1(){
/*TODO: implement sb2d algebra!!
    SBasis2d one(Linear2d(1,1,1,1));
    SBasis2d u(Linear2d(0,1,0,1));
    SBasis2d v(Linear2d(0,0,1,1));
    return(u*u+v*v-one);
*/
    SBasis2d result(Linear2d(-1,0,0,1));//x+y-1    
    result.push_back(Linear2d(-1,-1,-1,-1));
    result.push_back(Linear2d(-4,-1,-1,-1));
    result.push_back(Linear2d(0,0,0,0));
    result.us = 2;
    result.vs = 2;
    return result;
}

struct Frame
{
    Geom::Point O;
    Geom::Point x;
    Geom::Point y;
    Geom::Point z;
};

void
plot3d(cairo_t *cr, SBasis const &x, SBasis const &y, SBasis const &z, Frame frame){
    D2<SBasis> curve;
    for (unsigned dim=0; dim<2; dim++){
        curve[dim] = x*frame.x[dim] + y*frame.y[dim] + z*frame.z[dim];
        curve[dim] += frame.O[dim];
    }
    cairo_d2_sb(cr, curve);
}

void
plot3d(cairo_t *cr, 
       Piecewise<SBasis> const &x, 
       Piecewise<SBasis> const &y, 
       Piecewise<SBasis> const &z, Frame frame){
    
    Piecewise<SBasis> xx = partition(x,y.cuts);
    Piecewise<SBasis> xxx = partition(xx,z.cuts);
    Piecewise<SBasis> yyy = partition(y,xxx.cuts);
    Piecewise<SBasis> zzz = partition(z,xxx.cuts);
    
    for (unsigned i=0; i<xxx.size(); i++){
        plot3d(cr, xxx[i], yyy[i], zzz[i], frame);
    }
}

void
plot3d(cairo_t *cr, SBasis2d const &f, Frame frame, int NbRays=5){
        for (int i=0; i<=NbRays; i++){
            D2<SBasis> seg(SBasis(0.,1.), SBasis(i*1./NbRays, i*1./NbRays));
            SBasis f_on_seg = compose(f,seg);
            plot3d(cr,seg[X],seg[Y],f_on_seg,frame);
        }
        for (int i=0; i<NbRays; i++){
            D2<SBasis> seg(SBasis(i*1./NbRays, i*1./NbRays), SBasis(0.,1.));
            SBasis f_on_seg = compose(f,seg);
            plot3d(cr,seg[X],seg[Y],f_on_seg,frame);
        }
}

void
plot3d_top(cairo_t *cr, SBasis2d const &f, Frame frame, int NbRays=5){
        for (int i=0; i<=NbRays; i++){
            for(int j=0; j<2; j++){
                D2<SBasis> seg;
                if (j==0){
                    seg = D2<SBasis>(SBasis(0.,1.), SBasis(i*1./NbRays, i*1./NbRays));
                }else{
                    seg = D2<SBasis>(SBasis(i*1./NbRays,i*1./NbRays), SBasis(0.,1.));
                }
                SBasis f_on_seg = compose(f,seg);
                std::vector<double> rts = roots(f_on_seg);
                if (rts.size()==0||rts.back()<1) rts.push_back(1.);
                double t1,t0 = 0;
                for (unsigned i=(rts.front()<=0?1:0); i<rts.size(); i++){
                    t1 = rts[i];
                    if (f_on_seg((t0+t1)/2)>0) 
                        plot3d(cr,seg[X](Linear(t0,t1)),seg[Y](Linear(t0,t1)),f_on_seg(Linear(t0,t1)),frame);
                    t0=t1;
                }
            //plot3d(cr,seg[X],seg[Y],f_on_seg,frame);
            }
        }
}
#include <gsl/gsl_multimin.h>

class Sb2dSolverToy: public Toy {
public:
    PointSetHandle hand;
    Sb2dSolverToy() {
        handles.push_back(&hand);
    }

    class bits_n_bobs{
    public:
        SBasis2d * ff;
        Point A, B;
        Point dA, dB;
    };
    static double
    my_f (const gsl_vector *v, void *params)
    {
        double x, y;
        bits_n_bobs* bnb = (bits_n_bobs *)params;
       
        x = gsl_vector_get(v, 0);
        y = gsl_vector_get(v, 1);
        Bezier b0(bnb->B[0], bnb->B[0]+bnb->dB[0]*x, bnb->A[0]+bnb->dA[0]*y, bnb->A[0]);
        Bezier b1(bnb->B[1], bnb->B[1]+bnb->dB[1]*x, bnb->A[1]+bnb->dA[1]*y, bnb->A[1]);
            
        D2<SBasis> zeroset(b0.toSBasis(), b1.toSBasis());
            
        SBasis comp = compose((*bnb->ff),zeroset);
        Interval bounds = *bounds_fast(comp);
        double error = (bounds.max()>-bounds.min() ? bounds.max() : -bounds.min() );
        //printf("error = %g %g %g\n", bounds.max(), bounds.min(), error);
        return error*error;
    }
     


    void draw(cairo_t *cr, std::ostringstream *notify, int width, int height, bool save, std::ostringstream *timer_stream) override {

        double slider_top = width/4.;
        double slider_bot = width*3./4.;
        double slider_margin = width/8.;
        if(hand.pts.empty()) {
            hand.pts.emplace_back(width*3./16., 3*width/4.);
            hand.pts.push_back(hand.pts[0] + Geom::Point(width/2., 0));
            hand.pts.push_back(hand.pts[0] + Geom::Point(width/8., -width/12.));
            hand.pts.push_back(hand.pts[0] + Geom::Point(0,-width/4.));
            hand.pts.emplace_back(slider_margin,slider_bot);
            hand.pts.emplace_back(width-slider_margin,slider_top);
        }
        
        hand.pts[4][X] = slider_margin;
        if (hand.pts[4][Y]<slider_top) hand.pts[4][Y] = slider_top; 
        if (hand.pts[4][Y]>slider_bot) hand.pts[4][Y] = slider_bot; 
        hand.pts[5][X] = width-slider_margin;
        if (hand.pts[5][Y]<slider_top) hand.pts[5][Y] = slider_top; 
        if (hand.pts[5][Y]>slider_bot) hand.pts[5][Y] = slider_bot; 

        double tA = (slider_bot-hand.pts[4][Y])/(slider_bot-slider_top);
        double tB = (slider_bot-hand.pts[5][Y])/(slider_bot-slider_top);

        cairo_move_to(cr,Geom::Point(slider_margin,slider_bot));
        cairo_line_to(cr,Geom::Point(slider_margin,slider_top));
        cairo_move_to(cr,Geom::Point(width-slider_margin,slider_bot));
        cairo_line_to(cr,Geom::Point(width-slider_margin,slider_top));
        cairo_set_line_width(cr,.5);
        cairo_set_source_rgba (cr, 0., 0.3, 0., 1.);
        cairo_stroke(cr);
        
        Frame frame;
        frame.O = hand.pts[0];//
        frame.x = hand.pts[1]-hand.pts[0];//
        frame.y = hand.pts[2]-hand.pts[0];//
        frame.z = hand.pts[3]-hand.pts[0];// 

/*
        SBasis2d f = y_x2();
        D2<SBasis> true_solution(Linear(0,1),Linear(0,1));
        true_solution[Y].push_back(Linear(-1,-1));
        SBasis zero = SBasis(Linear(0.));
        Geom::Point A = true_solution(tA);
        Geom::Point B = true_solution(tB);
*/

        SBasis2d f = x2_plus_y2_1();
        D2<Piecewise<SBasis> > true_solution;
        true_solution[X] = cos(SBasis(Linear(0,3.141592/2)));
        true_solution[Y] = sin(SBasis(Linear(0,3.141592/2)));
        Piecewise<SBasis> zero = Piecewise<SBasis>(SBasis(Linear(0.)));
        //Geom::Point A(cos(tA*M_PI/2), sin(tA*M_PI/2));// = true_solution(tA);
        //Geom::Point B(cos(tB*M_PI/2), sin(tB*M_PI/2));// = true_solution(tB);
        Geom::Point A = true_solution(tA);
        Geom::Point B = true_solution(tB);
        Point dA(-sin(tA*M_PI/2), cos(tA*M_PI/2));
        Geom::Point dB(-sin(tB*M_PI/2), cos(tB*M_PI/2));
        SBasis2d dfdu = partial_derivative(f, 0);
        SBasis2d dfdv = partial_derivative(f, 1);
        Geom::Point dfA(dfdu.apply(A[X],A[Y]),dfdv.apply(A[X],A[Y]));
        Geom::Point dfB(dfdu.apply(B[X],B[Y]),dfdv.apply(B[X],B[Y]));
        dA = rot90(dfA);
        dB = rot90(dfB);

        plot3d(cr,Linear(0,1),Linear(0,0),Linear(0,0),frame);
        plot3d(cr,Linear(0,1),Linear(1,1),Linear(0,0),frame);
        plot3d(cr,Linear(0,0),Linear(0,1),Linear(0,0),frame);
        plot3d(cr,Linear(1,1),Linear(0,1),Linear(0,0),frame);
        cairo_set_line_width(cr,.2);
        cairo_set_source_rgba (cr, 0., 0., 0., 1.);
        cairo_stroke(cr);

        plot3d_top(cr,f,frame);
        cairo_set_line_width(cr,1);        
        cairo_set_source_rgba (cr, .5, 0.5, 0.5, 1.);
        cairo_stroke(cr);
        plot3d(cr,f,frame);
        cairo_set_line_width(cr,.2);        
        cairo_set_source_rgba (cr, .5, 0.5, 0.5, 1.);
        cairo_stroke(cr);

        plot3d(cr, true_solution[X], true_solution[Y], zero, frame);
        cairo_set_line_width(cr,.5);
        cairo_set_source_rgba (cr, 0., 0., 0., 1.);
        cairo_stroke(cr);
        double error;
        for(int degree = 2; degree < 2; degree++) {
            D2<SBasis> zeroset = sb2dsolve(f,A,B,degree);
            plot3d(cr, zeroset[X], zeroset[Y], SBasis(Linear(0.)),frame);
            cairo_set_line_width(cr,1);        
            cairo_set_source_rgba (cr, 0.9, 0., 0., 1.);
            cairo_stroke(cr);
            
            SBasis comp = compose(f,zeroset);
            plot3d(cr, zeroset[X], zeroset[Y], comp, frame);
            cairo_set_source_rgba (cr, 0.7, 0., 0.7, 1.);
            cairo_stroke(cr);
            //Fix Me: bounds_exact does not work here?!?!
            Interval bounds = *bounds_fast(comp);
            error = (bounds.max()>-bounds.min() ? bounds.max() : -bounds.min() );
        }
        if (1) {

            bits_n_bobs par = {&f, A, B, dA, dB};
            bits_n_bobs* bnb = &par;
            std::cout << f[0] << "= initial f \n";
            const gsl_multimin_fminimizer_type *T = 
                gsl_multimin_fminimizer_nmsimplex;
            gsl_multimin_fminimizer *s = NULL;
            gsl_vector *ss, *x;
            gsl_multimin_function minex_func;
     
            size_t iter = 0;
            int status;
            double size;
     
            /* Starting point */
            x = gsl_vector_alloc (2);
            gsl_vector_set (x, 0, 0.552); // magic number for quarter circle
            gsl_vector_set (x, 1, 0.552);
     
            /* Set initial step sizes to 1 */
            ss = gsl_vector_alloc (2);
            gsl_vector_set_all (ss, 0.1);
     
            /* Initialize method and iterate */
            minex_func.n = 2;
            minex_func.f = &my_f;
            minex_func.params = (void *)&par;
     
            s = gsl_multimin_fminimizer_alloc (T, 2);
            gsl_multimin_fminimizer_set (s, &minex_func, x, ss);
     
            do
            {
                iter++;
                status = gsl_multimin_fminimizer_iterate(s);
           
                if (status) 
                    break;
     
                size = gsl_multimin_fminimizer_size (s);
                status = gsl_multimin_test_size (size, 1e-7);
     
                if (status == GSL_SUCCESS)
                {
                    printf ("converged to minimum at\n");
                }
     
            }
            while (status == GSL_CONTINUE && iter < 100);
            printf ("%5lu %g %gf f() = %g size = %g\n", 
                    iter,
                    gsl_vector_get (s->x, 0), 
                    gsl_vector_get (s->x, 1), 
                    s->fval, size);
            {
                double x = gsl_vector_get(s->x, 0);
                double y = gsl_vector_get(s->x, 1);
                Bezier b0(bnb->B[0], bnb->B[0]+bnb->dB[0]*x, bnb->A[0]+bnb->dA[0]*y, bnb->A[0]);
                Bezier b1(bnb->B[1], bnb->B[1]+bnb->dB[1]*x, bnb->A[1]+bnb->dA[1]*y, bnb->A[1]);
            
                D2<SBasis> zeroset(b0.toSBasis(), b1.toSBasis());
                plot3d(cr, zeroset[X], zeroset[Y], SBasis(Linear(0.)),frame);
                cairo_set_line_width(cr,1);        
                cairo_set_source_rgba (cr, 0.9, 0., 0., 1.);
                cairo_stroke(cr);
            
                SBasis comp = compose(f,zeroset);
                plot3d(cr, zeroset[X], zeroset[Y], comp, frame);
                cairo_set_source_rgba (cr, 0.7, 0., 0.7, 1.);
                cairo_stroke(cr);
                //Fix Me: bounds_exact does not work here?!?!
                Interval bounds = *bounds_fast(comp);
                error = (bounds.max()>-bounds.min() ? bounds.max() : -bounds.min() );

            }        
       
            gsl_vector_free(x);
            gsl_vector_free(ss);
            gsl_multimin_fminimizer_free (s);
        }
        *notify << "Gray: f-graph and true solution,\n";
        *notify << "Red: solver solution,\n";
        *notify << "Purple: value of f over solver solution.\n";
        *notify << "  error: "<< error <<".\n";
        
        Toy::draw(cr, notify, width, height, save,timer_stream);
    }
};

int main(int argc, char **argv) {
        init(argc, argv, new Sb2dSolverToy());
        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 :