~jaspervdg/+junk/aem-diffusion-curves

#include <2geom/sbasis-2d.h>

#include <2geom/sbasis-geometric.h>

namespace Geom{

SBasis extract_u(SBasis2d const &a, double u) {

    SBasis sb(a.vs, Linear());

    double s = u*(1-u);

    for(unsigned vi = 0; vi < a.vs; vi++) {

        double sk = 1;

        Linear bo(0,0);

        for(unsigned ui = 0; ui < a.us; ui++) {

            bo += (extract_u(a.index(ui, vi), u))*sk;

            sk *= s;

        }

        sb[vi] = bo;

    }

    return sb;

}

SBasis extract_v(SBasis2d const &a, double v) {

    SBasis sb(a.us, Linear());

    double s = v*(1-v);

    for(unsigned ui = 0; ui < a.us; ui++) {

        double sk = 1;

        Linear bo(0,0);

        for(unsigned vi = 0; vi < a.vs; vi++) {

            bo += (extract_v(a.index(ui, vi), v))*sk;

            sk *= s;

        }

        sb[ui] = bo;

    }

    return sb;

}

SBasis compose(Linear2d const &a, D2<SBasis> const &p) {

    D2<SBasis> omp(-p[X] + 1, -p[Y] + 1);

    return multiply(omp[0], omp[1])*a[0] +

           multiply(p[0], omp[1])*a[1] +

           multiply(omp[0], p[1])*a[2] +

           multiply(p[0], p[1])*a[3];

}

SBasis 

compose(SBasis2d const &fg, D2<SBasis> const &p) {

    SBasis B;

    SBasis s[2];

    SBasis ss[2];

    for(unsigned dim = 0; dim < 2; dim++) 

        s[dim] = p[dim]*(Linear(1) - p[dim]);

    ss[1] = Linear(1);

    for(unsigned vi = 0; vi < fg.vs; vi++) {

        ss[0] = ss[1];

        for(unsigned ui = 0; ui < fg.us; ui++) {

            unsigned i = ui + vi*fg.us;

            B += ss[0]*compose(fg[i], p);

            ss[0] *= s[0];

        }

        ss[1] *= s[1];

    }

    return B;

}

D2<SBasis>

compose_each(D2<SBasis2d> const &fg, D2<SBasis> const &p) {

    return D2<SBasis>(compose(fg[X], p), compose(fg[Y], p));

}

SBasis2d partial_derivative(SBasis2d const &f, int dim) {

    SBasis2d result;

    for(unsigned i = 0; i < f.size(); i++) {

        result.push_back(Linear2d(0,0,0,0));

    }

    result.us = f.us;

    result.vs = f.vs;

    for(unsigned i = 0; i < f.us; i++) {

        for(unsigned j = 0; j < f.vs; j++) {

            Linear2d lin = f.index(i,j);

            Linear2d dlin(lin[1+dim]-lin[0], lin[1+2*dim]-lin[dim], lin[3-dim]-lin[2*(1-dim)], lin[3]-lin[2-dim]);

            result[i+j*result.us] += dlin;

            unsigned di = dim?j:i;

            if (di>=1){

                float motpi = dim?-1:1;

                Linear2d ds_lin_low( lin[0], -motpi*lin[1], motpi*lin[2], -lin[3] );

                result[(i+dim-1)+(j-dim)*result.us] += di*ds_lin_low;

                Linear2d ds_lin_hi( lin[1+dim]-lin[0], lin[1+2*dim]-lin[dim], lin[3]-lin[2-dim], lin[3-dim]-lin[2-dim] );

                result[i+j*result.us] += di*ds_lin_hi;                

            }

        }

    }

    return result;

}

/**

 * Finds a path which traces the 0 contour of f, traversing from A to B as a single d2<sbasis>.

 * degmax specifies the degree (degree = 2*degmax-1, so a degmax of 2 generates a cubic fit).

 * The algorithm is based on dividing out derivatives at each end point and does not use the curvature for fitting.

 * It is less accurate than sb2d_cubic_solve, although this may be fixed in the future. 

 */

D2<SBasis>

sb2dsolve(SBasis2d const &f, Geom::Point const &A, Geom::Point const &B, unsigned degmax){

    //g_warning("check f(A)= %f = f(B) = %f =0!", f.apply(A[X],A[Y]), f.apply(B[X],B[Y]));

    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]));

    Geom::Point nA = dfA/(dfA[X]*dfA[X]+dfA[Y]*dfA[Y]);

    Geom::Point nB = dfB/(dfB[X]*dfB[X]+dfB[Y]*dfB[Y]);

    D2<SBasis>result(SBasis(degmax, Linear()), SBasis(degmax, Linear()));

    double fact_k=1;

    double sign = 1.;

    for(int dim = 0; dim < 2; dim++)

        result[dim][0] = Linear(A[dim],B[dim]);

    for(unsigned k=1; k<degmax; k++){

        // these two lines make the solutions worse!

        //fact_k *= k;

        //sign = -sign;

        SBasis f_on_curve = compose(f,result);

        Linear reste = f_on_curve[k];

        double ax = -reste[0]/fact_k*nA[X];

        double ay = -reste[0]/fact_k*nA[Y];

        double bx = -sign*reste[1]/fact_k*nB[X];

        double by = -sign*reste[1]/fact_k*nB[Y];

        result[X][k] = Linear(ax,bx);

        result[Y][k] = Linear(ay,by);

        //sign *= 3;

    }    

    return result;

}

/**

 * Finds a path which traces the 0 contour of f, traversing from A to B as a single cubic d2<sbasis>.

 * The algorithm is based on matching direction and curvature at each end point.

 */

//TODO: handle the case when B is "behind" A for the natural orientation of the level set.

//TODO: more generally, there might be up to 4 solutions. Choose the best one!

D2<SBasis>

sb2d_cubic_solve(SBasis2d const &f, Geom::Point const &A, Geom::Point const &B){

    D2<SBasis>result;//(Linear(A[X],B[X]),Linear(A[Y],B[Y]));

    //g_warning("check 0 = %f = %f!", f.apply(A[X],A[Y]), f.apply(B[X],B[Y]));

    SBasis2d f_u  = partial_derivative(f  , 0);

    SBasis2d f_v  = partial_derivative(f  , 1);

    SBasis2d f_uu = partial_derivative(f_u, 0);

    SBasis2d f_uv = partial_derivative(f_v, 0);

    SBasis2d f_vv = partial_derivative(f_v, 1);

    Geom::Point dfA(f_u.apply(A[X],A[Y]),f_v.apply(A[X],A[Y]));

    Geom::Point dfB(f_u.apply(B[X],B[Y]),f_v.apply(B[X],B[Y]));

    Geom::Point V0 = rot90(dfA);

    Geom::Point V1 = rot90(dfB);

    double D2fVV0 = f_uu.apply(A[X],A[Y])*V0[X]*V0[X]+

                  2*f_uv.apply(A[X],A[Y])*V0[X]*V0[Y]+

                    f_vv.apply(A[X],A[Y])*V0[Y]*V0[Y];

    double D2fVV1 = f_uu.apply(B[X],B[Y])*V1[X]*V1[X]+

                  2*f_uv.apply(B[X],B[Y])*V1[X]*V1[Y]+

                    f_vv.apply(B[X],B[Y])*V1[Y]*V1[Y];

    std::vector<D2<SBasis> > candidates = cubics_fitting_curvature(A,B,V0,V1,D2fVV0,D2fVV1);

    if (candidates.size()==0) {

        return D2<SBasis>(Linear(A[X],B[X]),Linear(A[Y],B[Y]));

    }

    //TODO: I'm sure std algorithm could do that for me...

    double error = -1;

    unsigned best = 0;

    for (unsigned i=0; i<candidates.size(); i++){

        Interval bounds = *bounds_fast(compose(f,candidates[i]));

        double new_error = (fabs(bounds.max())>fabs(bounds.min()) ? fabs(bounds.max()) : fabs(bounds.min()) );

        if ( new_error < error || error < 0 ){

            error = new_error;

            best = i;

        }

    }

    return candidates[best];

}

};

/*

  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 :