static OptInterval
find_bounds_for_lambda0(double aa0,double aa1,double cc0,double cc1,
int insist_on_speeds_signs){
double a0=aa0,a1=aa1,c0=cc0,c1=cc1;
Interval result;
bool flip = a1<0;
if (a1<0){a1=-a1; c1=-c1;}
if (a0<0){a0=-a0; c0=-c0;}
double a = (a0<a1 ? a0 : a1);
double c = (c0<c1 ? c0 : c1);
double delta = 1-4*a*c;
if ( delta < 0 )
return OptInterval();//return empty interval
double lambda_max = (1+std::sqrt(delta))/2/a;
result = Interval(c,lambda_max);
if (flip)
result *= -1;
if (insist_on_speeds_signs == 1){
if (result.max() < 0)//Caution: setMin with max<new min...
return OptInterval();//return empty interval
result.setMin(0);
}
result = Interval(result.min()-.1,result.max()+.1);//just in case all our approx. were exact...
return result;
}
Piecewise<SBasis> convole(SBasisOf<double> const &f, Interval dom_f,
SBasisOf<double> const &g, Interval dom_g,
bool f_cst_ends = false){
if ( dom_f.extent() < dom_g.extent() ) return convole(g, dom_g, f, dom_f);
Piecewise<SBasis> result;
SBasisOf<SBasisOf<double> > u,v;
u.push_back(LinearOf<SBasisOf<double> >(SBasisOf<double>(LinearOf<double>(0,1))));
v.push_back(LinearOf<SBasisOf<double> >(SBasisOf<double>(LinearOf<double>(0,0)),
SBasisOf<double>(LinearOf<double>(1,1))));
SBasisOf<SBasisOf<double> > v_u = (v - u)*(dom_f.extent()/dom_g.extent());
v_u += SBasisOf<SBasisOf<double> >(SBasisOf<double>(-dom_g.min()/dom_g.extent()));
SBasisOf<SBasisOf<double> > gg = multi_compose(g,v_u);
SBasisOf<SBasisOf<double> > ff = SBasisOf<SBasisOf<double> >(f);
SBasisOf<SBasisOf<double> > hh = integral(ff*gg,0);
result.cuts.push_back(dom_f.min()+dom_g.min());
//Note: we know dom_f.extent() >= dom_g.extent()!!
//double rho = dom_f.extent()/dom_g.extent();
double t0 = dom_g.min()/dom_f.extent();
double t1 = dom_g.max()/dom_f.extent();
double t2 = t0+1;
double t3 = t1+1;
SBasisOf<double> a,b,t;
SBasis seg;
a = SBasisOf<double>(LinearOf<double>(0,0));
b = SBasisOf<double>(LinearOf<double>(0,t1-t0));
t = SBasisOf<double>(LinearOf<double>(t0,t1));
seg = toSBasis(compose(hh,b,t)-compose(hh,a,t));
result.push(seg,dom_f.min() + dom_g.max());
if (dom_f.extent() > dom_g.extent()){
a = SBasisOf<double>(LinearOf<double>(0,t2-t1));
b = SBasisOf<double>(LinearOf<double>(t1-t0,1));
t = SBasisOf<double>(LinearOf<double>(t1,t2));
seg = toSBasis(compose(hh,b,t)-compose(hh,a,t));
result.push(seg,dom_f.max() + dom_g.min());
}
a = SBasisOf<double>(LinearOf<double>(t2-t1,1.));
b = SBasisOf<double>(LinearOf<double>(1.,1.));
t = SBasisOf<double>(LinearOf<double>(t2,t3));
seg = toSBasis(compose(hh,b,t)-compose(hh,a,t));
result.push(seg,dom_f.max() + dom_g.max());
result*=dom_f.extent();
//--constant ends correction--------------
if (f_cst_ends){
SBasis ig = toSBasis(integraaal(g))*dom_g.extent();
ig -= ig.at0();
Piecewise<SBasis> cor;
cor.cuts.push_back(dom_f.min()+dom_g.min());
cor.push(reverse(ig)*f.at0(),dom_f.min()+dom_g.max());
cor.push(Linear(0),dom_f.max()+dom_g.min());
cor.push(ig*f.at1(),dom_f.max()+dom_g.max());
result+=cor;
}
//----------------------------------------
return result;
}
void IntensityDistributionHistogram::construct( const Billon &billon, const Interval<uint> &sliceInterval, const Interval<int> &intensityInterval, const uint &smoothingRadius )
{
const uint &width = billon.n_cols;
const uint &height = billon.n_rows;
const int &minVal = intensityInterval.min();
uint i, j, k;
clear();
resize(intensityInterval.size()+1);
for ( k=sliceInterval.min() ; k<=sliceInterval.max() ; ++k )
{
const Slice &slice = billon.slice(k);
for ( j=0 ; j<height ; ++j )
{
for ( i=0 ; i<width ; ++i )
{
if ( intensityInterval.containsClosed(slice.at(j,i)) ) ++((*this)[slice.at(j,i)-minVal]);
}
}
}
meansSmoothing(smoothingRadius,false);
}
void IntensityDistributionHistogram::construct( const Billon &billon, const Interval<uint> &sliceInterval, const Interval<uint> §orInterval,
const iCoord2D &pithCoord, const uint &maxDistance, const Interval<int> &intensityInterval,
const uint &smoothingRadius )
{
const uint &width = billon.n_cols;
const uint &height = billon.n_rows;
const int &minVal = intensityInterval.min();
uint i, j, k;
clear();
resize(intensityInterval.size()+1);
for ( j=0 ; j<height ; ++j )
{
for ( i=0 ; i<width ; ++i )
{
if ( sectorInterval.containsClosed(PieChartSingleton::getInstance()->sectorIndexOfAngle(pithCoord.angle(iCoord2D(i,j)))) && pithCoord.euclideanDistance(iCoord2D(i,j)) < maxDistance )
{
for ( k=sliceInterval.min() ; k<=sliceInterval.max() ; ++k )
{
if ( intensityInterval.containsClosed(billon.slice(k).at(j,i)) ) ++((*this)[billon.slice(k).at(j,i)-minVal]);
}
}
}
}
meansSmoothing(smoothingRadius,false);
}
Interval bounds_local(const SBasis &sb, const Interval &i, int order) {
double t0=i.min(), t1=i.max(), lo=0., hi=0.;
for(int j = sb.size()-1; j>=order; j--) {
double a=sb[j][0];
double b=sb[j][1];
double t = 0;
if (lo<0) t = ((b-a)/lo+1)*0.5;
if (lo>=0 || t<t0 || t>t1) {
lo = std::min(a*(1-t0)+b*t0+lo*t0*(1-t0),a*(1-t1)+b*t1+lo*t1*(1-t1));
}else{
lo = lerp(t, a+lo*t, b);
}
if (hi>0) t = ((b-a)/hi+1)*0.5;
if (hi<=0 || t<t0 || t>t1) {
hi = std::max(a*(1-t0)+b*t0+hi*t0*(1-t0),a*(1-t1)+b*t1+hi*t1*(1-t1));
}else{
hi = lerp(t, a+hi*t, b);
}
}
Interval res = Interval(lo,hi);
if (order>0) res*=pow(.25,order);
return res;
}
QVector<rCoord2D> restrictedAreaVertex( const Billon &billon, const Interval<uint> & sliceInterval, const uint & nbPolygonVertex, const int & intensityThreshold )
{
Q_ASSERT_X( nbPolygonVertex>0 , "BillonTpl<T>::getRestrictedAreaVertex", "nbPolygonVertex arguments equals to 0 => division by zero" );
QVector<rCoord2D> vectAllVertex;
if ( billon.hasPith() )
{
const int width = billon.n_cols;
const int height = billon.n_rows;
const qreal angleIncrement = TWO_PI/static_cast<qreal>(nbPolygonVertex);
rCoord2D edge, center;
rVec2D direction;
qreal orientation;
for ( uint indexSlice = sliceInterval.min() ; indexSlice<=sliceInterval.max() ; ++indexSlice )
{
const Slice & currentSlice = billon.slice(indexSlice);
center.x = billon.pithCoord(indexSlice).x;
center.y = billon.pithCoord(indexSlice).y;
orientation = 0.;
while (orientation < TWO_PI)
{
orientation += angleIncrement;
direction = rVec2D(qCos(orientation),qSin(orientation));
edge = center + direction*30;
while ( edge.x>0. && edge.y>0. && edge.x<width && edge.y<height && currentSlice(edge.y,edge.x) >= intensityThreshold )
{
edge += direction;
}
vectAllVertex.push_back(edge);
}
}
}
return vectAllVertex;
}
Piecewise<SBasis> reciprocalOnDomain(Interval range, double tol){
Piecewise<SBasis> reciprocal_fn;
//TODO: deduce R from tol...
double R=2.;
SBasis reciprocal1_R=reciprocal(Linear(1,R),3);
double a=range.min(), b=range.max();
if (a*b<0){
b=std::max(fabs(a),fabs(b));
a=0;
}else if (b<0){
a=-range.max();
b=-range.min();
}
if (a<=tol){
reciprocal_fn.push_cut(0);
int i0=(int) floor(std::log(tol)/std::log(R));
a=pow(R,i0);
reciprocal_fn.push(Linear(1/a),a);
}else{
int i0=(int) floor(std::log(a)/std::log(R));
a=pow(R,i0);
reciprocal_fn.cuts.push_back(a);
}
while (a<b){
reciprocal_fn.push(reciprocal1_R/a,R*a);
a*=R;
}
if (range.min()<0 || range.max()<0){
Piecewise<SBasis>reciprocal_fn_neg;
//TODO: define reverse(pw<sb>);
reciprocal_fn_neg.cuts.push_back(-reciprocal_fn.cuts.back());
for (unsigned i=0; i<reciprocal_fn.size(); i++){
int idx=reciprocal_fn.segs.size()-1-i;
reciprocal_fn_neg.push_seg(-reverse(reciprocal_fn.segs.at(idx)));
reciprocal_fn_neg.push_cut(-reciprocal_fn.cuts.at(idx));
}
if (range.max()>0){
reciprocal_fn_neg.concat(reciprocal_fn);
}
reciprocal_fn=reciprocal_fn_neg;
}
return(reciprocal_fn);
}
void SectorHistogram::construct( const Billon &billon, const Interval<uint> &sliceInterval, const Interval<int> &intensity,
const uint &zMotionMin, const int &radiusAroundPith )
{
clear();
if ( billon.hasPith() && sliceInterval.isValid() && sliceInterval.width() > 0 )
{
const int &width = billon.n_cols;
const int &height = billon.n_rows;
const qreal squareRadius = qPow(radiusAroundPith,2);
fill(0.,PieChartSingleton::getInstance()->nbSectors());
QVector<int> circleLines;
circleLines.reserve(2*radiusAroundPith+1);
for ( int lineIndex=-radiusAroundPith ; lineIndex<=radiusAroundPith ; ++lineIndex )
{
circleLines.append(qSqrt(squareRadius-qPow(lineIndex,2)));
}
QVector<int>::ConstIterator circlesLinesIterator;
int iRadius;
uint diff;
iCoord2D currentPos;
// Calcul du diagramme en parcourant les tranches du billon comprises dans l'intervalle
for ( uint k=sliceInterval.min() ; k<=sliceInterval.max() ; ++k )
{
const Slice ¤tSlice = billon.slice(k);
const Slice &previousSlice = billon.previousSlice(k);
const iCoord2D ¤tPithCoord = billon.pithCoord(k);
currentPos.y = currentPithCoord.y-radiusAroundPith;
for ( circlesLinesIterator = circleLines.constBegin() ; circlesLinesIterator != circleLines.constEnd() ; ++circlesLinesIterator )
{
iRadius = *circlesLinesIterator;
currentPos.x = currentPithCoord.x-iRadius;
iRadius += currentPithCoord.x;
while ( currentPos.x <= iRadius )
{
if ( currentPos.x < width && currentPos.y < height && intensity.containsOpen(currentSlice.at(currentPos.y,currentPos.x)) &&
intensity.containsOpen(previousSlice.at(currentPos.y,currentPos.x)) )
{
diff = billon.zMotion(currentPos.x,currentPos.y,k);
//if ( motionInterval.containsClosed(diff) )
if ( diff >= zMotionMin )
{
(*this)[PieChartSingleton::getInstance()->sectorIndexOfAngle( currentPithCoord.angle(currentPos) )] += diff-zMotionMin;
}
}
currentPos.x++;
}
currentPos.y++;
}
}
}
}
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;
}
//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.empty()) {
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];
}
void subdiv_sbasis(SBasis const & s,
std::vector<double> & roots,
double left, double right) {
Interval bs = bounds_fast(s);
if(bs.min() > 0 || bs.max() < 0)
return; // no roots here
if(s.tailError(1) < 1e-7) {
double t = s[0][0] / (s[0][0] - s[0][1]);
roots.push_back(left*(1-t) + t*right);
return;
}
double middle = (left + right)/2;
subdiv_sbasis(compose(s, Linear(0, 0.5)), roots, left, middle);
subdiv_sbasis(compose(s, Linear(0.5, 1.)), roots, middle, right);
}
Geom::Piecewise<Geom::D2<Geom::SBasis> >
doEffect_pwd2 (Geom::Piecewise<Geom::D2<Geom::SBasis> > & pwd2_in, Geom::Piecewise<Geom::D2<Geom::SBasis> > & pattern)
{
using namespace Geom;
Piecewise<D2<SBasis> > uskeleton = arc_length_parametrization(pwd2_in, 2, .1);
uskeleton = remove_short_cuts(uskeleton,.01);
Piecewise<D2<SBasis> > n = rot90(derivative(uskeleton));
n = force_continuity(remove_short_cuts(n,.1));
D2<Piecewise<SBasis> > patternd2 = make_cuts_independent(pattern);
Piecewise<SBasis> x = Piecewise<SBasis>(patternd2[0]);
Piecewise<SBasis> y = Piecewise<SBasis>(patternd2[1]);
Interval pattBnds = *bounds_exact(x);
x -= pattBnds.min();
Interval pattBndsY = *bounds_exact(y);
y -= (pattBndsY.max()+pattBndsY.min())/2;
int nbCopies = int(uskeleton.cuts.back()/pattBnds.extent());
double scaling = 1;
double pattWidth = pattBnds.extent() * scaling;
if (scaling != 1.0) {
x*=scaling;
}
double offs = 0;
Piecewise<D2<SBasis> > output;
for (int i=0; i<nbCopies; i++){
output.concat(compose(uskeleton,x+offs)+y*compose(n,x+offs));
offs+=pattWidth;
}
return output;
}
void PlotConcavityPointSerieCurve::update( const ConcavityPointSerieCurve &curve, const Interval<qreal> &angularInterval )
{
QVector<QPointF> datasMinConcavity(0);
QVector<QPointF> datasMaxConcavity(0);
QVector<QPointF> datasMinKnotArea(0);
QVector<QPointF> datasMaxKnotArea(0);
const int nbMaxConcavityPoints = curve.nbMaxConcavityPoints();
const int nbMinConcavityPoints = curve.nbMinConcavityPoints();
if ( nbMaxConcavityPoints || nbMinConcavityPoints )
{
const qreal minAngle = angularInterval.min();
const qreal maxAngle = angularInterval.isValid() ? angularInterval.max() : angularInterval.max()+TWO_PI;
int firstX, lastX;
firstX = lastX = 0;
if ( nbMaxConcavityPoints>0 && nbMinConcavityPoints>0 )
{
firstX = qMin(curve.maxConcavityPointsSerie().first().x,curve.minConcavityPointsSerie().first().x);
lastX = qMax(curve.maxConcavityPointsSerie().last().x,curve.minConcavityPointsSerie().last().x);
}
else if ( nbMaxConcavityPoints>0 )
{
firstX = curve.maxConcavityPointsSerie().first().x;
lastX = curve.maxConcavityPointsSerie().last().x;
}
else if ( nbMinConcavityPoints>0 )
{
firstX = curve.minConcavityPointsSerie().first().x;
lastX = curve.minConcavityPointsSerie().last().x;
}
if ( curve.nbMinConcavityPoints() > 0 )
{
datasMinConcavity.reserve(curve.nbMinConcavityPoints());
QVector<rCoord2D>::ConstIterator begin = curve.minConcavityPointsSerie().begin();
const QVector<rCoord2D>::ConstIterator end = curve.minConcavityPointsSerie().end();
while ( begin != end )
{
datasMinConcavity.append(QPointF(begin->x,begin->y));
++begin;
}
datasMinKnotArea.resize(2);
datasMinKnotArea[0] = QPointF( firstX, minAngle*RAD_TO_DEG_FACT );
datasMinKnotArea[1] = QPointF( lastX, minAngle*RAD_TO_DEG_FACT );
}
if ( curve.nbMaxConcavityPoints() > 0 )
{
datasMaxConcavity.reserve(curve.nbMaxConcavityPoints());
QVector<rCoord2D>::ConstIterator begin = curve.maxConcavityPointsSerie().begin();
const QVector<rCoord2D>::ConstIterator end = curve.maxConcavityPointsSerie().end();
while ( begin != end )
{
datasMaxConcavity.append(QPointF(begin->x,begin->y));
++begin;
}
datasMaxKnotArea.resize(2);
datasMaxKnotArea[0] = QPointF( firstX, maxAngle*RAD_TO_DEG_FACT );
datasMaxKnotArea[1] = QPointF( lastX, maxAngle*RAD_TO_DEG_FACT );
}
}
_minConcavityPointsData.setSamples(datasMinConcavity);
_maxConcavityPointsData.setSamples(datasMaxConcavity);
_minKnotAreaAngle.setSamples(datasMinKnotArea);
_maxKnotAreaAngle.setSamples(datasMaxKnotArea);
}
static void multi_roots_internal(SBasis const &f,
SBasis const &df,
std::vector<double> const &levels,
std::vector<std::vector<double> > &roots,
double htol,
double vtol,
double a,
double fa,
double b,
double fb){
if (f.size()==0){
int idx;
idx=upper_level(levels,0,vtol);
if (idx<(int)levels.size()&&fabs(levels.at(idx))<=vtol){
roots[idx].push_back(a);
roots[idx].push_back(b);
}
return;
}
////usefull?
// if (f.size()==1){
// int idxa=upper_level(levels,fa);
// int idxb=upper_level(levels,fb);
// if (fa==fb){
// if (fa==levels[idxa]){
// roots[a]=idxa;
// roots[b]=idxa;
// }
// return;
// }
// int idx_min=std::min(idxa,idxb);
// int idx_max=std::max(idxa,idxb);
// if (idx_max==levels.size()) idx_max-=1;
// for(int i=idx_min;i<=idx_max; i++){
// double t=a+(b-a)*(levels[i]-fa)/(fb-fa);
// if(a<t&&t<b) roots[t]=i;
// }
// return;
// }
if ((b-a)<htol){
//TODO: use different tol for t and f ?
//TODO: unsigned idx ? (remove int casts when fixed)
int idx=std::min(upper_level(levels,fa,vtol),upper_level(levels,fb,vtol));
if (idx==(int)levels.size()) idx-=1;
double c=levels.at(idx);
if((fa-c)*(fb-c)<=0||fabs(fa-c)<vtol||fabs(fb-c)<vtol){
roots[idx].push_back((a+b)/2);
}
return;
}
int idxa=upper_level(levels,fa,vtol);
int idxb=upper_level(levels,fb,vtol);
Interval bs = bounds_local(df,Interval(a,b));
//first times when a level (higher or lower) can be reached from a or b.
double ta_hi,tb_hi,ta_lo,tb_lo;
ta_hi=ta_lo=b+1;//default values => no root there.
tb_hi=tb_lo=a-1;//default values => no root there.
if (idxa<(int)levels.size() && fabs(fa-levels.at(idxa))<vtol){//a can be considered a root.
//ta_hi=ta_lo=a;
roots[idxa].push_back(a);
ta_hi=ta_lo=a+htol;
}else{
if (bs.max()>0 && idxa<(int)levels.size())
ta_hi=a+(levels.at(idxa )-fa)/bs.max();
if (bs.min()<0 && idxa>0)
ta_lo=a+(levels.at(idxa-1)-fa)/bs.min();
}
if (idxb<(int)levels.size() && fabs(fb-levels.at(idxb))<vtol){//b can be considered a root.
//tb_hi=tb_lo=b;
roots[idxb].push_back(b);
tb_hi=tb_lo=b-htol;
}else{
if (bs.min()<0 && idxb<(int)levels.size())
tb_hi=b+(levels.at(idxb )-fb)/bs.min();
if (bs.max()>0 && idxb>0)
tb_lo=b+(levels.at(idxb-1)-fb)/bs.max();
}
double t0,t1;
t0=std::min(ta_hi,ta_lo);
t1=std::max(tb_hi,tb_lo);
//hum, rounding errors frighten me! so I add this +tol...
if (t0>t1+htol) return;//no root here.
if (fabs(t1-t0)<htol){
multi_roots_internal(f,df,levels,roots,htol,vtol,t0,f(t0),t1,f(t1));
}else{
double t,t_left,t_right,ft,ft_left,ft_right;
t_left =t_right =t =(t0+t1)/2;
ft_left=ft_right=ft=f(t);
int idx=upper_level(levels,ft,vtol);
if (idx<(int)levels.size() && fabs(ft-levels.at(idx))<vtol){//t can be considered a root.
roots[idx].push_back(t);
//we do not want to count it twice (from the left and from the right)
t_left =t-htol/2;
t_right=t+htol/2;
ft_left =f(t_left);
ft_right=f(t_right);
}
multi_roots_internal(f,df,levels,roots,htol,vtol,t0 ,f(t0) ,t_left,ft_left);
multi_roots_internal(f,df,levels,roots,htol,vtol,t_right,ft_right,t1 ,f(t1) );
}
}
Piecewise<SBasis> log(Interval in) {
Piecewise<SBasis> I = integral(Geom::reciprocal(Linear(in.min(), in.max())));
return I + Piecewise<SBasis> (-I.segs[0][0] + log(in.min()));
}
bool operator == (const Interval<U>& v){ return min()==v.min() && max()==v.max(); }
virtual void draw(cairo_t *cr, std::ostringstream *notify, int width, int height, bool save, std::ostringstream *timer_stream) {
double slider_top = width/4.;
double slider_bot = width*3./4.;
double slider_margin = width/8.;
if(hand.pts.empty()) {
hand.pts.push_back(Geom::Point(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.push_back(Geom::Point(slider_margin,slider_bot));
hand.pts.push_back(Geom::Point(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 = ∥
std::cout << f[0] << "= intial 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 *)∥
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);
}
Crossings mono_intersect(Curve const & A, Interval const &Ad,
Curve const & B, Interval const &Bd) {
Crossings ret;
mono_intersect(A, Ad.min(), Ad.max(), B, Bd.min(), Bd.max(), ret);
return ret;
}
virtual void draw(cairo_t *cr, std::ostringstream *notify, int width, int height, bool save) {
double slider_top = width/4.;
double slider_bot = width*3./4.;
double slider_margin = width/8.;
if(hand.pts.empty()) {
hand.pts.push_back(Geom::Point(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.push_back(Geom::Point(slider_margin,slider_bot));
hand.pts.push_back(Geom::Point(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];//
#if 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);
#else
SBasis2d f = x2_plus_y2_1();
D2<Piecewise<SBasis> > true_solution;
true_solution[X] = cos(SBasis(Linear(0,3.14/2)));
true_solution[Y] = sin(SBasis(Linear(0,3.14/2)));
Piecewise<SBasis> zero = Piecewise<SBasis>(SBasis(Linear(0.)));
Geom::Point A = true_solution(tA);
Geom::Point B = true_solution(tB);
#endif
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 = 1; degree < 4; degree++) {
//D2<SBasis> zeroset = sb2dsolve(f,A,B,degree);
D2<SBasis> zeroset = sb2d_cubic_solve(f,A,B);
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() );
}
*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);
}
