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#include <2geom/d2.h>
#include <2geom/sbasis.h>
#include <2geom/sbasis-2d.h>
#include <2geom/sbasis-geometric.h>
#include <2geom/bezier-to-sbasis.h>
#include <toys/path-cairo.h>
#include <toys/toy-framework-2.h>
#include <vector>
using std::vector;
using namespace Geom;
class NormalBundle : public std::vector<D2<SBasis2d> >{
public:
vector<double> lengths;
NormalBundle(){lengths.push_back(0.);}
void setBase(D2<SBasis> const &B, double tol);
void draw(cairo_t* cr, unsigned NbSections =5,unsigned NbFibre=5);
};
vector<D2<SBasis> > compose(NormalBundle const &NB,
D2<SBasis> const &Binit,
Geom::Point Origin=Geom::Point(0,0));
//--------------------------------------------
void SBasis1d_to_2d(D2<SBasis> C0,
D2<SBasis> C1,
D2<SBasis2d> &S){
for(unsigned dim = 0; dim < 2; dim++) {
//**** C0 and C1 should have the same size...
for (unsigned i=C0[dim].size();i<C1[dim].size(); i++)
C0[dim].push_back(Linear(0));
for (unsigned i=C1[dim].size();i<C0[dim].size(); i++)
C1[dim].push_back(Linear(0));
S[dim].clear();
S[dim].us = C0[dim].size();
S[dim].vs = 1;
for(unsigned v = 0; v < S[dim].vs; v++)
for(unsigned u = 0; u < S[dim].us; u++)
S[dim].push_back(Linear2d(C0[dim][u][0],C0[dim][u][1],
C1[dim][u][0],C1[dim][u][1]));
}
}
void NormalBundle::setBase(D2<SBasis> const &B, double tol=0.01) {
D2<SBasis> dB = derivative(B);
vector<double> cuts;
Piecewise<D2<SBasis> > unitV=unitVector(dB);
//TODO: clean this up, use arc_length_parametrization...
cuts=unitV.cuts;
double t0=0,t1,L=0;
for(unsigned i=1;i<cuts.size();i++){
t1=cuts[i];
D2<SBasis> subB=compose(B,Linear(t0,t1));
D2<SBasis2d> S;
SBasis1d_to_2d(subB, subB+rot90(unitV[i]), S);
push_back(S);
SBasis s=integral(dot(compose(dB,Linear(t0,t1)),unitV[i]));
L+=(s(1)-s(0))*(t1-t0);
lengths.push_back(L);
t0=t1;
}
}
void NormalBundle::draw(cairo_t *cr, unsigned NbLi, unsigned NbCol) {
D2<SBasis> B;
vector<D2<SBasis> > tB;
//Geom::Point Seg[2];
B[1]=Linear(-100,100);
double width=*(lengths.rbegin());
if (NbCol>0)
for(unsigned ui = 0; ui <= NbCol; ui++) {
B[0]=Linear(ui*width/NbCol);
tB = compose(*this,B);
if (tB.size()>0) cairo_d2_sb(cr, tB[0]);
}
B[0]=SBasis(Linear(0,1));
for(unsigned ui = 0; ui <= NbLi; ui++) {
B[1]=Linear(-100+ui*200/NbLi);
for(unsigned i = 0; i <size(); i++) {
D2<SBasis> section=composeEach((*this)[i],B);
cairo_d2_sb(cr, section);
}
}
}
vector<D2<SBasis> > compose(NormalBundle const &NB,
D2<SBasis> const &Binit,
Geom::Point Origin){
vector<D2<SBasis> > result;
D2<SBasis> B=Binit;
D2<SBasis> Bcut;
vector<double> Roots;
std::map<double,unsigned> Cuts;
unsigned idx;
B = B + (-Origin);
//--Find intersections with fibers over segment ends.
for(unsigned i=0; i<=NB.size();i++){
Roots=roots(B[0]);
for (vector<double>::iterator root=Roots.begin();
root!=Roots.end();root++)
Cuts[*root]=i;
if((Cuts.count(0.)==0) and
((B[0].valueAt(0.)<=0) or i==NB.size()))
Cuts[0.]=i;
if((Cuts.count(1.)==0) and
((B[0].valueAt(1.)<=0) or i==NB.size()))
Cuts[1.]=i;
if (i<NB.size())
B[0]-=(NB.lengths[i+1]-NB.lengths[i]);
}
B[0]+=*(NB.lengths.rbegin());
//-- Compose each piece with the relevant sbasis2d.
// TODO: use a uniform parametrization of the base.
std::map<double,unsigned>::iterator cut=Cuts.begin();
std::map<double,unsigned>::iterator next=cut; next++;
while(next!=Cuts.end()){
double t0=(*cut).first;
unsigned idx0=(*cut).second;
double t1=(*next).first;
unsigned idx1=(*next).second;
if (idx0 != idx1){
idx=std::min(idx0,idx1);
} else if(B[0]((t0+t1)/2) < NB.lengths[idx0]) { // we have a left 'bump',
idx=idx0-1;
} else if(B[0]((t0+t1)/2) == NB.lengths[idx0]) { //we have a vertical segment!...
idx= (idx0==NB.size())? idx0-1:idx0;
} else //we have a right 'bump'.
idx=idx0;
//--trim version...
if (idx>=0 and idx<NB.size()) {
for (unsigned dim=0;dim<2;dim++)
Bcut[dim]=compose(B[dim], Linear(t0,t1));
double width=NB.lengths[idx+1]-NB.lengths[idx];
Bcut[0]=compose(Linear(-NB.lengths[idx]/width,
(1-NB.lengths[idx])/width),Bcut[0]);
Bcut = composeEach(NB[idx], Bcut);
result.push_back(Bcut);
}
cut++;
next++;
}
return(result);
}
class NormalBundleToy: public Toy {
PointSetHandle B_handle;
PointSetHandle P_handle;
PointHandle O_handle;
void draw(cairo_t *cr, std::ostringstream *notify, int width, int height, bool save, std::ostringstream *timer_stream) {
D2<SBasis> B = B_handle.asBezier();
D2<SBasis> P = P_handle.asBezier();
Geom::Point O = O_handle.pos;
NormalBundle NBdle;
NBdle.setBase(B);
Geom::Point Oo(O[0]+*(NBdle.lengths.rbegin()),O[1]);
vector<D2<SBasis> > Q=compose(NBdle,P,O);
cairo_set_line_width (cr, 0.5);
//Base lines
cairo_set_source_rgba (cr, 0.9, 0., 0., 1);
cairo_d2_sb(cr, B);
draw_line_seg(cr, O, Oo);
cairo_stroke(cr);
//Sections
cairo_set_source_rgba (cr, 0, 0, 0.9, 1);
cairo_d2_sb(cr, P);
for (unsigned i=0;i<Q.size();i++){
cairo_d2_sb(cr, Q[i]);
}
cairo_stroke(cr);
//Normal bundle
cairo_set_source_rgba (cr, 0., 0., 0., 1);
NBdle.draw(cr,3,5);
cairo_stroke(cr);
Toy::draw(cr, notify, width, height, save,timer_stream);
}
public:
NormalBundleToy(){
if(handles.empty()) {
handles.push_back(&B_handle);
handles.push_back(&P_handle);
handles.push_back(&O_handle);
for(unsigned i = 0; i < 4; i++)
B_handle.push_back(200+50*i,400);
for(unsigned i = 0; i < 4; i++)
P_handle.push_back(100+uniform()*400,
150+uniform()*100);
O_handle.pos = Geom::Point(200,200);
}
}
};
int main(int argc, char **argv) {
init(argc, argv, new NormalBundleToy);
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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