long double BaseOfPerpendicularIsInsideSegment(Pnt p, Pnt a, Pnt b) {
Pnt normal = Pnt((b - a).y, - (b - a).x);
normal = normal * (1 / normal.len());
long double l = distanceFromPointToLine(p, a, b);
return pointIsOnSegment(p + normal * l, a, b)
|| pointIsOnSegment(p - normal * l, a, b);
}
//Dini's Surface
void dini(GLVApp& app, bool reset = false){
static Dll dll = DLN(0,1,0);
static Frame frame(PT(0,2,0), Rot(1,0,0,0));
TOUCH(frame);
static Pnt p = Ro::null(1,0,0);
static float period, pitch, amt, nm, lz;
SET
Gui& gui = app.gui;
gui(period,"period",-10,10)(pitch,"pitch",-10,10)(amt,"amt",-10,10)(nm,"num",10,100);
gui(lz, "light_src",-100,100);
amt = -2;
period = 1;
pitch = 0;
lz = .35;
END
if (reset) bSet = false;
GL::lightPos(0, lz, lz);
DRAW(frame);//.draw();
Twist tw; tw.along(dll, PI*period, pitch);
Par par = frame.ty(frame.scale() * amt);
int num = nm;
UVMesh uvmesh(num+1,num+1);
ITJi(i,num)
Pnt tp = p.sp( tw.mot(-t) );
ITJi(j, num)
Par npar = par.trs(0,tp[1],0);
Bst pp = Gen::bst(npar*t);//Gen::trv(1,npar * t);
Pnt np = Ro::loc( tp.sp( pp ) );
uvmesh.add(np);
END
END
//DRAW
uvmesh.draw(1,0,0);
uvmesh.drawTri(1,1,0,.5);
app.text("Negatively Curved Surfaces: The Psuedosphere and Dini's Surface");
}
void Immediate (const Sph& s){
VT ta = Ro::size( s, false );
//Draw as dual Sphere (if |radius^2| > 0.000001);
if ( fabs(ta) > FPERROR ) {
// printf("spehere!!!!!!!!!!!!!!!!!!!!\n");
bool real = ta > 0 ? 1 : 0;
Pnt p = Ro::cen( s );
VT t = sqrt ( fabs ( ta ) );
gfx::GL::translate ( p.begin() );
(real) ? gfx::Glyph::SolidSphere(t, 5+ floor(t*30), 5+floor(t*30)) : Glyph::Sphere(t);
} else {
// printf("NOOOOOO\n");
gfx::Glyph::Point(s);
}
}
//Time that will take the point with a given speed to hit a circle
arrow::Vct::Mod tth (const Pnt &p, const arrow::Vct &pv, const Crl &c)
{
//If they are alredy at contact, the tth is 0
if (p.contact(c))
return 0;
else
if(!(pv))//If they are not at contact and the speed is null, they will never meet
return -1;
//Get the distance and the componets of the speed
arrow::Vct d(p.get_center()-c.get_center());
arrow::Vct::Mod dx(d.mod_tan_part(pv));
//Get the a, b and c coefficientes of the second degree ecuation
double
ac=pv.sq_mod(),
bc=2*dx*pv.mod(),
cc=d.sq_mod()-c.get_size()*c.get_size();
//Get the value of the discriminant
double disc=bc*bc-4*ac*cc;
//Check that the 2nd degree equation has solution
if (disc<0)//No solution
return -1;//No contact
else//Has solution
{
//Find the two solutions
double
sol1=(-bc-std::sqrt(disc))/(2*ac),
sol2=(-bc+std::sqrt(disc))/(2*ac);
double sol=std::min(sol1,sol2);//Find the final solution
if (sol<0) return -1;//No contact return value
return sol;
}
}
void hopf(al::VsrApp& app){
HopfFiber hf;
static int time = 0; time++; double tphase = PI * time/180.0;
//GUI Controlled Parameters
static int num = 2;
static int res = 3;
static bool handed, bDrawCir, bDrawPnt,bReset;
static double phase,amt,minDistance;
//SET UP Gui
static bool bSet = 0;
if (!bSet) {
bSet = 1;
app.glv.gui(num,"num",0,1000)(res,"res",0,1000)(phase,"phase",-100,100)(amt,"amt",0,10)(minDistance,"minDistance",0,1000);
app.glv.gui(handed)(bDrawCir, "drawcir")(bDrawPnt,"drawpnt")(bReset,"reset");
}
vector<Pnt> vp;
for (int i = 0; i < num; ++i){
double u = 1.0 * i/num;
for (int j = 0; j < res; ++j){
double v = 1.0 * j/res;
Cir tc = hf.fiber(-1.0 + 2*u, -.5 + v);
Pnt tp = Ro::pnt_cir( tc, tphase * Ro::cur(tc) * phase);
if(bDrawPnt)DRAW3(tp,u,v,1-u);
if(bDrawCir)DRAW3(tc,v,u,1-u);
vp.push_back( Ro::pnt_cir( tc, v * u * PI ) );
}
}
static Dll dll = DLN(0,1,0); app.interface.touch(dll); DRAW(dll);
static Point point = PT(2,0,0); app.interface.touch(point); DRAW3(point,1,0,0);
for (int i = 0; i <= 1; ++i){
double t = i/1.0;
Dll tdll = dll.sp( Gen::rot(Biv::xy * t*PIOVERTWO) );
Pnt pa = Ro::split( ( tdll ^ Ro::sur(hf.cir) ).dual(), true);
Pnt pb = Ro::split( ( tdll ^ Ro::sur(hf.cir) ).dual(), false);
DRAW3(pa,1,1,0); DRAW3(pb,1,1,0);
Coord::Sph spha = Coord::vec2sph( Vector(pa).unit() );
Coord::Sph sphb = Coord::vec2sph( Vector(pb).unit() );
Cir cca = hf.fiber( spha.theta / PI, spha.phi / PI );
Cir ccb = hf.fiber( sphb.theta / PI, sphb.phi / PI );
Bst bst = Gen::bst( (cca.dual() * PI/3.0 + ccb.dual() * PI/2.0 )* amt );
DRAW3(cca,0,1,0); DRAW3(ccb,0,0,1);
vector<Pnt> pp;
Pnt tp = point;//.trs(-t,0,0);
for (int i = 0; i<1000; ++i){
tp = Ro::loc( tp.sp( bst ) );
pp.push_back(tp);
}
glColor3f(1,0,0);
glBegin(GL_LINE_STRIP);
for (int i = 0; i<pp.size(); ++i ){
GL::vertex( pp[i].w() );
}
glEnd();
}
int tnum = 10;
// for (int j = 0; j < tnum; ++j){
//
// double t = 1.0 * j/tnum;
//
// Bst bst2 = hf.mtt( );
//
// for (int i = 0; i<pp.size(); ++i ){
// for(int k = 0; k < 10; ++k){
//
// }
// }
//
// }
}
//Contact between a point and a circle
bool collide (const Crl &c, const Pnt &p)
{
return (c.get_center()-p.get_center()).sq_mod()<=c.get_size()*c.get_size();
}
virtual void onDraw(){
getMouse();
static Dls dls = Ro::dls(5.0, 0,-5,0);
Touch(interface,dls);
static Dlp dlp = Vec(0,1,1).unit() + Inf(0);
Touch(interface,dlp);
Draw(dlp,0,1,0);
//some lines
int iter = 50;
float spacing = 10;
vector<Lin> lines(iter);
int it = 0;
for ( auto &i : lines ){
it += 1;
float t = -spacing/2.0 + spacing * (float) it / iter;
//Top curvature
Par tp = Par( Tnv(0,0,amtA) ).trs(0,3,0);
auto bstA = Gen::bst( tp );
Pnt tpnt = Ro::point( t, 3, 0 );
Dll dll = (tpnt ^ Vec::y ^ Inf(1) ).dual();
Pnt pa = Ro::loc( tpnt.spin( bstA ) );
//Bottom Curvature
Par bp = Par( Tnv(0,0,amtB) ).trs(0,-3,0);
auto bstB = Gen::bst( bp );
Pnt bpnt = Ro::point( t, -3, 0 );
Pnt pb = Ro::loc( bpnt.spin( bstB ) );
i = pa ^ pb ^ Inf(1); i = i.runit();
Draw(i);
Pnt rp = ( i.dual() ^ dlp ).dual().unit().null();
Draw(rp,1,0,1);
Draw(pa,1,0,0); Draw(tpnt,0,1,0); Draw(pb,1,0,0);
// Par itp = Par( Tnv(0,0,amtA) ).trs ( Fl::loc( LN(0,1,0), rp, false ) );
// auto ibst = Gen::bst(itp);
//
VT dist = Ro::dist( pa, rp );
Pnt rpp = Ro::loc( Ro::split( ( Ro::dls( tpnt, dist ) ^ dll ).dual(), false )) ;
VT dist2 = Ro::dist( tpnt, rpp );
// cout << dist << " " << dist2 << endl;
// Pnt rpp = Ro::loc( rp.spin( !ibst ) ); //inverse operation
Draw( rpp, 1,1, 0);
auto ri = i.reflect(dlp);
Draw(ri,0,0,1);
}
// Draw(dls,0,1,1,.2);
}
/*!
* \brief hyperbolic spin transformation from pa to pb by amt (0,1)
*/
Point hspin(const Pnt& pa, const Pnt& pb, double amt){
return Round::loc( pa.boost( hgen(pa,pb,amt) ) );
//versor * dist * amt * .5) );
}