load("draw");
load("vect");
z(x,y) := (x*y)^(1/3)*(sin(x-y)+3);
x(t) := t+3; y(t) := t^2+2;
a : 0; b : 4;
draw3d(
  xu_grid=50,yv_grid=50,
  explicit(z(x,y),x,0,7,y,0,18),
  color=red,line_width=3,parametric(x(t),y(t),z(x(t),y(t)),t,a,b),
    parametric(x(t),y(t),0,t,a,b),
    parametric(x(a),y(a),p,p,0,z(x(a),y(a))),
    parametric(x(b),y(b),p,p,0,z(x(b),y(b))),
  color=blue,parametric(x(t),0,z(x(t),y(t)),t,a,b),
    parametric(x(t),0,0,t,a,b),
    parametric(x(a),0,p,p,0,z(x(a),y(a))),
    parametric(x(b),0,p,p,0,z(x(b),y(b))),
  color=green,parametric(0,y(t),z(x(t),y(t)),t,a,b),
    parametric(0,y(t),0,t,a,b),
    parametric(0,y(a),p,p,0,z(x(a),y(a))),
    parametric(0,y(b),p,p,0,z(x(b),y(b))),
  xlabel="x", ylabel="y", zlabel="z",
  xyplane=0);

z(x,y) := (x*y)^(1/3)*(sin(x-y)+3);
x(t) := -1/10*(t-10)^2+5; y(t) := t;
a : 6; b : 15;
haript: 10;
draw3d(
  xu_grid=50,yv_grid=50,
  explicit(z(x,y),x,0,7,y,0,18),
  color=red,line_width=3,parametric(x(t),y(t),z(x(t),y(t)),t,a,b),
    parametric(x(t),y(t),0,t,a,b),
    parametric(x(a),y(a),p,p,0,z(x(a),y(a))),
    parametric(x(b),y(b),p,p,0,z(x(b),y(b))),
    parametric(x(haript), y(haript), p, p, 0, z(x(haript), y(haript))),
  color=blue,parametric(x(t),0,z(x(t),y(t)),t,a,b),
    parametric(x(t),0,0,t,a,b),
    parametric(x(a),0,p,p,0,z(x(a),y(a))),
    parametric(x(b),0,p,p,0,z(x(b),y(b))),
    parametric(x(haript),0,p,p,0,z(x(haript),y(haript))),
  color=green,parametric(0,y(t),z(x(t),y(t)),t,a,b),
    parametric(0,y(t),0,t,a,b),
    parametric(0,y(a),p,p,0,z(x(a),y(a))),
    parametric(0,y(b),p,p,0,z(x(b),y(b))),
  xlabel="x", ylabel="y", zlabel="z",
  xyplane=0);

k : 0.3;
x(t) := sin(t);
y(t) := cos(t);
z(t) := k*(t-%pi);
talg : 0;
tlopp : 1.8*%pi;
//puutx(t) := diff(x(t),t);
//puuty(t) := diff(y(t),t);
//puutz(t) := diff(z(t),t);
puutx(t) := cos(t);
puuty(t) := -sin(t);
puutz(t) := k;
//puutpik(t) := sqrt(puutx(t)**2+puuty(t)**2+puutz(t)**2);
puutpik(t) := sqrt(1+k**2);
//puutx(t) := puutx(t) / puutpik(t);
//puuty(t) := puuty(t) / puutpik(t);
//puutz(t) := puutz(t) / puutpik(t);
puutx(t) := cos(t) / sqrt(1+k**2);
puuty(t) := -sin(t) / sqrt(1+k**2);
puutz(t) := 1/sqrt(1+k**2);
//normx(t) := diff(puutx(t),t);
//normy(t) := diff(puuty(t),t);
//normz(t) := diff(puutz(t),t);
normx(t) := -sin(t)/sqrt(1+k**2);
normy(t) := -cos(t)/sqrt(1+k**2);
normz(t) := 0;
//normpik(t) := sqrt(normx(t)**2+normy(t)**2+normz(t)**2);
normpik(t) := 1/sqrt(1+k**2);
//normx(t) := normx(t) / normpik(t);
//normy(t) := normy(t) / normpik(t);
//normz(t) := normz(t) / normpik(t);
normx(t) := -sin(t);
normy(t) := -cos(t);
normz(t) := 0;
//abi(t) := [puutx(t),puuty(t),puutz(t)] ~ [normx(t),normy(t),normz(t)];
//binorm(t) := express(abi(t));
binormx(t) := cos(t)/sqrt(1+k**2);
binormy(t) := -sin(t)/sqrt(1+k**2);
binormz(t) := -1/sqrt(1+k**2);
spiraal:parametric(x(t), y(t), z(t) ,t, talg, tlopp);
f(t) := 0.1*(abs(sin(3*t))+1);
spiraal_paksusega:parametric_surface(x(t) + f(t)*(normx(t)*cos(fii)+binormx(t)*sin(fii)),
y(t) + f(t)*(normy(t)*cos(fii)+binormy(t)*sin(fii)),
z(t) + f(t)*(normz(t)*cos(fii)+binormz(t)*sin(fii)), t, talg, tlopp, fii,0,2*%pi);
draw3d(xu_grid=50,yv_grid=50,nticks=1000,surface_hide=true,
  color=orange,spiraal_paksusega,
  line_width=2,color=blue, spiraal,
  xlabel="x",ylabel="y",zlabel="z",
  xrange=[-1.5,1.5],yrange=[-1.5,1.5],zrange=[-1.5,1.5],
  xyplane=-1);