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% revolutionparaboloid.mp
% L. Nobre G.
% 2014
%outputformat := "png";
%outputformatoptions := "format=rgb antialias=best";
%hppp := 0.5;
%vppp := 0.5;
input featpost3Dplus2D;
%prologues := 1;
f := 0.7*(3,3,-5);
beginfig(1);
numeric u, r;
color b, t;
u = 2mm;
b = (-1.0,0.0,0.0);
t = (-0.4,0.3,0.9);
r = 0.6;
drawoptions(withpen pencircle scaled u);
revolparab( b, t, r );
endfig;
def parab( expr xis ) = (0.25*(xis**2)) enddef;
def oloid( expr xis ) = (1-(xis/2)**2) enddef;
def deriv( expr xis ) = (0.5*xis) enddef;
beginfig(2);
pair pzero, pone;
pzero = (-0.5,-5.5);
numeric u, delta, n, ste, minx, maxx, itex, tanx, marg, slope, sa, aux;
n = 50;
marg = 1;
u = 5mm;
delta = sqrt((xpart pzero)**2-4*(ypart pzero));
minx = (xpart pzero)-delta-marg;
tanx = (xpart pzero)+delta;
maxx = -minx;
ste = (maxx-minx)/(n+1);
z0 = (minx,parab(minx));
z1 = ((xpart pzero)-delta,parab((xpart pzero)-delta));
z2 = (tanx,parab(tanx));
z3 = 0.5[z1,z2];
draw z0 for itex=minx+ste step ste until maxx:
--(itex,parab(itex)) endfor withcolor blue;
draw pzero--z1--z2--cycle;
draw pzero--z3;
sa = -angle(z1-z2);
slope = sind(sa)/cosd(sa);
aux = 2*(-slope+(slope++1));
z4 = (aux,parab(aux));
z6 = z4+whatever*dir(angle(1,deriv(aux)));
aux := 2*(-slope-(slope++1));
z5 = (aux,parab(aux));
z6 = z5+whatever*dir(angle(1,deriv(aux)));
draw z6--z4--z5--cycle withcolor red;
%draw up withcolor blue;
picture scalpic;
scalpic = currentpicture;
currentpicture := nullpicture;
draw scalpic scaled u withpen pencircle scaled 0;
endfig;
beginfig(3);
% ParallelProj := true;
f := (7, 6, 5);
% f := (2, 1, 8);
% f := (7,6,8);
% f := (0.05,0,9.5);
% f := (0,9,0);
numeric ray, coneray, angrotparab, angrotfoc, steprotfoc, itex, xzer, yzer;
numeric tmpxzero, tmpdelta, tmpxtplu, tmpxtmin, stepx;
color focus, tmpxaxis, auxca, auxcb, auxcc, auxcd;
pen penone;
pair auxa, auxb;
penone = pencircle scaled 3mm;
xzer = 1;
yzer = -0.5;
stepx = 0.05;
ray = 3;
revolparab(blue*parab(ray),black,ray);
coneray = 4;
steprotfoc = 15;
focus = (xzer,0,yzer);
for angrotfoc=0 step steprotfoc until 360-steprotfoc:
angrotparab := 0.5*angrotfoc;
tmpxzero := xzer*cosd(angrotparab);
tmpxaxis := (cosd(angrotparab),sind(angrotparab),0);
z0 = (minx,parab(minx));
draw rp(-ray*tmpxaxis+blue*parab(-ray))
for itex=-ray+stepx step stepx until ray:
--rp(itex*tmpxaxis+blue*parab(itex)) endfor withcolor blue;
tmpdelta := sqrt(tmpxzero**2-4*yzer);
tmpxtplu := tmpxzero+tmpdelta;
tmpxtmin := tmpxzero-tmpdelta;
auxca := tmpxtplu*tmpxaxis+blue*parab(tmpxtplu);
auxcb := tmpxtmin*tmpxaxis+blue*parab(tmpxtmin);
auxa := rp(auxca);
auxb := rp(auxcb);
auxcc := auxca-focus;
auxcd := auxcb-focus;
draw auxa withpen penone;
draw auxb withpen penone;
endfor;
draw rp(focus) withpen penone withcolor green;
produce_auto_scale;
endfig;
beginfig(4);
numeric major, minor, focdi, rotaroun, steparoun, ra;
color majorc, minorc, focdic, garbac, vertec;
major = 4;
minor = 2.5;
f := (-5,0.5,0.4);
steparoun = 20;
ra = 0.35;
focdi = major +-+ minor;
majorc = major*red;
minorc = minor*green;
focdic = -focdi*red;
for rotaroun=0.5*steparoun step steparoun until 180-0.5*steparoun:
garbac := planarrotation(majorc,minorc,rotaroun);
vertec :=0.5[garbac,focdic];
revolparab( garbac, vertec, ra );
revolparab( (X(garbac),-Y(garbac),0), (X(vertec),-Y(vertec),0), ra );
endfor;
endfig;
beginfig(5);
f := (9,6,3);
numeric u, slo, delt, higx, lowx, cenx, rai, focz;
color cen, foc, low, base;
path ell, cir, both;
u = 2mm;
slo = 0.35;
delt = slo ++ 1;
lowx = 2*(slo-delt);
higx = 2*(slo+delt);
rai = 2*delt;
drawoptions(withpen pencircle scaled u withcolor blue);
revolparab( (0,0,-3), blue, 4 );
drawoptions(withpen pencircle scaled u);
z4 = (lowx,oloid(lowx));
z6 = z4+whatever*dir(angle(1,-deriv(lowx)));
z5 = (higx,oloid(higx));
z6 = z5+whatever*dir(angle(1,-deriv(higx)));
focz = ypart z6;
cen = (2*slo,0,ypart 0.5[z4,z5]);
foc = (2*slo,0,focz);
low = (lowx,0,ypart z4);
ell = ellipticpath( cen, low-cen, rai*green );
cir = fullcircle scaled u;
both = twocyclestogether( ell, cir shifted rp(foc) );
draw both;
draw ell;
draw rp(2*cen-low)--rp(low)--rp(foc)--cycle;
%draw rp(cen+rai*green)--rp(cen-rai*green);
fill cir shifted rp(black);
base = (2*slo,0,-3);
draw rigorouscircle( base, blue, rai );
draw rp(base)--rp(foc) dashed withdots withcolor red;
endfig;
end.
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