// Banana-like contours: ellipse bent by a parabola
r1 = 1;
r2 = 0.5;
theta = linspace(0, %pi/2, 20);
ct = cos(theta);
st = sin(theta);
x = r1*[ct, -st(2:$), -ct(2:$), st(2:$)];
y = r2*[st, ct(2:$), -st(2:$), -ct(2:$)] + x.^2;
z = 0:0.1:0.9;

taille =  size(z, "*")*size(x, "*");

// vertical trumpet-like profile: z = 1 - 1/(1 + R^2)
// => R = sqrt(1/(1 - z) - 1)
R = ones(x)'*sqrt(1 ./(1 - z) - 1);

X = matrix(R.*(x'*ones(z)), 1, taille);
Y = matrix(R.*(y'*ones(z)), 1, taille);
Z = matrix(ones(x)'*z, 1, taille);

figure(0);
clf();
param3d(X, Y, Z); // surface
param3d(X, Y, zeros(Z), theta=30, alpha=80); // projection des courbes de niveau