I have done some 3D shapes in the past. It may not be pretty, but it may be an option unless others have more efficient ways of coding. You will notice that the conditions you outlined above are "hard coded" into the function - anyone else have an idea how to make it more general (i.e., conditions defined as input arguments)? You can make the object more smooth by reducing the "dxyz" increment. I also have things in here that can change the way the object is illuminated, shaded, and colored. You will have to play around until you like the result.
Create and save this as an .m file, then run:
function plot_this
dxyz = 0.1;
x = 0 : dxyz : 1;
X = [];
for i = 1 : length(x)
y = x(i)^2;
while y <= x(i)
if isempty(X)
X(1,:) = [x(i),y,0];
X(2,:) = [x(i),y,x(i)+sqrt(y)];
else
X(end+1,:) = [x(i),y,0];
X(end+1,:) = [x(i),y,x(i)+sqrt(y)];
end
y = y + dxyz;
end
end
X = unique(X,'rows')
options = {'Qt','Qbb','Qc'};
Tes = delaunay3(X(:,1),X(:,2),X(:,3),options);
tetramesh(Tes,X);
colormap(white);
face_alpha = 1.0;
alpha(face_alpha)
shading flat
axis equal
light('Position',[-0.58674 -0.05336 0.80801],'Style','infinite')
light('Position',[-0.58674 -0.05336 -0.80801],'Style','infinite')
