Plotting 3D regions with constraints on x,y and z.

Hello,

I am trying to plot 3D solid regions based on certain constraints for x,y and z. Just as an example, the region of space bounded by 0<=x<=1, 0<=y<=2, 0<=z<=3 should obviously plot a rectangular prism, but my bounds may be more complicated such as: 0<=x<=1, x^2<=y<=x, 0<=z<=x+sqrt(y) .

How might I go about tackling this sort of problem? Any help would be appreciated.

Answer 1

[Dr. Seis]

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')

[Dr. Seis]

I edited to remove any rows in "X" that might repeat.

[Jeff]

Thanks very much. This worked quite well for me. I agree that with only small tweaks (keeping the basic structure you present in place), it may be made more flexible so that it could support a generic constraint of the form

a<=x<=b, f(x)<=y<=g(x), u(x,y)<=z<=v(x,y).

The function could be passed a,b,f(x),g(x),u(x,y),v(x,y) and the ordering of x,y,z to arrive at the desired result... I'll have to try it!