How can I get this function to take vector inputs for x

This function is to determine how much area a goat has to graze on when tied to a rope length x on the outside of a rectangular barn with sides length a and b. The rope can't be longer than a+b. It wont take vector inputs for x (to allow me to plot on a graph for a changing rope length) and I can't figure out why.

function[z] = goatgrazing(a,b,x)
if x <= a
    if x <= b
        z=(3/4).*pi.*(x).^2;
    end
end
if x > a
    if x <= b
        z=(3/4).*pi.*(x).^2+(1/4).*pi.*(x-a).^2;
    end
end
if x > b
    if x <= a
        z=(3/4).*pi.*(x).^2+(1/4).*pi.*(x-b).^2;
    end
end
if x > b
    if x > a
        z = (3/4).*pi.*(x).^2+(1/4).*pi*(x-b).^2+(1/4).*pi.*(x).^2;
    end
end
if x > a+b
    error("These dimensions are not valid")
end

Also, any improvements to the code you could suggest would be appreciated.

Answer 1

[Walter Roberson]

Use logical indexing. Your current code assumes that either x is a scalar or that exactly the same conditions apply to all x simultaneously.

 mask = x > b & x <= a;
 z(mask) = (3/4).*pi.*(x(mask)).^2+(1/4).*pi.*(x(mask)-b).^2;