How do I plot my function to a mesh - matlab

Question

I am a new MATLAB user and I am trying to plot a function:
function [ uncertainty ] = uncertain(s1, s2, p)
%UNCERTAIN calculates the measurement uncertainty of a triangulation
% provide two coordinates of known stations and a target coordinate
% of another point, then you get the uncertainty
[theta1, dist1] = cart2pol(p(1)-s1(1), p(2)-s1(2));
[theta2, dist2] = cart2pol(p(1)-s1(1), p(2)-s2(2));
theta=abs(pi-theta2-theta1);
uncertainty = dist1*dist2/abs(sin(theta));
end
called with:
uncertain([0 0],[8 0],[4 4])
I get a single result.
But i want a whole surface and called:
x=-2:.1:10;
y=-2:.1:10;
z = uncertain([0 0],[8 0],[x y]);
mesh(x,y,z)
I get the error: "Z must be a matrix, not a scalar or vector."
How can I modify my code so that my function draws a surface?
Thanks in advance.
Ralf.

Answer 1

First I think there's a mistake in your function: your [theta2, dist2] = cart2pol(p(1)-s1(1), p(2)-s2(2)); should have th first s1 being a s2.
Next, to get a vector answer out for your vector inputs, you have to change your p(i) (which selects the ith element of p) to p(i,:), which will select the first ith row of p.
After that, you change multiplication (*) to element-wise multiplication (.*).
In summary:
function [ uncertainty ] = uncertain(s1, s2, p)
%UNCERTAIN calculates the measurement uncertainty of a triangulation
% provide two coordinates of known stations and a target coordinate
% of another point, then you get the uncertainty
% target coordinates p are 2xn
% output uncertainty is 1xn
[theta1, dist1] = cart2pol(p(1,:)-s1(1), p(2,:)-s1(2));
[theta2, dist2] = cart2pol(p(1,:)-s2(1), p(2,:)-s2(2));
theta=abs(pi-theta2-theta1);
uncertainty = dist1.*dist2./abs(sin(theta));
end
The only changes are p(i) -> p(i,:), and *->.* and /->./.
To get a surface, you use meshgrid to get all sets of (x,y) coordinates in a grid, flatten them into a 2xn matrix for uncertain, and then expand them back out to the grid to plot. Example:
x=-2:.1:10; % 121 elements
y=-2:.1:10; % 121 elements
[xs,ys]=meshgrid(x,y); % xs and ys are each 121 x 121
zs = uncertain([0 0],[8 0],[xs(:) ys(:)]'); %get zs, being 1x(121*121) ie 1x14641
% Reshape zs to be 121x121 in order to plot with mesh
mesh(xs,ys,reshape(zs,size(xs)))
Note: you'll get lots of really big numbers because when theta is 0 or pi (or very nearly) because then you're dividing by (almost) 0.