create_flat_triangular_mesh(step, smoothness)

%good mesh to catch possible bugs in geodesic algorithms
%Copyright (c) 2007 Danil Kirsanov
function [p,tri] = create_flat_triangular_mesh(step, smoothness)

x = -1:step:1;
y = x;

N_p = length(x)*length(y);                  %regular grid
p = zeros(N_p,3);
N_t = (length(x)-1)*(length(y)-1)*2;        %two triangles per square
tri = zeros(N_t,3);

n_p = 1;
n_t = 1;
for i=1:length(x);
    for j=1:length(y);
        p(n_p,:) = [x(i) y(j) 0];
       
        if i<length(x) & j<length(y)
            tri(n_t,:) = [n_p, n_p + 1, n_p + length(y)];
            n_t = n_t + 1;
            tri(n_t,:) = [n_p + 1, n_p + length(y), n_p + length(y) + 1];
            n_t = n_t + 1;
        end;
        
        n_p = n_p+1;        
    end;
end;

if nargin < 2
    smoothness = 0;
end;
p(:,end) = smoothness*(0.5 - rand(size(p,1), 1));