How to plot a graph of a custom surface in Matlab? - matlab

Question

I would like to plot the surface of this function in Matlab:
w=(m*(1-p))/(h-1+m*(1-p))
Where
h=0.98;
P=[0.05:0.001:0.98];
M=[0:0.001:1];
The graph should look like this:
I tried to implement the graphing function as:
h=0.98;
P=[0.05:0.001:0.98];
M=[0:0.001:1];
W=[];
for i=1:size(P, 2)
for j=1:size(M, 2)
p=P(i);
m=M(j);
w=(m*(1-p))/(h-1+m*(1-p));
if w>1000
w=1000;
end
if w<0
w=0;
end
W(i, j) = w;
end
end
mesh(M, P, W);
But since the function changes rapidly around the boundary condition, my graph ended up looking like this:
How can I smooth out the curve and give it a nice, uniform grid like in the first picture?

Answer 1

Here's a way to do what you want. See comments in the code for more information.
%% //Definitions
w = #(h,m,p)(m.*(1-p))./(h-1+m.*(1-p)); %// w as a function handle
w_min = 0; w_max = 10; %// For plots
cMap = hot(200); cMap = cMap(floor(0.5*length(cMap)):ceil(0.7*length(cMap)),:);
h = 0.98;
m_start = 0; m_end = 1; m_step = [0.02 0.01 0.001];
p_start = 0.05; p_end = 0.98; p_step = [0.1 0.01 0.001];
%// Definitions of the mesh used in plotting (same for all charts)
mesh_m_step = 0.05; mesh_p_step = 0.05;
[meshM,meshP] = meshgrid(m_start:mesh_m_step:m_end,p_start:mesh_p_step:p_end);
meshW = w(h,meshM,meshP);
%% //Evaluation and plotting:
figure(); set(gcf,'Position',[240,500,1391,376]); subplot(1,3,1);
for ind1 = 1:3
%% // Evaluate equation
[MM,PP] = meshgrid(m_start:m_step(ind1):m_end,p_start:p_step(ind1):p_end);
WW = w(h,MM,PP);
%% // Plot
subplot(1,3,ind1);
surf(MM,PP,WW,'EdgeColor','none'); view([45,45]);
hold on; mesh(meshM,meshP,meshW,'EdgeColor','k','FaceColor','none');
colormap(cMap); %// Fix the colormap
zlim([w_min,w_max]); caxis(zlim) %// Modify zlim
end
Which results in: