remove sidewalls from surface plots

Hi, the quad mesh algorithm underlying the shaded surface plot 'surf(x,y,z,c)' creates unnatural sidewalls at height discontinuities of natural 3d objects. Is there a way to remove these sidewalls, e.g. by making them transparent?

Answer 1

[Teja Muppirala]

There are several ways, for example by replacing points with NaN, but they often give mixed results as far as appearance. The code below is another way to do it. This method is not simple, but it should look decent for most discontinuities. It involves looking at each face in turn and if the slope of the face exceeds some threshold, set it's alpha to zero.

I hope someone can come up with something a bit easier.

[X,Y] = ndgrid(linspace(-1,1,51));
Z = atan2(Y,X) + 3*round(atan2(Y,X)/2.5);

% For comparison
figure;
surf(X,Y,Z);

% Convert the "surf" into a "patch"
figure;
h = surf(X,Y,Z);
hp = patch(surf2patch(h));
delete(h);
V = get(hp,'Vertices');
F = get(hp,'Faces');
% Set the Alpha to be zero when the "slope" of a face is beyond a threshold
A = ones(prod(size(Z)-1),1);
thresh = 1.0;
for n = 1:size(F,1)
    z = V(F(n,:),3);
    dz = max(max(abs(bsxfun(@minus,z,z'))));
    if dz > thresh;
        A(n) = 0;
    end
end
set(hp,'FaceVertexAlphaData',A,'edgealpha','flat');
shading faceted;
alpha flat

[Bernhard Stroebel]

Hi Teja,

thanks a lot for the prompt and enlightening answer. I have meanwhile tried a slightly different solution which seems easier to me:

function d=saltus(z)

%map z discontinuities of a surface z(x,y).

%d = saltus(z)is the maximum absolute difference along the edges of each

%four-sided patch representing the surface z. The number of rows and

%columns of d is one less than those of z. If d exceeds some threshold,

%a discontinuity of z (a "saltus") can be assumed. In this case, the patch

%can be made transparent, to avoid sidewalls in the surf plot.

if ndims(z) ~= 2,error('input variable must be a matrix'),end

dx = abs(diff(z,1,2));%absolute differences along the x edges

dx = max(dx(1:end-1,:),dx(2:end,:));%max of x differences for each patch

dy = abs(diff(z,1,1));%absolute differences along the y edges

dy = max(dy(:,1:end-1),dy(:,2:end));%max of y differences for each patch

dxy = max(dx,dy);%maximum of all diffenences along the edges of each patch

d = zeros(size(dxy));

d(1:end-1,1:end-1) = dxy(2:end,2:end);%This shift is needed, reason unknown

[X,Y] = ndgrid(linspace(-1,1,51));

Z = atan2(Y,X) + 3*round(atan2(Y,X)/2.5);

% For comparison

figure(1);

surf(X,Y,Z);% Convert the "surf" into a "patch"

figure(2);

s=saltus(Z);

surf(X,Y,Z,'AlphaData',uint8(s<1),'FaceAlpha','flat');

There seem to remain some problems at the margins of the image, probably due to an error with the 'FaceAlpha' 'flat' property. (I am still using MATLAB 2006R). Anyway, the result looks great, thanks again!

Bernhard

[Theo]

Bernard, I tried to give your solution a shot, but the last command

surf(X,Y,Z,'AlphaData',uint8(s<1),'FaceAlpha','flat');

doesn't seem to change anything (the s matrix looks okay). Do you know whether there was a chance in the FaceAlpha implementation so that this no longer works? My current version of Matlab is R2014b.

The solution by Teja seems to work but requires conversion to patches.