How to extrude an image

I want to extrude a 2D image as attached by a value of 3 and make it 3D. I can create a 3D image by providing vertex values as given below but I couldn't read this image and extrude.

 %%Set up Coordinates

    XY1 = [-1 0; -4 0; -4 5; -1 5; -1 4; -3 4; -3 1; -1 1];
    fv1 = Extrude (XY1, -1, 1);

    %XY2 = [1 0; 3 0; 3 4; 4 4; 4 5; 1 5; 1 4; 2 4; 2 1; 1 1];

    %fv2 = Extrude (XY2, -1, 1);

    %%Set up the figure
    figure;
    axis ([-2 2 -1.5 1.5]);

    for i = 1:100

        % Set up the camera parameters
        yaw = i*(5*pi/180);
        pitch = (pi/6);

        Tz = 10 + 2*sin(yaw);
        T = [0 0 -Tz]';

        % Clear the axes
        cla;

        % Project the points into the camera
        uv = ProjectPoints (fv1.vertices', yaw, pitch, T);

        fv.Vertices = uv';
        fv.faces = fv1.faces;

        patch (fv, 'FaceColor', 'none');

        % Project the points into the camera
      %  uv = ProjectPoints (fv2.vertices', yaw, pitch, T);

       % fv.Vertices = uv';
       % fv.faces = fv2.faces;

       % patch (fv, 'FaceColor', 'none');

        % Pause so you can see the result
        %pause (0.2);
    end

function fv = Extrude (XY, Z1, Z2)
% Compute a 3D extrusion of a 2D polygon
% XY is an n x 2 array of the polygon vertices

n = size(XY,1);

v1 = XY;
v1(:,3) = Z1;

v2 = XY;
v2(:,3) = Z2;

vertices = [v1; v2];

faces = NaN(n+2, n);

% Front and back faces
faces(1,:) = 1:n;
faces(2,:) = (n+1):(2*n);

for i = 1:n
    if (i < n)
        next_index = i+1;
    else
        next_index = 1;
    end

      faces(i+2,1:4) = [i, next_index, next_index+n, i+n];
  end

fv.vertices = vertices;
fv.faces = faces;

Answer 1

[Michael Barrow]

If you make assumptions about the ordering of your points (say they are arranged in a clockwork order that they appear in the polygon) you could extrude the outline using the following example 'extrudeROI(x,y,d)' where d is the extrusion depth and x and y are the coordinates of your ordered point set:

function [pts,edges] = ROI2DtoPoly(x,y)
%ROI2DtoPoly converts an ordered set of points to a 2D polygon
%   you can draw the set of points using the function [binaryMaskn1, x, y] = roipoly
pts = [x,y];
edges = [1:length(x);[2:length(x),1]]'; %the connectivity list of x and y should be ordered 
end

function [pts,edges,tri] = extrudeROI(x,y,d)
%extrudeROI create an extruded 3D polygon of height d from an ROI drawn using: [binaryMaskn1, x, y] = roipoly

[bpts,bdg] = ROI2DtoPoly(x,y);
tpts = bpts;
tdg = bdg;
%add in third dimension
bpts3d = cat(2,tpts,zeros(length(x),1));
tpts3d = cat(2,bpts,ones(length(x),1)*d);
%create 3d points structure
pts = [bpts3d; tpts3d];
%fix the connectivity by offsetting one face's connectivity and adding side connector
tdg = tdg+length(x);                            %edges will be for points at the top
%define two triangulation edges, (v)ertical (d)iagonal [(b)ase is implied]
%vertical edges
sdgv = [1:length(x);(1:length(x))+length(x)]';   %connect the sides (extrude)
%diagonal edges
sdgd = [1:length(x);mod((1:length(x)),length(x))+length(x)+1]'; %construct connectivity list (diagonals, assumes closed poly)
%all edges
edges = [bdg; tdg; sdgv; sdgd]; %all edges, but not triangulation.
%triangulation
tri = [[sdgv,sdgd(:,2)];[sdgd,[2:length(x),1]']];%[lower triangles;upper triangles]
end