How can I create 2D projections from a 3D object?

I know I can use "radon" for creating 1D projections from 2D, but how can I get 2D projections from 3D objects (such as from a 3D file like an STL file).

Answer 1

[Mike Garrity]

One approach is the technique I showed in answers to this question, and this question.

The basic idea is that you take keep the faces of your geometry, but project the vertices onto the plane. That does mean that you've got multiple conincident polys, so it's not good for things like area computation. But if you just want the visual result, it works well and it's simple.

[Thomas Cornew]

Hello Mike,

How would I approach this problem if I was trying to solve for the area of the 2d projection?

[Naveen Pathak]

Hi Mike,

I have a simliar problem. Please, could you help me to plot the following:

https://www.mathworks.com/matlabcentral/answers/815765-2d-projection-of-a-3d-f-x-y-z-plot?s_tid=srchtitle

Thank you.

Answer 2

[Y.S.]

2 methods I found that I want to place here for future reference:

[1] fast, but only works for convex shapes. Assuming you have a struct (fvIn) with vertices & faces

fvIn.vertices(:,3)=0; % squash all Z coords
verts = fvIn.vertices;
faces = fvIn.faces;
a = verts(faces(:, 2), :) - verts(faces(:, 1), :); % compute area of all triangles
b = verts(faces(:, 3), :) - verts(faces(:, 1), :);
c = cross(a, b, 2);
area2 = 1/2 * sum(sqrt(sum(c.^2, 2))); % Calculate total area, but this gives double the area because the shape is squashed
Ap = area2/2; %

[2] slow, but works for all shapes

Loop over all triangles, project them on the Z=0 plane, create a polyshape and combine(union) it with the other projected triangles

P = fvIn.vertices(fvIn.faces(1,:),1:2);
psSurfTot = polyshape(P);
for N = 2:size(fvIn.faces,1)
    P = fvIn.vertices(fvIn.faces(N,:),1:2);
    psSurfTMP = polyshape(P);
    psSurfTot = union(psSurfTot,psSurfTMP);
end

% calculate projected area
Ap = area(psSurfTot);

I am still looking for a fast method that works for all shapes, but havent found any

[Naveen Pathak]

Thanks "Y.S." at least you showed a kind gesture.

Matlab people are worth-less to help.

However, I have already solved this problem few months ago :)

[Seung Jae Lee]

Hi, Naveen. How could you solve this problem? Can you please share your findings?

[DGM]

We can save some time in the polyshape example if we know our model is a closed surface.

unzip utahteapot.stl.zip % for the forum

% the model is a closed surface, but is self-occluding
T = stlread('utahteapot.stl');
[F V] = t2fv(T); % for conciseness

% just get the upper faces
N = faceNormal(T);
topfaces = N(:,3) > 0;
Ft = F(topfaces,:);

% combine as a polyshape vector
nfaces = size(Ft,1);
PS = repmat(polyshape(),[nfaces 1]); % preallocate
for k = 1:nfaces
    P = V(Ft(k,:),1:2);
    PS(k) = polyshape(P);
end
PS = union(PS); % then take the union at once

% results
plot(PS)

area(PS) % same answer

ans = 103.5117

At least for me, on this model, these two changes reduce the execution time by about 60%.

Obviously, if our model isn't a closed surface, then we can't make such a simple elimination of faces by orientation. We could still save some time by doing the union() outside the loop though.

One might be tempted to find the free boundaries of Ft and then construct a much shorter polyshape vector to save more time. The problem with that is that such a surface can still be self-occluding, so the projected boundary curve will be self-intersecting. It just creates new problems to solve.