Load stl file in matlab and convert to a 3D array

问题

I have a stl file and I've loaded it in Matlab using stlread function. At this point I have a set of faces and vertices. How can I convert these faces and vertices in a 3D binary array like 512x512x100 array to obtain a binary 3D volume?

回答1:

Ah lucky you. I am working with STL files recently and I coded some functions to do exactly this.

First, note that you lose precision. STL files represent arbitrary shapes with arbitrary precision and converting it into a volume results in discretization and losses.

That said, there is a very easy method to know if something is inside or outside a closed, connected triangulated surface, regardless if its convex or not: Throw a ray to the infinite and count intersection with the surface. If odd, its inside, if even, outside.

The only special code you need is the line-triangle intersection, and the Möller Trumbore algorithm is one of the most common ones.

function in=inmesh(fv,points)
%INMESH tells you if a point is inside a closed,connected triangulated surface mesh
% Author: Ander Biguri
maxZ=max(fv.vertices(:,3));
counts=zeros(size(points,1),1);
for ii=1:size(points,1)
    ray=[points(ii,:);points(ii,1:2) maxZ+1];
    for jj=1:size(fv.faces,1)
        v=fv.vertices(fv.faces(jj,:),:);
        if all(v(:,3)<ray(1,3))
            continue;
        end
        isin=mollerTrumbore(ray, fv.vertices(fv.faces(jj,:),:));
        counts(ii)=counts(ii)+isin;
    end

end
in=mod(counts,2);
end

From FileExchange, with small modifications:

function [flag, u, v, t] = mollerTrumbore (ray,tri)
% Ray/triangle intersection using the algorithm proposed by Moller and Trumbore (1997).
%
% IMPORTANT NOTE: Assumes infinite legth rays.
% Input:
%    ray(1,:) : origin.
%    d : direction.
%    tri(1,:), tri(2,:), tri(3,:): vertices of the triangle.
% Output:
%    flag: (0) Reject, (1) Intersect.
%    u,v: barycentric coordinates.
%    t: distance from the ray origin.
% Author: 
%    Jesus Mena

    d=ray(2,:)-ray(1,:);
    epsilon = 0.00001;

    e1 = tri(2,:)-tri(1,:);
    e2 = tri(3,:)-tri(1,:);
    q  = cross(d,e2);
    a  = dot(e1,q); % determinant of the matrix M

    if (a>-epsilon && a<epsilon) 
        % the vector is parallel to the plane (the intersection is at infinity)
        [flag, u, v, t] = deal(0,0,0,0);
        return;
    end

    f = 1/a;
    s = ray(1,:)-tri(1,:);
    u = f*dot(s,q);

    if (u<0.0)
        % the intersection is outside of the triangle
        [flag, u, v, t] = deal(0,0,0,0);
        return;          
    end

    r = cross(s,e1);
    v = f*dot(d,r);

    if (v<0.0 || u+v>1.0)
        % the intersection is outside of the triangle
        [flag, u, v, t] = deal(0,0,0,0);
        return;
    end
    if nargout>3
        t = f*dot(e2,r); % verified! 
    end
    flag = 1;
    return
end

Just generate your points:

yourboundaries=% get the range of your data from the STL file.
[x,y,z]=meshgrid(yourboundaries);
P=[x(:) y(:) z(:)];
in=inmesh(fv,P);
img=reshape(in,yourboundariesSize);

来源：https://stackoverflow.com/questions/51158078/load-stl-file-in-matlab-and-convert-to-a-3d-array

标签

arrays

matlab

stl-format