啊你真幸运。我最近正在处理 STL 文件,并且编写了一些函数来完成此任务。
首先,请注意您会失去精度。 STL 文件以任意精度表示任意形状,并将其转换为体积会导致离散化和损失。
也就是说,有一种非常简单的方法可以知道某物是在物体内部还是外部封闭的、连接的三角曲面,无论其是否凸:将光线投射到无限远并计算与曲面的交点。如果是奇数,则在内部;如果是偶数,则在外部。
您需要的唯一特殊代码是线-三角形相交,Möller Trumbore 算法是最常见的算法之一。
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 文件交换,稍作修改:
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
只需生成您的积分即可:
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);