Generates normals with multiple three-point coordinates

Hi！,I wanted to generate multiple three-dimensional coordinate normals in matlab and output them in fixed format to generate stl files, but I kept making mistakes. I want to know why, and I hope you can help me.

Nodes = [0 0 0;

4 0 0;

4 4 0;

0 4 0

4 0 2;

0 0 2;

4 1 2;

0 1 2;

0 1 1;

4 1 1;

4 2 1;

4 2 2;

0 2 2;

0 2 1;

0 4 2;

4 4 2];

singletriangle = [5 10 7;

5 2 10;

10 2 3;

3 11 10;

3 16 11;

16 12 11;

6 8 9;

6 1 9;

9 1 4;

9 4 14;

14 4 15;

14 15 13];

% Find the point coordinates according to the triangle index

points_triangles = [Nodes(singletriangle,1),Nodes(singletriangle,2),Nodes(singletriangle,3)];

% Find the point coordinates of each column (three-dimensional)

points_one=points_triangles(1:length(points_triangles)/3,:);

points_two=points_triangles(length(points_triangles)/3+1:length(points_triangles)/3*2,:);

points_three=points_triangles(length(points_triangles)/3*2+1:length(points_triangles),:);

% Subtract the matrix and compute the vector

vectors_one=points_two-points_one;

vectors_two=points_three-points_one;

% Take the cross product of two vectors

normal_vectors=cross(vectors_one,vectors_two);

% Normalizes the 3D vector so that its modulus is equal to 1

normalized_normal_vectors=normal_vectors./norm(normal_vectors);

% Initializes the empty array

output=zeros(length(points_one)*4,3);

% Write output data

for i=1:length(points_one)

output(i*4-3,:)=normalized_normal_vectors(i,:);

output(i*4-2,:)=points_one(i,:);

output(i*4-1,:)=points_two(i,:);

output(i*4,:)=points_three(i,:);

end

% Output content

output=output';

STL_file_name=['lin123','.stl'] ;

STL_file = fopen (STL_file_name,'wt');

fprintf (STL_file,'solid %s\n','solid');

fprintf (STL_file, ' facet normal %14e %14e %14e\n outer loop\n vertex %14e %14e %14e\n vertex %14e %14e %14e\n vertex %14e %14e %14e\n endloop\n endfacet\n',output);

fprintf (STL_file,'endsolid %s\n','solid' );

fclose (STL_file);

Answer 1

[William Rose]

@Chenglin Li,

[edit: I simplified the calculation of the normalized normal vectors]

I ran your code. It runs without error. It makes an STL file (attached). I can render the STL file at https://www.viewstl.com without getting an error. What is the problem?

The rendered object looks like two 2-D sheets, rather than a 3-D object. I don;t know what you expect your object to look like. I recommend that you start with a simple set of points. I re-ran your code with 4 points and 4 triangles, to make a tetrahedron. It works. The STL file produces a tetrahedron when viewed at https://www.viewstl.com.

Nodes = [0 0 0;
    1 0 0;
    0 1 0;
    0 0 1];
singletriangle = [1 3 2;
    1 2 4;
    1 4 3;
    2 3 4];
% Find the point coordinates according to the triangle index
points_triangles = [Nodes(singletriangle,1),Nodes(singletriangle,2),Nodes(singletriangle,3)];
% Find the point coordinates of each column (three-dimensional)
points_one=points_triangles(1:length(points_triangles)/3,:);    
points_two=points_triangles(length(points_triangles)/3+1:length(points_triangles)/3*2,:);       
points_three=points_triangles(length(points_triangles)/3*2+1:length(points_triangles),:);      
% Subtract the matrix and compute the vector
vectors_one=points_two-points_one;
vectors_two=points_three-points_one;
% Take the cross product of two vectors
normal_vectors=cross(vectors_one,vectors_two); 
% Normalizes the 3D vector so that its modulus is equal to 1
normalized_normal_vectors=normal_vectors./norm(normal_vectors);
% Initializes the empty array
output=zeros(length(points_one)*4,3);
% Write output data
for i=1:length(points_one)
    output(i*4-3,:)=normalized_normal_vectors(i,:);
    output(i*4-2,:)=points_one(i,:);
    output(i*4-1,:)=points_two(i,:);
    output(i*4,:)=points_three(i,:);
end
% Output content
output=output';
STL_file_name=['tetra.stl'] ;
STL_file = fopen (STL_file_name,'wt');
fprintf (STL_file,'solid %s\n','solid');
fprintf (STL_file, '  facet normal  %14e  %14e  %14e\n  outer loop\n      vertex %14e %14e %14e\n      vertex %14e %14e %14e\n      vertex %14e %14e %14e\n    endloop\n  endfacet\n',output);
fprintf (STL_file,'endsolid %s\n','solid' );
fclose (STL_file);

The code above makes a tetrahedron. Maybe you are not happy with the normal vectors. Let us inspect them:

disp(normal_vectors)

     0     0    -1
     0    -1     0
    -1     0     0
     1     1     1

These normal vectors point in the expected directions: outward from each face.

However, the normalized normal vectors do not have unit length:

disp(normalized_normal_vectors)

         0         0   -0.5000
         0   -0.5000         0
   -0.5000         0         0
    0.5000    0.5000    0.5000

That is a problem. Modify the normalization command. You did

normalized_normal_vectors=normal_vectors./norm(normal_vectors);

That does not give the desired result, because norm(X) returns a scalar when X is a matrix. Use vecnorm() instead:

nnv=normal_vectors./(vecnorm(normal_vectors'))';
disp(nnv)

         0         0   -1.0000
         0   -1.0000         0
   -1.0000         0         0
    0.5774    0.5774    0.5774

nnv looks like the correct set of normal vectors with unit length.

Good luck.

Answer 2

[Chenglin Li]

Thank you very much. I wanted to generate a concave surface before, but the figure was not what I wanted. After your program test, I found that it reached my expected effect, which helped me a lot, thank you！！！

[William Rose]

@Chenglin Li, you're welcome.