CGAL users discussion list

["Santosh Tiwari" <>]

This is how I got the correct normals for all the boundary facets.

The relevant code.


Alpha_shape_3 *as;
list<Facet> facets;
list<Vertex> vertices;
ostringstream facetStream;

as->get_alpha_shape_facets(back_inserter(facets), Alpha_shape_3::REGULAR);
as->get_alpha_shape_vertices(back_inserter(vertices),
Alpha_shape_3::REGULAR);

cout<<"\n Number of boundary facets = "<<facets.size();
cout<<"\n Number of vertices = "<<vertices.size();

facetStream<<vertices.size()<<endl;
facetStream<<facets.size()<<endl;
facetStream<<*as;


//You can now read the facetStream. Here is some code to read it. 

string facetString(facetstream.str());
istringstream in;
in.str(facetString);
in>>numVertices;
in>>numFacets;

vertices = new double*[numVertices];
for (i=0; i<numVertices; i++) {
        vertices[i] = new double[3];
        in>>x>>y>>z;
        vertices[i][0] = x;
        vertices[i][1] = y;
        vertices[i][2] = z;
}

facets = new unsigned long int*[numFacets];
for (i=0; i<numFacets; i++) {
        facets[i] = new unsigned long int[3];
        in>>v1>>v2>>v3;
        facets[i][0] = v1;
        facets[i][1] = v2;
        facets[i][2] = v3;
}

for(i=0; i<numFacets; i++) {
        x1 = vertices[facets[i][0]][0];
        y1 = vertices[facets[i][0]][1];
        z1 = vertices[facets[i][0]][2];

        x2 = vertices[facets[i][1]][0];
        y2 = vertices[facets[i][1]][1];
        z2 = vertices[facets[i][1]][2];

        x3 = vertices[facets[i][2]][0];
        y3 = vertices[facets[i][2]][1];
        z3 = vertices[facets[i][2]][2];
}

//You now have all the facets. You can write them to a STL file.
//You can compute the normals for every facet now.
//Here is some code to compute the normals.

a1 = x3 - x2;
a2 = y3 - y2;
a3 = z3 - z2;
b1 = x2 - x1;
b2 = y2 - y1;
b3 = z2 - z1;
n1 = a2*b3 - a3*b2;
n2 = a1*b3 - a3*b1;
n3 = a1*b2 - a2*b1;
res = sqrt(n1*n1 + n2*n2 + n3*n3);
n1 /= res;
n2 /= res;
n3 /= res;

I personally do not prefer accessing the internal data structure of a
library even if it permits that. It is very difficult to debug unless you
know the data structure really well.

__
Santosh Tiwari
EIB-326 Clemson University
http://www.clemson.edu/~stiwari/



-----Original Message-----
From: 

[mailto:]
 
Sent: Sunday, May 18, 2008 10:54 AM
To: 

Subject: Re: [cgal-discuss] Normal generation out of 3d alpha shapes

Andreas Fabri wrote:
> Jonas Schild wrote:
> 
>> Hi all,
>>
>> I have the following problem:
>>
>> I'm constructing a 3d alpha shape from a set of points using CGAL. 
>> After creation of the alpha shape, I'm iterating over all facets to 
>> extract the triangles. But:
>> The orientation of the normal (either by using cross product or using 
>> CGAL's ortho_vector(point, point, point) of which results are the 
>> same) is partially wrong. I've read that the orientation of the 
>> triangle is based on orientation of the cell (i.e. pointing into the 
>> cell). However, I'm not able to retrieve the normals pointing outside 
>> the alpha shape. Part of the problem is, that for certain alpha 
>> values, the constructed shape is no solid object. Is it possible to 
>> iterate only over alphas where the shape is solid, not necessarily 
>> convex?
>>
>> Furthermore, I don't understand how ccw(int) on the triangulation 
>> structure is supposed to work regarding finding the correct 
>> orientation thus the normals are pointing outside the volume.
>>
> 
> Hi Jonas,
> 
> Here comes a partial answer.
> 
> With ccw(int) you refer probably to the base class of all 3D 
> traingulations:
>
http://www.cgal.org/Manual/3.3/doc_html/cgal_manual/TriangulationDS_3_ref/Cl
ass_Triangulation_utils_3.html#Cross_link_anchor_994 
> 
> 
> 
> As the manual says ccw(int) only makes sense when it is 2D.
> 
> What you should use is the undocumented funcyion:
> 
> static int Triangulation_utils_3<..>::vertex_triple_index(const int i, 
> const int j)
>   {
>     // indexes of the  jth vertex  of the facet of a cell
>     // opposite to vertx i
>       CGAL_triangulation_precondition( ( i >= 0 && i < 4 ) &&
>                              ( j >= 0 && j < 3 ) );
>     return tab_vertex_triple_index[i][j];
>   }
> 
> The fact that it is undocumented is a bug.

really? I would say it is more like a matter of taste...

        Monique
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