SFCGAL generates incorrect 3D intersection

[danielcumberbatch]

SFCGAL appears to generate only single part results from the intersection of two input volumes.

The following test demonstrates this:

BOOST_AUTO_TEST_CASE(incorrect_intersection)
{
   std::auto_ptr<SFCGAL::Geometry> poly1 = SFCGAL::io::readWkt("POLYGON((0 0,1 0,1 1,0 1,0 0))");
   std::auto_ptr<SFCGAL::Geometry> solid1 = SFCGAL::algorithm::extrude(*poly1, 0.0, 0.0, 1.0);

   std::auto_ptr<SFCGAL::Geometry> poly2 = SFCGAL::io::readWkt("POLYGON((-1 0.2,1.8 0.2,1.8 0.4,-0.8 0.4,-0.8 0.6,1.8 0.6,1.8 0.8,-1 0.8,-1 0.2))");
   std::auto_ptr<SFCGAL::Geometry> solid2 = SFCGAL::algorithm::extrude(*poly2, 0.0, 0.0, 1.0);

   std::auto_ptr<SFCGAL::Geometry> inx = SFCGAL::algorithm::intersection3D(*solid1, *solid2);
   std::cout << inx->asText(5) << std::endl;

   std::cout << "Valid: " << SFCGAL::algorithm::isValid(*inx) << std::endl;
}

giving the result:

SOLID((((0.00000 0.40000 0.30769,0.40000 0.40000 0.00000,0.00000 0.40000 0.00000,0.00000 0.40000 0.30769)),((0.00000 0.40000 0.00000,0.00000 0.33846 0.00000,0.00000 0.40000 0.30769,0.00000 0.40000 0.00000)),((0.40000 0.40000 0.00000,0.31429 0.31429 0.00000,0.00000 0.40000 0.00000,0.40000 0.40000 0.00000)),((0.00000 0.40000 0.30769,1.00000 0.40000 0.69231,0.40000 0.40000 0.00000,0.00000 0.40000 0.30769)),((0.00000 0.33846 0.00000,0.00000 0.20000 0.20000,0.00000 0.40000 0.30769,0.00000 0.33846 0.00000)),((0.00000 0.40000 0.00000,0.31429 0.31429 0.00000,0.00000 0.33846 0.00000,0.00000 0.40000 0.00000)),((0.40000 0.40000 0.00000,1.00000 0.26154 0.00000,0.31429 0.31429 0.00000,0.40000 0.40000 0.00000)),((1.00000 0.40000 0.69231,1.00000 0.40000 0.60000,0.40000 0.40000 0.00000,1.00000 0.40000 0.69231)),((0.00000 0.40000 0.30769,0.60000 0.40000 1.00000,1.00000 0.40000 0.69231,0.00000 0.40000 0.30769)),((0.00000 0.20000 0.20000,0.00000 0.40000 0.40000,0.00000 0.40000 0.30769,0.00000 0.20000 0.20000)),((0.00000 0.33846 0.00000,0.00000 0.20000 0.00000,0.00000 0.20000 0.20000,0.00000 0.33846 0.00000)),((0.31429 0.31429 0.00000,0.20000 0.20000 0.00000,0.00000 0.33846 0.00000,0.31429 0.31429 0.00000)),((1.00000 0.26154 0.00000,1.00000 0.20000 0.00000,0.31429 0.31429 0.00000,1.00000 0.26154 0.00000)),((0.40000 0.40000 0.00000,1.00000 0.40000 0.00000,1.00000 0.26154 0.00000,0.40000 0.40000 0.00000)),((1.00000 0.40000 0.60000,1.00000 0.40000 0.00000,0.40000 0.40000 0.00000,1.00000 0.40000 0.60000)),((1.00000 0.40000 0.69231,1.00000 0.20000 0.80000,1.00000 0.40000 0.60000,1.00000 0.40000 0.69231)),((0.60000 0.40000 1.00000,1.00000 0.40000 1.00000,1.00000 0.40000 0.69231,0.60000 0.40000 1.00000)),((0.00000 0.40000 0.30769,0.00000 0.40000 0.40000,0.60000 0.40000 1.00000,0.00000 0.40000 0.30769)),((0.00000 0.20000 0.20000,0.00000 0.20000 0.64286,0.00000 0.40000 0.40000,0.00000 0.20000 0.20000)),((0.00000 0.20000 0.00000,0.20000 0.20000 0.00000,0.00000 0.20000 0.20000,0.00000 0.20000 0.00000)),((0.00000 0.33846 0.00000,0.20000 0.20000 0.00000,0.00000 0.20000 0.00000,0.00000 0.33846 0.00000)),((0.31429 0.31429 0.00000,1.00000 0.20000 0.00000,0.20000 0.20000 0.00000,0.31429 0.31429 0.00000)),((1.00000 0.26154 0.00000,1.00000 0.20000 0.28571,1.00000 0.20000 0.00000,1.00000 0.26154 0.00000)),((1.00000 0.40000 0.00000,1.00000 0.20000 0.28571,1.00000 0.26154 0.00000,1.00000 0.40000 0.00000)),((1.00000 0.40000 0.60000,1.00000 0.20000 0.28571,1.00000 0.40000 0.00000,1.00000 0.40000 0.60000)),((1.00000 0.20000 0.80000,1.00000 0.20000 0.28571,1.00000 0.40000 0.60000,1.00000 0.20000 0.80000)),((1.00000 0.40000 0.69231,1.00000 0.40000 1.00000,1.00000 0.20000 0.80000,1.00000 0.40000 0.69231)),((0.60000 0.40000 1.00000,0.71667 0.28333 1.00000,1.00000 0.40000 1.00000,0.60000 0.40000 1.00000)),((0.00000 0.40000 0.40000,0.00000 0.40000 1.00000,0.60000 0.40000 1.00000,0.00000 0.40000 0.40000)),((0.00000 0.20000 0.64286,0.00000 0.40000 1.00000,0.00000 0.40000 0.40000,0.00000 0.20000 0.64286)),((0.00000 0.20000 0.20000,0.20000 0.20000 0.00000,0.00000 0.20000 0.64286,0.00000 0.20000 0.20000)),((1.00000 0.20000 0.00000,1.00000 0.20000 0.28571,0.20000 0.20000 0.00000,1.00000 0.20000 0.00000)),((1.00000 0.20000 0.80000,0.80000 0.20000 1.00000,1.00000 0.20000 0.28571,1.00000 0.20000 0.80000)),((1.00000 0.40000 1.00000,1.00000 0.26154 1.00000,1.00000 0.20000 0.80000,1.00000 0.40000 1.00000)),((0.71667 0.28333 1.00000,1.00000 0.26154 1.00000,1.00000 0.40000 1.00000,0.71667 0.28333 1.00000)),((0.60000 0.40000 1.00000,0.00000 0.33846 1.00000,0.71667 0.28333 1.00000,0.60000 0.40000 1.00000)),((0.00000 0.40000 1.00000,0.00000 0.33846 1.00000,0.60000 0.40000 1.00000,0.00000 0.40000 1.00000)),((0.00000 0.20000 0.64286,0.00000 0.33846 1.00000,0.00000 0.40000 1.00000,0.00000 0.20000 0.64286)),((0.20000 0.20000 0.00000,1.00000 0.20000 0.28571,0.00000 0.20000 0.64286,0.20000 0.20000 0.00000)),((0.80000 0.20000 1.00000,0.00000 0.20000 0.64286,1.00000 0.20000 0.28571,0.80000 0.20000 1.00000)),((1.00000 0.20000 0.80000,1.00000 0.20000 1.00000,0.80000 0.20000 1.00000,1.00000 0.20000 0.80000)),((1.00000 0.26154 1.00000,1.00000 0.20000 1.00000,1.00000 0.20000 0.80000,1.00000 0.26154 1.00000)),((0.71667 0.28333 1.00000,0.80000 0.20000 1.00000,1.00000 0.26154 1.00000,0.71667 0.28333 1.00000)),((0.00000 0.33846 1.00000,0.00000 0.20000 1.00000,0.71667 0.28333 1.00000,0.00000 0.33846 1.00000)),((0.00000 0.20000 0.64286,0.00000 0.20000 1.00000,0.00000 0.33846 1.00000,0.00000 0.20000 0.64286)),((0.80000 0.20000 1.00000,0.00000 0.20000 1.00000,0.00000 0.20000 0.64286,0.80000 0.20000 1.00000)),((1.00000 0.20000 1.00000,1.00000 0.26154 1.00000,0.80000 0.20000 1.00000,1.00000 0.20000 1.00000)),((0.71667 0.28333 1.00000,0.00000 0.20000 1.00000,0.80000 0.20000 1.00000,0.71667 0.28333 1.00000)),((0.00000 0.80000 0.35714,0.80000 0.80000 0.00000,0.00000 0.80000 0.00000,0.00000 0.80000 0.35714)),((0.00000 0.80000 0.00000,0.00000 0.66154 0.00000,0.00000 0.80000 0.35714,0.00000 0.80000 0.00000)),((0.80000 0.80000 0.00000,0.71667 0.71667 0.00000,0.00000 0.80000 0.00000,0.80000 0.80000 0.00000)),((0.00000 0.80000 0.35714,1.00000 0.80000 0.71429,0.80000 0.80000 0.00000,0.00000 0.80000 0.35714)),((0.00000 0.66154 0.00000,0.00000 0.60000 0.00000,0.00000 0.80000 0.35714,0.00000 0.66154 0.00000)),((0.00000 0.80000 0.00000,0.71667 0.71667 0.00000,0.00000 0.66154 0.00000,0.00000 0.80000 0.00000)),((0.80000 0.80000 0.00000,1.00000 0.73846 0.00000,0.71667 0.71667 0.00000,0.80000 0.80000 0.00000)),((1.00000 0.80000 0.71429,1.00000 0.80000 0.20000,0.80000 0.80000 0.00000,1.00000 0.80000 0.71429)),((0.00000 0.80000 0.35714,0.20000 0.80000 1.00000,1.00000 0.80000 0.71429,0.00000 0.80000 0.35714)),((0.00000 0.60000 0.00000,0.00000 0.60000 0.60000,0.00000 0.80000 0.35714,0.00000 0.60000 0.00000)),((0.00000 0.66154 0.00000,0.60000 0.60000 0.00000,0.00000 0.60000 0.00000,0.00000 0.66154 0.00000)),((0.71667 0.71667 0.00000,0.60000 0.60000 0.00000,0.00000 0.66154 0.00000,0.71667 0.71667 0.00000)),((1.00000 0.73846 0.00000,1.00000 0.60000 0.00000,0.71667 0.71667 0.00000,1.00000 0.73846 0.00000)),((0.80000 0.80000 0.00000,1.00000 0.80000 0.00000,1.00000 0.73846 0.00000,0.80000 0.80000 0.00000)),((1.00000 0.80000 0.20000,1.00000 0.80000 0.00000,0.80000 0.80000 0.00000,1.00000 0.80000 0.20000)),((1.00000 0.80000 0.71429,1.00000 0.60000 0.40000,1.00000 0.80000 0.20000,1.00000 0.80000 0.71429)),((0.20000 0.80000 1.00000,1.00000 0.80000 1.00000,1.00000 0.80000 0.71429,0.20000 0.80000 1.00000)),((0.00000 0.80000 0.35714,0.00000 0.80000 0.80000,0.20000 0.80000 1.00000,0.00000 0.80000 0.35714)),((0.00000 0.60000 0.60000,0.00000 0.80000 0.80000,0.00000 0.80000 0.35714,0.00000 0.60000 0.60000)),((0.00000 0.60000 0.00000,0.60000 0.60000 0.00000,0.00000 0.60000 0.60000,0.00000 0.60000 0.00000)),((0.71667 0.71667 0.00000,1.00000 0.60000 0.00000,0.60000 0.60000 0.00000,0.71667 0.71667 0.00000)),((1.00000 0.73846 0.00000,1.00000 0.80000 0.20000,1.00000 0.60000 0.00000,1.00000 0.73846 0.00000)),((1.00000 0.80000 0.00000,1.00000 0.80000 0.20000,1.00000 0.73846 0.00000,1.00000 0.80000 0.00000)),((1.00000 0.60000 0.40000,1.00000 0.60000 0.30769,1.00000 0.80000 0.20000,1.00000 0.60000 0.40000)),((1.00000 0.80000 0.71429,1.00000 0.60000 1.00000,1.00000 0.60000 0.40000,1.00000 0.80000 0.71429)),((1.00000 0.80000 1.00000,1.00000 0.73846 1.00000,1.00000 0.80000 0.71429,1.00000 0.80000 1.00000)),((0.20000 0.80000 1.00000,0.31429 0.68571 1.00000,1.00000 0.80000 1.00000,0.20000 0.80000 1.00000)),((0.00000 0.80000 0.80000,0.00000 0.80000 1.00000,0.20000 0.80000 1.00000,0.00000 0.80000 0.80000)),((0.00000 0.60000 0.60000,0.00000 0.60000 0.69231,0.00000 0.80000 0.80000,0.00000 0.60000 0.60000)),((0.60000 0.60000 0.00000,0.00000 0.60000 0.69231,0.00000 0.60000 0.60000,0.60000 0.60000 0.00000)),((1.00000 0.60000 0.00000,1.00000 0.60000 0.30769,0.60000 0.60000 0.00000,1.00000 0.60000 0.00000)),((1.00000 0.80000 0.20000,1.00000 0.60000 0.30769,1.00000 0.60000 0.00000,1.00000 0.80000 0.20000)),((1.00000 0.60000 0.40000,0.40000 0.60000 1.00000,1.00000 0.60000 0.30769,1.00000 0.60000 0.40000)),((1.00000 0.60000 1.00000,0.40000 0.60000 1.00000,1.00000 0.60000 0.40000,1.00000 0.60000 1.00000)),((1.00000 0.80000 0.71429,1.00000 0.73846 1.00000,1.00000 0.60000 1.00000,1.00000 0.80000 0.71429)),((1.00000 0.80000 1.00000,0.31429 0.68571 1.00000,1.00000 0.73846 1.00000,1.00000 0.80000 1.00000)),((0.20000 0.80000 1.00000,0.00000 0.66154 1.00000,0.31429 0.68571 1.00000,0.20000 0.80000 1.00000)),((0.00000 0.80000 1.00000,0.00000 0.66154 1.00000,0.20000 0.80000 1.00000,0.00000 0.80000 1.00000)),((0.00000 0.80000 0.80000,0.00000 0.66154 1.00000,0.00000 0.80000 1.00000,0.00000 0.80000 0.80000)),((0.00000 0.60000 0.69231,0.00000 0.66154 1.00000,0.00000 0.80000 0.80000,0.00000 0.60000 0.69231)),((0.60000 0.60000 0.00000,1.00000 0.60000 0.30769,0.00000 0.60000 0.69231,0.60000 0.60000 0.00000)),((0.40000 0.60000 1.00000,0.00000 0.60000 0.69231,1.00000 0.60000 0.30769,0.40000 0.60000 1.00000)),((1.00000 0.60000 1.00000,1.00000 0.73846 1.00000,0.40000 0.60000 1.00000,1.00000 0.60000 1.00000)),((0.31429 0.68571 1.00000,0.40000 0.60000 1.00000,1.00000 0.73846 1.00000,0.31429 0.68571 1.00000)),((0.00000 0.66154 1.00000,0.00000 0.60000 1.00000,0.31429 0.68571 1.00000,0.00000 0.66154 1.00000)),((0.00000 0.60000 0.69231,0.00000 0.60000 1.00000,0.00000 0.66154 1.00000,0.00000 0.60000 0.69231)),((0.40000 0.60000 1.00000,0.00000 0.60000 1.00000,0.00000 0.60000 0.69231,0.40000 0.60000 1.00000)),((0.31429 0.68571 1.00000,0.00000 0.60000 1.00000,0.40000 0.60000 1.00000,0.31429 0.68571 1.00000))))
with the above SOLID being classified as invalid.

The result should be a MULTISOLID consisting of two valid SOLID parts, instead of the above result which is a single invalid SOLID with two disjoint components.

This bug comes about from the SFCGAL's use of CGAL's polyhedra_corefinement class, which, in this case, generates a single object consisting of two disjoint closed polyhedra. SFCGAL then wraps and returns these as a single component SOLID, whereas it should separate out the disjoint components and return them as SOLID parts of a single MULTISOLID.

[danielcumberbatch]

A fix has been engineered for this bug (and will be submitted shortly) consisting of:

• Decomposing the intersection polyhedron from Polyhedron_corefinement into separate parts before adding them to the geometry set returned from SFCGAL::algorithm::intersection3D.
• Adapting the SFCGAL client to accept multiple part results and returning them as a MULTISOLID.

[danielcumberbatch1]

We're getting two 3-cells being passed into the Volume_import_modifier. The modifier then is iterating over all 3-cells passed into it and collecting primitives associated with them in order to construct the faces of a single intersection polyhedron, leading to a Solid with disjoint parts. Looks like we need to process each 3-cell in the Volume_import_modifier individually and then the downstream call to filterCovered will remove any duplicate primitives and faces in the result.

[danielcumberbatch1]

The result is a GC with incomplete faces. This indicates that the resulting solids are Polyhedra that consist of contributions from more than a single 3-cell.

Clearly when the points from ALL 3-cells in the list passed to the Volume_import_modifier that index into the combinatorial map entry of one of those list entries we get the current bug with too many contributions.

Hence the list of 3-cells passed to the Volume_import_modifier needs better filtering before being used to construct the output polyhedra.