Work on geometry of primitives

We call primitives the elements that make up a mesh, such as facets, cells and lines (for a polyline). To give a few examples, in a triangular surface mesh, all facets will be triangles, in a quadrangular surface mesh, quads, and in a hexahedral volume mesh, hexahedrons.

Extracting the geometry of primitives provides access to functions for calculating some of their properties, such as the normal or area of a triangular facet.

Example of an extraction of the geometry of a tri facet:

// Init a Tri mesh
Triangles m;

// Create and place 8 points
m.points.create_points(3);
m.points[0] = vec3(0, 0, 0);
m.points[1] = vec3(1, 0, 0);
m.points[2] = vec3(1, 1, 0);

m.create_facets(1);

m.vert(0, 0) = 0;
m.vert(0, 1) = 1;
m.vert(0, 2) = 2;

// --- GET TRI3 ---

// Get facet at index 0
auto f = Triangles::Facet(m, 0);
// Extract tri geometry from facet f
auto tri_geo = f.geom<Triangle3>();
// Now, we could compute some info from geometry
auto n = tri_geo.normal(); // Get normal of quad
auto b = tri_geo.bary_verts(); // Get barycenter of quad
auto a = tri_geo.unsigned_area(); // Get area of quad
// and many other functions...
auto tri2_geo = tri_geo.xy(); // Get 2D quad from 3D (no projection, just truncate z)

// Display
std::cout 
    << "Tri facet geometry is defined by: [" 
    << tri_geo.v[0] << ", " 
    << tri_geo.v[1] << ", " 
    << tri_geo.v[2] << "]" 
    << std::endl;

std::cout << " - normal: " << n << std::endl;
std::cout << " - barycenter: " << b << std::endl;
std::cout << " - area: " << a << std::endl;

std::cout 
    << " - corresponding 2D Tri facet geometry is defined by: [" 
    << tri2_geo.v[0] << ", " 
    << tri2_geo.v[1] << ", " 
    << tri2_geo.v[2] << "]" 
    << std::endl;

Example of an extraction of the geometry of a quad facet:

// Init a Quad mesh
Quads m;

// Create and place 8 points
m.points.create_points(4);
m.points[0] = vec3(0, 0, 0);
m.points[1] = vec3(1, 0, 0);
m.points[2] = vec3(1, 1, 0);
m.points[3] = vec3(0, 1, 0);

m.create_facets(1);

m.vert(0, 0) = 0;
m.vert(0, 1) = 1;
m.vert(0, 2) = 2;
m.vert(0, 3) = 3;

// --- GET QUAD3 ---

// Get facet at index 0
auto f = Quads::Facet(m, 0);
// Extract quad geometry from facet f
auto quad_geo = f.geom<Quad3>();
// Now, we could compute some info from geometry
auto n = quad_geo.normal(); // Get normal of quad
auto b = quad_geo.bary_verts(); // Get barycenter of quad
auto a = quad_geo.unsigned_area(); // Get area of quad
auto quad2_geo = quad_geo.xy(); // Get 2D quad from 3D (no projection, just truncate z)

// Display
std::cout 
    << "Quad facet geometry is defined by: [" 
    << quad_geo.v[0] << ", " 
    << quad_geo.v[1] << ", " 
    << quad_geo.v[2] << ", " 
    << quad_geo.v[3] << "]" 
    << std::endl;

std::cout << " - normal: " << n << std::endl;
std::cout << " - barycenter: " << b << std::endl;
std::cout << " - area: " << a << std::endl;

std::cout 
    << " - corresponding 2D Quad facet geometry is defined by: [" 
    << quad2_geo.v[0] << ", " 
    << quad2_geo.v[1] << ", " 
    << quad2_geo.v[2] << ", " 
    << quad2_geo.v[3] << "]" 
    << std::endl;

Example of an extraction of the geometry of a hex cell:

// Init a Hex mesh
Hexahedra m;
m.points.create_points(8);
m.points[0] = vec3(-0.5,-0.5,-0.5);
m.points[1] = vec3(0.5,-0.5,-0.5);
m.points[2] = vec3(-0.5,0.5,-0.5);
m.points[3] = vec3(0.5,0.5,-0.5);
m.points[4] = vec3(-0.5,-0.5,0.5);
m.points[5] = vec3(0.5,-0.5,0.5);
m.points[6] = vec3(-0.5,0.5,0.5);
m.points[7] = vec3(0.5,0.5,0.5);

// Create 1 cell
m.create_cells(1);

m.vert(0, 0) = 0;
m.vert(0, 1) = 1;
m.vert(0, 2) = 2;
m.vert(0, 3) = 3;
m.vert(0, 4) = 4;
m.vert(0, 5) = 5;
m.vert(0, 6) = 6;
m.vert(0, 7) = 7;

// --- GET HEXAHEDRON ---
// Get cell at index 0
auto c = Hexahedra::Cell(m, 0);
// Extract tri geometry from facet f
auto hex_geo = c.geom<Hexahedron>();
// Now, we could compute some info from geometry
auto b = hex_geo.bary_verts(); // Get barycenter of quad
auto v = hex_geo.volume(); // Get volume
auto j = hex_geo.scaled_jacobian(); // Get scaled jacobian quality metrics

// Display
std::cout 
    << "Hex cell geometry is defined by: [" 
    << hex_geo.v[0] << ", " 
    << hex_geo.v[1] << ", " 
    << hex_geo.v[2] << ", " 
    << hex_geo.v[3] << ", " 
    << hex_geo.v[4] << ", " 
    << hex_geo.v[5] << ", " 
    << hex_geo.v[6] << ", " 
    << hex_geo.v[7] << "]" 
    << std::endl;

std::cout << " - barycenter: " << b << std::endl;
std::cout << " - volume: " << v << std::endl;
std::cout << " - scaled jacobian: " << j << std::endl;