public void TwelveFaces_ShouldHaveFiveVertices
(IPolyhedronOptions options)
{
// Fixture setup
var polyhedron = GeodesicSphereFactory.Build(options);
// Exercise system
var numberOfFacesWithFiveVertices = polyhedron.Faces.Count(face => face.Vertices.Count == 5);
// Verify outcome
Debug.WriteLine("Number of faces with five vertices is " + numberOfFacesWithFiveVertices);
Assert.True(numberOfFacesWithFiveVertices == 12);
// Teardown
}
// Icosaspheres are generated by repeatedly subdividing the faces of an icosahedron, then projecting the resultant
// vertices onto the sphere.
/// <summary>
/// Constructs the geodesic sphere with a number of faces exceeding the specified minimum.
/// </summary>
public static IPolyhedron Build(IPolyhedronOptions options)
{
// Build an icosasphere with a minimum number of faces.
var minimumNumberOfVertices = 2 * options.MinimumNumberOfFaces - 4;
var icosasphereOptions = new PolyhedronOptions
{
Radius = options.Radius,
MinimumNumberOfFaces = minimumNumberOfVertices
};
var icosasphere = IcosasphereFactory.Build(icosasphereOptions);
// Take the icosasphere's dual to get the geodesic sphere we want.
var faces = DualofIcosasphere(icosasphere);
return(new Polyhedron(faces));
}
// Icosaspheres are generated by repeatedly subdividing the faces of an icosahedron, then projecting the resultant
// vertices onto the sphere.
/// <summary>
/// Constructs the icosasphere with least number of vertices exceeding the specified minimum.
/// </summary>
public static IPolyhedron Build(IPolyhedronOptions options)
{
var icosahedron = IcosahedronFactory.Build();
// Calculate the number of times the icosahedron will have to be subdivided in order to meet the minimum
// number of faces specification.
var numberOfSubdivisions = NumberOfSubdivisionsRequired(options.MinimumNumberOfFaces);
// Keep subdividing the icosahedron until it meets the minimum number of faces specification.
for (int i = 0; i < numberOfSubdivisions; i++)
{
icosahedron = Subdivide(icosahedron);
}
// Project the subdivision of the icosahedron onto the sphere.
return(ProjectOntoSphere(icosahedron, options.Radius));
}
public void Vertices_ShouldHaveTheSameLengthsAsTheRadius
(IPolyhedronOptions options)
{
// Fixture setup
var polyhedron = GeodesicSphereFactory.Build(options);
// Exercise system
var vertices = polyhedron.Vertices;
// Verify outcome
var lengths = vertices.Select(vertex => vertex.Position.Norm()).ToList();
Debug.WriteLine("Lengths were " + TestUtilities.CollectionToString(lengths));
Assert.True(lengths.All(length => Number.AlmostEqual(length, options.Radius)));
// Teardown
}
public void EveryVertex_ShouldNeighbourThreeFaces
(IPolyhedronOptions options)
{
// Fixture setup
var polyhedron = GeodesicSphereFactory.Build(options);
// Exercise system
var numberOfVerticesWithThreeFaces = polyhedron.Vertices.Count(vertex => polyhedron.FacesOf(vertex).Count == 3);
// Verify outcome
var numberOfVertices = polyhedron.Vertices.Count;
Debug.WriteLine("Number of vertices is " + numberOfVertices);
Debug.WriteLine("Number of vertices neighbouring three faces is " + numberOfVerticesWithThreeFaces);
Assert.True(numberOfVerticesWithThreeFaces == numberOfVertices);
// Teardown
}
public void EveryEdge_ShouldNeighbourTwoFaces
(IPolyhedronOptions options)
{
// Fixture setup
var polyhedron = GeodesicSphereFactory.Build(options);
// Exercise system
var numberOfEdgesWithThreeFaces = polyhedron.Edges.Count(edge => polyhedron.FacesOf(edge).Count == 2);
// Verify outcome
var numberOfEdges = polyhedron.Edges.Count;
Debug.WriteLine("Number of edges is " + numberOfEdges);
Debug.WriteLine("Number of edges neighbouring two faces is " + numberOfEdgesWithThreeFaces);
Assert.True(numberOfEdgesWithThreeFaces == numberOfEdges);
// Teardown
}
public void NumbersOfVerticesAndEdgesAndFaces_ShouldSatisfyEulersFormula
(IPolyhedronOptions options)
{
// Fixture setup
var polyhedron = GeodesicSphereFactory.Build(options);
// Exercise system
var v = polyhedron.Vertices.Count;
var e = polyhedron.Edges.Count;
var f = polyhedron.Faces.Count;
// Verify outcome
Debug.WriteLine("Number of vertices: " + v);
Debug.WriteLine("Number of edges: " + e);
Debug.WriteLine("Number of faces: " + f);
Assert.True(v - e + f == 2);
// Teardown
}
