/// <summary>
/// Constructs a FieldManipulator instance that allows the cursor tracked by cursorTracker to interact with
/// fields defined on polyhedron.
/// </summary>
/// <param name="polyhedron"></param>
/// <param name="cursorTracker"></param>
/// <param name="options"></param>
public FieldManipulator(IPolyhedron polyhedron, CursorTracker cursorTracker, IFieldManipulatorOptions options)
{
_polyhedron = polyhedron;
_cursorTracker = cursorTracker;
_settings = new FieldManipulatorSettings(options);
_options = options;
}
private static Mesh BuildMesh(IPolyhedron surface)
{
var vertices = CreateVertexArray(surface);
var triangles = CreateTriangleArray(surface);
return(CreateMesh(vertices, triangles));
}
public static ScalarField <Face> RandomScalarField(IPolyhedron polyhedron, double average, double deviation)
{
var prng = new Random();
var values = Enumerable.Repeat(deviation, polyhedron.Faces.Count).Select(i => average + (prng.NextDouble() - 0.5) * deviation).ToArray();
return(new ScalarField <Face>(polyhedron.IndexOf, values));
}
public void Faces_OfEachVertex_ShouldHaveTheSameOrderAsEdgesOfEachVertex
(IPolyhedron polyhedron)
{
// Fixture setup
// Exercise system
var faces = VertexIndexedTableFactory.Faces(polyhedron);
// Verify outcome
for (int vertex = 0; vertex < polyhedron.Vertices.Count; vertex++)
{
var faceList = faces[vertex];
var edgeList = polyhedron.EdgesOf(polyhedron.Vertices[vertex]);
var firstFace = polyhedron.Faces[faceList[0]];
var lastEdge = edgeList[edgeList.Count - 1];
var firstEdge = edgeList[0];
Assert.True(polyhedron.EdgesOf(firstFace).Contains(lastEdge));
Assert.True(polyhedron.EdgesOf(firstFace).Contains(firstEdge));
for (int i = 1; i < edgeList.Count; i++)
{
var thisFace = polyhedron.Faces[faceList[i]];
var previousEdge = edgeList[i - 1];
var thisEdge = edgeList[i];
Assert.True(polyhedron.EdgesOf(thisFace).Contains(previousEdge));
Assert.True(polyhedron.EdgesOf(thisFace).Contains(thisEdge));
}
}
// Teardown
}
public static VectorField <Vertex> RandomVectorField(IPolyhedron polyhedron, Vector average, double maxDeviation)
{
var prng = new Random();
var values = polyhedron.Vertices.Select(vertex => RandomLocalVector(prng, vertex.Position, average, maxDeviation)).ToArray();
return(new VectorField <Vertex>(polyhedron.IndexOf, values));
}
public static ScalarField <Face> XDependentScalarField(IPolyhedron polyhedron, double average, double deviation)
{
var normals = FaceIndexedTableFactory.Normals(polyhedron);
var values = polyhedron.Faces.Select(face => average + deviation * normals[polyhedron.IndexOf(face)][0]).ToArray();
return(new ScalarField <Face>(polyhedron.IndexOf, values));
}
/// <summary>
/// Construct a color mapper for the given polyhedron and maintain the running averages of the extrema for
/// the specified length of time.
/// </summary>
/// <param name="polyhedron"></param>
/// <param name="lengthOfHistory"></param>
public FieldColorer(IPolyhedron polyhedron, int lengthOfHistory)
{
_polyhedron = polyhedron;
_faces = VertexIndexedTableFactory.Faces(polyhedron);
_maxAndMinTracker = new MaxAndMinTracker(lengthOfHistory);
}
private static int IndexOfFaceInVertex(IPolyhedron surface, Face face, Vertex vertex)
{
var facesAroundVertex = surface.FacesOf(vertex);
var indexOfFace = facesAroundVertex.IndexOf(face);
return(indexOfFace);
}
/// <summary>
/// Constructs a table of the spherical areas associated with each vertex.
///
/// Only valid for degree-3 vertices.
/// </summary>
public static double[] Areas(IPolyhedron surface)
{
var areasInEachFace = AreaInEachFace(surface);
var areas = surface.Vertices.Select((vertex, i) => areasInEachFace[i].Sum()).ToArray();
return(areas);
}
/// <summary>
/// Calculates the Coriolis acceleration field for the given surface rotating at the given frequency.
/// </summary>
/// <param name="surface"></param>
/// <param name="rotationFrequency"></param>
/// <returns></returns>
public static ScalarField <Face> CoriolisField(IPolyhedron surface, double rotationFrequency)
{
var angularVelocity = 2 * Math.PI * rotationFrequency;
var values = surface.Faces.Select(face => 2 * angularVelocity * face.SphericalCenter().Normalize()[2]).ToArray();
return(new ScalarField <Face>(surface.IndexOf, values));
}
/// <summary>
/// Calculates the size of the area that's both in the specified face and closer to the specified vertex than any other vertex.
/// </summary>
public static double AreaSharedByVertexAndFace(IPolyhedron surface, Vertex vertex, Face face)
{
var vertexPosition = vertex.Position;
var faces = surface.FacesOf(vertex);
var edges = surface.EdgesOf(vertex);
var index = faces.IndexOf(face);
if (!faces.Contains(face))
{
return(0.0);
}
var midpointOfFace = face.Center();
var previousEdge = edges.AtCyclicIndex(index - 1);
var midpointOfPreviousEdge = BisectionPoint(surface, previousEdge);
var nextEdge = edges.AtCyclicIndex(index);
var midpointOfNextEdge = BisectionPoint(surface, nextEdge);
var crossProductOfFirstSegment = Vector.CrossProduct(midpointOfPreviousEdge - vertexPosition, midpointOfFace - vertexPosition);
var areaOfFirstSegment = Vector.ScalarProduct(crossProductOfFirstSegment, midpointOfFace.Normalize()) / 2;
var crossProductOfSecondSegment = Vector.CrossProduct(midpointOfFace - vertexPosition, midpointOfNextEdge - vertexPosition);
var areaOfSecondSegment = Vector.ScalarProduct(crossProductOfSecondSegment, midpointOfFace.Normalize()) / 2;
return(areaOfFirstSegment + areaOfSecondSegment);
}
/// <summary>
/// Constructs a table of the areas of the faces.
/// </summary>
public static double[] Areas(IPolyhedron surface)
{
var areasInEachVertex = AreaInEachVertex(surface);
var areas = surface.Faces.Select((face, i) => areasInEachVertex[i].Sum()).ToArray();
return(areas);
}
//TODO: Fix the dependency on the specific ordering of vertex vectors then face vectors.
// Constructs Vector3 for at each Vertex and at the center of each Face. Returns an array which contains
// the Vertex vectors followed by the Face vectors.
private static Vector3[] CreateVertexArray(IPolyhedron surface)
{
var vertexVectors = surface.Vertices.Select(vertex => GraphicsUtilities.Vector3(vertex.Position));
var faceVectors = surface.Faces.Select(face => GraphicsUtilities.Vector3(face.SphericalCenter()));
return(vertexVectors.Concat(faceVectors).ToArray());
}
/// <summary>
/// Returns the neighbours of a vertex in the same order that their connecting edges are listed by the
/// polyhedron's vertexToEdge lookup.
/// </summary>
/// <param name="polyhedron"></param>
/// <param name="vertex"></param>
/// <returns></returns>
public static IEnumerable <Vertex> NeighboursOf(this IPolyhedron polyhedron, Vertex vertex)
{
var vertexSingleton = new[] { vertex };
var edges = polyhedron.EdgesOf(vertex);
var neighbours = edges.SelectMany(edge => edge.Vertices().Except(vertexSingleton));
return(neighbours.Where(neighbour => neighbour != vertex));
}
/// <summary>
/// Returns the neighbours of a face in the same order that the edges they have in common appear.
/// </summary>
public static IEnumerable <Face> NeighboursOf(this IPolyhedron polyhedron, Face face)
{
var faceSingleton = new[] { face };
var edges = polyhedron.EdgesOf(face);
var neighbours = edges.SelectMany(edge => polyhedron.FacesOf(edge).Except(faceSingleton));
return(neighbours);
}
/// <summary>
/// Constructs an updater for the provided geometry.
/// </summary>
/// <param name="polyhedron"></param>
/// <param name="options"></param>
public ParticlePositionUpdater(IPolyhedron polyhedron, IParticleMapOptions options)
{
_scaleFactor = (float)(options.ParticleSpeedScaleFactor * options.Timestep);
_tracker = new ParticleNeighbourhoodTracker(polyhedron, options.ParticleCount);
_vertexPositions = GetVertexPositions(polyhedron);
_vertexVelocities = new Vector3[polyhedron.Vertices.Count];
_particleVelocities = new Vector3[options.ParticleCount];
}
// Creates a new icosahedron by subdividing the provided icosasphere.
private static IPolyhedron Subdivide(IPolyhedron icosasphere)
{
// Map each edge of the old icosasphere to a new vertex
var oldEdgesToNewVertices = CreateNewVerticesFrom(icosasphere.Edges);
// Create the new faces (each represented by a list of vertices) from the old icosasphere and the new vertices
var newFaces = CreateFacesFrom(icosasphere.Faces, icosasphere.EdgesOf, oldEdgesToNewVertices);
return(new Polyhedron(newFaces));
}
/// <summary>
/// Construct a particle map for the given simulation geometry.
/// </summary>
/// <param name="polyhedron"></param>
/// <param name="options"></param>
public ParticleMapView(IPolyhedron polyhedron, IParticleMapOptions options)
{
_options = options;
_radius = (float)_options.Radius;
_positions = CreateParticles(options.ParticleCount, _radius);
_renewalScheduler = new ParticleRenewalScheduler(options);
_positionUpdater = new ParticlePositionUpdater(polyhedron, options);
_renderingManager = new ParticleRenderingManager(options);
}
/// <summary>
/// Constructs a table of the normals to the sphere at the center of each face.
/// </summary>
public static Vector[] Normals(IPolyhedron surface)
{
var normals = new Vector[surface.Faces.Count];
foreach (var face in surface.Faces)
{
normals[surface.IndexOf(face)] = face.SphericalCenter().Normalize();
}
return(normals);
}
/// <summary>
/// Constructs a table of the faces around each vertex.
///
/// The ith edge given by surface.EdgesOf is anticlockwise of the ith face.
/// </summary>
public static int[][] Faces(IPolyhedron surface)
{
var faceTable = new int[surface.Vertices.Count][];
foreach (var vertex in surface.Vertices)
{
faceTable[surface.IndexOf(vertex)] = FacesAroundVertex(vertex, surface);
}
return(faceTable);
}
// Constructs the dual of the provided icosasphere, returning a list of lists in which each list represents the
// vertices of a face.
private static List <List <Vertex> > DualofIcosasphere(IPolyhedron icosasphere)
{
// Map each icosasphere face to a geodesic sphere vertex
var newVertexDict = icosasphere.Faces.ToDictionary(face => face, face => VertexAtCenterOf(face));
// Gather the new vertices into lists that represent the faces of the geodesic sphere.
var vertexLists =
icosasphere.Vertices.
Select(oldVertex => CreateFaceAbout(oldVertex, newVertexDict, icosasphere.FacesOf)).ToList();
return(vertexLists);
}
/// <summary>
/// Construct a field updated for the given surface.
/// </summary>
/// <param name="surface"></param>
/// <param name="options"></param>
public PrognosticFieldsUpdater(IPolyhedron surface, IModelParameters options)
{
_options = options;
_coriolisField = SimulationUtilities.CoriolisField(surface, _options.RotationFrequency);
_faceNormalsField = SimulationUtilities.FaceNormalsField(surface);
_vertexNormalsField = SimulationUtilities.VertexNormalsField(surface);
_operators = new VectorFieldOperators(surface);
_gravity = options.Gravity;
}
// Project the vertices of the given polyhedron onto a sphere of the specified radius.
private static IPolyhedron ProjectOntoSphere(IPolyhedron polyhedron, double radius)
{
var newVertex =
polyhedron.Vertices.
ToDictionary(oldVertex => oldVertex, oldVertex => new Vertex(radius * oldVertex.Position.Normalize()));
var newFaces =
from face in polyhedron.Faces
select face.Vertices.Select(oldVertex => newVertex[oldVertex]).ToList();
return(new Polyhedron(newFaces.ToList()));
}
/// <summary>
/// Constructs a table of the neighbours of each face.
/// Neighbours are listed in the same order as given by surface.NeighboursOf.
/// </summary>
public static int[][] Neighbours(IPolyhedron surface)
{
var neighbours = new int[surface.Faces.Count][];
foreach (var face in surface.Faces)
{
var indicesOfNeighbours = surface.NeighboursOf(face).Select(neighbour => surface.IndexOf(neighbour));
neighbours[surface.IndexOf(face)] = indicesOfNeighbours.ToArray();
}
return(neighbours);
}
/// <summary>
/// Constructs a table of the lengths of edges surrounding each face.
/// Edges are listed in the same order as the opposing faces are given by surface.NeighboursOf.
/// </summary>
public static double[][] EdgeLengths(IPolyhedron surface)
{
var edgeLengths = new double[surface.Faces.Count][];
foreach (var face in surface.Faces)
{
var lengths = surface.EdgesOf(face).Select(edge => edge.Length());
edgeLengths[surface.IndexOf(face)] = lengths.ToArray();
}
return(edgeLengths);
}
/// <summary>
/// Calculates the point at which the specified edge is closest to the line between its neighbouring faces' centers.
/// </summary>
public static Vector BisectionPoint(IPolyhedron polyhedron, Edge edge)
{
var aFace = polyhedron.FacesOf(edge).First();
var origin = edge.A.Position;
var edgeVector = edge.B.Position - origin;
var vectorToFace = aFace.SphericalCenter() - origin;
var vectorToBisector = Vector.ScalarProduct(vectorToFace, edgeVector.Normalize()) * edgeVector.Normalize();
return(vectorToBisector + origin);
}
public static Vector[] Normals(IPolyhedron surface)
{
var normals = new Vector[surface.Vertices.Count];
foreach (var vertex in surface.Vertices)
{
var normal = vertex.Position.Normalize();
normals[surface.IndexOf(vertex)] = normal;
}
return(normals);
}
/// <summary>
/// Constructs a table of the index of each face in surface.Faces(vertex) for each vertex around that face.
/// </summary>
public static int[][] FaceInFacesOfVertices(IPolyhedron surface)
{
var indices = new int[surface.Faces.Count][];
foreach (var face in surface.Faces)
{
var indicesOfFace = face.Vertices.Select(vertex => IndexOfFaceInVertex(surface, face, vertex)).ToArray();
indices[surface.IndexOf(face)] = indicesOfFace;
}
return(indices);
}
/// <summary>
/// Constructs a table of the indices of the vertices around each face.
/// </summary>
public static int[][] Vertices(IPolyhedron surface)
{
var indices = new int[surface.Faces.Count][];
foreach (var face in surface.Faces)
{
var vertexIndices = face.Vertices.Select(vertex => surface.IndexOf(vertex)).ToArray();
indices[surface.IndexOf(face)] = vertexIndices;
}
return(indices);
}
/// <summary>
/// Constructs a table of the directions towards the faces neighbours in the face's tangent space.
/// </summary>
public static Vector[][] Directions(IPolyhedron surface)
{
var directions = new Vector[surface.Faces.Count][];
foreach (var face in surface.Faces)
{
var neighboursOfFace = surface.NeighboursOf(face);
var localDirections = neighboursOfFace.Select(neighbour => Direction(face, neighbour));
directions[surface.IndexOf(face)] = localDirections.ToArray();
}
return(directions);
}
