//Vertices need to be reduced to 2D
//see Akenine-Möller, Tomas; Haines, Eric; Hoffman, Naty (2016): Real-Time Rendering, p. 754
/// <summary>
/// Tests if a point/vertex lies inside or outside a face - Only use this if you know the face AND vertex lie in the same plane and this plane is parallel to xy or xz or yz!
/// </summary>
/// <param name="geometry">The geometry the polygon (here: face) belongs to.</param>
/// <param name="face">The faces to be tested. It will not be Reduced2D!</param>
/// <param name="v">The vertex to be tested.</param>
/// <returns></returns>
public static bool IsPointInPolygon(this Geometry geometry, Face face, float3 v)
{
var inside = false;
var faceVerts = geometry.GetFaceVertices(face.Handle).ToList();
var v1 = geometry.GetVertexByHandle(faceVerts.Last().Handle);
var v1Pos = geometry.Get2DVertPos(face, v1.Handle);
var y0 = v1Pos.y >= v.y;
foreach (var vert in faceVerts)
{
var e1Pos = geometry.Get2DVertPos(face, vert.Handle);
var y1 = e1Pos.y >= v.y;
if (y0 != y1)
{
if ((e1Pos.y - v.y) * (v1Pos.x - e1Pos.x) >=
(e1Pos.x - v.x) * (v1Pos.y - e1Pos.y) == y1)
{
inside = !inside;
}
}
y0 = y1;
v1Pos = e1Pos;
}
return(inside);
}
private static Dictionary <int, Vertex> GetEdgeVertices(Geometry geometry, Dictionary <int, Vertex> faceVertices)
{
var allEdges = geometry.GetAllHalfEdges();
var doneHe = new int[allEdges.Count() + 1];
var allEdgeVertices = new Dictionary <int, Vertex>();
foreach (var edge in allEdges)
{
if (doneHe[edge.Handle] == edge.TwinHalfEdge)
{
continue;
}
var face1 = edge.IncidentFace;
var twin = geometry.GetHalfEdgeByHandle(edge.TwinHalfEdge);
var face2 = twin.IncidentFace;
var vertex1 = geometry.GetVertexByHandle(edge.OriginVertex);
var vertex2 = geometry.GetVertexByHandle(twin.OriginVertex);
var cVertex1 = faceVertices[face1];
var cVertex2 = faceVertices[face2];
var temp = new List <Vertex> {
vertex1, vertex2, cVertex1, cVertex2
};
var finalVertex = new Vertex(edge.Handle, GeometricOperations.GetVerticesMeanPos(temp))
{
IncidentHalfEdge = edge.Handle
};
allEdgeVertices.Add(edge.Handle, finalVertex);
doneHe[edge.TwinHalfEdge] = edge.Handle;
}
return(allEdgeVertices);
}
private static void AssignFaceHandle(this Geometry geometry, int heHandle, Face newFace)
{
var oldFaceHandle = geometry.GetHalfEdgeByHandle(heHandle).IncidentFace;
var currentHe = geometry.GetHalfEdgeByHandle(heHandle);
do
{
currentHe.IncidentFace = newFace.Handle;
geometry.DictHalfEdges[currentHe.Handle] = currentHe;
currentHe = geometry.GetHalfEdgeByHandle(currentHe.NextHalfEdge);
} while (currentHe.Handle != heHandle);
//Assign newFace to possible holes in the "old" face.
var oldFace = geometry.GetFaceByHandle(oldFaceHandle);
if (oldFace.InnerHalfEdges.Count == 0)
{
return;
}
var inner = new List <int>();
inner.AddRange(oldFace.InnerHalfEdges);
foreach (var heh in inner)
{
var origin = geometry.GetHalfEdgeByHandle(heh).OriginVertex;
if (!geometry.IsPointInPolygon(newFace, geometry.GetVertexByHandle(origin)))
{
continue;
}
oldFace.InnerHalfEdges.Remove(heh);
newFace.InnerHalfEdges.Add(heh);
var curHe = geometry.GetHalfEdgeByHandle(heh);
do
{
curHe.IncidentFace = newFace.Handle;
geometry.DictHalfEdges[curHe.Handle] = curHe;
curHe = geometry.GetHalfEdgeByHandle(curHe.NextHalfEdge);
} while (curHe.Handle != heh);
}
}
private static IEnumerable <Vertex> GetLeftChain(IList <Vertex> sortedVerts, Face face)
{
var heHandle = new int();
var endOfChain = sortedVerts.Last();
var startingAtFirstV = _geometry.GetVertexStartingHalfEdges(sortedVerts[0].Handle).ToList();
if (startingAtFirstV.Count > 1)
{
foreach (var heh in startingAtFirstV)
{
var he = heh;
if (he.IncidentFace == face.Handle)
{
heHandle = heh.Handle;
}
}
}
else
{
heHandle = sortedVerts[0].IncidentHalfEdge;
}
do
{
var halfEdge = _geometry.GetHalfEdgeByHandle(heHandle);
yield return(_geometry.GetVertexByHandle(halfEdge.OriginVertex));
heHandle = halfEdge.NextHalfEdge;
} while (_geometry.GetHalfEdgeByHandle(heHandle).OriginVertex != endOfChain.Handle);
}
private static Geometry ExtrudeFaceByHandle(Geometry geometry, int faceHandle, float offset, float3 extrusionVector)
{
var face = geometry.GetFaceByHandle(faceHandle);
//get HE of Face
var start = geometry.GetHalfEdgeByHandle(face.OuterHalfEdge);
var next = start;
var vertexIncHe = new Dictionary <int, List <HalfEdge> >();
var allFaceVertices = geometry.GetFaceVertices(faceHandle);
foreach (var vertex in allFaceVertices)
{
vertexIncHe.Add(vertex.Handle, geometry.GetVertexStartingHalfEdges(vertex.Handle).ToList());
}
var allH2NEdges = new List <HalfEdge>();
do
{
var nextOriginV = geometry.GetVertexByHandle(next.OriginVertex);
var newVertex = new Vertex(geometry.CreateVertHandleId(), nextOriginV.VertData.Pos);
var twinEdge = geometry.GetHalfEdgeByHandle(next.TwinHalfEdge);
var prevEdge = geometry.GetHalfEdgeByHandle(next.PrevHalfEdge);
var prevTwinEdge = geometry.GetHalfEdgeByHandle(prevEdge.TwinHalfEdge);
nextOriginV.VertData.Pos = nextOriginV.VertData.Pos + extrusionVector * offset;
var h4 = new HalfEdge(geometry.CreateHalfEdgeHandleId());
var h2n = new HalfEdge(geometry.CreateHalfEdgeHandleId());
var h1 = new HalfEdge(geometry.CreateHalfEdgeHandleId());
var currentList = vertexIncHe[nextOriginV.Handle];
foreach (var halfEdge in currentList)
{
if (halfEdge == next)
{
continue;
}
var edge = GeomEditing.UpdateHalfEdgeOrigin(halfEdge, newVertex.Handle);
geometry.ReplaceHalfEdge(edge);
}
nextOriginV.IncidentHalfEdge = next.Handle;
h4.OriginVertex = nextOriginV.Handle;
h2n.OriginVertex = newVertex.Handle;
h1.OriginVertex = newVertex.Handle;
h4.TwinHalfEdge = h2n.Handle;
h2n.TwinHalfEdge = h4.Handle;
h4.NextHalfEdge = h1.Handle;
h1.PrevHalfEdge = h4.Handle;
h1.TwinHalfEdge = next.TwinHalfEdge;
twinEdge.TwinHalfEdge = h1.Handle;
prevTwinEdge.OriginVertex = newVertex.Handle;
newVertex.IncidentHalfEdge = h2n.Handle;
geometry.ReplaceHalfEdge(twinEdge);
geometry.ReplaceHalfEdge(prevTwinEdge);
geometry.ReplaceVertex(nextOriginV);
geometry.DictVertices.Add(newVertex.Handle, newVertex);
geometry.DictHalfEdges.Add(h4.Handle, h4);
geometry.DictHalfEdges.Add(h1.Handle, h1);
geometry.DictHalfEdges.Add(h2n.Handle, h2n);
allH2NEdges.Add(h2n);
next = geometry.GetHalfEdgeByHandle(next.NextHalfEdge);
} while (start != next);
start = geometry.GetHalfEdgeByHandle(face.OuterHalfEdge);
next = start;
do
{
var newFace = new Face(geometry.CreateFaceHandleId());
var twinEdge = geometry.GetHalfEdgeByHandle(next.TwinHalfEdge);
var h1 = geometry.GetHalfEdgeByHandle(twinEdge.TwinHalfEdge);
var h2 = allH2NEdges.First(n => n.OriginVertex == twinEdge.OriginVertex);
var h3 = new HalfEdge(geometry.CreateHalfEdgeHandleId());
var h4 = geometry.GetHalfEdgeByHandle(h1.PrevHalfEdge);
//set Face
h1.IncidentFace = newFace.Handle;
h2.IncidentFace = newFace.Handle;
h3.IncidentFace = newFace.Handle;
h4.IncidentFace = newFace.Handle;
h1.NextHalfEdge = h2.Handle;
h2.NextHalfEdge = h3.Handle;
h3.NextHalfEdge = h4.Handle;
h4.NextHalfEdge = h1.Handle;
h1.PrevHalfEdge = h4.Handle;
h2.PrevHalfEdge = h1.Handle;
h3.PrevHalfEdge = h2.Handle;
h4.PrevHalfEdge = h3.Handle;
h3.TwinHalfEdge = next.Handle;
h3.OriginVertex = geometry.GetHalfEdgeByHandle(next.NextHalfEdge).OriginVertex;
next.TwinHalfEdge = h3.Handle;
newFace.OuterHalfEdge = h1.Handle;
//write all changes
geometry.ReplaceHalfEdge(h1);
geometry.ReplaceHalfEdge(h2);
geometry.ReplaceHalfEdge(h4);
geometry.ReplaceHalfEdge(next);
geometry.DictHalfEdges.Add(h3.Handle, h3);
geometry.DictFaces.Add(newFace.Handle, newFace);
newFace.FaceData.FaceNormal = GeometricOperations.CalculateFaceNormal(geometry.GetFaceVertices(newFace.Handle).ToList());
geometry.ReplaceFace(newFace);
next = geometry.GetHalfEdgeByHandle(next.NextHalfEdge);
} while (start != next);
return(geometry);
}
/// <summary>
/// Insets a Face with a given offset. The new, center Face has the same Handle as the original Face.
/// </summary>
/// <param name="geometry">The geometry on which to perform a face inset.</param>
/// <param name="faceHandle">The Handle of the face, the new one will be inseted to.</param>
/// <param name="insetOffset">The offset of the inset in percent. Use values between 0 and 1. A value of 0.5f means 50% of the original face remains.</param>
/// <returns>Returns the geometry with edited faces.</returns>
public static Geometry InsetFace(this Geometry geometry, int faceHandle, float insetOffset)
{
if (insetOffset >= 1)
{
throw new ArgumentException("insetOffset can not be greate or equal to 1.");
}
if (insetOffset <= 0)
{
throw new ArgumentException("insetOffset can not be smaller or equal to 0.");
}
var face = geometry.GetFaceByHandle(faceHandle);
var allFaceVertices = geometry.GetFaceVertices(faceHandle).ToList();
var meanPos = GeometricOperations.GetVerticesMeanPos(allFaceVertices);
//Dict sotres countEdges; [0] = edge1.handle, [1] = edge2twin.handle, [2] = edge3.handle, [3] = vertex.Handle
var edgeStorage = new Dictionary <int, int[]>();
var countEdges = 0;
var start = geometry.GetHalfEdgeByHandle(face.OuterHalfEdge);
var next = start;
do
{
var nextEdge = next.NextHalfEdge;
var currentVertex = geometry.GetVertexByHandle(next.OriginVertex);
var currentPos = currentVertex.VertData.Pos;
var newPos = (currentPos - meanPos) * insetOffset + meanPos;
var newVertex = new Vertex(geometry.CreateVertHandleId(), newPos);
var nextNext = geometry.GetHalfEdgeByHandle(next.NextHalfEdge);
var edge1 = new HalfEdge(geometry.CreateHalfEdgeHandleId());
var edge2Twin = new HalfEdge(geometry.CreateHalfEdgeHandleId());
var edge2 = new HalfEdge(geometry.CreateHalfEdgeHandleId());
var edge3 = new HalfEdge(geometry.CreateHalfEdgeHandleId());
var newFace = new Face(geometry.CreateFaceHandleId());
//store info
edgeStorage.Add(countEdges, new[] { edge1.Handle, edge2Twin.Handle, edge3.Handle, newVertex.Handle });
newVertex.IncidentHalfEdge = edge3.Handle;
newFace.OuterHalfEdge = edge1.Handle;
edge1.OriginVertex = nextNext.OriginVertex;
edge3.OriginVertex = newVertex.Handle;
edge2Twin.OriginVertex = newVertex.Handle;
//twins
edge2.TwinHalfEdge = edge2Twin.Handle;
edge2Twin.TwinHalfEdge = edge2.Handle;
//nexts
edge1.NextHalfEdge = edge2.Handle;
edge2.NextHalfEdge = edge3.Handle;
edge3.NextHalfEdge = next.Handle;
next.NextHalfEdge = edge1.Handle;
//prevs
edge1.PrevHalfEdge = next.Handle;
edge2.PrevHalfEdge = edge1.Handle;
edge3.PrevHalfEdge = edge2.Handle;
next.PrevHalfEdge = edge3.Handle;
//face
edge1.IncidentFace = newFace.Handle;
edge2.IncidentFace = newFace.Handle;
edge3.IncidentFace = newFace.Handle;
next.IncidentFace = newFace.Handle;
edge2Twin.IncidentFace = face.Handle;
newFace.FaceData.FaceNormal = face.FaceData.FaceNormal;
//write changes
geometry.DictVertices.Add(newVertex.Handle, newVertex);
geometry.DictFaces.Add(newFace.Handle, newFace);
geometry.DictHalfEdges.Add(edge1.Handle, edge1);
geometry.DictHalfEdges.Add(edge2Twin.Handle, edge2Twin);
geometry.DictHalfEdges.Add(edge2.Handle, edge2);
geometry.DictHalfEdges.Add(edge3.Handle, edge3);
geometry.ReplaceHalfEdge(next);
countEdges++;
next = geometry.GetHalfEdgeByHandle(nextEdge);
} while (start != next);
for (var i = 0; i < countEdges; i++)
{
var prevFace = i - 1;
var nextFace = i + 1;
var faceData = edgeStorage[i];
if (i == 0)
{
prevFace = countEdges - 1;
}
if (i == countEdges - 1)
{
nextFace = 0;
face.OuterHalfEdge = faceData[1];
geometry.ReplaceFace(face);
}
var prevFaceData = edgeStorage[prevFace];
var nextFaceData = edgeStorage[nextFace];
var edge2Twin = geometry.GetHalfEdgeByHandle(faceData[1]);
var edge3 = geometry.GetHalfEdgeByHandle(faceData[2]);
var edge3Twin = geometry.GetHalfEdgeByHandle(prevFaceData[0]);
var edge2 = geometry.GetHalfEdgeByHandle(edge2Twin.TwinHalfEdge);
edge2Twin.PrevHalfEdge = prevFaceData[1];
edge2Twin.NextHalfEdge = nextFaceData[1];
edge2.OriginVertex = nextFaceData[3];
edge3Twin.TwinHalfEdge = edge3.Handle;
edge3.TwinHalfEdge = edge3Twin.Handle;
//write
geometry.ReplaceHalfEdge(edge2Twin);
geometry.ReplaceHalfEdge(edge2);
geometry.ReplaceHalfEdge(edge3Twin);
geometry.ReplaceHalfEdge(edge3);
}
return(geometry);
}
/// <summary>
/// Inserts a new Vertex between two given exsisting Vertices.
/// </summary>
/// <param name="geometry">The Geometry to insert a Vertex.</param>
/// <param name="p">Handle of Vertex one.</param>
/// <param name="q">Handle of Vertex two.</param>
/// <param name="pos">Position of the new Vertex</param>
/// <returns>New Vertex Handle.</returns>
public static int InsertVertex(this Geometry geometry, int p, int q, float3 pos)
{
var adjacentVertices = geometry.GetVertexAdjacentVertices(p).ToList();
for (var i = 0; i < adjacentVertices.Count; i++)
{
if (adjacentVertices[i].Handle == q)
{
break;
}
if (i == adjacentVertices.Count - 1)
{
throw new ArgumentException("Vertices with Handle q=" + q + " and p=" + p + " are not adjacent!");
}
}
var newVertex = new Vertex(geometry.CreateVertHandleId(), pos);
//add two new Half Edges
var newHalfEdge1 = new HalfEdge(geometry.CreateHalfEdgeHandleId());
var newHalfEdge2 = new HalfEdge(geometry.CreateHalfEdgeHandleId());
//set origin to new Vertex
newHalfEdge1.OriginVertex = newVertex.Handle;
newHalfEdge2.OriginVertex = newVertex.Handle;
newVertex.IncidentHalfEdge = newHalfEdge2.Handle;
var vertexP = geometry.GetVertexByHandle(p);
var vertexQ = geometry.GetVertexByHandle(q);
//Find Half Edge between p and q
var incomingEdges = geometry.GetVertexStartingHalfEdges(vertexP.Handle);
var he1 = new HalfEdge();
var he2 = new HalfEdge();
foreach (var halfEdge in incomingEdges)
{
var twinEdge = geometry.GetHalfEdgeByHandle(halfEdge.TwinHalfEdge);
if (twinEdge.OriginVertex != vertexQ.Handle)
{
continue;
}
he1 = halfEdge;
he2 = twinEdge;
}
var next1 = geometry.GetHalfEdgeByHandle(he2.NextHalfEdge);
var next2 = geometry.GetHalfEdgeByHandle(he1.NextHalfEdge);
//change Handels
he1.TwinHalfEdge = newHalfEdge1.Handle;
newHalfEdge1.TwinHalfEdge = he1.Handle;
newHalfEdge1.NextHalfEdge = he2.NextHalfEdge;
he2.NextHalfEdge = newHalfEdge1.Handle;
newHalfEdge1.PrevHalfEdge = he2.Handle;
next1.PrevHalfEdge = newHalfEdge1.Handle;
he2.TwinHalfEdge = newHalfEdge2.Handle;
newHalfEdge2.TwinHalfEdge = he2.Handle;
newHalfEdge2.NextHalfEdge = he1.NextHalfEdge;
he1.NextHalfEdge = newHalfEdge2.Handle;
newHalfEdge2.PrevHalfEdge = he1.Handle;
next2.PrevHalfEdge = newHalfEdge2.Handle;
//reconnect faces
newHalfEdge1.IncidentFace = he2.IncidentFace;
newHalfEdge2.IncidentFace = he1.IncidentFace;
//replace exsisnting Edges
geometry.ReplaceHalfEdge(he1);
geometry.ReplaceHalfEdge(he2);
geometry.ReplaceHalfEdge(next1);
geometry.ReplaceHalfEdge(next2);
//add to dict
geometry.DictVertices.Add(newVertex.Handle, newVertex);
geometry.DictHalfEdges.Add(newHalfEdge1.Handle, newHalfEdge1);
geometry.DictHalfEdges.Add(newHalfEdge2.Handle, newHalfEdge2);
return(newVertex.Handle);
}
private static void AddFaceVerticesAndNewFaces(Geometry geometry, Geometry newGeometry, Dictionary <int, Vertex> allFaceVertices)
{
var allFaces = geometry.GetAllFaces();
foreach (var face in allFaces)
{
Vertex faceVertex = new Vertex(newGeometry.CreateVertHandleId(), allFaceVertices[face.Handle].VertData.Pos);
HalfEdge startEdge = geometry.GetHalfEdgeByHandle(face.OuterHalfEdge);
HalfEdge nextEdge = startEdge;
//stores Halfedges without Twin
Dictionary <int, HalfEdge> halfEdges2 = new Dictionary <int, HalfEdge>();
Dictionary <int, HalfEdge> halfEdges1 = new Dictionary <int, HalfEdge>();
newGeometry.DictVertices.Add(faceVertex.Handle, faceVertex);
int i = 0;
do
{
HalfEdge h1 = new HalfEdge(newGeometry.CreateHalfEdgeHandleId());
HalfEdge h2 = new HalfEdge(newGeometry.CreateHalfEdgeHandleId());
HalfEdge h3 = newGeometry.GetHalfEdgeByHandle(nextEdge.PrevHalfEdge);
HalfEdge h4 = newGeometry.GetHalfEdgeByHandle(nextEdge.Handle);
//create new quad face
Face newFace;
newFace = i == 0 ? face : new Face(newGeometry.CreateFaceHandleId());
nextEdge = geometry.GetHalfEdgeByHandle(nextEdge.NextHalfEdge);
h1.NextHalfEdge = h2.Handle;
h2.NextHalfEdge = h3.Handle;
h3.NextHalfEdge = h4.Handle;
h4.NextHalfEdge = h1.Handle;
h1.PrevHalfEdge = h4.Handle;
h2.PrevHalfEdge = h1.Handle;
h3.PrevHalfEdge = h2.Handle;
h4.PrevHalfEdge = h3.Handle;
h1.OriginVertex = nextEdge.OriginVertex;
h2.OriginVertex = faceVertex.Handle;
h1.IncidentFace = newFace.Handle;
h2.IncidentFace = newFace.Handle;
h3.IncidentFace = newFace.Handle;
h4.IncidentFace = newFace.Handle;
faceVertex.IncidentHalfEdge = h2.Handle;
newFace.OuterHalfEdge = h1.Handle;
//add and replace changed
newGeometry.DictHalfEdges.Add(h1.Handle, h1);
newGeometry.DictHalfEdges.Add(h2.Handle, h2);
newGeometry.ReplaceHalfEdge(h3);
newGeometry.ReplaceHalfEdge(h4);
newGeometry.ReplaceVertex(faceVertex);
if (i == 0) // the old face becomes the first quad, so no new face to create
{
newGeometry.ReplaceFace(newFace);
}
else //create new face
{
newGeometry.DictFaces.Add(newFace.Handle, newFace);
}
//Stores Vertices to get the face normal
List <Vertex> faceVertices = new List <Vertex>
{
newGeometry.GetVertexByHandle(h1.OriginVertex),
newGeometry.GetVertexByHandle(h2.OriginVertex),
newGeometry.GetVertexByHandle(h3.OriginVertex),
newGeometry.GetVertexByHandle(h4.OriginVertex)
};
newGeometry.SetFaceNormal(faceVertices, newFace);
halfEdges2.Add(i, h2);
halfEdges1.Add(i, h1);
//for the second Edge per Face connect the twin
if (i > 0)
{
HalfEdge h1N = halfEdges1[i - 1];
h1N.TwinHalfEdge = halfEdges2[i].Handle;
HalfEdge h2N = halfEdges2[i];
h2N.TwinHalfEdge = h1N.Handle;
newGeometry.ReplaceHalfEdge(h1N);
newGeometry.ReplaceHalfEdge(h2N);
}
i++;
nextEdge = geometry.GetHalfEdgeByHandle(nextEdge.NextHalfEdge);
} while (startEdge != nextEdge);
//set Twin of firsts and lasts of each new Face
var h2Firts = halfEdges2[0];
var h1Last = halfEdges1[i - 1];
h2Firts.TwinHalfEdge = h1Last.Handle;
h1Last.TwinHalfEdge = h2Firts.Handle;
newGeometry.ReplaceHalfEdge(h2Firts);
newGeometry.ReplaceHalfEdge(h1Last);
}
}
/// <summary>
/// Creates and returns a UV-Sphere as a DCEL with the specified dimensions centered in the worlds coordinate system.
/// </summary>
/// <param name="radius">Radius of the sphere.</param>
/// <param name="horizontalResolution">Lines of latitude, smallest value is 3.</param>
/// <param name="verticalResolution">Lines of longitude, smallest value is 3.</param>
/// <returns>A UV-Sphere centered in the world coordinate system as a DCEL.</returns>
public static Geometry CreateSpehreGeometry(float radius, int horizontalResolution, int verticalResolution)
{
//check input
if (radius <= 0)
{
throw new ArgumentException("Radius can not be <= 0");
}
if (horizontalResolution <= 3)
{
horizontalResolution = 3;
}
if (verticalResolution <= 2)
{
verticalResolution = 2;
}
var sphere = new Geometry();
var northPole = new Vertex(sphere.CreateVertHandleId(), new float3(0, radius, 0));
var southPole = new Vertex(sphere.CreateVertHandleId(), new float3(0, -radius, 0));
var horizontalAngleStep = System.Math.PI * 2 / horizontalResolution; // s
var verrticalAngleStep = System.Math.PI / verticalResolution; // t
var currentLatitudeVerticesHandles = new int[horizontalResolution];
var lastlatitudeVerticesHandles = new int[horizontalResolution]; //stores last vertices to connect them later with the next latitude vertices
for (var i = 1; i < verticalResolution + 1; i++)
{
//create all vertices
if (i < verticalResolution)
{
for (var j = 0; j < horizontalResolution; j++)
{
//create all Vertices of current latitude
var xPos = (float)(radius * System.Math.Sin(horizontalAngleStep * j) * System.Math.Sin(verrticalAngleStep * i));
var yPos = (float)(radius * System.Math.Cos(verrticalAngleStep * (i)));
var zPos = (float)(radius * System.Math.Cos(horizontalAngleStep * j) * System.Math.Sin(verrticalAngleStep * i));
var circleVertex = new Vertex(sphere.CreateVertHandleId(), new float3(xPos, yPos, zPos));
sphere.DictVertices.Add(circleVertex.Handle, circleVertex);
currentLatitudeVerticesHandles[j] = circleVertex.Handle;
}
}
//create faces
var topHeHandles = new int[horizontalResolution];
for (var j = 0; j < horizontalResolution; j++)
{
// bottom triangles of sphere
if (i == verticalResolution)
{
var bottomTriangle = new Face(sphere.CreateFaceHandleId());
var h1 = new HalfEdge(sphere.CreateHalfEdgeHandleId());
var h2 = new HalfEdge(sphere.CreateHalfEdgeHandleId());
var h3 = new HalfEdge(sphere.CreateHalfEdgeHandleId());
topHeHandles[j] = h1.Handle;
h1.NextHalfEdge = h2.Handle;
h2.NextHalfEdge = h3.Handle;
h3.NextHalfEdge = h1.Handle;
h1.PrevHalfEdge = h3.Handle;
h2.PrevHalfEdge = h1.Handle;
h3.PrevHalfEdge = h2.Handle;
h1.IncidentFace = bottomTriangle.Handle;
h2.IncidentFace = bottomTriangle.Handle;
h3.IncidentFace = bottomTriangle.Handle;
h1.OriginVertex = currentLatitudeVerticesHandles[j];
h2.OriginVertex = j == horizontalResolution - 1 ? currentLatitudeVerticesHandles[0] : currentLatitudeVerticesHandles[j + 1];
h3.OriginVertex = southPole.Handle;
bottomTriangle.OuterHalfEdge = h1.Handle;
southPole.IncidentHalfEdge = h3.Handle;
//write changes
sphere.DictHalfEdges.Add(h1.Handle, h1);
sphere.DictHalfEdges.Add(h2.Handle, h2);
sphere.DictHalfEdges.Add(h3.Handle, h3);
sphere.DictFaces.Add(bottomTriangle.Handle, bottomTriangle);
}
// top triangles of sphere
else if (i == 1)
{
var topTriangle = new Face(sphere.CreateFaceHandleId());
var h1 = new HalfEdge(sphere.CreateHalfEdgeHandleId());
var h2 = new HalfEdge(sphere.CreateHalfEdgeHandleId());
var h3 = new HalfEdge(sphere.CreateHalfEdgeHandleId());
topHeHandles[j] = h1.Handle;
h1.NextHalfEdge = h2.Handle;
h2.NextHalfEdge = h3.Handle;
h3.NextHalfEdge = h1.Handle;
h1.PrevHalfEdge = h3.Handle;
h2.PrevHalfEdge = h1.Handle;
h3.PrevHalfEdge = h2.Handle;
h1.IncidentFace = topTriangle.Handle;
h2.IncidentFace = topTriangle.Handle;
h3.IncidentFace = topTriangle.Handle;
h1.OriginVertex = j == horizontalResolution - 1 ? currentLatitudeVerticesHandles[0] : currentLatitudeVerticesHandles[j + 1];
h2.OriginVertex = currentLatitudeVerticesHandles[j];
h3.OriginVertex = northPole.Handle;
topTriangle.OuterHalfEdge = h1.Handle;
var currentVertex = sphere.GetVertexByHandle(currentLatitudeVerticesHandles[j]);
currentVertex.IncidentHalfEdge = h2.Handle;
northPole.IncidentHalfEdge = h3.Handle;
//write changes
sphere.DictHalfEdges.Add(h1.Handle, h1);
sphere.DictHalfEdges.Add(h2.Handle, h2);
sphere.DictHalfEdges.Add(h3.Handle, h3);
sphere.DictFaces.Add(topTriangle.Handle, topTriangle);
sphere.ReplaceVertex(currentVertex);
}
// middle quads of sphere
else
{
var quad = new Face(sphere.CreateFaceHandleId());
var h1 = new HalfEdge(sphere.CreateHalfEdgeHandleId());
var h2 = new HalfEdge(sphere.CreateHalfEdgeHandleId());
var h3 = new HalfEdge(sphere.CreateHalfEdgeHandleId());
var h4 = new HalfEdge(sphere.CreateHalfEdgeHandleId());
topHeHandles[j] = h1.Handle;
h1.NextHalfEdge = h2.Handle;
h2.NextHalfEdge = h3.Handle;
h3.NextHalfEdge = h4.Handle;
h4.NextHalfEdge = h1.Handle;
h1.PrevHalfEdge = h4.Handle;
h2.PrevHalfEdge = h1.Handle;
h3.PrevHalfEdge = h2.Handle;
h4.PrevHalfEdge = h3.Handle;
h1.IncidentFace = quad.Handle;
h2.IncidentFace = quad.Handle;
h3.IncidentFace = quad.Handle;
h4.IncidentFace = quad.Handle;
quad.OuterHalfEdge = h1.Handle;
h4.OriginVertex = currentLatitudeVerticesHandles[j];
h3.OriginVertex = j == horizontalResolution - 1 ? currentLatitudeVerticesHandles[0] : currentLatitudeVerticesHandles[j + 1];
h2.OriginVertex = j == horizontalResolution - 1 ? lastlatitudeVerticesHandles[0] : lastlatitudeVerticesHandles[j + 1];
h1.OriginVertex = lastlatitudeVerticesHandles[j];
var currentVertex = sphere.GetVertexByHandle(currentLatitudeVerticesHandles[j]);
currentVertex.IncidentHalfEdge = h4.Handle;
//write changes
sphere.DictFaces.Add(quad.Handle, quad);
sphere.DictHalfEdges.Add(h1.Handle, h1);
sphere.DictHalfEdges.Add(h2.Handle, h2);
sphere.DictHalfEdges.Add(h3.Handle, h3);
sphere.DictHalfEdges.Add(h4.Handle, h4);
sphere.ReplaceVertex(currentVertex);
}
}
//set twins
for (int j = 0; j < horizontalResolution; j++)
{
//set twins of adjacent triangles bottom
if (i == 1)
{
int nextH1Index;
nextH1Index = j == 0 ? horizontalResolution - 1 : j - 1;
var h1 = sphere.GetHalfEdgeByHandle(topHeHandles[j]);
var h2 = sphere.GetHalfEdgeByHandle(h1.NextHalfEdge);
var nextH1 = sphere.GetHalfEdgeByHandle(topHeHandles[nextH1Index]);
var nextH3 = sphere.GetHalfEdgeByHandle(nextH1.PrevHalfEdge);
nextH3.TwinHalfEdge = h2.Handle;
h2.TwinHalfEdge = nextH3.Handle;
sphere.ReplaceHalfEdge(nextH3);
sphere.ReplaceHalfEdge(h2);
}
else if (i == verticalResolution)
{
int nextH1Index;
nextH1Index = j == 0 ? horizontalResolution - 1 : j - 1;
var h1 = sphere.GetHalfEdgeByHandle(topHeHandles[j]);
var h3 = sphere.GetHalfEdgeByHandle(h1.PrevHalfEdge);
var nextH1 = sphere.GetHalfEdgeByHandle(topHeHandles[nextH1Index]);
var nextH2 = sphere.GetHalfEdgeByHandle(nextH1.NextHalfEdge);
nextH2.TwinHalfEdge = h3.Handle;
h3.TwinHalfEdge = nextH2.Handle;
sphere.ReplaceHalfEdge(nextH2);
sphere.ReplaceHalfEdge(h3);
}
else //set twins of adjacent quads
{
var h1 = sphere.GetHalfEdgeByHandle(topHeHandles[j]);
var h4 = sphere.GetHalfEdgeByHandle(h1.PrevHalfEdge);
int nextH1Index;
nextH1Index = j == 0 ? horizontalResolution - 1 : j - 1;
var nextH1 = sphere.GetHalfEdgeByHandle(topHeHandles[nextH1Index]);
var nextH2 = sphere.GetHalfEdgeByHandle(nextH1.NextHalfEdge);
nextH2.TwinHalfEdge = h4.Handle;
h4.TwinHalfEdge = nextH2.Handle;
sphere.ReplaceHalfEdge(nextH2);
sphere.ReplaceHalfEdge(h4);
}
//set twin of face on top
if (i > 1)
{
var h1 = sphere.GetHalfEdgeByHandle(topHeHandles[j]);
var lastVertex = sphere.GetVertexByHandle(lastlatitudeVerticesHandles[j]);
var topH1 = sphere.GetHalfEdgeByHandle(lastVertex.IncidentHalfEdge);
while (true)
{
if (topH1.TwinHalfEdge == 0)
{
break;
}
topH1 = sphere.GetHalfEdgeByHandle(topH1.NextHalfEdge);
}
topH1.TwinHalfEdge = h1.Handle;
h1.TwinHalfEdge = topH1.Handle;
sphere.ReplaceHalfEdge(h1);
sphere.ReplaceHalfEdge(topH1);
}
}
Array.Copy(currentLatitudeVerticesHandles, lastlatitudeVerticesHandles,
currentLatitudeVerticesHandles.Length);
}
sphere.DictVertices.Add(northPole.Handle, northPole);
sphere.DictVertices.Add(southPole.Handle, southPole);
//calculate normals
var allFaces = sphere.GetAllFaces().ToList();
foreach (var face in allFaces)
{
sphere.SetFaceNormal(sphere.GetFaceVertices(face.Handle).ToList(), face);
}
return(sphere);
}
/// <summary>
/// Creates and returns a cone with the given dimensions.
/// </summary>
/// <param name="baseRadius">The radius of the base circle.</param>
/// <param name="dimensionY">The height of the cone.</param>
/// <param name="sliceCount">The horizontal resolution of the base circle. Min value is 3. For a basic cone 15.</param>
/// <returns></returns>
public static Geometry CreateConeGeometry(float baseRadius, float dimensionY, int sliceCount)
{
//check input
if (sliceCount < 3)
{
sliceCount = 3;
}
if (baseRadius <= 0 || dimensionY <= 0)
{
throw new ArgumentException("You can not input parameters <= 0");
}
var cone = new Geometry();
var northPole = new Vertex(cone.CreateVertHandleId(), new float3(0, dimensionY / 2, 0));
var southPole = new Vertex(cone.CreateVertHandleId(), new float3(0, -dimensionY / 2, 0));
var angleStep = System.Math.PI * 2 / sliceCount;
var yPos = -dimensionY / 2.0f;
int[] firstHandles = null; //stores the handles of the first slice to connect it later with the last slice
var lastH3 = new HalfEdge();
var lastH2 = new HalfEdge();
var lastVertex = southPole;
for (var i = 1; i < sliceCount + 1; i++)
{
var x = (float)System.Math.Cos(angleStep * i) * baseRadius;
var z = (float)System.Math.Sin(angleStep * i) * baseRadius;
var tempVertex = new Vertex(cone.CreateVertHandleId(), new float3(x, yPos, z));
//south to temp
var h1 = new HalfEdge(cone.CreateHalfEdgeHandleId());
var h2 = new HalfEdge(cone.CreateHalfEdgeHandleId()); //twin of h1
tempVertex.IncidentHalfEdge = h2.Handle;
h1.OriginVertex = southPole.Handle;
h2.OriginVertex = tempVertex.Handle;
h1.TwinHalfEdge = h2.Handle;
h2.TwinHalfEdge = h1.Handle;
//temp to north
var h3 = new HalfEdge(cone.CreateHalfEdgeHandleId());
var h4 = new HalfEdge(cone.CreateHalfEdgeHandleId());
northPole.IncidentHalfEdge = h3.Handle;
southPole.IncidentHalfEdge = h1.Handle;
h3.OriginVertex = northPole.Handle;
h4.OriginVertex = tempVertex.Handle;
h3.TwinHalfEdge = h4.Handle;
h4.TwinHalfEdge = h3.Handle;
if (lastVertex == southPole)
{
firstHandles = new[] { tempVertex.Handle, h1.Handle, h4.Handle };
lastH3 = h3;
lastH2 = h2;
cone.DictVertices.Add(tempVertex.Handle, tempVertex);
cone.DictHalfEdges.Add(h1.Handle, h1);
cone.DictHalfEdges.Add(h2.Handle, h2);
cone.DictHalfEdges.Add(h3.Handle, h3);
cone.DictHalfEdges.Add(h4.Handle, h4);
lastVertex = tempVertex;
continue;
}
//temp to last
var h5 = new HalfEdge(cone.CreateHalfEdgeHandleId());
var h6 = new HalfEdge(cone.CreateHalfEdgeHandleId());
h5.OriginVertex = lastVertex.Handle;
h6.OriginVertex = tempVertex.Handle;
h5.TwinHalfEdge = h6.Handle;
h6.TwinHalfEdge = h5.Handle;
//create top triangles south-temp-last
var triangle1 = new Face(cone.CreateFaceHandleId());
h5.NextHalfEdge = h4.Handle;
triangle1.OuterHalfEdge = h5.Handle;
h4.NextHalfEdge = lastH3.Handle;
lastH3.NextHalfEdge = h5.Handle;
h5.IncidentFace = triangle1.Handle;
h4.IncidentFace = triangle1.Handle;
lastH3.IncidentFace = triangle1.Handle;
h5.PrevHalfEdge = lastH3.Handle;
lastH3.PrevHalfEdge = h4.Handle;
h4.PrevHalfEdge = h5.Handle;
//north-last-temp
var triangle2 = new Face(cone.CreateFaceHandleId());
h6.NextHalfEdge = lastH2.Handle;
triangle2.OuterHalfEdge = h6.Handle;
lastH2.NextHalfEdge = h1.Handle;
h1.NextHalfEdge = h6.Handle;
h6.IncidentFace = triangle2.Handle;
lastH2.IncidentFace = triangle2.Handle;
h1.IncidentFace = triangle2.Handle;
h6.PrevHalfEdge = h1.Handle;
h1.PrevHalfEdge = lastH2.Handle;
lastH2.PrevHalfEdge = h6.Handle;
//write
cone.DictVertices.Add(tempVertex.Handle, tempVertex);
cone.DictHalfEdges.Add(h1.Handle, h1);
cone.DictHalfEdges.Add(h2.Handle, h2);
cone.DictHalfEdges.Add(h3.Handle, h3);
cone.DictHalfEdges.Add(h4.Handle, h4);
cone.DictHalfEdges.Add(h5.Handle, h5);
cone.DictHalfEdges.Add(h6.Handle, h6);
cone.ReplaceHalfEdge(lastH2);
cone.ReplaceHalfEdge(lastH3);
cone.DictFaces.Add(triangle1.Handle, triangle1);
cone.DictFaces.Add(triangle2.Handle, triangle2);
lastH2 = h2;
lastH3 = h3;
lastVertex = tempVertex;
}
//add south and north pole
cone.DictVertices.Add(southPole.Handle, southPole);
cone.DictVertices.Add(northPole.Handle, northPole);
//create last 2 triangles
var firstVertex = cone.GetVertexByHandle(firstHandles[0]);
var firtstH1 = cone.GetHalfEdgeByHandle(firstHandles[1]);
var firstH4 = cone.GetHalfEdgeByHandle(firstHandles[2]);
var lastH5 = new HalfEdge(cone.CreateHalfEdgeHandleId());
var lastH6 = new HalfEdge(cone.CreateHalfEdgeHandleId());
lastH5.OriginVertex = lastVertex.Handle;
lastH6.OriginVertex = firstVertex.Handle;
lastH5.TwinHalfEdge = lastH6.Handle;
lastH6.TwinHalfEdge = lastH5.Handle;
//create to triangles south-temp-last, north-last-temp
var triangleL1 = new Face(cone.CreateFaceHandleId())
{
OuterHalfEdge = lastH5.Handle
};
lastH5.NextHalfEdge = firstH4.Handle;
firstH4.NextHalfEdge = lastH3.Handle;
lastH3.NextHalfEdge = lastH5.Handle;
lastH5.IncidentFace = triangleL1.Handle;
firstH4.IncidentFace = triangleL1.Handle;
lastH3.IncidentFace = triangleL1.Handle;
lastH5.PrevHalfEdge = lastH3.Handle;
lastH3.PrevHalfEdge = firstH4.Handle;
firstH4.PrevHalfEdge = lastH5.Handle;
var triangleL2 = new Face(cone.CreateFaceHandleId())
{
OuterHalfEdge = lastH6.Handle
};
lastH6.NextHalfEdge = lastH2.Handle;
lastH2.NextHalfEdge = firtstH1.Handle;
firtstH1.NextHalfEdge = lastH6.Handle;
lastH6.IncidentFace = triangleL2.Handle;
lastH2.IncidentFace = triangleL2.Handle;
firtstH1.IncidentFace = triangleL2.Handle;
lastH6.PrevHalfEdge = firtstH1.Handle;
firtstH1.PrevHalfEdge = lastH2.Handle;
lastH2.PrevHalfEdge = lastH6.Handle;
//write
cone.ReplaceHalfEdge(firtstH1);
cone.DictHalfEdges.Add(lastH5.Handle, lastH5);
cone.DictHalfEdges.Add(lastH6.Handle, lastH6);
cone.ReplaceHalfEdge(lastH2);
cone.ReplaceHalfEdge(lastH3);
cone.ReplaceHalfEdge(firstH4);
cone.DictFaces.Add(triangleL1.Handle, triangleL1);
cone.DictFaces.Add(triangleL2.Handle, triangleL2);
//face normals
var allFaces = cone.GetAllFaces().ToList();
foreach (var face in allFaces)
{
cone.SetFaceNormal(cone.GetFaceVertices(face.Handle).ToList(), face);
}
return(cone);
}
