/// <summary>
/// Инициализировать корпус, если Vertices.Length == Dimension.
/// </summary>
void InitSingle()
{
var vertices = new int[Dimension];
for (int i = 0; i < Vertices.Length; i++)
{
vertices[i] = i;
}
var newFace = FacePool[ObjectManager.GetFace()];
newFace.Vertices = vertices;
Array.Sort(vertices);
MathHelper.CalculateFacePlane(newFace, Center);
// Убедиться, что нормальная точка внизу в случае, если это используется для триангуляции
if (newFace.Normal[Dimension - 1] >= 0.0)
{
for (int i = 0; i < Dimension; i++)
{
newFace.Normal[i] *= -1.0;
}
newFace.Offset = -newFace.Offset;
newFace.IsNormalFlipped = !newFace.IsNormalFlipped;
}
ConvexFaces.Add(newFace.Index);
}
/// <summary>
/// Init the hull if Vertices.Length == Dimension.
/// </summary>
void InitSingle()
{
var vertices = new int[Dimension];
for (int i = 0; i < Vertices.Length; i++)
{
vertices[i] = i;
}
var newFace = FacePool[ObjectManager.GetFace()];
newFace.Vertices = vertices;
Array.Sort(vertices);
MathHelper.CalculateFacePlane(newFace, Center);
// Make sure the normal point downwards in case this is used for triangulation
if (newFace.Normal[Dimension - 1] >= 0.0)
{
for (int i = 0; i < Dimension; i++)
{
newFace.Normal[i] *= -1.0;
}
newFace.Offset = -newFace.Offset;
newFace.IsNormalFlipped = !newFace.IsNormalFlipped;
}
ConvexFaces.Add(newFace.Index);
}
/// <summary>
/// Find the (dimension+1) initial points and create the simplexes.
/// Creates the initial simplex of n+1 vertices by using points from the bounding box.
/// Special care is taken to ensure that the vertices chosen do not result in a degenerate shape
/// where vertices are collinear (co-planar, etc). This would technically be resolved when additional
/// vertices are checked in the main loop, but: 1) a degenerate simplex would not eliminate any other
/// vertices (thus no savings there), 2) the creation of the face normal is prone to error.
/// </summary>
private void CreateInitialSimplex()
{
var initialPoints = FindInitialPoints();
#region Create the first faces from (dimension + 1) vertices.
var faces = new int[NumOfDimensions + 1];
for (var i = 0; i < NumOfDimensions + 1; i++)
{
var vertices = new int[NumOfDimensions];
for (int j = 0, k = 0; j <= NumOfDimensions; j++)
{
if (i != j)
{
vertices[k++] = initialPoints[j];
}
}
var newFace = FacePool[ObjectManager.GetFace()];
newFace.Vertices = vertices;
Array.Sort(vertices);
mathHelper.CalculateFacePlane(newFace, Center);
faces[i] = newFace.Index;
}
// update the adjacency (check all pairs of faces)
for (var i = 0; i < NumOfDimensions; i++)
{
for (var j = i + 1; j < NumOfDimensions + 1; j++)
{
UpdateAdjacency(FacePool[faces[i]], FacePool[faces[j]]);
}
}
#endregion
#region Init the vertex beyond buffers.
foreach (var faceIndex in faces)
{
var face = FacePool[faceIndex];
FindBeyondVertices(face);
if (face.VerticesBeyond.Count == 0)
{
ConvexFaces.Add(face.Index); // The face is on the hull
}
else
{
UnprocessedFaces.Add(face);
}
}
#endregion
// Set all vertices to false (unvisited).
foreach (var vertex in initialPoints)
{
VertexVisited[vertex] = false;
}
}
/// <summary>
/// Commits a cone and adds a vertex to the convex hull.
/// </summary>
private void CommitCone()
{
// Fill the adjacency.
for (var i = 0; i < ConeFaceBuffer.Count; i++)
{
var face = ConeFaceBuffer[i];
var newFace = face.Face;
var adjacentFace = face.Pivot;
var oldFace = face.OldFace;
var orderedPivotIndex = face.FaceIndex;
newFace.AdjacentFaces[orderedPivotIndex] = adjacentFace.Index;
adjacentFace.AdjacentFaces[face.PivotIndex] = newFace.Index;
// let there be a connection.
for (var j = 0; j < NumOfDimensions; j++)
{
if (j == orderedPivotIndex) continue;
var connector = ObjectManager.GetConnector();
connector.Update(newFace, j, NumOfDimensions);
ConnectFace(connector);
}
// the id adjacent face on the hull? If so, we can use simple method to find beyond vertices.
if (adjacentFace.VerticesBeyond.Count == 0)
FindBeyondVertices(newFace, oldFace.VerticesBeyond);
// it is slightly more effective if the face with the lower number of beyond vertices comes first.
else if (adjacentFace.VerticesBeyond.Count < oldFace.VerticesBeyond.Count)
FindBeyondVertices(newFace, adjacentFace.VerticesBeyond, oldFace.VerticesBeyond);
else
FindBeyondVertices(newFace, oldFace.VerticesBeyond, adjacentFace.VerticesBeyond);
// This face will definitely lie on the hull
if (newFace.VerticesBeyond.Count == 0)
{
ConvexFaces.Add(newFace.Index);
UnprocessedFaces.Remove(newFace);
ObjectManager.DepositVertexBuffer(newFace.VerticesBeyond);
newFace.VerticesBeyond = EmptyBuffer;
}
else // Add the face to the list
{
UnprocessedFaces.Add(newFace);
}
// recycle the object.
ObjectManager.DepositDeferredFace(face);
}
// Recycle the affected faces.
for (var fIndex = 0; fIndex < AffectedFaceBuffer.Count; fIndex++)
{
var face = AffectedFaceBuffer[fIndex];
UnprocessedFaces.Remove(FacePool[face]);
ObjectManager.DepositFace(face);
}
}
/// <summary>
/// Find the (dimension+1) initial points and create the simplexes.
/// </summary>
void InitConvexHull()
{
if (Vertices.Length < Dimension)
{
// In this case, there cannot be a single convex face, so we return an empty result.
return;
}
else if (Vertices.Length == Dimension)
{
// The vertices are all on the hull and form a single simplex.
InitSingle();
return;
}
var extremes = FindExtremes();
var initialPoints = FindInitialPoints(extremes);
// Add the initial points to the convex hull.
foreach (var vertex in initialPoints)
{
CurrentVertex = vertex;
// update center must be called before adding the vertex.
UpdateCenter();
AddConvexVertex(vertex);
// Mark the vertex so that it's not included in any beyond set.
VertexMarks[vertex] = true;
}
// Create the initial simplexes.
var faces = CreateInitialHull();
// Init the vertex beyond buffers.
foreach (var faceIndex in faces)
{
var face = FacePool[faceIndex];
FindBeyondVertices(face);
if (face.VerticesBeyond.Count == 0)
{
ConvexFaces.Add(face.Index); // The face is on the hull
}
else
{
UnprocessedFaces.Add(face);
}
}
// Unmark the vertices
foreach (var vertex in initialPoints)
{
VertexMarks[vertex] = false;
}
}
/// <summary>
/// Найти (размер + 1) начальных точек и создать симплексы
/// </summary>
void InitConvexHull()
{
if (Vertices.Length < Dimension)
{
// В этом случае не может быть одной выпуклой поверхности, так что мы возвращаем пустой результат
return;
}
else if (Vertices.Length == Dimension)
{
// Все вершины на корпусе и образуют единый симплекс
InitSingle();
return;
}
var extremes = FindExtremes();
var initialPoints = FindInitialPoints(extremes);
// Добавление начальных точек в выпуклую оболочку
foreach (var vertex in initialPoints)
{
CurrentVertex = vertex;
// Центр обновления должен быть вызван, прежде чем добавить вершину
UpdateCenter();
// Отметьте вершину так, чтобы она не была включена за пределы
VertexMarks[vertex] = true;
}
// Создать начальный симплекс
var faces = CreateInitialHull(initialPoints);
// Инициализировать вершины за пределами буфера
foreach (var faceIndex in faces)
{
var face = FacePool[faceIndex];
FindBeyondVertices(face);
if (face.VerticesBeyond.Count == 0)
{
ConvexFaces.Add(face.Index); // The face is on the hull
}
else
{
UnprocessedFaces.Add(face);
}
}
// Снять выделение с вершин
foreach (var vertex in initialPoints)
{
VertexMarks[vertex] = false;
}
}
/// <summary>
/// Handles singular vertex.
/// </summary>
private void HandleSingular()
{
SingularVertices.Add(CurrentVertex);
// This means that all the affected faces must be on the hull and that all their "vertices beyond" are singular.
for (var fIndex = 0; fIndex < AffectedFaceBuffer.Count; fIndex++)
{
var face = FacePool[AffectedFaceBuffer[fIndex]];
var vb = face.VerticesBeyond;
for (var i = 0; i < vb.Count; i++)
{
SingularVertices.Add(vb[i]);
}
ConvexFaces.Add(face.Index);
UnprocessedFaces.Remove(face);
ObjectManager.DepositVertexBuffer(face.VerticesBeyond);
face.VerticesBeyond = EmptyBuffer;
}
}
/// <summary>
/// Рукоятки исключительных вершин
/// </summary>
void HandleSingular()
{
RollbackCenter();
SingularVertices.Add(CurrentVertex);
// Это означает, что все затронутые грани должны находиться на корпусе и что все "вершины за пределами" единичны
for (int fIndex = 0; fIndex < AffectedFaceBuffer.Count; fIndex++)
{
var face = FacePool[AffectedFaceBuffer[fIndex]];
var vb = face.VerticesBeyond;
for (int i = 0; i < vb.Count; i++)
{
SingularVertices.Add(vb[i]);
}
ConvexFaces.Add(face.Index);
UnprocessedFaces.Remove(face);
ObjectManager.DepositVertexBuffer(face.VerticesBeyond);
face.VerticesBeyond = EmptyBuffer;
}
}
/// <summary>
/// Фиксирует конус и добавляет вершину к выпуклой оболочки
/// </summary>
void CommitCone()
{
// Заполнение смежностей
for (int i = 0; i < ConeFaceBuffer.Count; i++)
{
var face = ConeFaceBuffer[i];
var newFace = face.Face;
var adjacentFace = face.Pivot;
var oldFace = face.OldFace;
var orderedPivotIndex = face.FaceIndex;
newFace.AdjacentFaces[orderedPivotIndex] = adjacentFace.Index;
adjacentFace.AdjacentFaces[face.PivotIndex] = newFace.Index;
// Пусть здесь будет соединение
for (int j = 0; j < Dimension; j++)
{
if (j == orderedPivotIndex)
{
continue;
}
var connector = ObjectManager.GetConnector();
connector.Update(newFace, j, Dimension);
ConnectFace(connector);
}
// Идентификатор смежной грани на корпусе? Если да, то мы можем использовать простой метод, чтобы найти вершины за пределами
if (adjacentFace.VerticesBeyond.Count == 0)
{
FindBeyondVertices(newFace, oldFace.VerticesBeyond);
}
// Это более эффективно, если грань с меньшим числом вершин не приходит первой
else if (adjacentFace.VerticesBeyond.Count < oldFace.VerticesBeyond.Count)
{
FindBeyondVertices(newFace, adjacentFace.VerticesBeyond, oldFace.VerticesBeyond);
}
else
{
FindBeyondVertices(newFace, oldFace.VerticesBeyond, adjacentFace.VerticesBeyond);
}
// Это лицо, грань, лежит на холме
if (newFace.VerticesBeyond.Count == 0)
{
ConvexFaces.Add(newFace.Index);
UnprocessedFaces.Remove(newFace);
ObjectManager.DepositVertexBuffer(newFace.VerticesBeyond);
newFace.VerticesBeyond = EmptyBuffer;
}
else // Добавить грань в список
{
UnprocessedFaces.Add(newFace);
}
// Утилизировать объект
ObjectManager.DepositDeferredFace(face);
}
// Утилизировать поврежденные грани
for (int fIndex = 0; fIndex < AffectedFaceBuffer.Count; fIndex++)
{
var face = AffectedFaceBuffer[fIndex];
UnprocessedFaces.Remove(FacePool[face]);
ObjectManager.DepositFace(face);
}
}