/// <summary>
/// Shows the specified tessellated solid in a Helix toolkit window.
/// </summary>
/// <param name="tessellatedSolid">The tessellated solid.</param>
public static void Show(TessellatedSolid tessellatedSolid)
{
var window = new MainWindow();
window.view1.Children.Add(MakeModelVisual3D(tessellatedSolid));
window.view1.ZoomExtentsWhenLoaded = true;
window.ShowDialog();
}
/// <summary>
/// When the tessellated solid is sliced at the specified plane, the contact surfaces are
/// described by the return ContactData object. This is a non-destructive function typically
/// used to find the shape and size of 2D surface on the prescribed plane..
/// </summary>
/// <param name="plane">The plane.</param>
/// <param name="ts">The ts.</param>
/// <returns>ContactData.</returns>
/// <exception cref="System.Exception">Contact Edges found that are not contained in loop.</exception>
public static ContactData DefineContact(Flat plane, TessellatedSolid ts)
{
var vertexDistancesToPlane = new double[ts.NumberOfVertices];
for (int i = 0; i < ts.NumberOfVertices; i++)
vertexDistancesToPlane[i] = ts.Vertices[i].Position.dotProduct(plane.Normal) - plane.DistanceToOrigin;
// the edges serve as the easiest way to identify where the solid is interacting with the plane.
// Instead of a foreach, the while loop lets us look ahead to known edges that are irrelevant.
var edgeHashSet = new HashSet<Edge>(ts.Edges);
// Contact elements are constructed and then later arranged into loops. Loops make up the returned object, ContactData.
var straddleContactElts = new List<ContactElement>();
var inPlaneContactElts = new List<CoincidentEdgeContactElement>();
while (edgeHashSet.Any())
{
// instead of the foreach, we have this while statement and these first 2 lines to enumerate over the edges.
var edge = edgeHashSet.First();
edgeHashSet.Remove(edge);
var toDistance = vertexDistancesToPlane[edge.To.IndexInList];
var fromDistance = vertexDistancesToPlane[edge.From.IndexInList];
if (StarMath.IsNegligible(toDistance) && StarMath.IsNegligible(fromDistance))
ContactElement.MakeInPlaneContactElement(plane, edge, edgeHashSet, vertexDistancesToPlane,
inPlaneContactElts);
else if ((toDistance > 0 && fromDistance < 0)
|| (toDistance < 0 && fromDistance > 0))
straddleContactElts.Add(new ThroughFaceContactElement(plane, edge, toDistance));
}
foreach (var contactElement in inPlaneContactElts)
{
// next, we find any additional vertices that just touch the plane but don't have in-plane edges
// to facilitate this we negate all vertices already captures in the inPlaneContactElts
vertexDistancesToPlane[contactElement.StartVertex.IndexInList] = double.NaN;
vertexDistancesToPlane[contactElement.EndVertex.IndexInList] = double.NaN;
}
for (int i = 0; i < ts.NumberOfVertices; i++)
{
if (!StarMath.IsNegligible(vertexDistancesToPlane[i])) continue;
var v = ts.Vertices[i];
PolygonalFace negativeFace, positiveFace;
if (ThroughVertexContactElement.FindNegativeAndPositiveFaces(plane, v, vertexDistancesToPlane,
out negativeFace, out positiveFace))
straddleContactElts.Add(new ThroughVertexContactElement(v, negativeFace, positiveFace));
}
straddleContactElts.AddRange(inPlaneContactElts);
var loops = new List<Loop>();
var numberOfTries = 0;
while (straddleContactElts.Any() && numberOfTries < straddleContactElts.Count)
{
// now build loops from stringing together contact elements
var loop = FindLoop(plane, straddleContactElts, vertexDistancesToPlane);
if (loop != null)
{
Debug.WriteLine(loops.Count + ": " + loop.MakeDebugContactString() + " ");
loops.Add(loop);
numberOfTries = 0;
}
else numberOfTries++;
}
if (straddleContactElts.Any()) Debug.WriteLine("Contact Edges found that are not contained in loop.");
return new ContactData(loops);
}
private static Visual3D MakeModelVisual3D(TessellatedSolid ts)
{
var defaultMaterial = MaterialHelper.CreateMaterial(
new Color
{
A = ts.SolidColor.A,
B = ts.SolidColor.B,
G = ts.SolidColor.G,
R = ts.SolidColor.R
});
if (ts.HasUniformColor)
{
var positions = ts.Faces.SelectMany(f => f.Vertices.Select(v => new Point3D(v.Position[0], v.Position[1], v.Position[2])));
var normals = ts.Faces.SelectMany(f => f.Vertices.Select(v => new Vector3D(f.Normal[0], f.Normal[1], f.Normal[2])));
return new ModelVisual3D
{
Content =
new GeometryModel3D
{
Geometry = new MeshGeometry3D
{
Positions = new Point3DCollection(positions),
// TriangleIndices = new Int32Collection(triIndices),
Normals = new Vector3DCollection(normals)
},
Material = defaultMaterial
}
};
}
var result = new ModelVisual3D();
foreach (var f in ts.Faces)
{
var vOrder = new Point3DCollection();
for (var i = 0; i < 3; i++)
vOrder.Add(new Point3D(f.Vertices[i].X, f.Vertices[i].Y, f.Vertices[i].Z));
var c = (f.color == null)
? defaultMaterial
: MaterialHelper.CreateMaterial(new Color { A = f.color.A, B = f.color.B, G = f.color.G, R = f.color.R });
result.Children.Add(new ModelVisual3D
{
Content =
new GeometryModel3D
{
Geometry = new MeshGeometry3D { Positions = vOrder },
Material = c
}
});
}
return result;
}
/// <summary>
/// Divides up contact.
/// </summary>
/// <param name="ts">The ts.</param>
/// <param name="contactData">The contact data.</param>
/// <param name="plane">The plane.</param>
/// <exception cref="System.Exception">face is supposed to be split at plane but lives only on one side</exception>
private static void DivideUpContact(TessellatedSolid ts, ContactData contactData, Flat plane)
{
var edgesToAdd = new List<Edge>();
var facesToAdd = new List<PolygonalFace>();
var verticesToAdd = new List<Vertex>();
var edgesToDelete = new List<Edge>();
var facesToDelete = new List<PolygonalFace>();
var edgesToModify = new List<Edge>();
foreach (var loop in contactData.AllLoops)
{
for (int i = 0; i < loop.Count; i++)
{
var ce = loop[i];
if (ce is CoincidentEdgeContactElement)
// If the contact element is at a coincident edge, then there is nothing to do in this stage. When contact element was
// created, it properly defined SplitFacePositive and SplitFaceNegative.
continue;
edgesToAdd.Add(ce.ContactEdge); // the contact edge is a new edge for the solid
edgesToModify.Add(ce.ContactEdge); // the contact edge will need to be linked to vertices and faces further down.
var faceToSplit = ce.SplitFacePositive; //faceToSplit will be removed, but before we do that, we use
facesToDelete.Add(faceToSplit); // use it to build the new 2 to 3 triangles
PolygonalFace positiveFace, negativeFace;
if (ce is ThroughVertexContactElement)
{
var vertPlaneDistances = //signed distances of faceToSplit's vertices from the plane
faceToSplit.Vertices.Select(
v => v.Position.dotProduct(plane.Normal) - plane.DistanceToOrigin).ToArray();
var maxIndex = vertPlaneDistances.FindIndex(vertPlaneDistances.Max());
var maxVert = faceToSplit.Vertices[maxIndex];
var minIndex = vertPlaneDistances.FindIndex(vertPlaneDistances.Min());
var minVert = faceToSplit.Vertices[minIndex];
positiveFace = new PolygonalFace(new[] { ce.ContactEdge.From, ce.ContactEdge.To, maxVert });
facesToAdd.Add(positiveFace);
negativeFace = new PolygonalFace(new[] { ce.ContactEdge.To, ce.ContactEdge.From, minVert });
facesToAdd.Add(negativeFace);
} //#+1 add v to f (both of these are done in the preceding PolygonalFace
//#+2 add f to v constructors as well as the one for thirdFace below)
else // then ce is a ThroughFaceContactElement
{
var tfce = (ThroughFaceContactElement)ce; // ce is renamed and recast as tfce
edgesToDelete.Add(tfce.SplitEdge);
verticesToAdd.Add(tfce.StartVertex);
Vertex positiveVertex, negativeVertex;
if (tfce.SplitEdge.To.Position.dotProduct(plane.Normal) > plane.DistanceToOrigin)
{
positiveVertex = tfce.SplitEdge.To;
negativeVertex = tfce.SplitEdge.From;
}
else
{
positiveVertex = tfce.SplitEdge.From;
negativeVertex = tfce.SplitEdge.To;
}
positiveFace =
new PolygonalFace(new[] { ce.ContactEdge.From, ce.ContactEdge.To, positiveVertex });
facesToAdd.Add(positiveFace);
negativeFace =
new PolygonalFace(new[] { ce.ContactEdge.To, ce.ContactEdge.From, negativeVertex });
facesToAdd.Add(negativeFace);
var positiveEdge = new Edge(positiveVertex, ce.ContactEdge.From, positiveFace, null, true,
true);
edgesToAdd.Add(positiveEdge);
edgesToModify.Add(positiveEdge);
var negativeEdge = new Edge(ce.ContactEdge.From, negativeVertex, negativeFace, null, true,
true);
edgesToAdd.Add(negativeEdge);
edgesToModify.Add(negativeEdge);
var otherVertex = faceToSplit.Vertices.First(v => v != positiveVertex && v != negativeVertex);
PolygonalFace thirdFace;
if (otherVertex.Position.dotProduct(plane.Normal) > plane.DistanceToOrigin)
{
thirdFace = new PolygonalFace(new[] { ce.ContactEdge.To, otherVertex, positiveVertex });
facesToAdd.Add(thirdFace);
edgesToAdd.Add(new Edge(ce.ContactEdge.To, positiveVertex, positiveFace, thirdFace, true, true));
}
else
{
thirdFace = new PolygonalFace(new[] { ce.ContactEdge.To, negativeVertex, otherVertex });
facesToAdd.Add(thirdFace);
edgesToAdd.Add(new Edge(negativeVertex, ce.ContactEdge.To, negativeFace, thirdFace, true, true));
}
// for the new edges in a through face this line accomplishes: +3 add f to e; +4 add e to f; +5 add v to e;
// +6 add e to v
}
loop[i] = new CoincidentEdgeContactElement
{
ContactEdge = ce.ContactEdge,
EndVertex = ce.ContactEdge.To,
StartVertex = ce.ContactEdge.From,
SplitFaceNegative = negativeFace,
SplitFacePositive = positiveFace
};
}
}
// -1 remove v from f - no need to do this as no v's are removed
foreach (var face in facesToDelete)
{
foreach (var vertex in face.Vertices)
vertex.Faces.Remove(face); //-2 remove f from v
foreach (var edge in face.Edges)
{
if (edgesToDelete.Contains(edge)) continue;
edgesToModify.Add(edge);
if (edge.OwnedFace == face) edge.OwnedFace = null; //-3 remove f from e
else edge.OtherFace = null;
}
}
//-4 remove e from f - no need to do as the only edges deleted are the ones between deleted faces
ts.RemoveFaces(facesToDelete);
// -5 remove v from e - not needed as no vertices are deleted (like -1 above)
foreach (var edge in edgesToDelete)
{
edge.From.Edges.Remove(edge); //-6 remove e from v
edge.To.Edges.Remove(edge);
}
ts.RemoveEdges(edgesToDelete);
// now to add new faces to modified edges
ts.AddVertices(verticesToAdd);
ts.AddFaces(facesToAdd);
foreach (var edge in edgesToModify)
{
var facesToAttach = facesToAdd.Where(f => f.Vertices.Contains(edge.To) && f.Vertices.Contains(edge.From)
&& !f.Edges.Contains(edge));
if (facesToAttach.Count() > 2) throw new Exception();
foreach (var face in facesToAttach)
{
face.Edges.Add(edge); //+4 add e to f
var fromIndex = face.Vertices.IndexOf(edge.From);
if ((fromIndex == face.Vertices.Count - 1 && face.Vertices[0] == edge.To)
|| (fromIndex < face.Vertices.Count - 1 && face.Vertices[fromIndex + 1] == edge.To))
edge.OwnedFace = face; //+3 add f to e
else edge.OtherFace = face;
}
}
ts.AddEdges(edgesToAdd);
}
private static List<TessellatedSolid> convertFaceListsToSolids(TessellatedSolid ts, List<List<PolygonalFace>> facesLists,
List<Loop> loops, Boolean onPositiveSide, Flat plane)
{
List<TessellatedSolid> solids = new List<TessellatedSolid>();
foreach (var facesList in facesLists)
{
// get a list of the vertex indices from the original solid
var vertIndices = facesList.SelectMany(f => f.Vertices.Select(v => v.IndexInList))
.Distinct().OrderBy(index => index).ToArray();
var numVertices = vertIndices.Count();
// get the set of connected loops for this list of faces. it could be one or it could be all
var connectedLoops = loops.Where(loop =>
(onPositiveSide && loop.Any(ce => facesList.Contains(ce.SplitFacePositive)))
|| (!onPositiveSide && loop.Any(ce => facesList.Contains(ce.SplitFaceNegative))))
.ToList();
// put the vertices from vertIndices in subSolidVertices, except those that are on the loop.
// you'll need to copy those.
var subSolidVertices = new Vertex[numVertices];
var indicesToCopy = connectedLoops.SelectMany(loop => loop.Select(ce => ce.StartVertex.IndexInList))
.OrderBy(index => index).ToArray();
var numIndicesToCopy = indicesToCopy.GetLength(0);
var newEdgeVertices = new Vertex[connectedLoops.Count][];
for (int i = 0; i < connectedLoops.Count; i++)
newEdgeVertices[i] = new Vertex[connectedLoops[i].Count];
var copyIndex = 0;
for (int i = 0; i < numVertices; i++)
{
Vertex vertexCopy;
if (copyIndex < numIndicesToCopy && vertIndices[i] == indicesToCopy[copyIndex])
{
var oldVertex = ts.Vertices[vertIndices[i]];
vertexCopy = oldVertex.Copy();
for (int j = 0; j < connectedLoops.Count; j++)
{
var k = connectedLoops[j].FindIndex(ce => ce.StartVertex == oldVertex);
newEdgeVertices[j][k] = vertexCopy;
}
foreach (var face in oldVertex.Faces.Where(face => facesList.Contains(face)))
{
face.Vertices.Remove(oldVertex);
face.Vertices.Add(vertexCopy);
vertexCopy.Faces.Add(face);
}
while (copyIndex < numIndicesToCopy && vertIndices[i] >= indicesToCopy[copyIndex])
copyIndex++;
}
else vertexCopy = ts.Vertices[vertIndices[i]];
vertexCopy.IndexInList = i;
subSolidVertices[i] = vertexCopy;
}
solids.Add(new TessellatedSolid(facesList, subSolidVertices, newEdgeVertices, onPositiveSide ? plane.Normal.multiply(-1) : plane.Normal,
connectedLoops.Select(loop => loop.IsPositive).ToArray()));
}
return solids;
}
/// <summary>
/// Performs the slicing operation on the prescribed flat plane. This destructively alters
/// the tessellated solid into one or more solids which are returned in the "out" parameter
/// lists.
/// </summary>
/// <param name="oldSolid">The old solid.</param>
/// <param name="plane">The plane.</param>
/// <param name="positiveSideSolids">The solids that are on the positive side of the plane
/// This means that are on the side that the normal faces.</param>
/// <param name="negativeSideSolids">The solids on the negative side of the plane.</param>
public static void OnFlat(TessellatedSolid ts, Flat plane,
out List<TessellatedSolid> positiveSideSolids, out List<TessellatedSolid> negativeSideSolids)
{
var contactData = DefineContact(plane, ts);
DivideUpContact(ts, contactData, plane);
var loops =
contactData.AllLoops.Where(loop => loop.All(
ce => !(ce.ContactEdge.Curvature == CurvatureType.Convex && ce is CoincidentEdgeContactElement))).ToList();
var allNegativeStartingFaces =
loops.SelectMany(loop => loop.Select(ce => ce.SplitFaceNegative)).ToList();
var allPositiveStartingFaces =
loops.SelectMany(loop => loop.Select(ce => ce.SplitFacePositive)).ToList();
var negativeSideFaceList = FindAllSolidsWithTheseFaces(allNegativeStartingFaces, allPositiveStartingFaces);
var positiveSideFaceList = FindAllSolidsWithTheseFaces(allPositiveStartingFaces, allNegativeStartingFaces);
negativeSideSolids = convertFaceListsToSolids(ts, negativeSideFaceList, loops, false, plane);
positiveSideSolids = convertFaceListsToSolids(ts, positiveSideFaceList, loops, true, plane);
}
private static BoundingBox Find_via_MC_ApproachOne(TessellatedSolid ts)
{
BoundingBox minBox = new BoundingBox();
var minVolume = double.PositiveInfinity;
foreach (var convexHullEdge in ts.ConvexHullEdges)
{
var rotAxis = convexHullEdge.Vector.normalize();
var n = convexHullEdge.OwnedFace.Normal;
var numSamples = (int)Math.Ceiling((Math.PI - convexHullEdge.InternalAngle) / MaxDeltaAngle);
var deltaAngle = (Math.PI - convexHullEdge.InternalAngle) / numSamples;
var edgeBBs = new BoundingBox[numSamples];
for (var i = 0; i < numSamples; i++)
{
double[] direction;
if (i == 0) direction = n;
else
{
var angleChange = i * deltaAngle;
var invCrossMatrix = new[,]
{
{n[0]*n[0], n[0]*n[1], n[0]*n[2]},
{n[1]*n[0], n[1]*n[1], n[1]*n[2]},
{n[2]*n[0], n[2]*n[1], n[2]*n[2]}
};
direction = invCrossMatrix.multiply(rotAxis.multiply(Math.Sin(angleChange)));
}
edgeBBs[i] = FindOBBAlongDirection(ts.ConvexHullVertices, direction);
if (edgeBBs[i].Volume < minVolume)
{
minBox = edgeBBs[i];
minVolume = minBox.Volume;
}
}
}
return minBox;
}
private static BoundingBox Find_via_PCA_Approach(TessellatedSolid ts)
{
throw new NotImplementedException();
}
/// <summary>
/// Orienteds the bounding box.
/// </summary>
/// <param name="ts">The ts.</param>
/// <returns>BoundingBox.</returns>
public static BoundingBox OrientedBoundingBox(TessellatedSolid ts)
{
return Find_via_MC_ApproachOne(ts);
}
/// <summary>
/// Copies this instance.
/// </summary>
/// <returns>TessellatedSolid.</returns>
public TessellatedSolid Copy()
{
var copyOfFaces = new PolygonalFace[NumberOfFaces];
for (var i = 0; i < NumberOfFaces; i++)
copyOfFaces[i] = Faces[i].Copy();
var copyOfVertices = new Vertex[NumberOfVertices];
for (var i = 0; i < NumberOfVertices; i++)
copyOfVertices[i] = Vertices[i].Copy();
for (var fIndex = 0; fIndex < NumberOfFaces; fIndex++)
{
var thisFace = copyOfFaces[fIndex];
var oldFace = Faces[fIndex];
var vertexIndices = new List<int>();
foreach (var oldVertex in oldFace.Vertices)
{
var vIndex = oldVertex.IndexInList;
vertexIndices.Add(vIndex);
var thisVertex = copyOfVertices[vIndex];
thisFace.Vertices.Add(thisVertex);
thisVertex.Faces.Add(thisFace);
}
}
Edge[] copyOfEdges = MakeEdges(copyOfFaces, copyOfVertices);
var copy = new TessellatedSolid
{
SurfaceArea = SurfaceArea,
Center = (double[])Center.Clone(),
Faces = copyOfFaces,
Vertices = copyOfVertices,
Edges = copyOfEdges,
Name = Name,
NumberOfFaces = NumberOfFaces,
NumberOfVertices = NumberOfVertices,
Volume = Volume,
XMax = XMax,
XMin = XMin,
YMax = YMax,
YMin = YMin,
ZMax = ZMax,
ZMin = ZMin
};
copy.CreateConvexHull();
return copy;
}
private static void TestSlice(TessellatedSolid ts)
{
//var a= ContactData.Divide(new Flat { DistanceToOrigin = 40 , Normal = new []{0,1.0,0} }, ts).Area;
// Debug.WriteLine(a);
//Console.ReadKey();
//return;
var now = DateTime.Now;
Debug.WriteLine("start...");
var crossAreas = new double[3][,];
List<TessellatedSolid> positiveSideSolids, negativeSideSolids;
Slice.OnFlat(ts, new Flat(0, new[] { 1.0, 0, 0 }), out positiveSideSolids, out negativeSideSolids);
}
//private static void TestClassification(TessellatedSolid ts)
//{
// TesselationToPrimitives.Run(ts);
//}
private static void TestOBB(TessellatedSolid ts)
{
var obb = MinimumEnclosure.OrientedBoundingBox(ts);
}
private static void TestXSections(TessellatedSolid ts)
{
var now = DateTime.Now;
Debug.WriteLine("start...");
var crossAreas = new double[3][,];
var maxSlices = 100;
var delta = Math.Max((ts.Bounds[1][0] - ts.Bounds[0][0]) / maxSlices,
Math.Max((ts.Bounds[1][1] - ts.Bounds[0][1]) / maxSlices,
(ts.Bounds[1][2] - ts.Bounds[0][2]) / maxSlices));
//Parallel.For(0, 3, i =>
for (int i = 0; i < 3; i++)
{
//var max = ts.Bounds[1][i];
//var min = ts.Bounds[0][i];
//var numSteps = (int)Math.Ceiling((max - min) / delta);
var coordValues = ts.Vertices.Select(v => v.Position[i]).Distinct().OrderBy(x => x).ToList();
var numSteps = coordValues.Count;
var direction = new double[3];
direction[i] = 1.0;
crossAreas[i] = new double[numSteps, 2];
for (var j = 0; j < numSteps; j++)
{
var dist = crossAreas[i][j, 0] = coordValues[j];
Console.WriteLine("slice at Coord " + i + " at " + coordValues[j]);
crossAreas[i][j, 1] = Slice.DefineContact(new Flat(dist, direction), ts).Area;
}
}//);
Debug.WriteLine("end...Time Elapsed = " + (DateTime.Now - now));
Console.ReadKey();
for (var i = 0; i < 3; i++)
{
Debug.WriteLine("\nfor direction " + i);
for (var j = 0; j < crossAreas[i].GetLength(0); j++)
{
Debug.WriteLine(crossAreas[i][j, 0] + ", " + crossAreas[i][j, 1]);
}
}
}
