public double NormaErrorW2(Function u, Function du, FEMContext FEMContext)
{
double norma = 0;
for (int e = 0; e < FEMContext.Data.NT.GetLength(0); e++)
{
Point i = FEMContext.Data.CT[FEMContext.Data.NT[e].GetVertexID(0)];
Point j = FEMContext.Data.CT[FEMContext.Data.NT[e].GetVertexID(1)];
Point m = FEMContext.Data.CT[FEMContext.Data.NT[e].GetVertexID(2)];
Point point = new Point((i.X + j.X + m.X) / 3, (i.Y + j.Y + m.Y) / 3);
if (TriangleOnPoint(point, i, j, m))
{
double fi = CalculateArea(point, j, m) * FEMContext.X[FEMContext.Data.NT[e].GetVertexID(0)];
double fj = CalculateArea(i, point, m) * FEMContext.X[FEMContext.Data.NT[e].GetVertexID(1)];
double fm = CalculateArea(i, j, point) * FEMContext.X[FEMContext.Data.NT[e].GetVertexID(2)];
double Uh = (fi + fj + fm) / AreaTriangles[e];
double dUh = UhDerivative(e, FEMContext);
norma += (Math.Abs(Math.Pow(Uh - u(point.X), 2)) + Math.Abs(Math.Pow(dUh - du(point.X), 2))) * AreaTriangles[e];
}
else
{
MessageBox.Show("Exception - (NormaErrorW2)");
}
}
return(norma);
}
private double CalculateArea(Point i, Point j, Point m)
{
var matrix = new Matrix(new double[3, 3] {
{ 1, i.X, i.Y }, { 1, j.X, j.Y }, { 1, m.X, m.Y }
});
var result = matrix.Determinant3x3();
return(result / 2);
}
private TriangleNet.Geometry.Point Echelle(TriangleNet.Geometry.Point centre, TriangleNet.Geometry.Point point, double f)
{
gVecteur v = new gVecteur(point.X - centre.X, point.Y - centre.Y, 0);
v.Multiplier(f);
double x = centre.X + v.X;
double y = centre.Y + v.Y;
return(new TriangleNet.Geometry.Point(x, y));
}
private Point GetIncenter(ITriangle triangle)
{
Point incenter = new Point();
Vertex A = triangle.GetVertex(0), B = triangle.GetVertex(1), C = triangle.GetVertex(2);
double a = GetLength(B, C), b = GetLength(A, C), c = GetLength(A, B);
double p = a + b + c;
incenter.X = (a * A.X + b * B.X + c * C.X) / p;
incenter.Y = (a * A.Y + b * B.Y + c * C.Y) / p;
return(incenter);
}
private void CalculateAreas(FEMContext FEMContext)
{
this.AreaTriangles = new double[FEMContext.Data.NT.GetLength(0)];
for (int k = 0; k < FEMContext.Data.NT.GetLength(0); k++)
{
Point i = FEMContext.Data.CT[FEMContext.Data.NT[k].GetVertexID(0)];
Point j = FEMContext.Data.CT[FEMContext.Data.NT[k].GetVertexID(1)];
Point m = FEMContext.Data.CT[FEMContext.Data.NT[k].GetVertexID(2)];
AreaTriangles[k] = CalculateArea(i, j, m);
}
}
private TriangleNet.Geometry.Point TransformPt(TriangleNet.Geometry.Point Pt)
{
double[] arr = new double[3];
arr[0] = Pt.X;
arr[1] = Pt.Y;
arr[2] = 0;
MathPoint swPt = (MathPoint)Mu.CreatePoint(arr);
swPt = swPt.MultiplyTransform(xForm);
arr = swPt.ArrayData;
return(new TriangleNet.Geometry.Point(arr[0], arr[1]));
}
private void CalculateLength(FEMContext FEMContext)
{
this.LengthSegments = new double[FEMContext.Data.GT.Length][];
for (int border = 0; border < FEMContext.Data.GT.Length; border++)
{
LengthSegments[border] = new double[FEMContext.Data.GT[border].GetLength(0)];
for (int k = 0; k < FEMContext.Data.GT[border].GetLength(0); k++)
{
Point p1 = FEMContext.Data.CT[FEMContext.Data.GT[border][k, 0]];
Point p2 = FEMContext.Data.CT[FEMContext.Data.GT[border][k, 1]];
LengthSegments[border][k] = Length(p1, p2);
}
}
}
private bool TriangleOnPoint(Point point, Point i, Point j, Point m)
{
double a = Math.Round((i.X - point.X) * (j.Y - i.Y) - (j.X - i.X) * (i.Y - point.Y), 13);
double b = Math.Round((j.X - point.X) * (m.Y - j.Y) - (m.X - j.X) * (j.Y - point.Y), 13);
double c = Math.Round((m.X - point.X) * (i.Y - m.Y) - (i.X - m.X) * (m.Y - point.Y), 13);
if ((a >= 0 && b >= 0 && c >= 0) || (a <= 0 && b <= 0 && c <= 0))
{
return(true);
}
else
{
return(false);
}
}
private TriangleNet.Geometry.Point CalculateCenterOfGravity()
{
TriangleNet.Geometry.Point[] TVert = new TriangleNet.Geometry.Point[3];
double[] TSide = new double[4];
double[] Sum_TCenterXS_TCenterYS_S = new double[3];
TriangleNet.Geometry.Point ObjCenter = new TriangleNet.Geometry.Point();
foreach (Triangle triangle in mesh.Triangles)
{
//ulozim vrcholy trojuholnika do pola
for (int i = 0; i < 3; i++)
{
TVert[i] = new TriangleNet.Geometry.Point();
TVert[i].X = triangle.GetVertex(i).X;
TVert[i].Y = triangle.GetVertex(i).Y;
}
//dlzka stran do pola + obvod
TSide[3] = 0;
for (int i = 0; i < 3; i++)
{
TSide[i] = Math.Sqrt(Math.Pow((TVert[i].X - TVert[(i + 1) % 3].X), 2) + Math.Pow((TVert[i].Y - TVert[(i + 1) % 3].Y), 2));
TSide[3] += TSide[i];
}
//ratame obsah - heronov vzorec
TSide[3] = TSide[3] / 2;
double TS = 0;
TS = Math.Sqrt(TSide[3] * (TSide[3] - TSide[0]) * (TSide[3] - TSide[1]) * (TSide[3] - TSide[2]));
//ratame tazisko trojuholnika
double[] TC = new double[2];
TC[0] = TVert[0].X + 2 * ((TVert[1].X + (double)(TVert[2].X - TVert[1].X) / 2) - TVert[0].X) / 3;
TC[1] = TVert[0].Y + 2 * ((TVert[1].Y + (double)(TVert[2].Y - TVert[1].Y) / 2) - TVert[0].Y) / 3;
//pomocne sumy pre vyratanie taziska polygonu
Sum_TCenterXS_TCenterYS_S[0] += TC[0] * TS;
Sum_TCenterXS_TCenterYS_S[1] += TC[1] * TS;
Sum_TCenterXS_TCenterYS_S[2] += TS;
}
//suradnice taziska polygonu
ObjCenter.X = Sum_TCenterXS_TCenterYS_S[0] / Sum_TCenterXS_TCenterYS_S[2];
ObjCenter.Y = Sum_TCenterXS_TCenterYS_S[1] / Sum_TCenterXS_TCenterYS_S[2];
//procedura vypluje bod = tazisko
return(new TriangleNet.Geometry.Point(ObjCenter.X, ObjCenter.Y));
}
private double UhDerivative(int numberTriangle, FEMContext FEMContext)
{
double UhDer;
Point i = FEMContext.Data.CT[FEMContext.Data.NT[numberTriangle].GetVertexID(0)];
Point j = FEMContext.Data.CT[FEMContext.Data.NT[numberTriangle].GetVertexID(1)];
Point m = FEMContext.Data.CT[FEMContext.Data.NT[numberTriangle].GetVertexID(2)];
double bI = j.Y - m.Y;
double bJ = m.Y - i.Y;
double bM = i.Y - j.Y;
double Ui = FEMContext.X[FEMContext.Data.NT[numberTriangle].GetVertexID(0)];
double Uj = FEMContext.X[FEMContext.Data.NT[numberTriangle].GetVertexID(1)];
double Um = FEMContext.X[FEMContext.Data.NT[numberTriangle].GetVertexID(2)];
double sigma = 2 * AreaTriangles[numberTriangle];
UhDer = (Ui * bI + Uj * bJ + Um * bM) / sigma;
return(UhDer);
}
private void DrawCircle(ITriangle triangle)
{
Point incenter = GetIncenter(triangle);
var k = 80.0;
System.Windows.Point center = new System.Windows.Point
{
X = k * incenter.X + 250.0,
Y = k * incenter.Y + 100.0
};
double size = 10;
//add circle
Ellipse circle = new Ellipse()
{
Width = size,
Height = size,
Stroke = Brushes.Red
};
circle.SetValue(Canvas.LeftProperty, center.X - circle.Width / 2);
circle.SetValue(Canvas.TopProperty, center.Y - circle.Height / 2);
MainCanvas.Children.Add(circle);
//add ID
TextBlock triangleId = new TextBlock();
triangleId.Text = triangle.ID.ToString();
triangleId.Foreground = circle.Stroke;
Viewbox viewbox = new Viewbox();
viewbox.Visibility = Visibility.Visible;
viewbox.Stretch = Stretch.Uniform;
viewbox.Child = triangleId;
viewbox.Height = circle.Height / 2;
viewbox.Width = circle.Width / 2;
viewbox.MouseEnter += ViewBoxOnMouseDown;
viewbox.SetValue(Canvas.LeftProperty, center.X - viewbox.Width / 2);
viewbox.SetValue(Canvas.TopProperty, center.Y - viewbox.Height / 2);
MainCanvas.Children.Add(viewbox);
}
public double NormaW2Exact(Function u, Function du, FEMContext FEMContext)
{
double norma = 0;
for (int e = 0; e < FEMContext.Data.NT.GetLength(0); e++)
{
Point i = FEMContext.Data.CT[FEMContext.Data.NT[e].GetVertexID(0)];
Point j = FEMContext.Data.CT[FEMContext.Data.NT[e].GetVertexID(1)];
Point m = FEMContext.Data.CT[FEMContext.Data.NT[e].GetVertexID(2)];
Point point = new Point((i.X + j.X + m.X) / 3, (i.Y + j.Y + m.Y) / 3);
if (TriangleOnPoint(point, i, j, m))
{
norma += (Math.Pow(u(point.X), 2) + Math.Pow(du(point.X), 2)) * AreaTriangles[e];
}
else
{
MessageBox.Show("Exception - (NormaW2_Exact)");
}
}
return(Math.Sqrt(norma));
}
public static bool IsPointInPolygon(TriangleNet.Geometry.Point point, List <Vertex> poly)
{
bool inside = false;
double x = point.X;
double y = point.Y;
int count = poly.Count;
for (int i = 0, j = count - 1; i < count; i++)
{
if (((poly[i].Y < y && poly[j].Y >= y) || (poly[j].Y < y && poly[i].Y >= y)) &&
(poly[i].X <= x || poly[j].X <= x))
{
inside ^= (poly[i].X + (y - poly[i].Y) / (poly[j].Y - poly[i].Y) * (poly[j].X - poly[i].X) < x);
}
j = i;
}
return(inside);
}
public double NormaL2(FEMContext FEMContext)
{
double norma = 0;
for (int e = 0; e < FEMContext.Data.NT.GetLength(0); e++)
{
Point i = FEMContext.Data.CT[FEMContext.Data.NT[e].GetVertexID(0)];
Point j = FEMContext.Data.CT[FEMContext.Data.NT[e].GetVertexID(1)];
Point m = FEMContext.Data.CT[FEMContext.Data.NT[e].GetVertexID(2)];
Point point = new Point((i.X + j.X + m.X) / 3, (i.Y + j.Y + m.Y) / 3);
if (TriangleOnPoint(point, i, j, m))
{
double fi = CalculateArea(point, j, m) * FEMContext.X[FEMContext.Data.NT[e].GetVertexID(0)];
double fj = CalculateArea(point, m, i) * FEMContext.X[FEMContext.Data.NT[e].GetVertexID(1)];
double fm = CalculateArea(point, i, j) * FEMContext.X[FEMContext.Data.NT[e].GetVertexID(2)];
norma += Math.Pow((fi + fj + fm) / AreaTriangles[e], 2) * AreaTriangles[e];
}
else
{
MessageBox.Show("Exception - (NormaL2)");
}
}
return(Math.Sqrt(norma));
}
/// <summary>
/// Return true if the given point is inside the polygon, or false if it is not.
/// </summary>
/// <param name="point">The point to check.</param>
/// <param name="poly">The polygon (list of contour points).</param>
/// <returns></returns>
/// <remarks>
/// WARNING: If the point is exactly on the edge of the polygon, then the function
/// may return true or false.
///
/// See http://alienryderflex.com/polygon/
/// </remarks>
public static bool IsPointInPolygon(TriangleNet.Geometry.Point point, SectionContour contour,
List <SectionContour> otherContours)
{
bool inside = false;
double x = point.X;
double y = point.Y;
List <Vertex> poly = contour.Points.Select(p => new Vertex(p.X, p.Y)).ToList();
inside = IsPointInPolygon(point, poly);
if (inside)
{
foreach (var item in otherContours)
{
if (IsPointInPolygon(point, item.Points.Select(p => new Vertex(p.X, p.Y)).ToList()))
{
inside = false;
break;
}
}
}
return(inside);
}
protected override void Command()
{
Feature Fonction = MdlBase.eSelect_RecupererObjet <Feature>(1, -1);
MdlBase.eEffacerSelection();
Esquisse = Fonction.GetSpecificFeature2();
xForm = Esquisse.ModelToSketchTransform.Inverse();
Mu = App.Sw.GetMathUtility();
String fact = "0.8";
if (Interaction.InputBox("Facteur de décalage", "F :", ref fact) == DialogResult.OK)
{
if (!String.IsNullOrWhiteSpace(fact))
{
Double r = fact.eToDouble();
if (r != 0)
{
FacteurDecal = r;
}
}
}
var polygon = new Polygon();
if (Esquisse.GetSketchRegionCount() == 0)
{
return;
}
// On ajoute les contours
SketchRegion region = Esquisse.GetSketchRegions()[0];
Loop2 loop = region.GetFirstLoop();
int i = 0;
while (loop != null)
{
var ListPt = new List <TriangleNet.Geometry.Vertex>();
foreach (SolidWorks.Interop.sldworks.Vertex v in loop.GetVertices())
{
double[] pt = (double[])v.GetPoint();
ListPt.Add(new TriangleNet.Geometry.Vertex(pt[0], pt[1]));
}
polygon.Add(new Contour(ListPt, i++), !loop.IsOuter());
loop = loop.GetNext();
}
foreach (SketchPoint pt in Esquisse.GetSketchPoints2())
{
polygon.Add(new TriangleNet.Geometry.Vertex(pt.X, pt.Y));
}
var contraintes = new ConstraintOptions();
contraintes.ConformingDelaunay = true;
contraintes.SegmentSplitting = 0;
//var Qualite = new QualityOptions();
//Qualite.SteinerPoints = 0;
Mesh mesh = (Mesh)polygon.Triangulate(contraintes);
var voronoi = new BoundedVoronoi(mesh);
var SM = MdlBase.SketchManager;
SelectionnerSupportEsquisse();
SM.InsertSketch(false);
SM.AddToDB = true;
SM.DisplayWhenAdded = false;
List <TriangleNet.Geometry.Vertex> lstVertex = new List <TriangleNet.Geometry.Vertex>();
foreach (var v in mesh.Vertices)
{
lstVertex.Add(v);
}
foreach (var edge in mesh.Edges)
{
try
{
TriangleNet.Geometry.Point p1 = TransformPt(lstVertex[edge.P0]);
TriangleNet.Geometry.Point p2 = TransformPt(lstVertex[edge.P1]);
SM.CreateLine(p1.X, p1.Y, 0, p2.X, p2.Y, 0);
}
catch (Exception errDesc)
{ this.LogMethode(new Object[] { errDesc }); }
}
SM.DisplayWhenAdded = true;
SM.AddToDB = false;
SM.InsertSketch(true);
MdlBase.eEffacerSelection();
SelectionnerSupportEsquisse();
SM.InsertSketch(false);
SM.AddToDB = true;
SM.DisplayWhenAdded = false;
foreach (var t in mesh.Triangles)
{
try
{
TriangleNet.Geometry.Point p1 = TransformPt(lstVertex[t.GetVertexID(0)]);
TriangleNet.Geometry.Point p2 = TransformPt(lstVertex[t.GetVertexID(1)]);
TriangleNet.Geometry.Point p3 = TransformPt(lstVertex[t.GetVertexID(2)]);
TriangleNet.Geometry.Point centre = new TriangleNet.Geometry.Point();
centre.X = (p1.X + p2.X + p3.X) / 3.0;
centre.Y = (p1.Y + p2.Y + p3.Y) / 3.0;
TriangleNet.Geometry.Point pt1;
TriangleNet.Geometry.Point pt2;
pt1 = TransformPt(Echelle(centre, t.GetVertex(0), FacteurDecal));
pt2 = TransformPt(Echelle(centre, t.GetVertex(1), FacteurDecal));
SM.CreateLine(pt1.X, pt1.Y, 0, pt2.X, pt2.Y, 0);
pt1 = TransformPt(Echelle(centre, t.GetVertex(1), FacteurDecal));
pt2 = TransformPt(Echelle(centre, t.GetVertex(2), FacteurDecal));
SM.CreateLine(pt1.X, pt1.Y, 0, pt2.X, pt2.Y, 0);
pt1 = TransformPt(Echelle(centre, t.GetVertex(2), FacteurDecal));
pt2 = TransformPt(Echelle(centre, t.GetVertex(0), FacteurDecal));
SM.CreateLine(pt1.X, pt1.Y, 0, pt2.X, pt2.Y, 0);
}
catch (Exception errDesc)
{ this.LogMethode(new Object[] { errDesc }); }
}
SM.DisplayWhenAdded = true;
SM.AddToDB = false;
SM.InsertSketch(true);
MdlBase.eEffacerSelection();
SelectionnerSupportEsquisse();
SM.InsertSketch(false);
SM.AddToDB = true;
SM.DisplayWhenAdded = false;
foreach (var f in voronoi.Faces)
{
try
{
TriangleNet.Geometry.Point centre = f.generator;
foreach (var e in f.EnumerateEdges())
{
var pt1 = TransformPt(Echelle(centre, e.Origin, FacteurDecal));
var pt2 = TransformPt(Echelle(centre, e.Twin.Origin, FacteurDecal));
SM.CreateLine(pt1.X, pt1.Y, 0, pt2.X, pt2.Y, 0);
}
}
catch (Exception errDesc)
{ this.LogMethode(new Object[] { errDesc }); }
}
SM.DisplayWhenAdded = true;
SM.AddToDB = false;
SM.InsertSketch(true);
}
public static MyMath.Point getPoint(this TriangleNet.Geometry.Point p)
{
return(new MyMath.Point((float)p.X, (float)p.Y));
}
private double Length(Point p1, Point p2)
{
return(Math.Sqrt(Math.Pow(p1.X - p2.X, 2) + Math.Pow(p1.Y - p2.Y, 2)));
}
public static TriangleNet.Geometry.Point FindPointInPolygon(SectionContour contour, List <SectionContour> otherContours,
int limit, double eps = 2e-5)
{
List <Vertex> poly = contour.Points.Select(p => new Vertex(p.X, p.Y)).ToList();
var bounds = new TriangleNet.Geometry.Rectangle();
bounds.Expand(poly);
int length = poly.Count;
var test = new TriangleNet.Geometry.Point();
TriangleNet.Geometry.Point a, b, c; // Current corner points.
double bx, by;
double dx, dy;
double h;
var predicates = new RobustPredicates();
a = poly[0];
b = poly[1];
for (int i = 0; i < length; i++)
{
c = poly[(i + 2) % length];
// Corner point.
bx = b.X;
by = b.Y;
// NOTE: if we knew the contour points were in counterclockwise order, we
// could skip concave corners and search only in one direction.
h = predicates.CounterClockwise(a, b, c);
if (Math.Abs(h) < eps)
{
// Points are nearly co-linear. Use perpendicular direction.
dx = (c.Y - a.Y) / 2;
dy = (a.X - c.X) / 2;
}
else
{
// Direction [midpoint(a-c) -> corner point]
dx = (a.X + c.X) / 2 - bx;
dy = (a.Y + c.Y) / 2 - by;
}
// Move around the contour.
a = b;
b = c;
h = 1.0;
for (int j = 0; j < limit; j++)
{
// Search in direction.
test.X = bx + dx * h;
test.Y = by + dy * h;
if (bounds.Contains(test) && IsPointInPolygon(test, contour, otherContours))
{
return(test);
}
// Search in opposite direction (see NOTE above).
test.X = bx - dx * h;
test.Y = by - dy * h;
if (bounds.Contains(test) && IsPointInPolygon(test, contour, otherContours))
{
return(test);
}
h = h / 2;
}
}
throw new Exception();
}
