public IReadOnlyList <GaussPoint> GenerateIntegrationPoints(XContinuumElement2D element)
{
SortedSet <CartesianPoint> cartesianDelaunyPoints = crack.FindTriangleVertices(element);
IReadOnlyList <NaturalPoint> naturalDelaunyPoints =
FindNaturalPointsForTriangulation(element, cartesianDelaunyPoints);
IReadOnlyList <Triangle2D <NaturalPoint> > subtriangles;
if (double.IsPositiveInfinity(triangleOverElementArea))
{
subtriangles = triangulator.CreateMesh(naturalDelaunyPoints);
}
else
{
double elementArea = (ConvexPolygon2D.CreateUnsafe(element.Nodes)).ComputeArea();
subtriangles = triangulator.CreateMesh(naturalDelaunyPoints, triangleOverElementArea * elementArea);
}
var integrationPoints = new List <GaussPoint>();
foreach (Triangle2D <NaturalPoint> triangle in subtriangles)
{
integrationPoints.AddRange(GenerateIntegrationPointsOfTriangle(triangle));
}
return(integrationPoints);
}
// TODO: I should really cache these somehow, so that they can be accessible from the crack object. They are used at various points.
private (double positiveArea, double negativeArea) FindSignedAreasOfElement(ISingleCrack crack,
XContinuumElement2D element)
{
SortedSet <CartesianPoint> triangleVertices = crack.FindTriangleVertices(element);
IReadOnlyList <Triangle2D <CartesianPoint> > triangles = triangulator.CreateMesh(triangleVertices);
double positiveArea = 0.0;
double negativeArea = 0.0;
foreach (var triangle in triangles)
{
CartesianPoint v0 = triangle.Vertices[0];
CartesianPoint v1 = triangle.Vertices[1];
CartesianPoint v2 = triangle.Vertices[2];
double area = 0.5 * Math.Abs(v0.X * (v1.Y - v2.Y) + v1.X * (v2.Y - v0.Y) + v2.X * (v0.Y - v1.Y));
// The sign of the area can be derived from any node with body level set != 0
int sign = 0;
foreach (var vertex in triangle.Vertices)
{
XNode vertexAsNode = null;
foreach (var node in element.Nodes) // TODO: find a faster way to do this
{
if ((vertex.X == node.X) && (vertex.Y == node.Y))
{
vertexAsNode = node;
break;
}
}
if (vertexAsNode != null)
{
double distance = crack.SignedDistanceOf(vertexAsNode);
if (Math.Abs(distance) <= zeroDistanceTolerance)
{
sign = 0;
}
else
{
sign = Math.Sign(distance);
}
if (sign != 0)
{
break;
}
}
}
// If no node with non-zero body level set is found, then find the body level set of its centroid
if (sign == 0)
{
// Report this instance in DEBUG messages. It should not happen with linear level sets and only 1 crack.
//if (reports)
//{
// Console.WriteLine("--- DEBUG: Triangulation resulted in a triangle where no vertex is an element node. ---");
//}
var centroid = new CartesianPoint((v0.X + v1.X + v2.X) / 3.0, (v0.Y + v1.Y + v2.Y) / 3.0);
NaturalPoint centroidNatural = element.Interpolation.
CreateInverseMappingFor(element.Nodes).TransformPointCartesianToNatural(centroid);
EvalInterpolation2D centroidInterpolation =
element.Interpolation.EvaluateAllAt(element.Nodes, centroidNatural);
sign = Math.Sign(crack.SignedDistanceOf(centroidNatural, element, centroidInterpolation));
}
if (sign > 0)
{
positiveArea += area;
}
else if (sign < 0)
{
negativeArea += area;
}
else
{
throw new Exception(
"Even after finding the signed distance of its centroid, the sign of the area is unidentified");
}
}
return(positiveArea, negativeArea);
}