| public static FindCircumcenter ( System.Point torg, System.Point tdest, System.Point tapex, double &xi, double &eta ) : System.Point | ||
| torg | System.Point | Triangle point. |
| tdest | System.Point | Triangle point. |
| tapex | System.Point | Triangle point. |
| xi | double | Relative coordinate of new location. |
| eta | double | Relative coordinate of new location. |
| return | System.Point | |
public static Point FindCircumcenter(Point torg, Point tdest, Point tapex,
ref double xi, ref double eta)
{
double xdo, ydo, xao, yao;
double dodist, aodist;
double denominator;
double dx, dy;
Statistic.CircumcenterCount++;
// Compute the circumcenter of the triangle.
xdo = tdest.x - torg.x;
ydo = tdest.y - torg.y;
xao = tapex.x - torg.x;
yao = tapex.y - torg.y;
dodist = xdo * xdo + ydo * ydo;
aodist = xao * xao + yao * yao;
if (Behavior.NoExact)
{
denominator = 0.5 / (xdo * yao - xao * ydo);
}
else
{
// Use the counterclockwise() routine to ensure a positive (and
// reasonably accurate) result, avoiding any possibility of
// division by zero.
denominator = 0.5 / CounterClockwise(tdest, tapex, torg);
// Don't count the above as an orientation test.
Statistic.CounterClockwiseCount--;
}
dx = (yao * dodist - ydo * aodist) * denominator;
dy = (xdo * aodist - xao * dodist) * denominator;
// To interpolate vertex attributes for the new vertex inserted at
// the circumcenter, define a coordinate system with a xi-axis,
// directed from the triangle's origin to its destination, and
// an eta-axis, directed from its origin to its apex.
// Calculate the xi and eta coordinates of the circumcenter.
xi = (yao * dx - xao * dy) * (2.0 * denominator);
eta = (xdo * dy - ydo * dx) * (2.0 * denominator);
return new Point(torg.x + dx, torg.y + dy);
}
| Primitives::FindCircumcenter ( System.Point torg, System.Point tdest, System.Point tapex, double &xi, double &eta, double offconstant ) : System.Point |
/// <summary>
/// Inserts a vertex at the circumcenter of a triangle. Deletes
/// the newly inserted vertex if it encroaches upon a segment.
/// </summary>
/// <param name="badtri"></param>
private void SplitTriangle(BadTriangle badtri)
{
Otri badotri = default(Otri);
Vertex borg, bdest, bapex;
Point newloc; // Location of the new vertex
float xi = 0, eta = 0;
InsertVertexResult success;
bool errorflag;
badotri = badtri.poortri;
borg = badotri.Org();
bdest = badotri.Dest();
bapex = badotri.Apex();
// Make sure that this triangle is still the same triangle it was
// when it was tested and determined to be of bad quality.
// Subsequent transformations may have made it a different triangle.
if (!Otri.IsDead(badotri.triangle) && (borg == badtri.triangorg) &&
(bdest == badtri.triangdest) && (bapex == badtri.triangapex))
{
errorflag = false;
// Create a new vertex at the triangle's circumcenter.
// Using the original (simpler) Steiner point location method
// for mesh refinement.
// TODO: NewLocation doesn't work for refinement. Why? Maybe
// reset VertexType?
if (behavior.fixedArea || behavior.VarArea)
{
newloc = Primitives.FindCircumcenter(borg, bdest, bapex, ref xi, ref eta, behavior.offconstant);
}
else
{
newloc = newLocation.FindLocation(borg, bdest, bapex, ref xi, ref eta, true, badotri);
}
// Check whether the new vertex lies on a triangle vertex.
if (((newloc.x == borg.x) && (newloc.y == borg.y)) ||
((newloc.x == bdest.x) && (newloc.y == bdest.y)) ||
((newloc.x == bapex.x) && (newloc.y == bapex.y)))
{
if (Behavior.Verbose)
{
logger.Warning("New vertex falls on existing vertex.", "Quality.SplitTriangle()");
errorflag = true;
}
}
else
{
// The new vertex must be in the interior, and therefore is a
// free vertex with a marker of zero.
Vertex newvertex = new Vertex(newloc.x, newloc.y, 0, mesh.nextras);
newvertex.type = VertexType.FreeVertex;
for (int i = 0; i < mesh.nextras; i++)
{
// Interpolate the vertex attributes at the circumcenter.
newvertex.attributes[i] = borg.attributes[i]
+ xi * (bdest.attributes[i] - borg.attributes[i])
+ eta * (bapex.attributes[i] - borg.attributes[i]);
}
// Ensure that the handle 'badotri' does not represent the longest
// edge of the triangle. This ensures that the circumcenter must
// fall to the left of this edge, so point location will work.
// (If the angle org-apex-dest exceeds 90 degrees, then the
// circumcenter lies outside the org-dest edge, and eta is
// negative. Roundoff error might prevent eta from being
// negative when it should be, so I test eta against xi.)
if (eta < xi)
{
badotri.LprevSelf();
}
// Insert the circumcenter, searching from the edge of the triangle,
// and maintain the Delaunay property of the triangulation.
Osub tmp = default(Osub);
success = mesh.InsertVertex(newvertex, ref badotri, ref tmp, true, true);
if (success == InsertVertexResult.Successful)
{
newvertex.hash = mesh.hash_vtx++;
newvertex.id = newvertex.hash;
mesh.vertices.Add(newvertex.hash, newvertex);
if (mesh.steinerleft > 0)
{
mesh.steinerleft--;
}
}
else if (success == InsertVertexResult.Encroaching)
{
// If the newly inserted vertex encroaches upon a subsegment,
// delete the new vertex.
mesh.UndoVertex();
}
else if (success == InsertVertexResult.Violating)
{
// Failed to insert the new vertex, but some subsegment was
// marked as being encroached.
}
else
{ // success == DUPLICATEVERTEX
// Couldn't insert the new vertex because a vertex is already there.
if (Behavior.Verbose)
{
logger.Warning("New vertex falls on existing vertex.", "Quality.SplitTriangle()");
errorflag = true;
}
}
}
if (errorflag)
{
logger.Error("The new vertex is at the circumcenter of triangle: This probably "
+ "means that I am trying to refine triangles to a smaller size than can be "
+ "accommodated by the finite precision of floating point arithmetic.",
"Quality.SplitTriangle()");
throw new Exception("The new vertex is at the circumcenter of triangle.");
}
}
}