More code reorganization (for beta 4)
git-svn-id: https://triangle.svn.codeplex.com/svn@75021 0e2699bc-83d4-4a8f-98e7-55e24ab8c7a5
This commit is contained in:
SND\wo80_cp
@@ -0,0 +1,900 @@
|
||||
// -----------------------------------------------------------------------
|
||||
// <copyright file="Dwyer.cs">
|
||||
// Original Triangle code by Jonathan Richard Shewchuk, http://www.cs.cmu.edu/~quake/triangle.html
|
||||
// Triangle.NET code by Christian Woltering, http://triangle.codeplex.com/
|
||||
// </copyright>
|
||||
// -----------------------------------------------------------------------
|
||||
|
||||
namespace TriangleNet.Meshing.Algorithm
|
||||
{
|
||||
using System;
|
||||
using TriangleNet.Data;
|
||||
using TriangleNet.Log;
|
||||
|
||||
/// <summary>
|
||||
/// Builds a delaunay triangulation using the divide-and-conquer algorithm.
|
||||
/// </summary>
|
||||
/// <remarks>
|
||||
/// The divide-and-conquer bounding box
|
||||
///
|
||||
/// I originally implemented the divide-and-conquer and incremental Delaunay
|
||||
/// triangulations using the edge-based data structure presented by Guibas
|
||||
/// and Stolfi. Switching to a triangle-based data structure doubled the
|
||||
/// speed. However, I had to think of a few extra tricks to maintain the
|
||||
/// elegance of the original algorithms.
|
||||
///
|
||||
/// The "bounding box" used by my variant of the divide-and-conquer
|
||||
/// algorithm uses one triangle for each edge of the convex hull of the
|
||||
/// triangulation. These bounding triangles all share a common apical
|
||||
/// vertex, which is represented by NULL and which represents nothing.
|
||||
/// The bounding triangles are linked in a circular fan about this NULL
|
||||
/// vertex, and the edges on the convex hull of the triangulation appear
|
||||
/// opposite the NULL vertex. You might find it easiest to imagine that
|
||||
/// the NULL vertex is a point in 3D space behind the center of the
|
||||
/// triangulation, and that the bounding triangles form a sort of cone.
|
||||
///
|
||||
/// This bounding box makes it easy to represent degenerate cases. For
|
||||
/// instance, the triangulation of two vertices is a single edge. This edge
|
||||
/// is represented by two bounding box triangles, one on each "side" of the
|
||||
/// edge. These triangles are also linked together in a fan about the NULL
|
||||
/// vertex.
|
||||
///
|
||||
/// The bounding box also makes it easy to traverse the convex hull, as the
|
||||
/// divide-and-conquer algorithm needs to do.
|
||||
/// </remarks>
|
||||
class Dwyer
|
||||
{
|
||||
static Random rand = new Random(DateTime.Now.Millisecond);
|
||||
bool useDwyer = true;
|
||||
|
||||
Vertex[] sortarray;
|
||||
Mesh mesh;
|
||||
|
||||
/// <summary>
|
||||
/// Sort an array of vertices by x-coordinate, using the y-coordinate as a secondary key.
|
||||
/// </summary>
|
||||
/// <param name="left"></param>
|
||||
/// <param name="right"></param>
|
||||
/// <remarks>
|
||||
/// Uses quicksort. Randomized O(n log n) time. No, I did not make any of
|
||||
/// the usual quicksort mistakes.
|
||||
/// </remarks>
|
||||
void VertexSort(int left, int right)
|
||||
{
|
||||
int oleft = left;
|
||||
int oright = right;
|
||||
int arraysize = right - left + 1;
|
||||
int pivot;
|
||||
double pivotx, pivoty;
|
||||
Vertex temp;
|
||||
|
||||
if (arraysize < 32)
|
||||
{
|
||||
// Insertion sort
|
||||
for (int i = left + 1; i <= right; i++)
|
||||
{
|
||||
var a = sortarray[i];
|
||||
int j = i - 1;
|
||||
while (j >= left && (sortarray[j].x > a.x || (sortarray[j].x == a.x && sortarray[j].y > a.y)))
|
||||
{
|
||||
sortarray[j + 1] = sortarray[j];
|
||||
j--;
|
||||
}
|
||||
sortarray[j + 1] = a;
|
||||
}
|
||||
|
||||
return;
|
||||
}
|
||||
|
||||
// Choose a random pivot to split the array.
|
||||
pivot = rand.Next(left, right);
|
||||
pivotx = sortarray[pivot].x;
|
||||
pivoty = sortarray[pivot].y;
|
||||
// Split the array.
|
||||
left--;
|
||||
right++;
|
||||
while (left < right)
|
||||
{
|
||||
// Search for a vertex whose x-coordinate is too large for the left.
|
||||
do
|
||||
{
|
||||
left++;
|
||||
}
|
||||
while ((left <= right) && ((sortarray[left].x < pivotx) ||
|
||||
((sortarray[left].x == pivotx) &&
|
||||
(sortarray[left].y < pivoty))));
|
||||
// Search for a vertex whose x-coordinate is too small for the right.
|
||||
do
|
||||
{
|
||||
right--;
|
||||
}
|
||||
while ((left <= right) && ((sortarray[right].x > pivotx) ||
|
||||
((sortarray[right].x == pivotx) &&
|
||||
(sortarray[right].y > pivoty))));
|
||||
|
||||
if (left < right)
|
||||
{
|
||||
// Swap the left and right vertices.
|
||||
temp = sortarray[left];
|
||||
sortarray[left] = sortarray[right];
|
||||
sortarray[right] = temp;
|
||||
}
|
||||
}
|
||||
if (left > oleft)
|
||||
{
|
||||
// Recursively sort the left subset.
|
||||
VertexSort(oleft, left);
|
||||
}
|
||||
if (oright > right + 1)
|
||||
{
|
||||
// Recursively sort the right subset.
|
||||
VertexSort(right + 1, oright);
|
||||
}
|
||||
}
|
||||
|
||||
/// <summary>
|
||||
/// An order statistic algorithm, almost. Shuffles an array of vertices so that
|
||||
/// the first 'median' vertices occur lexicographically before the remaining vertices.
|
||||
/// </summary>
|
||||
/// <param name="left"></param>
|
||||
/// <param name="right"></param>
|
||||
/// <param name="median"></param>
|
||||
/// <param name="axis"></param>
|
||||
/// <remarks>
|
||||
/// Uses the x-coordinate as the primary key if axis == 0; the y-coordinate
|
||||
/// if axis == 1. Very similar to the vertexsort() procedure, but runs in
|
||||
/// randomized linear time.
|
||||
/// </remarks>
|
||||
void VertexMedian(int left, int right, int median, int axis)
|
||||
{
|
||||
int arraysize = right - left + 1;
|
||||
int oleft = left, oright = right;
|
||||
int pivot;
|
||||
double pivot1, pivot2;
|
||||
Vertex temp;
|
||||
|
||||
if (arraysize == 2)
|
||||
{
|
||||
// Recursive base case.
|
||||
if ((sortarray[left][axis] > sortarray[right][axis]) ||
|
||||
((sortarray[left][axis] == sortarray[right][axis]) &&
|
||||
(sortarray[left][1 - axis] > sortarray[right][1 - axis])))
|
||||
{
|
||||
temp = sortarray[right];
|
||||
sortarray[right] = sortarray[left];
|
||||
sortarray[left] = temp;
|
||||
}
|
||||
return;
|
||||
}
|
||||
// Choose a random pivot to split the array.
|
||||
pivot = rand.Next(left, right); //left + arraysize / 2;
|
||||
pivot1 = sortarray[pivot][axis];
|
||||
pivot2 = sortarray[pivot][1 - axis];
|
||||
|
||||
left--;
|
||||
right++;
|
||||
while (left < right)
|
||||
{
|
||||
// Search for a vertex whose x-coordinate is too large for the left.
|
||||
do
|
||||
{
|
||||
left++;
|
||||
}
|
||||
while ((left <= right) && ((sortarray[left][axis] < pivot1) ||
|
||||
((sortarray[left][axis] == pivot1) &&
|
||||
(sortarray[left][1 - axis] < pivot2))));
|
||||
// Search for a vertex whose x-coordinate is too small for the right.
|
||||
do
|
||||
{
|
||||
right--;
|
||||
}
|
||||
while ((left <= right) && ((sortarray[right][axis] > pivot1) ||
|
||||
((sortarray[right][axis] == pivot1) &&
|
||||
(sortarray[right][1 - axis] > pivot2))));
|
||||
if (left < right)
|
||||
{
|
||||
// Swap the left and right vertices.
|
||||
temp = sortarray[left];
|
||||
sortarray[left] = sortarray[right];
|
||||
sortarray[right] = temp;
|
||||
}
|
||||
}
|
||||
|
||||
// Unlike in vertexsort(), at most one of the following conditionals is true.
|
||||
if (left > median)
|
||||
{
|
||||
// Recursively shuffle the left subset.
|
||||
VertexMedian(oleft, left - 1, median, axis);
|
||||
}
|
||||
if (right < median - 1)
|
||||
{
|
||||
// Recursively shuffle the right subset.
|
||||
VertexMedian(right + 1, oright, median, axis);
|
||||
}
|
||||
}
|
||||
|
||||
/// <summary>
|
||||
/// Sorts the vertices as appropriate for the divide-and-conquer algorithm with
|
||||
/// alternating cuts.
|
||||
/// </summary>
|
||||
/// <param name="left"></param>
|
||||
/// <param name="right"></param>
|
||||
/// <param name="axis"></param>
|
||||
/// <remarks>
|
||||
/// Partitions by x-coordinate if axis == 0; by y-coordinate if axis == 1.
|
||||
/// For the base case, subsets containing only two or three vertices are
|
||||
/// always sorted by x-coordinate.
|
||||
/// </remarks>
|
||||
void AlternateAxes(int left, int right, int axis)
|
||||
{
|
||||
int arraysize = right - left + 1;
|
||||
int divider;
|
||||
|
||||
divider = arraysize >> 1;
|
||||
//divider += left; // TODO: check
|
||||
if (arraysize <= 3)
|
||||
{
|
||||
// Recursive base case: subsets of two or three vertices will be
|
||||
// handled specially, and should always be sorted by x-coordinate.
|
||||
axis = 0;
|
||||
}
|
||||
// Partition with a horizontal or vertical cut.
|
||||
VertexMedian(left, right, left + divider, axis);
|
||||
// Recursively partition the subsets with a cross cut.
|
||||
if (arraysize - divider >= 2)
|
||||
{
|
||||
if (divider >= 2)
|
||||
{
|
||||
AlternateAxes(left, left + divider - 1, 1 - axis);
|
||||
}
|
||||
AlternateAxes(left + divider, right, 1 - axis);
|
||||
}
|
||||
}
|
||||
|
||||
/// <summary>
|
||||
/// Merge two adjacent Delaunay triangulations into a single Delaunay triangulation.
|
||||
/// </summary>
|
||||
/// <param name="farleft">Bounding triangles of the left triangulation.</param>
|
||||
/// <param name="innerleft">Bounding triangles of the left triangulation.</param>
|
||||
/// <param name="innerright">Bounding triangles of the right triangulation.</param>
|
||||
/// <param name="farright">Bounding triangles of the right triangulation.</param>
|
||||
/// <param name="axis"></param>
|
||||
/// <remarks>
|
||||
/// This is similar to the algorithm given by Guibas and Stolfi, but uses
|
||||
/// a triangle-based, rather than edge-based, data structure.
|
||||
///
|
||||
/// The algorithm walks up the gap between the two triangulations, knitting
|
||||
/// them together. As they are merged, some of their bounding triangles
|
||||
/// are converted into real triangles of the triangulation. The procedure
|
||||
/// pulls each hull's bounding triangles apart, then knits them together
|
||||
/// like the teeth of two gears. The Delaunay property determines, at each
|
||||
/// step, whether the next "tooth" is a bounding triangle of the left hull
|
||||
/// or the right. When a bounding triangle becomes real, its apex is
|
||||
/// changed from NULL to a real vertex.
|
||||
///
|
||||
/// Only two new triangles need to be allocated. These become new bounding
|
||||
/// triangles at the top and bottom of the seam. They are used to connect
|
||||
/// the remaining bounding triangles (those that have not been converted
|
||||
/// into real triangles) into a single fan.
|
||||
///
|
||||
/// On entry, 'farleft' and 'innerleft' are bounding triangles of the left
|
||||
/// triangulation. The origin of 'farleft' is the leftmost vertex, and
|
||||
/// the destination of 'innerleft' is the rightmost vertex of the
|
||||
/// triangulation. Similarly, 'innerright' and 'farright' are bounding
|
||||
/// triangles of the right triangulation. The origin of 'innerright' and
|
||||
/// destination of 'farright' are the leftmost and rightmost vertices.
|
||||
///
|
||||
/// On completion, the origin of 'farleft' is the leftmost vertex of the
|
||||
/// merged triangulation, and the destination of 'farright' is the rightmost
|
||||
/// vertex.
|
||||
/// </remarks>
|
||||
void MergeHulls(ref Otri farleft, ref Otri innerleft, ref Otri innerright,
|
||||
ref Otri farright, int axis)
|
||||
{
|
||||
Otri leftcand = default(Otri), rightcand = default(Otri);
|
||||
Otri nextedge = default(Otri);
|
||||
Otri sidecasing = default(Otri), topcasing = default(Otri), outercasing = default(Otri);
|
||||
Otri checkedge = default(Otri);
|
||||
Otri baseedge = default(Otri);
|
||||
Vertex innerleftdest;
|
||||
Vertex innerrightorg;
|
||||
Vertex innerleftapex, innerrightapex;
|
||||
Vertex farleftpt, farrightpt;
|
||||
Vertex farleftapex, farrightapex;
|
||||
Vertex lowerleft, lowerright;
|
||||
Vertex upperleft, upperright;
|
||||
Vertex nextapex;
|
||||
Vertex checkvertex;
|
||||
bool changemade;
|
||||
bool badedge;
|
||||
bool leftfinished, rightfinished;
|
||||
|
||||
innerleftdest = innerleft.Dest();
|
||||
innerleftapex = innerleft.Apex();
|
||||
innerrightorg = innerright.Org();
|
||||
innerrightapex = innerright.Apex();
|
||||
// Special treatment for horizontal cuts.
|
||||
if (useDwyer && (axis == 1))
|
||||
{
|
||||
farleftpt = farleft.Org();
|
||||
farleftapex = farleft.Apex();
|
||||
farrightpt = farright.Dest();
|
||||
farrightapex = farright.Apex();
|
||||
// The pointers to the extremal vertices are shifted to point to the
|
||||
// topmost and bottommost vertex of each hull, rather than the
|
||||
// leftmost and rightmost vertices.
|
||||
while (farleftapex.y < farleftpt.y)
|
||||
{
|
||||
farleft.LnextSelf();
|
||||
farleft.SymSelf();
|
||||
farleftpt = farleftapex;
|
||||
farleftapex = farleft.Apex();
|
||||
}
|
||||
innerleft.Sym(ref checkedge);
|
||||
checkvertex = checkedge.Apex();
|
||||
while (checkvertex.y > innerleftdest.y)
|
||||
{
|
||||
checkedge.Lnext(ref innerleft);
|
||||
innerleftapex = innerleftdest;
|
||||
innerleftdest = checkvertex;
|
||||
innerleft.Sym(ref checkedge);
|
||||
checkvertex = checkedge.Apex();
|
||||
}
|
||||
while (innerrightapex.y < innerrightorg.y)
|
||||
{
|
||||
innerright.LnextSelf();
|
||||
innerright.SymSelf();
|
||||
innerrightorg = innerrightapex;
|
||||
innerrightapex = innerright.Apex();
|
||||
}
|
||||
farright.Sym(ref checkedge);
|
||||
checkvertex = checkedge.Apex();
|
||||
while (checkvertex.y > farrightpt.y)
|
||||
{
|
||||
checkedge.Lnext(ref farright);
|
||||
farrightapex = farrightpt;
|
||||
farrightpt = checkvertex;
|
||||
farright.Sym(ref checkedge);
|
||||
checkvertex = checkedge.Apex();
|
||||
}
|
||||
}
|
||||
// Find a line tangent to and below both hulls.
|
||||
do
|
||||
{
|
||||
changemade = false;
|
||||
// Make innerleftdest the "bottommost" vertex of the left hull.
|
||||
if (Primitives.CounterClockwise(innerleftdest, innerleftapex, innerrightorg) > 0.0)
|
||||
{
|
||||
innerleft.LprevSelf();
|
||||
innerleft.SymSelf();
|
||||
innerleftdest = innerleftapex;
|
||||
innerleftapex = innerleft.Apex();
|
||||
changemade = true;
|
||||
}
|
||||
// Make innerrightorg the "bottommost" vertex of the right hull.
|
||||
if (Primitives.CounterClockwise(innerrightapex, innerrightorg, innerleftdest) > 0.0)
|
||||
{
|
||||
innerright.LnextSelf();
|
||||
innerright.SymSelf();
|
||||
innerrightorg = innerrightapex;
|
||||
innerrightapex = innerright.Apex();
|
||||
changemade = true;
|
||||
}
|
||||
} while (changemade);
|
||||
|
||||
// Find the two candidates to be the next "gear tooth."
|
||||
innerleft.Sym(ref leftcand);
|
||||
innerright.Sym(ref rightcand);
|
||||
// Create the bottom new bounding triangle.
|
||||
mesh.MakeTriangle(ref baseedge);
|
||||
// Connect it to the bounding boxes of the left and right triangulations.
|
||||
baseedge.Bond(ref innerleft);
|
||||
baseedge.LnextSelf();
|
||||
baseedge.Bond(ref innerright);
|
||||
baseedge.LnextSelf();
|
||||
baseedge.SetOrg(innerrightorg);
|
||||
baseedge.SetDest(innerleftdest);
|
||||
// Apex is intentionally left NULL.
|
||||
|
||||
// Fix the extreme triangles if necessary.
|
||||
farleftpt = farleft.Org();
|
||||
if (innerleftdest == farleftpt)
|
||||
{
|
||||
baseedge.Lnext(ref farleft);
|
||||
}
|
||||
farrightpt = farright.Dest();
|
||||
if (innerrightorg == farrightpt)
|
||||
{
|
||||
baseedge.Lprev(ref farright);
|
||||
}
|
||||
// The vertices of the current knitting edge.
|
||||
lowerleft = innerleftdest;
|
||||
lowerright = innerrightorg;
|
||||
// The candidate vertices for knitting.
|
||||
upperleft = leftcand.Apex();
|
||||
upperright = rightcand.Apex();
|
||||
// Walk up the gap between the two triangulations, knitting them together.
|
||||
while (true)
|
||||
{
|
||||
// Have we reached the top? (This isn't quite the right question,
|
||||
// because even though the left triangulation might seem finished now,
|
||||
// moving up on the right triangulation might reveal a new vertex of
|
||||
// the left triangulation. And vice-versa.)
|
||||
leftfinished = Primitives.CounterClockwise(upperleft, lowerleft, lowerright) <= 0.0;
|
||||
rightfinished = Primitives.CounterClockwise(upperright, lowerleft, lowerright) <= 0.0;
|
||||
if (leftfinished && rightfinished)
|
||||
{
|
||||
// Create the top new bounding triangle.
|
||||
mesh.MakeTriangle(ref nextedge);
|
||||
nextedge.SetOrg(lowerleft);
|
||||
nextedge.SetDest(lowerright);
|
||||
// Apex is intentionally left NULL.
|
||||
// Connect it to the bounding boxes of the two triangulations.
|
||||
nextedge.Bond(ref baseedge);
|
||||
nextedge.LnextSelf();
|
||||
nextedge.Bond(ref rightcand);
|
||||
nextedge.LnextSelf();
|
||||
nextedge.Bond(ref leftcand);
|
||||
|
||||
// Special treatment for horizontal cuts.
|
||||
if (useDwyer && (axis == 1))
|
||||
{
|
||||
farleftpt = farleft.Org();
|
||||
farleftapex = farleft.Apex();
|
||||
farrightpt = farright.Dest();
|
||||
farrightapex = farright.Apex();
|
||||
farleft.Sym(ref checkedge);
|
||||
checkvertex = checkedge.Apex();
|
||||
// The pointers to the extremal vertices are restored to the
|
||||
// leftmost and rightmost vertices (rather than topmost and
|
||||
// bottommost).
|
||||
while (checkvertex.x < farleftpt.x)
|
||||
{
|
||||
checkedge.Lprev(ref farleft);
|
||||
farleftapex = farleftpt;
|
||||
farleftpt = checkvertex;
|
||||
farleft.Sym(ref checkedge);
|
||||
checkvertex = checkedge.Apex();
|
||||
}
|
||||
while (farrightapex.x > farrightpt.x)
|
||||
{
|
||||
farright.LprevSelf();
|
||||
farright.SymSelf();
|
||||
farrightpt = farrightapex;
|
||||
farrightapex = farright.Apex();
|
||||
}
|
||||
}
|
||||
return;
|
||||
}
|
||||
// Consider eliminating edges from the left triangulation.
|
||||
if (!leftfinished)
|
||||
{
|
||||
// What vertex would be exposed if an edge were deleted?
|
||||
leftcand.Lprev(ref nextedge);
|
||||
nextedge.SymSelf();
|
||||
nextapex = nextedge.Apex();
|
||||
// If nextapex is NULL, then no vertex would be exposed; the
|
||||
// triangulation would have been eaten right through.
|
||||
if (nextapex != null)
|
||||
{
|
||||
// Check whether the edge is Delaunay.
|
||||
badedge = Primitives.InCircle(lowerleft, lowerright, upperleft, nextapex) > 0.0;
|
||||
while (badedge)
|
||||
{
|
||||
// Eliminate the edge with an edge flip. As a result, the
|
||||
// left triangulation will have one more boundary triangle.
|
||||
nextedge.LnextSelf();
|
||||
nextedge.Sym(ref topcasing);
|
||||
nextedge.LnextSelf();
|
||||
nextedge.Sym(ref sidecasing);
|
||||
nextedge.Bond(ref topcasing);
|
||||
leftcand.Bond(ref sidecasing);
|
||||
leftcand.LnextSelf();
|
||||
leftcand.Sym(ref outercasing);
|
||||
nextedge.LprevSelf();
|
||||
nextedge.Bond(ref outercasing);
|
||||
// Correct the vertices to reflect the edge flip.
|
||||
leftcand.SetOrg(lowerleft);
|
||||
leftcand.SetDest(null);
|
||||
leftcand.SetApex(nextapex);
|
||||
nextedge.SetOrg(null);
|
||||
nextedge.SetDest(upperleft);
|
||||
nextedge.SetApex(nextapex);
|
||||
// Consider the newly exposed vertex.
|
||||
upperleft = nextapex;
|
||||
// What vertex would be exposed if another edge were deleted?
|
||||
sidecasing.Copy(ref nextedge);
|
||||
nextapex = nextedge.Apex();
|
||||
if (nextapex != null)
|
||||
{
|
||||
// Check whether the edge is Delaunay.
|
||||
badedge = Primitives.InCircle(lowerleft, lowerright, upperleft, nextapex) > 0.0;
|
||||
}
|
||||
else
|
||||
{
|
||||
// Avoid eating right through the triangulation.
|
||||
badedge = false;
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
// Consider eliminating edges from the right triangulation.
|
||||
if (!rightfinished)
|
||||
{
|
||||
// What vertex would be exposed if an edge were deleted?
|
||||
rightcand.Lnext(ref nextedge);
|
||||
nextedge.SymSelf();
|
||||
nextapex = nextedge.Apex();
|
||||
// If nextapex is NULL, then no vertex would be exposed; the
|
||||
// triangulation would have been eaten right through.
|
||||
if (nextapex != null)
|
||||
{
|
||||
// Check whether the edge is Delaunay.
|
||||
badedge = Primitives.InCircle(lowerleft, lowerright, upperright, nextapex) > 0.0;
|
||||
while (badedge)
|
||||
{
|
||||
// Eliminate the edge with an edge flip. As a result, the
|
||||
// right triangulation will have one more boundary triangle.
|
||||
nextedge.LprevSelf();
|
||||
nextedge.Sym(ref topcasing);
|
||||
nextedge.LprevSelf();
|
||||
nextedge.Sym(ref sidecasing);
|
||||
nextedge.Bond(ref topcasing);
|
||||
rightcand.Bond(ref sidecasing);
|
||||
rightcand.LprevSelf();
|
||||
rightcand.Sym(ref outercasing);
|
||||
nextedge.LnextSelf();
|
||||
nextedge.Bond(ref outercasing);
|
||||
// Correct the vertices to reflect the edge flip.
|
||||
rightcand.SetOrg(null);
|
||||
rightcand.SetDest(lowerright);
|
||||
rightcand.SetApex(nextapex);
|
||||
nextedge.SetOrg(upperright);
|
||||
nextedge.SetDest(null);
|
||||
nextedge.SetApex(nextapex);
|
||||
// Consider the newly exposed vertex.
|
||||
upperright = nextapex;
|
||||
// What vertex would be exposed if another edge were deleted?
|
||||
sidecasing.Copy(ref nextedge);
|
||||
nextapex = nextedge.Apex();
|
||||
if (nextapex != null)
|
||||
{
|
||||
// Check whether the edge is Delaunay.
|
||||
badedge = Primitives.InCircle(lowerleft, lowerright, upperright, nextapex) > 0.0;
|
||||
}
|
||||
else
|
||||
{
|
||||
// Avoid eating right through the triangulation.
|
||||
badedge = false;
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
if (leftfinished || (!rightfinished &&
|
||||
(Primitives.InCircle(upperleft, lowerleft, lowerright, upperright) > 0.0)))
|
||||
{
|
||||
// Knit the triangulations, adding an edge from 'lowerleft'
|
||||
// to 'upperright'.
|
||||
baseedge.Bond(ref rightcand);
|
||||
rightcand.Lprev(ref baseedge);
|
||||
baseedge.SetDest(lowerleft);
|
||||
lowerright = upperright;
|
||||
baseedge.Sym(ref rightcand);
|
||||
upperright = rightcand.Apex();
|
||||
}
|
||||
else
|
||||
{
|
||||
// Knit the triangulations, adding an edge from 'upperleft'
|
||||
// to 'lowerright'.
|
||||
baseedge.Bond(ref leftcand);
|
||||
leftcand.Lnext(ref baseedge);
|
||||
baseedge.SetOrg(lowerright);
|
||||
lowerleft = upperleft;
|
||||
baseedge.Sym(ref leftcand);
|
||||
upperleft = leftcand.Apex();
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
/// <summary>
|
||||
/// Recursively form a Delaunay triangulation by the divide-and-conquer method.
|
||||
/// </summary>
|
||||
/// <param name="left"></param>
|
||||
/// <param name="right"></param>
|
||||
/// <param name="axis"></param>
|
||||
/// <param name="farleft"></param>
|
||||
/// <param name="farright"></param>
|
||||
/// <remarks>
|
||||
/// Recursively breaks down the problem into smaller pieces, which are
|
||||
/// knitted together by mergehulls(). The base cases (problems of two or
|
||||
/// three vertices) are handled specially here.
|
||||
///
|
||||
/// On completion, 'farleft' and 'farright' are bounding triangles such that
|
||||
/// the origin of 'farleft' is the leftmost vertex (breaking ties by
|
||||
/// choosing the highest leftmost vertex), and the destination of
|
||||
/// 'farright' is the rightmost vertex (breaking ties by choosing the
|
||||
/// lowest rightmost vertex).
|
||||
/// </remarks>
|
||||
void DivconqRecurse(int left, int right, int axis,
|
||||
ref Otri farleft, ref Otri farright)
|
||||
{
|
||||
Otri midtri = default(Otri);
|
||||
Otri tri1 = default(Otri);
|
||||
Otri tri2 = default(Otri);
|
||||
Otri tri3 = default(Otri);
|
||||
Otri innerleft = default(Otri), innerright = default(Otri);
|
||||
double area;
|
||||
int vertices = right - left + 1;
|
||||
int divider;
|
||||
|
||||
if (vertices == 2)
|
||||
{
|
||||
// The triangulation of two vertices is an edge. An edge is
|
||||
// represented by two bounding triangles.
|
||||
mesh.MakeTriangle(ref farleft);
|
||||
farleft.SetOrg(sortarray[left]);
|
||||
farleft.SetDest(sortarray[left + 1]);
|
||||
// The apex is intentionally left NULL.
|
||||
mesh.MakeTriangle(ref farright);
|
||||
farright.SetOrg(sortarray[left + 1]);
|
||||
farright.SetDest(sortarray[left]);
|
||||
// The apex is intentionally left NULL.
|
||||
farleft.Bond(ref farright);
|
||||
farleft.LprevSelf();
|
||||
farright.LnextSelf();
|
||||
farleft.Bond(ref farright);
|
||||
farleft.LprevSelf();
|
||||
farright.LnextSelf();
|
||||
farleft.Bond(ref farright);
|
||||
|
||||
// Ensure that the origin of 'farleft' is sortarray[0].
|
||||
farright.Lprev(ref farleft);
|
||||
return;
|
||||
}
|
||||
else if (vertices == 3)
|
||||
{
|
||||
// The triangulation of three vertices is either a triangle (with
|
||||
// three bounding triangles) or two edges (with four bounding
|
||||
// triangles). In either case, four triangles are created.
|
||||
mesh.MakeTriangle(ref midtri);
|
||||
mesh.MakeTriangle(ref tri1);
|
||||
mesh.MakeTriangle(ref tri2);
|
||||
mesh.MakeTriangle(ref tri3);
|
||||
area = Primitives.CounterClockwise(sortarray[left], sortarray[left + 1], sortarray[left + 2]);
|
||||
if (area == 0.0)
|
||||
{
|
||||
// Three collinear vertices; the triangulation is two edges.
|
||||
midtri.SetOrg(sortarray[left]);
|
||||
midtri.SetDest(sortarray[left + 1]);
|
||||
tri1.SetOrg(sortarray[left + 1]);
|
||||
tri1.SetDest(sortarray[left]);
|
||||
tri2.SetOrg(sortarray[left + 2]);
|
||||
tri2.SetDest(sortarray[left + 1]);
|
||||
tri3.SetOrg(sortarray[left + 1]);
|
||||
tri3.SetDest(sortarray[left + 2]);
|
||||
// All apices are intentionally left NULL.
|
||||
midtri.Bond(ref tri1);
|
||||
tri2.Bond(ref tri3);
|
||||
midtri.LnextSelf();
|
||||
tri1.LprevSelf();
|
||||
tri2.LnextSelf();
|
||||
tri3.LprevSelf();
|
||||
midtri.Bond(ref tri3);
|
||||
tri1.Bond(ref tri2);
|
||||
midtri.LnextSelf();
|
||||
tri1.LprevSelf();
|
||||
tri2.LnextSelf();
|
||||
tri3.LprevSelf();
|
||||
midtri.Bond(ref tri1);
|
||||
tri2.Bond(ref tri3);
|
||||
// Ensure that the origin of 'farleft' is sortarray[0].
|
||||
tri1.Copy(ref farleft);
|
||||
// Ensure that the destination of 'farright' is sortarray[2].
|
||||
tri2.Copy(ref farright);
|
||||
}
|
||||
else
|
||||
{
|
||||
// The three vertices are not collinear; the triangulation is one
|
||||
// triangle, namely 'midtri'.
|
||||
midtri.SetOrg(sortarray[left]);
|
||||
tri1.SetDest(sortarray[left]);
|
||||
tri3.SetOrg(sortarray[left]);
|
||||
// Apices of tri1, tri2, and tri3 are left NULL.
|
||||
if (area > 0.0)
|
||||
{
|
||||
// The vertices are in counterclockwise order.
|
||||
midtri.SetDest(sortarray[left + 1]);
|
||||
tri1.SetOrg(sortarray[left + 1]);
|
||||
tri2.SetDest(sortarray[left + 1]);
|
||||
midtri.SetApex(sortarray[left + 2]);
|
||||
tri2.SetOrg(sortarray[left + 2]);
|
||||
tri3.SetDest(sortarray[left + 2]);
|
||||
}
|
||||
else
|
||||
{
|
||||
// The vertices are in clockwise order.
|
||||
midtri.SetDest(sortarray[left + 2]);
|
||||
tri1.SetOrg(sortarray[left + 2]);
|
||||
tri2.SetDest(sortarray[left + 2]);
|
||||
midtri.SetApex(sortarray[left + 1]);
|
||||
tri2.SetOrg(sortarray[left + 1]);
|
||||
tri3.SetDest(sortarray[left + 1]);
|
||||
}
|
||||
// The topology does not depend on how the vertices are ordered.
|
||||
midtri.Bond(ref tri1);
|
||||
midtri.LnextSelf();
|
||||
midtri.Bond(ref tri2);
|
||||
midtri.LnextSelf();
|
||||
midtri.Bond(ref tri3);
|
||||
tri1.LprevSelf();
|
||||
tri2.LnextSelf();
|
||||
tri1.Bond(ref tri2);
|
||||
tri1.LprevSelf();
|
||||
tri3.LprevSelf();
|
||||
tri1.Bond(ref tri3);
|
||||
tri2.LnextSelf();
|
||||
tri3.LprevSelf();
|
||||
tri2.Bond(ref tri3);
|
||||
// Ensure that the origin of 'farleft' is sortarray[0].
|
||||
tri1.Copy(ref farleft);
|
||||
// Ensure that the destination of 'farright' is sortarray[2].
|
||||
if (area > 0.0)
|
||||
{
|
||||
tri2.Copy(ref farright);
|
||||
}
|
||||
else
|
||||
{
|
||||
farleft.Lnext(ref farright);
|
||||
}
|
||||
}
|
||||
|
||||
return;
|
||||
}
|
||||
else
|
||||
{
|
||||
// Split the vertices in half.
|
||||
divider = vertices >> 1;
|
||||
// Recursively triangulate each half.
|
||||
DivconqRecurse(left, left + divider - 1, 1 - axis, ref farleft, ref innerleft);
|
||||
//DebugWriter.Session.Write(mesh, true);
|
||||
DivconqRecurse(left + divider, right, 1 - axis, ref innerright, ref farright);
|
||||
//DebugWriter.Session.Write(mesh, true);
|
||||
|
||||
// Merge the two triangulations into one.
|
||||
MergeHulls(ref farleft, ref innerleft, ref innerright, ref farright, axis);
|
||||
//DebugWriter.Session.Write(mesh, true);
|
||||
}
|
||||
}
|
||||
|
||||
/// <summary>
|
||||
/// Removes ghost triangles.
|
||||
/// </summary>
|
||||
/// <param name="startghost"></param>
|
||||
/// <returns>Number of vertices on the hull.</returns>
|
||||
int RemoveGhosts(ref Otri startghost)
|
||||
{
|
||||
Otri searchedge = default(Otri);
|
||||
Otri dissolveedge = default(Otri);
|
||||
Otri deadtriangle = default(Otri);
|
||||
Vertex markorg;
|
||||
|
||||
int hullsize;
|
||||
|
||||
bool noPoly = !mesh.behavior.Poly;
|
||||
|
||||
// Find an edge on the convex hull to start point location from.
|
||||
startghost.Lprev(ref searchedge);
|
||||
searchedge.SymSelf();
|
||||
Mesh.dummytri.neighbors[0] = searchedge;
|
||||
// Remove the bounding box and count the convex hull edges.
|
||||
startghost.Copy(ref dissolveedge);
|
||||
hullsize = 0;
|
||||
do
|
||||
{
|
||||
hullsize++;
|
||||
dissolveedge.Lnext(ref deadtriangle);
|
||||
dissolveedge.LprevSelf();
|
||||
dissolveedge.SymSelf();
|
||||
|
||||
// If no PSLG is involved, set the boundary markers of all the vertices
|
||||
// on the convex hull. If a PSLG is used, this step is done later.
|
||||
if (noPoly)
|
||||
{
|
||||
// Watch out for the case where all the input vertices are collinear.
|
||||
if (dissolveedge.triangle != Mesh.dummytri)
|
||||
{
|
||||
markorg = dissolveedge.Org();
|
||||
if (markorg.mark == 0)
|
||||
{
|
||||
markorg.mark = 1;
|
||||
}
|
||||
}
|
||||
}
|
||||
// Remove a bounding triangle from a convex hull triangle.
|
||||
dissolveedge.Dissolve();
|
||||
// Find the next bounding triangle.
|
||||
deadtriangle.Sym(ref dissolveedge);
|
||||
|
||||
// Delete the bounding triangle.
|
||||
mesh.TriangleDealloc(deadtriangle.triangle);
|
||||
} while (!dissolveedge.Equal(startghost));
|
||||
|
||||
return hullsize;
|
||||
}
|
||||
|
||||
/// <summary>
|
||||
/// Form a Delaunay triangulation by the divide-and-conquer method.
|
||||
/// </summary>
|
||||
/// <returns></returns>
|
||||
/// <remarks>
|
||||
/// Sorts the vertices, calls a recursive procedure to triangulate them, and
|
||||
/// removes the bounding box, setting boundary markers as appropriate.
|
||||
/// </remarks>
|
||||
public int Triangulate(Mesh m)
|
||||
{
|
||||
Otri hullleft = default(Otri), hullright = default(Otri);
|
||||
int divider;
|
||||
int i, j;
|
||||
|
||||
this.mesh = m;
|
||||
|
||||
//DebugWriter.Session.Start("test-dbg");
|
||||
|
||||
// Allocate an array of pointers to vertices for sorting.
|
||||
// TODO: use ToArray
|
||||
this.sortarray = new Vertex[m.invertices];
|
||||
i = 0;
|
||||
foreach (var v in m.vertices.Values)
|
||||
{
|
||||
sortarray[i++] = v;
|
||||
}
|
||||
// Sort the vertices.
|
||||
//Array.Sort(sortarray);
|
||||
VertexSort(0, m.invertices - 1);
|
||||
// Discard duplicate vertices, which can really mess up the algorithm.
|
||||
i = 0;
|
||||
for (j = 1; j < m.invertices; j++)
|
||||
{
|
||||
if ((sortarray[i].x == sortarray[j].x)
|
||||
&& (sortarray[i].y == sortarray[j].y))
|
||||
{
|
||||
if (Behavior.Verbose)
|
||||
{
|
||||
SimpleLog.Instance.Warning(
|
||||
String.Format("A duplicate vertex appeared and was ignored (ID {0}).", sortarray[j].hash),
|
||||
"DivConquer.DivconqDelaunay()");
|
||||
}
|
||||
sortarray[j].type = VertexType.UndeadVertex;
|
||||
m.undeads++;
|
||||
}
|
||||
else
|
||||
{
|
||||
i++;
|
||||
sortarray[i] = sortarray[j];
|
||||
}
|
||||
}
|
||||
i++;
|
||||
if (useDwyer)
|
||||
{
|
||||
// Re-sort the array of vertices to accommodate alternating cuts.
|
||||
divider = i >> 1;
|
||||
if (i - divider >= 2)
|
||||
{
|
||||
if (divider >= 2)
|
||||
{
|
||||
AlternateAxes(0, divider - 1, 1);
|
||||
}
|
||||
AlternateAxes(divider, i - 1, 1);
|
||||
}
|
||||
}
|
||||
|
||||
// Form the Delaunay triangulation.
|
||||
DivconqRecurse(0, i-1, 0, ref hullleft, ref hullright);
|
||||
|
||||
//DebugWriter.Session.Write(mesh);
|
||||
//DebugWriter.Session.Finish();
|
||||
|
||||
return RemoveGhosts(ref hullleft);
|
||||
}
|
||||
}
|
||||
}
|
||||
Reference in New Issue
Block a user