C# Otri.Apex方法代码示例

        /// <summary>
        /// Transform two triangles to two different triangles by flipping an edge 
        /// counterclockwise within a quadrilateral.
        /// </summary>
        /// <param name="flipedge">Handle to the edge that will be flipped.</param>
        /// <remarks>Imagine the original triangles, abc and bad, oriented so that the
        /// shared edge ab lies in a horizontal plane, with the vertex b on the left
        /// and the vertex a on the right. The vertex c lies below the edge, and
        /// the vertex d lies above the edge. The 'flipedge' handle holds the edge
        /// ab of triangle abc, and is directed left, from vertex a to vertex b.
        ///
        /// The triangles abc and bad are deleted and replaced by the triangles cdb
        /// and dca.  The triangles that represent abc and bad are NOT deallocated;
        /// they are reused for dca and cdb, respectively.  Hence, any handles that
        /// may have held the original triangles are still valid, although not
        /// directed as they were before.
        ///
        /// Upon completion of this routine, the 'flipedge' handle holds the edge
        /// dc of triangle dca, and is directed down, from vertex d to vertex c.
        /// (Hence, the two triangles have rotated counterclockwise.)
        ///
        /// WARNING:  This transformation is geometrically valid only if the
        /// quadrilateral adbc is convex.  Furthermore, this transformation is
        /// valid only if there is not a subsegment between the triangles abc and
        /// bad.  This routine does not check either of these preconditions, and
        /// it is the responsibility of the calling routine to ensure that they are
        /// met.  If they are not, the streets shall be filled with wailing and
        /// gnashing of teeth.
        /// 
        /// Terminology
        ///
        /// A "local transformation" replaces a small set of triangles with another
        /// set of triangles.  This may or may not involve inserting or deleting a
        /// vertex.
        ///
        /// The term "casing" is used to describe the set of triangles that are
        /// attached to the triangles being transformed, but are not transformed
        /// themselves.  Think of the casing as a fixed hollow structure inside
        /// which all the action happens.  A "casing" is only defined relative to
        /// a single transformation; each occurrence of a transformation will
        /// involve a different casing.
        /// </remarks>
        internal void Flip(ref Otri flipedge)
        {
            Otri botleft = default(Otri), botright = default(Otri);
            Otri topleft = default(Otri), topright = default(Otri);
            Otri top = default(Otri);
            Otri botlcasing = default(Otri), botrcasing = default(Otri);
            Otri toplcasing = default(Otri), toprcasing = default(Otri);
            Osub botlsubseg = default(Osub), botrsubseg = default(Osub);
            Osub toplsubseg = default(Osub), toprsubseg = default(Osub);
            Vertex leftvertex, rightvertex, botvertex;
            Vertex farvertex;

            // Identify the vertices of the quadrilateral.
            rightvertex = flipedge.Org();
            leftvertex = flipedge.Dest();
            botvertex = flipedge.Apex();
            flipedge.Sym(ref top);

            // SELF CHECK

            //if (top.triangle == dummytri)
            //{
            //    logger.Error("Attempt to flip on boundary.", "Mesh.Flip()");
            //    flipedge.LnextSelf();
            //    return;
            //}

            //if (checksegments)
            //{
            //    flipedge.SegPivot(ref toplsubseg);
            //    if (toplsubseg.ss != dummysub)
            //    {
            //        logger.Error("Attempt to flip a segment.", "Mesh.Flip()");
            //        flipedge.LnextSelf();
            //        return;
            //    }
            //}

            farvertex = top.Apex();

            // Identify the casing of the quadrilateral.
            top.Lprev(ref topleft);
            topleft.Sym(ref toplcasing);
            top.Lnext(ref topright);
            topright.Sym(ref toprcasing);
            flipedge.Lnext(ref botleft);
            botleft.Sym(ref botlcasing);
            flipedge.Lprev(ref botright);
            botright.Sym(ref botrcasing);
            // Rotate the quadrilateral one-quarter turn counterclockwise.
            topleft.Bond(ref botlcasing);
            botleft.Bond(ref botrcasing);
            botright.Bond(ref toprcasing);
            topright.Bond(ref toplcasing);

            if (checksegments)
            {
                // Check for subsegments and rebond them to the quadrilateral.
//.........这里部分代码省略.........

        bool RightOfHyperbola(ref Otri fronttri, Point newsite)
        {
            Vertex leftvertex, rightvertex;
            double dxa, dya, dxb, dyb;

            Statistic.HyperbolaCount++;

            leftvertex = fronttri.Dest();
            rightvertex = fronttri.Apex();
            if ((leftvertex.y < rightvertex.y) ||
                ((leftvertex.y == rightvertex.y) &&
                 (leftvertex.x < rightvertex.x)))
            {
                if (newsite.x >= rightvertex.x)
                {
                    return true;
                }
            }
            else
            {
                if (newsite.x <= leftvertex.x)
                {
                    return false;
                }
            }
            dxa = leftvertex.x - newsite.x;
            dya = leftvertex.y - newsite.y;
            dxb = rightvertex.x - newsite.x;
            dyb = rightvertex.y - newsite.y;
            return dya * (dxb * dxb + dyb * dyb) > dyb * (dxa * dxa + dya * dya);
        }

        /// <summary>
        /// Find the intersection of an existing segment and a segment that is being 
        /// inserted. Insert a vertex at the intersection, splitting an existing subsegment.
        /// </summary>
        /// <param name="splittri"></param>
        /// <param name="splitsubseg"></param>
        /// <param name="endpoint2"></param>
        /// <remarks>
        /// The segment being inserted connects the apex of splittri to endpoint2.
        /// splitsubseg is the subsegment being split, and MUST adjoin splittri.
        /// Hence, endpoints of the subsegment being split are the origin and
        /// destination of splittri.
        ///
        /// On completion, splittri is a handle having the newly inserted
        /// intersection point as its origin, and endpoint1 as its destination.
        /// </remarks>
        private void SegmentIntersection(ref Otri splittri, ref Osub splitsubseg, Vertex endpoint2)
        {
            Osub opposubseg = default(Osub);
            Vertex endpoint1;
            Vertex torg, tdest;
            Vertex leftvertex, rightvertex;
            Vertex newvertex;
            InsertVertexResult success;

            double ex, ey;
            double tx, ty;
            double etx, ety;
            double split, denom;

            // Find the other three segment endpoints.
            endpoint1 = splittri.Apex();
            torg = splittri.Org();
            tdest = splittri.Dest();
            // Segment intersection formulae; see the Antonio reference.
            tx = tdest.x - torg.x;
            ty = tdest.y - torg.y;
            ex = endpoint2.x - endpoint1.x;
            ey = endpoint2.y - endpoint1.y;
            etx = torg.x - endpoint2.x;
            ety = torg.y - endpoint2.y;
            denom = ty * ex - tx * ey;
            if (denom == 0.0)
            {
                logger.Error("Attempt to find intersection of parallel segments.",
                    "Mesh.SegmentIntersection()");
                throw new Exception("Attempt to find intersection of parallel segments.");
            }
            split = (ey * etx - ex * ety) / denom;

            // Create the new vertex.
            newvertex = new Vertex(
                torg.x + split * (tdest.x - torg.x),
                torg.y + split * (tdest.y - torg.y),
                splitsubseg.seg.boundary,
                this.nextras);

            newvertex.hash = this.hash_vtx++;
            newvertex.id = newvertex.hash;

            // Interpolate its attributes.
            for (int i = 0; i < nextras; i++)
            {
                newvertex.attributes[i] = torg.attributes[i] + split * (tdest.attributes[i] - torg.attributes[i]);
            }

            vertices.Add(newvertex.hash, newvertex);

            // Insert the intersection vertex.  This should always succeed.
            success = InsertVertex(newvertex, ref splittri, ref splitsubseg, false, false);
            if (success != InsertVertexResult.Successful)
            {
                logger.Error("Failure to split a segment.", "Mesh.SegmentIntersection()");
                throw new Exception("Failure to split a segment.");
            }
            // Record a triangle whose origin is the new vertex.
            newvertex.tri = splittri;
            if (steinerleft > 0)
            {
                steinerleft--;
            }

            // Divide the segment into two, and correct the segment endpoints.
            splitsubseg.SymSelf();
            splitsubseg.Pivot(ref opposubseg);
            splitsubseg.Dissolve();
            opposubseg.Dissolve();
            do
            {
                splitsubseg.SetSegOrg(newvertex);
                splitsubseg.NextSelf();
            } while (splitsubseg.seg != Mesh.dummysub);
            do
            {
                opposubseg.SetSegOrg(newvertex);
                opposubseg.NextSelf();
            } while (opposubseg.seg != Mesh.dummysub);

            // Inserting the vertex may have caused edge flips.  We wish to rediscover
            // the edge connecting endpoint1 to the new intersection vertex.
//.........这里部分代码省略.........

        /// <summary>
        /// Find the Delaunay triangulation of a polygon that has a certain "nice" shape. 
        /// This includes the polygons that result from deletion of a vertex or insertion 
        /// of a segment.
        /// </summary>
        /// <param name="firstedge">The primary edge of the first triangle.</param>
        /// <param name="lastedge">The primary edge of the last triangle.</param>
        /// <param name="edgecount">The number of sides of the polygon, including its 
        /// base.</param>
        /// <param name="doflip">A flag, wether to perform the last flip.</param>
        /// <param name="triflaws">A flag that determines whether the new triangles should 
        /// be tested for quality, and enqueued if they are bad.</param>
        /// <remarks>
        //  This is a conceptually difficult routine. The starting assumption is
        //  that we have a polygon with n sides. n - 1 of these sides are currently
        //  represented as edges in the mesh. One side, called the "base", need not
        //  be.
        //
        //  Inside the polygon is a structure I call a "fan", consisting of n - 1
        //  triangles that share a common origin. For each of these triangles, the
        //  edge opposite the origin is one of the sides of the polygon. The
        //  primary edge of each triangle is the edge directed from the origin to
        //  the destination; note that this is not the same edge that is a side of
        //  the polygon. 'firstedge' is the primary edge of the first triangle.
        //  From there, the triangles follow in counterclockwise order about the
        //  polygon, until 'lastedge', the primary edge of the last triangle.
        //  'firstedge' and 'lastedge' are probably connected to other triangles
        //  beyond the extremes of the fan, but their identity is not important, as
        //  long as the fan remains connected to them.
        //
        //  Imagine the polygon oriented so that its base is at the bottom.  This
        //  puts 'firstedge' on the far right, and 'lastedge' on the far left.
        //  The right vertex of the base is the destination of 'firstedge', and the
        //  left vertex of the base is the apex of 'lastedge'.
        //
        //  The challenge now is to find the right sequence of edge flips to
        //  transform the fan into a Delaunay triangulation of the polygon.  Each
        //  edge flip effectively removes one triangle from the fan, committing it
        //  to the polygon.  The resulting polygon has one fewer edge. If 'doflip'
        //  is set, the final flip will be performed, resulting in a fan of one
        //  (useless?) triangle. If 'doflip' is not set, the final flip is not
        //  performed, resulting in a fan of two triangles, and an unfinished
        //  triangular polygon that is not yet filled out with a single triangle.
        //  On completion of the routine, 'lastedge' is the last remaining triangle,
        //  or the leftmost of the last two.
        //
        //  Although the flips are performed in the order described above, the
        //  decisions about what flips to perform are made in precisely the reverse
        //  order. The recursive triangulatepolygon() procedure makes a decision,
        //  uses up to two recursive calls to triangulate the "subproblems"
        //  (polygons with fewer edges), and then performs an edge flip.
        //
        //  The "decision" it makes is which vertex of the polygon should be
        //  connected to the base. This decision is made by testing every possible
        //  vertex.  Once the best vertex is found, the two edges that connect this
        //  vertex to the base become the bases for two smaller polygons. These
        //  are triangulated recursively. Unfortunately, this approach can take
        //  O(n^2) time not only in the worst case, but in many common cases. It's
        //  rarely a big deal for vertex deletion, where n is rarely larger than
        //  ten, but it could be a big deal for segment insertion, especially if
        //  there's a lot of long segments that each cut many triangles. I ought to
        //  code a faster algorithm some day.
        /// </remarks>
        private void TriangulatePolygon(Otri firstedge, Otri lastedge,
                                int edgecount, bool doflip, bool triflaws)
        {
            Otri testtri = default(Otri);
            Otri besttri = default(Otri);
            Otri tempedge = default(Otri);
            Vertex leftbasevertex, rightbasevertex;
            Vertex testvertex;
            Vertex bestvertex;

            int bestnumber = 1;

            // Identify the base vertices.
            leftbasevertex = lastedge.Apex();
            rightbasevertex = firstedge.Dest();

            // Find the best vertex to connect the base to.
            firstedge.Onext(ref besttri);
            bestvertex = besttri.Dest();
            besttri.Copy(ref testtri);

            for (int i = 2; i <= edgecount - 2; i++)
            {
                testtri.OnextSelf();
                testvertex = testtri.Dest();
                // Is this a better vertex?
                if (Primitives.InCircle(leftbasevertex, rightbasevertex, bestvertex, testvertex) > 0.0)
                {
                    testtri.Copy(ref besttri);
                    bestvertex = testvertex;
                    bestnumber = i;
                }
            }

            if (bestnumber > 1)
            {
                // Recursively triangulate the smaller polygon on the right.
//.........这里部分代码省略.........

        /// <summary>
        /// Find the first triangle on the path from one point to another.
        /// </summary>
        /// <param name="searchtri"></param>
        /// <param name="searchpoint"></param>
        /// <returns>
        /// The return value notes whether the destination or apex of the found
        /// triangle is collinear with the two points in question.</returns>
        /// <remarks>
        /// Finds the triangle that intersects a line segment drawn from the
        /// origin of 'searchtri' to the point 'searchpoint', and returns the result
        /// in 'searchtri'. The origin of 'searchtri' does not change, even though
        /// the triangle returned may differ from the one passed in. This routine
        /// is used to find the direction to move in to get from one point to
        /// another.
        /// </remarks>
        private FindDirectionResult FindDirection(ref Otri searchtri, Vertex searchpoint)
        {
            Otri checktri = default(Otri);
            Vertex startvertex;
            Vertex leftvertex, rightvertex;
            double leftccw, rightccw;
            bool leftflag, rightflag;

            startvertex = searchtri.Org();
            rightvertex = searchtri.Dest();
            leftvertex = searchtri.Apex();
            // Is 'searchpoint' to the left?
            leftccw = Primitives.CounterClockwise(searchpoint, startvertex, leftvertex);
            leftflag = leftccw > 0.0;
            // Is 'searchpoint' to the right?
            rightccw = Primitives.CounterClockwise(startvertex, searchpoint, rightvertex);
            rightflag = rightccw > 0.0;
            if (leftflag && rightflag)
            {
                // 'searchtri' faces directly away from 'searchpoint'. We could go left
                // or right. Ask whether it's a triangle or a boundary on the left.
                searchtri.Onext(ref checktri);
                if (checktri.triangle == Mesh.dummytri)
                {
                    leftflag = false;
                }
                else
                {
                    rightflag = false;
                }
            }
            while (leftflag)
            {
                // Turn left until satisfied.
                searchtri.OnextSelf();
                if (searchtri.triangle == Mesh.dummytri)
                {
                    logger.Error("Unable to find a triangle on path.", "Mesh.FindDirection().1");
                    throw new Exception("Unable to find a triangle on path.");
                }
                leftvertex = searchtri.Apex();
                rightccw = leftccw;
                leftccw = Primitives.CounterClockwise(searchpoint, startvertex, leftvertex);
                leftflag = leftccw > 0.0;
            }
            while (rightflag)
            {
                // Turn right until satisfied.
                searchtri.OprevSelf();
                if (searchtri.triangle == Mesh.dummytri)
                {
                    logger.Error("Unable to find a triangle on path.", "Mesh.FindDirection().2");
                    throw new Exception("Unable to find a triangle on path.");
                }
                rightvertex = searchtri.Dest();
                leftccw = rightccw;
                rightccw = Primitives.CounterClockwise(startvertex, searchpoint, rightvertex);
                rightflag = rightccw > 0.0;
            }
            if (leftccw == 0.0)
            {
                return FindDirectionResult.Leftcollinear;
            }
            else if (rightccw == 0.0)
            {
                return FindDirectionResult.Rightcollinear;
            }
            else
            {
                return FindDirectionResult.Within;
            }
        }

        /// <summary>
        /// Scout the first triangle on the path from one endpoint to another, and check 
        /// for completion (reaching the second endpoint), a collinear vertex, or the 
        /// intersection of two segments.
        /// </summary>
        /// <param name="searchtri"></param>
        /// <param name="endpoint2"></param>
        /// <param name="newmark"></param>
        /// <returns>Returns true if the entire segment is successfully inserted, and false 
        /// if the job must be finished by ConstrainedEdge().</returns>
        /// <remarks>
        /// If the first triangle on the path has the second endpoint as its
        /// destination or apex, a subsegment is inserted and the job is done.
        ///
        /// If the first triangle on the path has a destination or apex that lies on
        /// the segment, a subsegment is inserted connecting the first endpoint to
        /// the collinear vertex, and the search is continued from the collinear
        /// vertex.
        ///
        /// If the first triangle on the path has a subsegment opposite its origin,
        /// then there is a segment that intersects the segment being inserted.
        /// Their intersection vertex is inserted, splitting the subsegment.
        /// </remarks>
        private bool ScoutSegment(ref Otri searchtri, Vertex endpoint2, int newmark)
        {
            Otri crosstri = default(Otri);
            Osub crosssubseg = default(Osub);
            Vertex leftvertex, rightvertex;
            FindDirectionResult collinear;

            collinear = FindDirection(ref searchtri, endpoint2);
            rightvertex = searchtri.Dest();
            leftvertex = searchtri.Apex();
            if (((leftvertex.x == endpoint2.x) && (leftvertex.y == endpoint2.y)) ||
                ((rightvertex.x == endpoint2.x) && (rightvertex.y == endpoint2.y)))
            {
                // The segment is already an edge in the mesh.
                if ((leftvertex.x == endpoint2.x) && (leftvertex.y == endpoint2.y))
                {
                    searchtri.LprevSelf();
                }
                // Insert a subsegment, if there isn't already one there.
                InsertSubseg(ref searchtri, newmark);
                return true;
            }
            else if (collinear == FindDirectionResult.Leftcollinear)
            {
                // We've collided with a vertex between the segment's endpoints.
                // Make the collinear vertex be the triangle's origin.
                searchtri.LprevSelf();
                InsertSubseg(ref searchtri, newmark);
                // Insert the remainder of the segment.
                return ScoutSegment(ref searchtri, endpoint2, newmark);
            }
            else if (collinear == FindDirectionResult.Rightcollinear)
            {
                // We've collided with a vertex between the segment's endpoints.
                InsertSubseg(ref searchtri, newmark);
                // Make the collinear vertex be the triangle's origin.
                searchtri.LnextSelf();
                // Insert the remainder of the segment.
                return ScoutSegment(ref searchtri, endpoint2, newmark);
            }
            else
            {
                searchtri.Lnext(ref crosstri);
                crosstri.SegPivot(ref crosssubseg);
                // Check for a crossing segment.
                if (crosssubseg.seg == Mesh.dummysub)
                {
                    return false;
                }
                else
                {
                    // Insert a vertex at the intersection.
                    SegmentIntersection(ref crosstri, ref crosssubseg, endpoint2);
                    crosstri.Copy(ref searchtri);
                    InsertSubseg(ref searchtri, newmark);
                    // Insert the remainder of the segment.
                    return ScoutSegment(ref searchtri, endpoint2, newmark);
                }
            }
        }

        /// <summary>
        /// Transform two triangles to two different triangles by flipping an edge 
        /// clockwise within a quadrilateral. Reverses the flip() operation so that 
        /// the data structures representing the triangles are back where they were 
        /// before the flip().
        /// </summary>
        /// <param name="flipedge"></param>
        /// <remarks>
        /// See above Flip() remarks for more information.
        ///
        /// Upon completion of this routine, the 'flipedge' handle holds the edge
        /// cd of triangle cdb, and is directed up, from vertex c to vertex d.
        /// (Hence, the two triangles have rotated clockwise.)
        /// </remarks>
        internal void Unflip(ref Otri flipedge)
        {
            Otri botleft = default(Otri), botright = default(Otri);
            Otri topleft = default(Otri), topright = default(Otri);
            Otri top = default(Otri);
            Otri botlcasing = default(Otri), botrcasing = default(Otri);
            Otri toplcasing = default(Otri), toprcasing = default(Otri);
            Osub botlsubseg = default(Osub), botrsubseg = default(Osub);
            Osub toplsubseg = default(Osub), toprsubseg = default(Osub);
            Vertex leftvertex, rightvertex, botvertex;
            Vertex farvertex;

            // Identify the vertices of the quadrilateral.
            rightvertex = flipedge.Org();
            leftvertex = flipedge.Dest();
            botvertex = flipedge.Apex();
            flipedge.Sym(ref top);

            farvertex = top.Apex();

            // Identify the casing of the quadrilateral.
            top.Lprev(ref topleft);
            topleft.Sym(ref toplcasing);
            top.Lnext(ref topright);
            topright.Sym(ref toprcasing);
            flipedge.Lnext(ref botleft);
            botleft.Sym(ref botlcasing);
            flipedge.Lprev(ref botright);
            botright.Sym(ref botrcasing);
            // Rotate the quadrilateral one-quarter turn clockwise.
            topleft.Bond(ref toprcasing);
            botleft.Bond(ref toplcasing);
            botright.Bond(ref botlcasing);
            topright.Bond(ref botrcasing);

            if (checksegments)
            {
                // Check for subsegments and rebond them to the quadrilateral.
                topleft.SegPivot(ref toplsubseg);
                botleft.SegPivot(ref botlsubseg);
                botright.SegPivot(ref botrsubseg);
                topright.SegPivot(ref toprsubseg);
                if (toplsubseg.seg == Mesh.dummysub)
                {
                    botleft.SegDissolve();
                }
                else
                {
                    botleft.SegBond(ref toplsubseg);
                }
                if (botlsubseg.seg == Mesh.dummysub)
                {
                    botright.SegDissolve();
                }
                else
                {
                    botright.SegBond(ref botlsubseg);
                }
                if (botrsubseg.seg == Mesh.dummysub)
                {
                    topright.SegDissolve();
                }
                else
                {
                    topright.SegBond(ref botrsubseg);
                }
                if (toprsubseg.seg == Mesh.dummysub)
                {
                    topleft.SegDissolve();
                }
                else
                {
                    topleft.SegBond(ref toprsubseg);
                }
            }

            // New vertex assignments for the rotated quadrilateral.
            flipedge.SetOrg(botvertex);
            flipedge.SetDest(farvertex);
            flipedge.SetApex(leftvertex);
            top.SetOrg(farvertex);
            top.SetDest(botvertex);
            top.SetApex(rightvertex);
        }

        /// <summary>
        /// Find a triangle or edge containing a given point.
        /// </summary>
        /// <param name="searchpoint">The point to locate.</param>
        /// <param name="searchtri">The triangle to start the search at.</param>
        /// <param name="stopatsubsegment"> If 'stopatsubsegment' is set, the search 
        /// will stop if it tries to walk through a subsegment, and will return OUTSIDE.</param>
        /// <returns>Location information.</returns>
        /// <remarks>
        /// Begins its search from 'searchtri'. It is important that 'searchtri'
        /// be a handle with the property that 'searchpoint' is strictly to the left
        /// of the edge denoted by 'searchtri', or is collinear with that edge and
        /// does not intersect that edge. (In particular, 'searchpoint' should not
        /// be the origin or destination of that edge.)
        ///
        /// These conditions are imposed because preciselocate() is normally used in
        /// one of two situations:
        ///
        /// (1)  To try to find the location to insert a new point.  Normally, we
        ///      know an edge that the point is strictly to the left of. In the
        ///      incremental Delaunay algorithm, that edge is a bounding box edge.
        ///      In Ruppert's Delaunay refinement algorithm for quality meshing,
        ///      that edge is the shortest edge of the triangle whose circumcenter
        ///      is being inserted.
        ///
        /// (2)  To try to find an existing point.  In this case, any edge on the
        ///      convex hull is a good starting edge. You must screen out the
        ///      possibility that the vertex sought is an endpoint of the starting
        ///      edge before you call preciselocate().
        ///
        /// On completion, 'searchtri' is a triangle that contains 'searchpoint'.
        ///
        /// This implementation differs from that given by Guibas and Stolfi.  It
        /// walks from triangle to triangle, crossing an edge only if 'searchpoint'
        /// is on the other side of the line containing that edge. After entering
        /// a triangle, there are two edges by which one can leave that triangle.
        /// If both edges are valid ('searchpoint' is on the other side of both
        /// edges), one of the two is chosen by drawing a line perpendicular to
        /// the entry edge (whose endpoints are 'forg' and 'fdest') passing through
        /// 'fapex'. Depending on which side of this perpendicular 'searchpoint'
        /// falls on, an exit edge is chosen.
        ///
        /// This implementation is empirically faster than the Guibas and Stolfi
        /// point location routine (which I originally used), which tends to spiral
        /// in toward its target.
        ///
        /// Returns ONVERTEX if the point lies on an existing vertex. 'searchtri'
        /// is a handle whose origin is the existing vertex.
        ///
        /// Returns ONEDGE if the point lies on a mesh edge. 'searchtri' is a
        /// handle whose primary edge is the edge on which the point lies.
        ///
        /// Returns INTRIANGLE if the point lies strictly within a triangle.
        /// 'searchtri' is a handle on the triangle that contains the point.
        ///
        /// Returns OUTSIDE if the point lies outside the mesh. 'searchtri' is a
        /// handle whose primary edge the point is to the right of.  This might
        /// occur when the circumcenter of a triangle falls just slightly outside
        /// the mesh due to floating-point roundoff error. It also occurs when
        /// seeking a hole or region point that a foolish user has placed outside
        /// the mesh.
        ///
        /// WARNING:  This routine is designed for convex triangulations, and will
        /// not generally work after the holes and concavities have been carved.
        /// However, it can still be used to find the circumcenter of a triangle, as
        /// long as the search is begun from the triangle in question.</remarks>
        public LocateResult PreciseLocate(Point searchpoint, ref Otri searchtri,
                                        bool stopatsubsegment)
        {
            Otri backtracktri = default(Otri);
            Osub checkedge = default(Osub);
            Vertex forg, fdest, fapex;
            float orgorient, destorient;
            bool moveleft;

            // Where are we?
            forg = searchtri.Org();
            fdest = searchtri.Dest();
            fapex = searchtri.Apex();
            while (true)
            {
                // Check whether the apex is the point we seek.
                if ((fapex.x == searchpoint.X) && (fapex.y == searchpoint.Y))
                {
                    searchtri.LprevSelf();
                    return LocateResult.OnVertex;
                }
                // Does the point lie on the other side of the line defined by the
                // triangle edge opposite the triangle's destination?
                destorient = Primitives.CounterClockwise(forg, fapex, searchpoint);
                // Does the point lie on the other side of the line defined by the
                // triangle edge opposite the triangle's origin?
                orgorient = Primitives.CounterClockwise(fapex, fdest, searchpoint);
                if (destorient > 0.0)
                {
                    if (orgorient > 0.0)
                    {
                        // Move left if the inner product of (fapex - searchpoint) and
                        // (fdest - forg) is positive.  This is equivalent to drawing
                        // a line perpendicular to the line (forg, fdest) and passing
//.........这里部分代码省略.........

        /// <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)
                {
//.........这里部分代码省略.........

        /// <summary>
        /// Check if given triangle is blinded by given segment.
        /// </summary>
        /// <param name="tri">Triangle.</param>
        /// <param name="seg">Segments</param>
        /// <returns>Returns true, if the triangle is blinded.</returns>
        private bool TriangleIsBlinded(ref Otri tri, ref Osub seg)
        {
            Point c, pt;

            Vertex torg = tri.Org();
            Vertex tdest = tri.Dest();
            Vertex tapex = tri.Apex();

            Vertex sorg = seg.Org();
            Vertex sdest = seg.Dest();

            c = this.points[tri.triangle.id];

            if (SegmentsIntersect(sorg, sdest, c, torg, out pt, true))
            {
                return true;
            }

            if (SegmentsIntersect(sorg, sdest, c, tdest, out pt, true))
            {
                return true;
            }

            if (SegmentsIntersect(sorg, sdest, c, tapex, out pt, true))
            {
                return true;
            }

            return false;
        }

        /// <summary>
        /// Test a triangle for quality and size.
        /// </summary>
        /// <param name="testtri">Triangle to check.</param>
        /// <remarks>
        /// Tests a triangle to see if it satisfies the minimum angle condition and
        /// the maximum area condition.  Triangles that aren't up to spec are added
        /// to the bad triangle queue.
        /// </remarks>
        public void TestTriangle(ref Otri testtri)
        {
            Otri tri1 = default(Otri), tri2 = default(Otri);
            Osub testsub = default(Osub);
            Vertex torg, tdest, tapex;
            Vertex base1, base2;
            Vertex org1, dest1, org2, dest2;
            Vertex joinvertex;
            double dxod, dyod, dxda, dyda, dxao, dyao;
            double dxod2, dyod2, dxda2, dyda2, dxao2, dyao2;
            double apexlen, orglen, destlen, minedge;
            double angle;
            double area;
            double dist1, dist2;

            double maxangle;

            torg = testtri.Org();
            tdest = testtri.Dest();
            tapex = testtri.Apex();
            dxod = torg.x - tdest.x;
            dyod = torg.y - tdest.y;
            dxda = tdest.x - tapex.x;
            dyda = tdest.y - tapex.y;
            dxao = tapex.x - torg.x;
            dyao = tapex.y - torg.y;
            dxod2 = dxod * dxod;
            dyod2 = dyod * dyod;
            dxda2 = dxda * dxda;
            dyda2 = dyda * dyda;
            dxao2 = dxao * dxao;
            dyao2 = dyao * dyao;
            // Find the lengths of the triangle's three edges.
            apexlen = dxod2 + dyod2;
            orglen = dxda2 + dyda2;
            destlen = dxao2 + dyao2;

            if ((apexlen < orglen) && (apexlen < destlen))
            {
                // The edge opposite the apex is shortest.
                minedge = apexlen;
                // Find the square of the cosine of the angle at the apex.
                angle = dxda * dxao + dyda * dyao;
                angle = angle * angle / (orglen * destlen);
                base1 = torg;
                base2 = tdest;
                testtri.Copy(ref tri1);
            }
            else if (orglen < destlen)
            {
                // The edge opposite the origin is shortest.
                minedge = orglen;
                // Find the square of the cosine of the angle at the origin.
                angle = dxod * dxao + dyod * dyao;
                angle = angle * angle / (apexlen * destlen);
                base1 = tdest;
                base2 = tapex;
                testtri.Lnext(ref tri1);
            }
            else
            {
                // The edge opposite the destination is shortest.
                minedge = destlen;
                // Find the square of the cosine of the angle at the destination.
                angle = dxod * dxda + dyod * dyda;
                angle = angle * angle / (apexlen * orglen);
                base1 = tapex;
                base2 = torg;
                testtri.Lprev(ref tri1);
            }

            if (behavior.VarArea || behavior.fixedArea || behavior.Usertest)
            {
                // Check whether the area is larger than permitted.
                area = 0.5 * (dxod * dyda - dyod * dxda);
                if (behavior.fixedArea && (area > behavior.MaxArea))
                {
                    // Add this triangle to the list of bad triangles.
                    queue.Enqueue(ref testtri, minedge, tapex, torg, tdest);
                    return;
                }

                // Nonpositive area constraints are treated as unconstrained.
                if ((behavior.VarArea) && (area > testtri.triangle.area) && (testtri.triangle.area > 0.0))
                {
                    // Add this triangle to the list of bad triangles.
                    queue.Enqueue(ref testtri, minedge, tapex, torg, tdest);
                    return;
                }

                // Check whether the user thinks this triangle is too large.
//.........这里部分代码省略.........