C# Otri.LprevSelf方法代码示例

        /// <summary>
        /// Enforce the Delaunay condition at an edge, fanning out recursively from 
        /// an existing vertex. Pay special attention to stacking inverted triangles.
        /// </summary>
        /// <param name="fixuptri"></param>
        /// <param name="leftside">Indicates whether or not fixuptri is to the left of 
        /// the segment being inserted. (Imagine that the segment is pointing up from
        /// endpoint1 to endpoint2.)</param>
        /// <remarks>
        /// This is a support routine for inserting segments into a constrained
        /// Delaunay triangulation.
        ///
        /// The origin of fixuptri is treated as if it has just been inserted, and
        /// the local Delaunay condition needs to be enforced. It is only enforced
        /// in one sector, however, that being the angular range defined by
        /// fixuptri.
        ///
        /// This routine also needs to make decisions regarding the "stacking" of
        /// triangles. (Read the description of ConstrainedEdge() below before
        /// reading on here, so you understand the algorithm.) If the position of
        /// the new vertex (the origin of fixuptri) indicates that the vertex before
        /// it on the polygon is a reflex vertex, then "stack" the triangle by
        /// doing nothing.  (fixuptri is an inverted triangle, which is how stacked
        /// triangles are identified.)
        ///
        /// Otherwise, check whether the vertex before that was a reflex vertex.
        /// If so, perform an edge flip, thereby eliminating an inverted triangle
        /// (popping it off the stack). The edge flip may result in the creation
        /// of a new inverted triangle, depending on whether or not the new vertex
        /// is visible to the vertex three edges behind on the polygon.
        ///
        /// If neither of the two vertices behind the new vertex are reflex
        /// vertices, fixuptri and fartri, the triangle opposite it, are not
        /// inverted; hence, ensure that the edge between them is locally Delaunay.
        /// </remarks>
        private void DelaunayFixup(ref Otri fixuptri, bool leftside)
        {
            Otri neartri = default(Otri);
            Otri fartri = default(Otri);
            Osub faredge = default(Osub);
            Vertex nearvertex, leftvertex, rightvertex, farvertex;

            fixuptri.Lnext(ref neartri);
            neartri.Sym(ref fartri);
            // Check if the edge opposite the origin of fixuptri can be flipped.
            if (fartri.triangle == Mesh.dummytri)
            {
                return;
            }
            neartri.SegPivot(ref faredge);
            if (faredge.seg != Mesh.dummysub)
            {
                return;
            }
            // Find all the relevant vertices.
            nearvertex = neartri.Apex();
            leftvertex = neartri.Org();
            rightvertex = neartri.Dest();
            farvertex = fartri.Apex();
            // Check whether the previous polygon vertex is a reflex vertex.
            if (leftside)
            {
                if (Primitives.CounterClockwise(nearvertex, leftvertex, farvertex) <= 0.0)
                {
                    // leftvertex is a reflex vertex too. Nothing can
                    // be done until a convex section is found.
                    return;
                }
            }
            else
            {
                if (Primitives.CounterClockwise(farvertex, rightvertex, nearvertex) <= 0.0)
                {
                    // rightvertex is a reflex vertex too.  Nothing can
                    // be done until a convex section is found.
                    return;
                }
            }
            if (Primitives.CounterClockwise(rightvertex, leftvertex, farvertex) > 0.0)
            {
                // fartri is not an inverted triangle, and farvertex is not a reflex
                // vertex.  As there are no reflex vertices, fixuptri isn't an
                // inverted triangle, either.  Hence, test the edge between the
                // triangles to ensure it is locally Delaunay.
                if (Primitives.InCircle(leftvertex, farvertex, rightvertex, nearvertex) <= 0.0)
                {
                    return;
                }
                // Not locally Delaunay; go on to an edge flip.
            }
            // else fartri is inverted; remove it from the stack by flipping.
            Flip(ref neartri);
            fixuptri.LprevSelf();    // Restore the origin of fixuptri after the flip.
            // Recursively process the two triangles that result from the flip.
            DelaunayFixup(ref fixuptri, leftside);
            DelaunayFixup(ref fartri, leftside);
        }

        /// <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>
        /// 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.........

//.........这里部分代码省略.........
                    // right triangle (largest angle is 90 degrees)
                    isObtuse = true;
                }
                else
                {
                    // nonobtuse
                    isObtuse = false;
                }
                /// RELOCATION	(LOCAL SMOOTHING) ///
                /// check for possible relocation of one of triangle's points ///				
                relocated = DoSmoothing(delotri, torg, tdest, tapex, ref newloc);
                /// if relocation is possible, delete that vertex and insert a vertex at the new location ///		
                if (relocated > 0)
                {
                    Statistic.RelocationCount++;

                    dx = newloc[0] - torg.x;
                    dy = newloc[1] - torg.y;
                    origin_x = torg.x;	// keep for later use
                    origin_y = torg.y;
                    switch (relocated)
                    {
                        case 1:
                            //printf("Relocate: (%f,%f)\n", torg[0],torg[1]);			
                            mesh.DeleteVertex(ref delotri);
                            break;
                        case 2:
                            //printf("Relocate: (%f,%f)\n", tdest[0],tdest[1]);			
                            delotri.LnextSelf();
                            mesh.DeleteVertex(ref delotri);
                            break;
                        case 3:
                            //printf("Relocate: (%f,%f)\n", tapex[0],tapex[1]);						
                            delotri.LprevSelf();
                            mesh.DeleteVertex(ref delotri);
                            break;
                    }
                }
                else
                {
                    // calculate radius of the petal according to angle constraint
                    // first find the visible region, PETAL
                    // find the center of the circle and radius
                    // choose minimum angle as the maximum of quality angle and the minimum angle of the bad triangle
                    minangle = Math.Acos((middleEdgeDist + longestEdgeDist - shortestEdgeDist) / (2 * Math.Sqrt(middleEdgeDist) * Math.Sqrt(longestEdgeDist))) * 180.0 / Math.PI;
                    if (behavior.MinAngle > minangle)
                    {
                        minangle = behavior.MinAngle;
                    }
                    else
                    {
                        minangle = minangle + 0.5;
                    }
                    petalRadius = Math.Sqrt(shortestEdgeDist) / (2 * Math.Sin(minangle * Math.PI / 180.0));
                    /// compute two possible centers of the petal ///
                    // finding the center
                    // first find the middle point of smallest edge
                    xMidOfShortestEdge = (middleAngleCorner.x + largestAngleCorner.x) / 2.0;
                    yMidOfShortestEdge = (middleAngleCorner.y + largestAngleCorner.y) / 2.0;
                    // two possible centers
                    xPetalCtr_1 = xMidOfShortestEdge + Math.Sqrt(petalRadius * petalRadius - (shortestEdgeDist / 4)) * (middleAngleCorner.y -
                        largestAngleCorner.y) / Math.Sqrt(shortestEdgeDist);
                    yPetalCtr_1 = yMidOfShortestEdge + Math.Sqrt(petalRadius * petalRadius - (shortestEdgeDist / 4)) * (largestAngleCorner.x -
                        middleAngleCorner.x) / Math.Sqrt(shortestEdgeDist);

                    xPetalCtr_2 = xMidOfShortestEdge - Math.Sqrt(petalRadius * petalRadius - (shortestEdgeDist / 4)) * (middleAngleCorner.y -

        /// <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'.
//.........这里部分代码省略.........

//.........这里部分代码省略.........
                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();

//.........这里部分代码省略.........
                    // right triangle (largest angle is 90 degrees)
                    isObtuse = true;
                }
                else
                {
                    // nonobtuse
                    isObtuse = false;
                }
                /// RELOCATION	(LOCAL SMOOTHING) ///
                /// check for possible relocation of one of triangle's points ///				
                relocated = DoSmoothing(delotri, torg, tdest, tapex, ref newloc);
                /// if relocation is possible, delete that vertex and insert a vertex at the new location ///		
                if (relocated > 0)
                {
                    Statistic.RelocationCount++;

                    dx = newloc[0] - torg.x;
                    dy = newloc[1] - torg.y;
                    origin_x = torg.x;	// keep for later use
                    origin_y = torg.y;
                    switch (relocated)
                    {
                        case 1:
                            //printf("Relocate: (%f,%f)\n", torg[0],torg[1]);			
                            mesh.DeleteVertex(ref delotri);
                            break;
                        case 2:
                            //printf("Relocate: (%f,%f)\n", tdest[0],tdest[1]);			
                            delotri.LnextSelf();
                            mesh.DeleteVertex(ref delotri);
                            break;
                        case 3:
                            //printf("Relocate: (%f,%f)\n", tapex[0],tapex[1]);						
                            delotri.LprevSelf();
                            mesh.DeleteVertex(ref delotri);
                            break;

                    }
                }
                else
                {
                    // calculate radius of the petal according to angle constraint
                    // first find the visible region, PETAL
                    // find the center of the circle and radius
                    petalRadius = UnityEngine.Mathf.Sqrt(shortestEdgeDist) / (2f * UnityEngine.Mathf.Sin(behavior.MinAngle * UnityEngine.Mathf.PI / 180.0f));
                    /// compute two possible centers of the petal ///
                    // finding the center
                    // first find the middle point of smallest edge
                    xMidOfShortestEdge = (middleAngleCorner.x + largestAngleCorner.x) / 2.0f;
                    yMidOfShortestEdge = (middleAngleCorner.y + largestAngleCorner.y) / 2.0f;
                    // two possible centers
                    xPetalCtr_1 = xMidOfShortestEdge + UnityEngine.Mathf.Sqrt(petalRadius * petalRadius - (shortestEdgeDist / 4)) * (middleAngleCorner.y -
                        largestAngleCorner.y) / UnityEngine.Mathf.Sqrt(shortestEdgeDist);
                    yPetalCtr_1 = yMidOfShortestEdge + UnityEngine.Mathf.Sqrt(petalRadius * petalRadius - (shortestEdgeDist / 4)) * (largestAngleCorner.x -
                        middleAngleCorner.x) / UnityEngine.Mathf.Sqrt(shortestEdgeDist);

                    xPetalCtr_2 = xMidOfShortestEdge - UnityEngine.Mathf.Sqrt(petalRadius * petalRadius - (shortestEdgeDist / 4)) * (middleAngleCorner.y -
                        largestAngleCorner.y) / UnityEngine.Mathf.Sqrt(shortestEdgeDist);
                    yPetalCtr_2 = yMidOfShortestEdge - UnityEngine.Mathf.Sqrt(petalRadius * petalRadius - (shortestEdgeDist / 4)) * (largestAngleCorner.x -
                        middleAngleCorner.x) / UnityEngine.Mathf.Sqrt(shortestEdgeDist);
                    // find the correct circle since there will be two possible circles
                    // calculate the distance to smallest angle corner
                    dxcenter1 = (xPetalCtr_1 - smallestAngleCorner.x) * (xPetalCtr_1 - smallestAngleCorner.x);
                    dycenter1 = (yPetalCtr_1 - smallestAngleCorner.y) * (yPetalCtr_1 - smallestAngleCorner.y);
                    dxcenter2 = (xPetalCtr_2 - smallestAngleCorner.x) * (xPetalCtr_2 - smallestAngleCorner.x);
                    dycenter2 = (yPetalCtr_2 - smallestAngleCorner.y) * (yPetalCtr_2 - smallestAngleCorner.y);