예제 #1
0
        /// <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 != null))
            {
                // 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.
                if (behavior.UserTest != null)
                {
                    if (behavior.UserTest(testtri.triangle, area))
                    {
                        queue.Enqueue(ref testtri, minedge, tapex, torg, tdest);
                        return;
                    }
                }
            }

            // find the maximum edge and accordingly the pqr orientation
            if ((apexlen > orglen) && (apexlen > destlen))
            {
                // The edge opposite the apex is longest.
                // maxedge = apexlen;
                // Find the cosine of the angle at the apex.
                maxangle = (orglen + destlen - apexlen) / (2 * Math.Sqrt(orglen * destlen));
            }
            else if (orglen > destlen)
            {
                // The edge opposite the origin is longest.
                // maxedge = orglen;
                // Find the cosine of the angle at the origin.
                maxangle = (apexlen + destlen - orglen) / (2 * Math.Sqrt(apexlen * destlen));
            }
            else
            {
                // The edge opposite the destination is longest.
                // maxedge = destlen;
                // Find the cosine of the angle at the destination.
                maxangle = (apexlen + orglen - destlen) / (2 * Math.Sqrt(apexlen * orglen));
            }

            // Check whether the angle is smaller than permitted.
            if ((angle > behavior.goodAngle) || (maxangle < behavior.maxGoodAngle && behavior.MaxAngle != 0.0))
            {
                // Use the rules of Miller, Pav, and Walkington to decide that certain
                // triangles should not be split, even if they have bad angles.
                // A skinny triangle is not split if its shortest edge subtends a
                // small input angle, and both endpoints of the edge lie on a
                // concentric circular shell.  For convenience, I make a small
                // adjustment to that rule:  I check if the endpoints of the edge
                // both lie in segment interiors, equidistant from the apex where
                // the two segments meet.
                // First, check if both points lie in segment interiors.
                if ((base1.type == VertexType.SegmentVertex) &&
                    (base2.type == VertexType.SegmentVertex))
                {
                    // Check if both points lie in a common segment. If they do, the
                    // skinny triangle is enqueued to be split as usual.
                    tri1.SegPivot(ref testsub);
                    if (testsub.seg == Mesh.dummysub)
                    {
                        // No common segment.  Find a subsegment that contains 'torg'.
                        tri1.Copy(ref tri2);
                        do
                        {
                            tri1.OprevSelf();
                            tri1.SegPivot(ref testsub);
                        } while (testsub.seg == Mesh.dummysub);
                        // Find the endpoints of the containing segment.
                        org1  = testsub.SegOrg();
                        dest1 = testsub.SegDest();
                        // Find a subsegment that contains 'tdest'.
                        do
                        {
                            tri2.DnextSelf();
                            tri2.SegPivot(ref testsub);
                        } while (testsub.seg == Mesh.dummysub);
                        // Find the endpoints of the containing segment.
                        org2  = testsub.SegOrg();
                        dest2 = testsub.SegDest();
                        // Check if the two containing segments have an endpoint in common.
                        joinvertex = null;
                        if ((dest1.x == org2.x) && (dest1.y == org2.y))
                        {
                            joinvertex = dest1;
                        }
                        else if ((org1.x == dest2.x) && (org1.y == dest2.y))
                        {
                            joinvertex = org1;
                        }
                        if (joinvertex != null)
                        {
                            // Compute the distance from the common endpoint (of the two
                            // segments) to each of the endpoints of the shortest edge.
                            dist1 = ((base1.x - joinvertex.x) * (base1.x - joinvertex.x) +
                                     (base1.y - joinvertex.y) * (base1.y - joinvertex.y));
                            dist2 = ((base2.x - joinvertex.x) * (base2.x - joinvertex.x) +
                                     (base2.y - joinvertex.y) * (base2.y - joinvertex.y));
                            // If the two distances are equal, don't split the triangle.
                            if ((dist1 < 1.001 * dist2) && (dist1 > 0.999 * dist2))
                            {
                                // Return now to avoid enqueueing the bad triangle.
                                return;
                            }
                        }
                    }
                }

                // Add this triangle to the list of bad triangles.
                queue.Enqueue(ref testtri, minedge, tapex, torg, tdest);
            }
        }