/* * Poly2Tri Copyright (c) 2009-2018, Poly2Tri Contributors * https://github.com/jhasse/poly2tri * * All rights reserved. * * Redistribution and use in source and binary forms, with or without modification, * are permitted provided that the following conditions are met: * * * Redistributions of source code must retain the above copyright notice, * this list of conditions and the following disclaimer. * * Redistributions in binary form must reproduce the above copyright notice, * this list of conditions and the following disclaimer in the documentation * and/or other materials provided with the distribution. * * Neither the name of Poly2Tri nor the names of its contributors may be * used to endorse or promote products derived from this software without specific * prior written permission. * * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR * A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR * CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, * EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, * PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR * PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF * LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING * NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS * SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. */ #include "sweep.h" #include "sweep_context.h" #include "advancing_front.h" #include "../common/utils.h" #include #include namespace p2t { // Triangulate simple polygon with holes void Sweep::Triangulate(SweepContext& tcx) { tcx.InitTriangulation(); tcx.CreateAdvancingFront(); // Sweep points; build mesh SweepPoints(tcx); // Clean up FinalizationPolygon(tcx); } void Sweep::SweepPoints(SweepContext& tcx) { for (size_t i = 1; i < tcx.point_count(); i++) { Point& point = *tcx.GetPoint(i); Node* node = &PointEvent(tcx, point); for (unsigned int j = 0; j < point.edge_list.size(); j++) { EdgeEvent(tcx, point.edge_list[j], node); } } } void Sweep::FinalizationPolygon(SweepContext& tcx) { // Get an Internal triangle to start with Triangle* t = tcx.front()->head()->next->triangle; Point* p = tcx.front()->head()->next->point; while (!t->GetConstrainedEdgeCW(*p)) { t = t->NeighborCCW(*p); } // Collect interior triangles constrained by edges tcx.MeshClean(*t); } Node& Sweep::PointEvent(SweepContext& tcx, Point& point) { Node& node = tcx.LocateNode(point); Node& new_node = NewFrontTriangle(tcx, point, node); // Only need to check +epsilon since point never have smaller // x value than node due to how we fetch nodes from the front if (point.x <= node.point->x + EPSILON) { Fill(tcx, node); } //tcx.AddNode(new_node); FillAdvancingFront(tcx, new_node); return new_node; } void Sweep::EdgeEvent(SweepContext& tcx, Edge* edge, Node* node) { tcx.edge_event.constrained_edge = edge; tcx.edge_event.right = (edge->p->x > edge->q->x); if (IsEdgeSideOfTriangle(*node->triangle, *edge->p, *edge->q)) { return; } // For now we will do all needed filling // TODO: integrate with flip process might give some better performance // but for now this avoid the issue with cases that needs both flips and fills FillEdgeEvent(tcx, edge, node); EdgeEvent(tcx, *edge->p, *edge->q, node->triangle, *edge->q); } void Sweep::EdgeEvent(SweepContext& tcx, Point& ep, Point& eq, Triangle* triangle, Point& point) { if (triangle == nullptr) { throw std::runtime_error("EdgeEvent - null triangle"); } if (IsEdgeSideOfTriangle(*triangle, ep, eq)) { return; } Point* p1 = triangle->PointCCW(point); Orientation o1 = Orient2d(eq, *p1, ep); if (o1 == COLLINEAR) { if (triangle->Contains(&eq, p1)) { triangle->MarkConstrainedEdge(&eq, p1); // We are modifying the constraint maybe it would be better to // not change the given constraint and just keep a variable for the new constraint tcx.edge_event.constrained_edge->q = p1; triangle = triangle->NeighborAcross(point); EdgeEvent(tcx, ep, *p1, triangle, *p1); } else { throw std::runtime_error("EdgeEvent - collinear points not supported"); } return; } Point* p2 = triangle->PointCW(point); Orientation o2 = Orient2d(eq, *p2, ep); if (o2 == COLLINEAR) { if (triangle->Contains(&eq, p2)) { triangle->MarkConstrainedEdge(&eq, p2); // We are modifying the constraint maybe it would be better to // not change the given constraint and just keep a variable for the new constraint tcx.edge_event.constrained_edge->q = p2; triangle = triangle->NeighborAcross(point); EdgeEvent(tcx, ep, *p2, triangle, *p2); } else { throw std::runtime_error("EdgeEvent - collinear points not supported"); } return; } if (o1 == o2) { // Need to decide if we are rotating CW or CCW to get to a triangle // that will cross edge if (o1 == CW) { triangle = triangle->NeighborCCW(point); } else { triangle = triangle->NeighborCW(point); } EdgeEvent(tcx, ep, eq, triangle, point); } else { // This triangle crosses constraint so lets flippin start! assert(triangle); FlipEdgeEvent(tcx, ep, eq, triangle, point); } } bool Sweep::IsEdgeSideOfTriangle(Triangle& triangle, Point& ep, Point& eq) { const int index = triangle.EdgeIndex(&ep, &eq); if (index != -1) { triangle.MarkConstrainedEdge(index); Triangle* t = triangle.GetNeighbor(index); if (t) { t->MarkConstrainedEdge(&ep, &eq); } return true; } return false; } Node& Sweep::NewFrontTriangle(SweepContext& tcx, Point& point, Node& node) { Triangle* triangle = new Triangle(point, *node.point, *node.next->point); triangle->MarkNeighbor(*node.triangle); tcx.AddToMap(triangle); Node* new_node = new Node(point); nodes_.push_back(new_node); new_node->next = node.next; new_node->prev = &node; node.next->prev = new_node; node.next = new_node; if (!Legalize(tcx, *triangle)) { tcx.MapTriangleToNodes(*triangle); } return *new_node; } void Sweep::Fill(SweepContext& tcx, Node& node) { Triangle* triangle = new Triangle(*node.prev->point, *node.point, *node.next->point); // TODO: should copy the constrained_edge value from neighbor triangles // for now constrained_edge values are copied during the legalize triangle->MarkNeighbor(*node.prev->triangle); triangle->MarkNeighbor(*node.triangle); tcx.AddToMap(triangle); // Update the advancing front node.prev->next = node.next; node.next->prev = node.prev; // If it was legalized the triangle has already been mapped if (!Legalize(tcx, *triangle)) { tcx.MapTriangleToNodes(*triangle); } } void Sweep::FillAdvancingFront(SweepContext& tcx, Node& n) { // Fill right holes Node* node = n.next; while (node->next) { // if HoleAngle exceeds 90 degrees then break. if (LargeHole_DontFill(node)) break; Fill(tcx, *node); node = node->next; } // Fill left holes node = n.prev; while (node->prev) { // if HoleAngle exceeds 90 degrees then break. if (LargeHole_DontFill(node)) break; Fill(tcx, *node); node = node->prev; } // Fill right basins if (n.next && n.next->next) { const double angle = BasinAngle(n); if (angle < PI_3div4) { FillBasin(tcx, n); } } } // True if HoleAngle exceeds 90 degrees. bool Sweep::LargeHole_DontFill(const Node* node) const { const Node* nextNode = node->next; const Node* prevNode = node->prev; if (!AngleExceeds90Degrees(node->point, nextNode->point, prevNode->point)) return false; // Check additional points on front. const Node* next2Node = nextNode->next; // "..Plus.." because only want angles on same side as point being added. if ((next2Node != nullptr) && !AngleExceedsPlus90DegreesOrIsNegative(node->point, next2Node->point, prevNode->point)) return false; const Node* prev2Node = prevNode->prev; // "..Plus.." because only want angles on same side as point being added. if ((prev2Node != nullptr) && !AngleExceedsPlus90DegreesOrIsNegative(node->point, nextNode->point, prev2Node->point)) return false; return true; } bool Sweep::AngleExceeds90Degrees(const Point* origin, const Point* pa, const Point* pb) const { const double angle = Angle(origin, pa, pb); return ((angle > PI_div2) || (angle < -PI_div2)); } bool Sweep::AngleExceedsPlus90DegreesOrIsNegative(const Point* origin, const Point* pa, const Point* pb) const { const double angle = Angle(origin, pa, pb); return (angle > PI_div2) || (angle < 0); } double Sweep::Angle(const Point* origin, const Point* pa, const Point* pb) const { /* Complex plane * ab = cosA +i*sinA * ab = (ax + ay*i)(bx + by*i) = (ax*bx + ay*by) + i(ax*by-ay*bx) * atan2(y,x) computes the principal value of the argument function * applied to the complex number x+iy * Where x = ax*bx + ay*by * y = ax*by - ay*bx */ const double px = origin->x; const double py = origin->y; const double ax = pa->x - px; const double ay = pa->y - py; const double bx = pb->x - px; const double by = pb->y - py; const double x = ax * by - ay * bx; const double y = ax * bx + ay * by; return atan2(x, y); } double Sweep::BasinAngle(const Node& node) const { const double ax = node.point->x - node.next->next->point->x; const double ay = node.point->y - node.next->next->point->y; return atan2(ay, ax); } double Sweep::HoleAngle(const Node& node) const { /* Complex plane * ab = cosA +i*sinA * ab = (ax + ay*i)(bx + by*i) = (ax*bx + ay*by) + i(ax*by-ay*bx) * atan2(y,x) computes the principal value of the argument function * applied to the complex number x+iy * Where x = ax*bx + ay*by * y = ax*by - ay*bx */ const double ax = node.next->point->x - node.point->x; const double ay = node.next->point->y - node.point->y; const double bx = node.prev->point->x - node.point->x; const double by = node.prev->point->y - node.point->y; return atan2(ax * by - ay * bx, ax * bx + ay * by); } bool Sweep::Legalize(SweepContext& tcx, Triangle& t) { // To legalize a triangle we start by finding if any of the three edges // violate the Delaunay condition for (int i = 0; i < 3; i++) { if (t.delaunay_edge[i]) continue; Triangle* ot = t.GetNeighbor(i); if (ot) { Point* p = t.GetPoint(i); Point* op = ot->OppositePoint(t, *p); int oi = ot->Index(op); // If this is a Constrained Edge or a Delaunay Edge(only during recursive legalization) // then we should not try to legalize if (ot->constrained_edge[oi] || ot->delaunay_edge[oi]) { t.constrained_edge[i] = ot->constrained_edge[oi]; continue; } bool inside = Incircle(*p, *t.PointCCW(*p), *t.PointCW(*p), *op); if (inside) { // Lets mark this shared edge as Delaunay t.delaunay_edge[i] = true; ot->delaunay_edge[oi] = true; // Lets rotate shared edge one vertex CW to legalize it RotateTrianglePair(t, *p, *ot, *op); // We now got one valid Delaunay Edge shared by two triangles // This gives us 4 new edges to check for Delaunay // Make sure that triangle to node mapping is done only one time for a specific triangle bool not_legalized = !Legalize(tcx, t); if (not_legalized) { tcx.MapTriangleToNodes(t); } not_legalized = !Legalize(tcx, *ot); if (not_legalized) tcx.MapTriangleToNodes(*ot); // Reset the Delaunay edges, since they only are valid Delaunay edges // until we add a new triangle or point. // XXX: need to think about this. Can these edges be tried after we // return to previous recursive level? t.delaunay_edge[i] = false; ot->delaunay_edge[oi] = false; // If triangle have been legalized no need to check the other edges since // the recursive legalization will handles those so we can end here. return true; } } } return false; } bool Sweep::Incircle(const Point& pa, const Point& pb, const Point& pc, const Point& pd) const { const double adx = pa.x - pd.x; const double ady = pa.y - pd.y; const double bdx = pb.x - pd.x; const double bdy = pb.y - pd.y; const double adxbdy = adx * bdy; const double bdxady = bdx * ady; const double oabd = adxbdy - bdxady; if (oabd <= 0) return false; const double cdx = pc.x - pd.x; const double cdy = pc.y - pd.y; const double cdxady = cdx * ady; const double adxcdy = adx * cdy; const double ocad = cdxady - adxcdy; if (ocad <= 0) return false; const double bdxcdy = bdx * cdy; const double cdxbdy = cdx * bdy; const double alift = adx * adx + ady * ady; const double blift = bdx * bdx + bdy * bdy; const double clift = cdx * cdx + cdy * cdy; const double det = alift * (bdxcdy - cdxbdy) + blift * ocad + clift * oabd; return det > 0; } void Sweep::RotateTrianglePair(Triangle& t, Point& p, Triangle& ot, Point& op) const { Triangle* n1, *n2, *n3, *n4; n1 = t.NeighborCCW(p); n2 = t.NeighborCW(p); n3 = ot.NeighborCCW(op); n4 = ot.NeighborCW(op); bool ce1, ce2, ce3, ce4; ce1 = t.GetConstrainedEdgeCCW(p); ce2 = t.GetConstrainedEdgeCW(p); ce3 = ot.GetConstrainedEdgeCCW(op); ce4 = ot.GetConstrainedEdgeCW(op); bool de1, de2, de3, de4; de1 = t.GetDelunayEdgeCCW(p); de2 = t.GetDelunayEdgeCW(p); de3 = ot.GetDelunayEdgeCCW(op); de4 = ot.GetDelunayEdgeCW(op); t.Legalize(p, op); ot.Legalize(op, p); // Remap delaunay_edge ot.SetDelunayEdgeCCW(p, de1); t.SetDelunayEdgeCW(p, de2); t.SetDelunayEdgeCCW(op, de3); ot.SetDelunayEdgeCW(op, de4); // Remap constrained_edge ot.SetConstrainedEdgeCCW(p, ce1); t.SetConstrainedEdgeCW(p, ce2); t.SetConstrainedEdgeCCW(op, ce3); ot.SetConstrainedEdgeCW(op, ce4); // Remap neighbors // XXX: might optimize the markNeighbor by keeping track of // what side should be assigned to what neighbor after the // rotation. Now mark neighbor does lots of testing to find // the right side. t.ClearNeighbors(); ot.ClearNeighbors(); if (n1) ot.MarkNeighbor(*n1); if (n2) t.MarkNeighbor(*n2); if (n3) t.MarkNeighbor(*n3); if (n4) ot.MarkNeighbor(*n4); t.MarkNeighbor(ot); } void Sweep::FillBasin(SweepContext& tcx, Node& node) { if (Orient2d(*node.point, *node.next->point, *node.next->next->point) == CCW) { tcx.basin.left_node = node.next->next; } else { tcx.basin.left_node = node.next; } // Find the bottom and right node tcx.basin.bottom_node = tcx.basin.left_node; while (tcx.basin.bottom_node->next && tcx.basin.bottom_node->point->y >= tcx.basin.bottom_node->next->point->y) { tcx.basin.bottom_node = tcx.basin.bottom_node->next; } if (tcx.basin.bottom_node == tcx.basin.left_node) { // No valid basin return; } tcx.basin.right_node = tcx.basin.bottom_node; while (tcx.basin.right_node->next && tcx.basin.right_node->point->y < tcx.basin.right_node->next->point->y) { tcx.basin.right_node = tcx.basin.right_node->next; } if (tcx.basin.right_node == tcx.basin.bottom_node) { // No valid basins return; } tcx.basin.width = tcx.basin.right_node->point->x - tcx.basin.left_node->point->x; tcx.basin.left_highest = tcx.basin.left_node->point->y > tcx.basin.right_node->point->y; FillBasinReq(tcx, tcx.basin.bottom_node); } void Sweep::FillBasinReq(SweepContext& tcx, Node* node) { // if shallow stop filling if (IsShallow(tcx, *node)) { return; } Fill(tcx, *node); if (node->prev == tcx.basin.left_node && node->next == tcx.basin.right_node) { return; } else if (node->prev == tcx.basin.left_node) { Orientation o = Orient2d(*node->point, *node->next->point, *node->next->next->point); if (o == CW) { return; } node = node->next; } else if (node->next == tcx.basin.right_node) { Orientation o = Orient2d(*node->point, *node->prev->point, *node->prev->prev->point); if (o == CCW) { return; } node = node->prev; } else { // Continue with the neighbor node with lowest Y value if (node->prev->point->y < node->next->point->y) { node = node->prev; } else { node = node->next; } } FillBasinReq(tcx, node); } bool Sweep::IsShallow(SweepContext& tcx, Node& node) { double height; if (tcx.basin.left_highest) { height = tcx.basin.left_node->point->y - node.point->y; } else { height = tcx.basin.right_node->point->y - node.point->y; } // if shallow stop filling if (tcx.basin.width > height) { return true; } return false; } void Sweep::FillEdgeEvent(SweepContext& tcx, Edge* edge, Node* node) { if (tcx.edge_event.right) { FillRightAboveEdgeEvent(tcx, edge, node); } else { FillLeftAboveEdgeEvent(tcx, edge, node); } } void Sweep::FillRightAboveEdgeEvent(SweepContext& tcx, Edge* edge, Node* node) { while (node->next->point->x < edge->p->x) { // Check if next node is below the edge if (Orient2d(*edge->q, *node->next->point, *edge->p) == CCW) { FillRightBelowEdgeEvent(tcx, edge, *node); } else { node = node->next; } } } void Sweep::FillRightBelowEdgeEvent(SweepContext& tcx, Edge* edge, Node& node) { if (node.point->x < edge->p->x) { if (Orient2d(*node.point, *node.next->point, *node.next->next->point) == CCW) { // Concave FillRightConcaveEdgeEvent(tcx, edge, node); } else { // Convex FillRightConvexEdgeEvent(tcx, edge, node); // Retry this one FillRightBelowEdgeEvent(tcx, edge, node); } } } void Sweep::FillRightConcaveEdgeEvent(SweepContext& tcx, Edge* edge, Node& node) { Fill(tcx, *node.next); if (node.next->point != edge->p) { // Next above or below edge? if (Orient2d(*edge->q, *node.next->point, *edge->p) == CCW) { // Below if (Orient2d(*node.point, *node.next->point, *node.next->next->point) == CCW) { // Next is concave FillRightConcaveEdgeEvent(tcx, edge, node); } else { // Next is convex } } } } void Sweep::FillRightConvexEdgeEvent(SweepContext& tcx, Edge* edge, Node& node) { // Next concave or convex? if (Orient2d(*node.next->point, *node.next->next->point, *node.next->next->next->point) == CCW) { // Concave FillRightConcaveEdgeEvent(tcx, edge, *node.next); } else { // Convex // Next above or below edge? if (Orient2d(*edge->q, *node.next->next->point, *edge->p) == CCW) { // Below FillRightConvexEdgeEvent(tcx, edge, *node.next); } else { // Above } } } void Sweep::FillLeftAboveEdgeEvent(SweepContext& tcx, Edge* edge, Node* node) { while (node->prev->point->x > edge->p->x) { // Check if next node is below the edge if (Orient2d(*edge->q, *node->prev->point, *edge->p) == CW) { FillLeftBelowEdgeEvent(tcx, edge, *node); } else { node = node->prev; } } } void Sweep::FillLeftBelowEdgeEvent(SweepContext& tcx, Edge* edge, Node& node) { if (node.point->x > edge->p->x) { if (Orient2d(*node.point, *node.prev->point, *node.prev->prev->point) == CW) { // Concave FillLeftConcaveEdgeEvent(tcx, edge, node); } else { // Convex FillLeftConvexEdgeEvent(tcx, edge, node); // Retry this one FillLeftBelowEdgeEvent(tcx, edge, node); } } } void Sweep::FillLeftConvexEdgeEvent(SweepContext& tcx, Edge* edge, Node& node) { // Next concave or convex? if (Orient2d(*node.prev->point, *node.prev->prev->point, *node.prev->prev->prev->point) == CW) { // Concave FillLeftConcaveEdgeEvent(tcx, edge, *node.prev); } else { // Convex // Next above or below edge? if (Orient2d(*edge->q, *node.prev->prev->point, *edge->p) == CW) { // Below FillLeftConvexEdgeEvent(tcx, edge, *node.prev); } else { // Above } } } void Sweep::FillLeftConcaveEdgeEvent(SweepContext& tcx, Edge* edge, Node& node) { Fill(tcx, *node.prev); if (node.prev->point != edge->p) { // Next above or below edge? if (Orient2d(*edge->q, *node.prev->point, *edge->p) == CW) { // Below if (Orient2d(*node.point, *node.prev->point, *node.prev->prev->point) == CW) { // Next is concave FillLeftConcaveEdgeEvent(tcx, edge, node); } else { // Next is convex } } } } void Sweep::FlipEdgeEvent(SweepContext& tcx, Point& ep, Point& eq, Triangle* t, Point& p) { assert(t); Triangle* ot_ptr = t->NeighborAcross(p); if (ot_ptr == nullptr) { throw std::runtime_error("FlipEdgeEvent - null neighbor across"); } Triangle& ot = *ot_ptr; Point& op = *ot.OppositePoint(*t, p); if (InScanArea(p, *t->PointCCW(p), *t->PointCW(p), op)) { // Lets rotate shared edge one vertex CW RotateTrianglePair(*t, p, ot, op); tcx.MapTriangleToNodes(*t); tcx.MapTriangleToNodes(ot); if (p == eq && op == ep) { if (eq == *tcx.edge_event.constrained_edge->q && ep == *tcx.edge_event.constrained_edge->p) { t->MarkConstrainedEdge(&ep, &eq); ot.MarkConstrainedEdge(&ep, &eq); Legalize(tcx, *t); Legalize(tcx, ot); } else { // XXX: I think one of the triangles should be legalized here? } } else { Orientation o = Orient2d(eq, op, ep); t = &NextFlipTriangle(tcx, (int)o, *t, ot, p, op); FlipEdgeEvent(tcx, ep, eq, t, p); } } else { Point& newP = NextFlipPoint(ep, eq, ot, op); FlipScanEdgeEvent(tcx, ep, eq, *t, ot, newP); EdgeEvent(tcx, ep, eq, t, p); } } Triangle& Sweep::NextFlipTriangle(SweepContext& tcx, int o, Triangle& t, Triangle& ot, Point& p, Point& op) { if (o == CCW) { // ot is not crossing edge after flip int edge_index = ot.EdgeIndex(&p, &op); ot.delaunay_edge[edge_index] = true; Legalize(tcx, ot); ot.ClearDelunayEdges(); return t; } // t is not crossing edge after flip int edge_index = t.EdgeIndex(&p, &op); t.delaunay_edge[edge_index] = true; Legalize(tcx, t); t.ClearDelunayEdges(); return ot; } Point& Sweep::NextFlipPoint(Point& ep, Point& eq, Triangle& ot, Point& op) { Orientation o2d = Orient2d(eq, op, ep); if (o2d == CW) { // Right return *ot.PointCCW(op); } else if (o2d == CCW) { // Left return *ot.PointCW(op); } throw std::runtime_error("[Unsupported] Opposing point on constrained edge"); } void Sweep::FlipScanEdgeEvent(SweepContext& tcx, Point& ep, Point& eq, Triangle& flip_triangle, Triangle& t, Point& p) { Triangle* ot_ptr = t.NeighborAcross(p); if (ot_ptr == nullptr) { throw std::runtime_error("FlipScanEdgeEvent - null neighbor across"); } Triangle& ot = *ot_ptr; Point& op = *ot.OppositePoint(t, p); if (InScanArea(eq, *flip_triangle.PointCCW(eq), *flip_triangle.PointCW(eq), op)) { // flip with new edge op->eq FlipEdgeEvent(tcx, eq, op, &ot, op); // TODO: Actually I just figured out that it should be possible to // improve this by getting the next ot and op before the the above // flip and continue the flipScanEdgeEvent here // set new ot and op here and loop back to inScanArea test // also need to set a new flip_triangle first // Turns out at first glance that this is somewhat complicated // so it will have to wait. } else { Point& newP = NextFlipPoint(ep, eq, ot, op); FlipScanEdgeEvent(tcx, ep, eq, flip_triangle, ot, newP); } } Sweep::~Sweep() { // Clean up memory for(size_t i = 0; i < nodes_.size(); i++) { delete nodes_[i]; } } } // namespace p2t