/* =========================================================================== Copyright (C) 2000 - 2013, Raven Software, Inc. Copyright (C) 2001 - 2013, Activision, Inc. Copyright (C) 2013 - 2015, OpenJK contributors This file is part of the OpenJK source code. OpenJK is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License version 2 as published by the Free Software Foundation. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with this program; if not, see . =========================================================================== */ //////////////////////////////////////////////////////////////////////////////////////// // RAVEN STANDARD TEMPLATE LIBRARY // (c) 2002 Activision // // // Graph Triangulate // ----------------- // Triangulation is the process of generating graph edges between "nearby" points. // // This class is designed to work with the ragl_graph template class, and requires that // the same template parameters for that class be used here. The memory requirements // of this class are not inconsequential, so it is best to allocate this class during // a preprocess step and then throw it away. // // NOTE: This is a 2D triangulation! All Z Coordinates are ignored! // // // // // How Do I Triangulate A Raw Set Of Points? // ----------------------------------------- // First of all, in order to construct a triangulation, you need to have your graph and // pass it in to the constructor: // // typedef ragl::graph_triangulate TTriangulation // TTriangulation MyTriangulation(mMyGraph); // // Next, you are free to call any of the public functions in any order, but the best use // is to call them in this order: // // MyTriangulation.insertion_hull(); // MyTriangulation.delaunay_edge_flip(); // MyTriangulation.alpha_shape(MyGraphUser, , ); // // For documentation on the above functions, look at their def below. Also, the doc on // the Graph User class is in graph_vs.h // // // Finally, when you are ready, call the finish() function. That will populate your // graph (which has not been altered in any way up until now). After calling finish() // you can dump the triangulation class, as it has done it's job and all the data is // now stored in the class. // // MyTriangulation.finish(); // // // // // How Does It Work? (Overview) // ----------------------------- // The details of how each step works are outlined below, however, here is the general // idea: // // - Call insertion hull to generate a "rough and dirty" triangulation of the point set. // The algorithm is relativly fast, and as a handy bi-product, generates the convex // hull of the points. The resulting mesh is ugly though. You probably won't want // to use it in the rough state. The basic idea of this algorithm is to iterativly // add points which have been presorted along the x-axis into the triangulation. It // is easy to do so, because you always know it will be on the right side of any edge // it needs to connect with. // // - Now that you have a functional triangulation with edges and faces, there is fairly // simple and fast algorithm to "clean it up" called EdgeFlipping. The idea is simple. // Just scan through the edges, if you find one that is "bad", flip it! Continue until // you find no "bad" edges. NOTE: This algorithm can lock up if any four points are // colinear! // // - Finally, Alpha Shape is just a simple prune scan of the edges for anything that is // too big or too small. This step is totally optional. // // //////////////////////////////////////////////////////////////////////////////////////// #if !defined(RATL_GRAPH_TRIANGULATE_INC) #define RATL_GRAPH_TRIANGULATE_INC //////////////////////////////////////////////////////////////////////////////////////// // Includes //////////////////////////////////////////////////////////////////////////////////////// #if defined(RA_DEBUG_LINKING) #pragma message("...including graph_triangulate.h") #endif #if !defined(RAGL_COMMON_INC) #include "ragl_common.h" #endif #if !defined(RAGL_GRAPH_VS_INC) #include "graph_vs.h" #endif #if !defined(RATL_LIST_VS_INC) #include "..\Ratl\list_vs.h" #endif namespace ragl { //////////////////////////////////////////////////////////////////////////////////////// // The Graph Class //////////////////////////////////////////////////////////////////////////////////////// template class graph_triangulate : public ratl::ratl_base { public: //////////////////////////////////////////////////////////////////////////////////// // Capacity Enum //////////////////////////////////////////////////////////////////////////////////// enum { CAPACITY = MAXNODES, MAXFACES = MAXEDGES*2, NULLEDGE = -1 }; typedef graph_vs TGraph; public: //////////////////////////////////////////////////////////////////////////////////// // Constructor //////////////////////////////////////////////////////////////////////////////////// graph_triangulate(TGraph& Graph) : mGraph(Graph), mHull(), mHullIter(mHull.begin()) { mLinks.init(0); } //////////////////////////////////////////////////////////////////////////////////// // Clear Out All Temp Data So We Can Triangulate Again //////////////////////////////////////////////////////////////////////////////////// void clear() { mLinks.init(0); mEdges.clear(); mFaces.clear(); mHull.clear(); mHullIter = mHull.begin(); mSortNodes.clear(); } //////////////////////////////////////////////////////////////////////////////////// // Insertion Hull // // This is a "quick and dirty" triangulation technique. It does not give you a very // nice looking or terribly useful mesh, but it is a good place to start. Once // you have an insertion hull triangulation, you can call delauny_edge_flip() to // clean it up some. // // This algorithm's complexity isbounded in the worst case where all the points in // the mesh are on the "hull", in which case it is O(n^2). However the number of // points on the hull for most common point clouds is more likely to be log n. // //////////////////////////////////////////////////////////////////////////////////// void insertion_hull() { assert(mGraph.size_nodes()>3); // We Need More Than 3 Points To Triangulate // STEP ONE: Sort all points along the x axis in increasing order //---------------------------------------------------------------- // COMPLEXITY: O(n log n) Heapsort sort_points(); // STEP TWO: Manually constructe the first face of the triangulation out of the 3 rightmost points //-------------------------------------------------------------------------------------------------- // COMPLEXITY: O(1) add_face(mSortNodes[0].mNodeHandle, mSortNodes[1].mNodeHandle, mSortNodes[2].mNodeHandle); // STEP THREE: Add each remaining point to the hull, constructing new faces as we go //----------------------------------------------------------------------------------- // COMPLEXITY: O(n*c) (n = num nodes, c = num nodes on hull) for (int i=3; i CullEdges; int nEdge; TEdges::iterator stop=mEdges.end(); for (TEdges::iterator it=mEdges.begin(); it!=mEdges.end(); it++) { if (!(*it).mOnHull) { edge& EdgeAt = *it; face& FaceR = mFaces[EdgeAt.mRight]; face& FaceL = mFaces[EdgeAt.mLeft]; // int Edge = mEdges.index_to_handle(it.index()); int R = FaceR.opposing_node(EdgeAt.mA, EdgeAt.mB); int L = FaceL.opposing_node(EdgeAt.mA, EdgeAt.mB); int RInd = mGraph.node_index(R); int LInd = mGraph.node_index(L); TNODE& PtA = mGraph.get_node(EdgeAt.mA); TNODE& PtB = mGraph.get_node(EdgeAt.mB); TNODE& PtR = mGraph.get_node(R); TNODE& PtL = mGraph.get_node(L); if ( (user.on_same_floor(PtR, PtL)) && (mLinks.get(RInd, LInd)==0) && (mLinks.get(LInd, RInd)==0) && (!user.on_same_floor(PtL, PtA) || !user.on_same_floor(PtL, PtB)) ) { nEdge= mEdges.alloc(); mEdges[nEdge].mA = R; mEdges[nEdge].mB = L; mEdges[nEdge].mHullLoc = mHullIter; mEdges[nEdge].mOnHull = true; mEdges[nEdge].mFlips = 0; mEdges[nEdge].mLeft = 0; mEdges[nEdge].mRight = 0; mLinks.get(RInd, LInd) = nEdge; mLinks.get(LInd, RInd) = nEdge; } if (!user.on_same_floor(PtA, PtB)) { mLinks.get(mGraph.node_index(EdgeAt.mA), mGraph.node_index(EdgeAt.mB)) = 0; mLinks.get(mGraph.node_index(EdgeAt.mB), mGraph.node_index(EdgeAt.mA)) = 0; CullEdges.push_back(it.index()); } } } for (int i=0; i CullEdges; float cost; for (TEdges::iterator it=mEdges.begin(); it!=mEdges.end(); it++) { cost = user.cost(mGraph.get_node((*it).mA), mGraph.get_node((*it).mB)); if (costmax) { mLinks.get(mGraph.node_index((*it).mA), mGraph.node_index((*it).mB)) = 0; mLinks.get(mGraph.node_index((*it).mB), mGraph.node_index((*it).mA)) = 0; CullEdges.push_back(it.index()); } } for (int i=0; i THull; typedef typename ratl::list_vs::iterator THullIter; typedef typename ratl::grid2_vs TLinks; //////////////////////////////////////////////////////////////////////////////////// // The Local Edge Class // // RIGHT // B<-<-<-<-<-<-A // LEFT // //////////////////////////////////////////////////////////////////////////////////// class edge { public: int mA; int mB; int mLeft; int mRight; int mFlips; THullIter mHullLoc; bool mOnHull; void flip_face(int OldFace, int NewFace) { assert(mRight!=mLeft); assert(mLeft!=NewFace && mRight!=NewFace); if (mLeft==OldFace) { mLeft=NewFace; } else { assert(mRight==OldFace); mRight = NewFace; } assert(mRight!=mLeft); } void verify(int PtA, int PtB, int Edge) { assert(PtA==mA || PtA==mB); assert(PtB==mA || PtB==mB); assert(mRight==Edge || mLeft==Edge); assert(mRight!=mLeft); assert(mA!=mB); } void verify(int PtA, int PtB, int PtC, int Edge) { assert((PtC==mA && (PtA==mB || PtB==mB)) || (PtC==mB && (PtA==mA || PtB==mA))); assert(mRight==Edge || mLeft==Edge); assert(mRight!=mLeft); assert(mA!=mB); } }; //////////////////////////////////////////////////////////////////////////////////// // The Local Face Class // // _ C // /| \ // LEFT/ \RIGHT // / \ // B-<-<-<-<-A // BOTTOM // //////////////////////////////////////////////////////////////////////////////////// class face { public: int mA; int mB; int mC; int mLeft; int mRight; int mBottom; int mFlips; int& opposing_node(int A, int B) { if (mA!=A && mA!=B) { return mA; } if (mB!=A && mB!=B) { return mB; } assert(mC!=A && mC!=B); return mC; } int& relative_left(int edge) { if (edge==mLeft) { return mRight; } if (edge==mRight) { return mBottom; } assert(edge==mBottom); // If you hit this assert, then the edge is not in this face return mLeft; } int& relative_right(int edge) { if (edge==mLeft) { return mBottom; } if (edge==mRight) { return mLeft; } assert(edge==mBottom); // If you hit this assert, then the edge is not in this face return mRight; } }; //////////////////////////////////////////////////////////////////////////////////// // The Sort Node Class // // Used To Sort Nodes In Increasing X Order //////////////////////////////////////////////////////////////////////////////////// class sort_node { public: bool operator<(const sort_node& r) const { return ((*r.mNodePointer)[0] < (*mNodePointer)[0]); } int mNodeHandle; TNODE* mNodePointer; }; //////////////////////////////////////////////////////////////////////////////////// // //////////////////////////////////////////////////////////////////////////////////// typedef typename ratl::handle_pool_vs TEdges; typedef typename ratl::handle_pool_vs::iterator TEdgesIter; typedef typename ratl::handle_pool_vs TFaces; typedef typename ratl::vector_vs TSortNodes; TGraph& mGraph; // A Reference To The Graph Points To Triangulate TLinks mLinks; TEdges mEdges; TFaces mFaces; THull mHull; // The Convex Hull THullIter mHullIter; TSortNodes mSortNodes; // Need To Presort Nodes On (x-Axis) For Insertion Hull sort_node mSortNode; private: //////////////////////////////////////////////////////////////////////////////////// // Copy All The Graph Nodes To Our Sort Node Class And Run Heap Sort //////////////////////////////////////////////////////////////////////////////////// void sort_points() { mSortNodes.clear(); for (TGraph::TNodes::iterator i=mGraph.nodes_begin(); i!=mGraph.nodes_end(); i++) { mSortNode.mNodeHandle = mGraph.node_handle(i); mSortNode.mNodePointer = &(*i); mSortNodes.push_back(mSortNode); } mSortNodes.sort(); } //////////////////////////////////////////////////////////////////////////////////// // Create A New Edge A->B, And Fix Up The Face //////////////////////////////////////////////////////////////////////////////////// int add_edge(int A, int B, int Face=0, bool OnHull=true) { assert(A!=B ); int nEdge = mLinks.get(mGraph.node_index(A), mGraph.node_index(B)); // Apparently This Edge Does Not Exist, So Make A New One //-------------------------------------------------------- if (nEdge==0) { nEdge= mEdges.alloc(); mHull.insert_after(mHullIter, nEdge); assert(mHullIter!=mHull.end()); mEdges[nEdge].mA = A; mEdges[nEdge].mB = B; mEdges[nEdge].mHullLoc = mHullIter; mEdges[nEdge].mOnHull = true; mEdges[nEdge].mFlips = 0; mEdges[nEdge].mLeft = 0; mEdges[nEdge].mRight = 0; mLinks.get(mGraph.node_index(A), mGraph.node_index(B)) = nEdge; mLinks.get(mGraph.node_index(B), mGraph.node_index(A)) = nEdge; } // If This Edge DOES Already Exist, Then We Need To Remove It From The Hull //-------------------------------------------------------------------------- else if (mEdges[nEdge].mOnHull) { assert(mEdges[nEdge].mHullLoc!=mHull.end()); if (mHullIter==mEdges[nEdge].mHullLoc) { mHull.erase(mHullIter); // Make Sure To Fix Up The Hull Iter If That Is What We Are Removing } else { mHull.erase(mEdges[nEdge].mHullLoc); } mEdges[nEdge].mOnHull = false; } // If The Edge Was Made With The Same Orientation Currently Asked For (A->B), Then Mark Face As Right //---------------------------------------------------------------------------------------------------- if (mEdges[nEdge].mA==A) { mEdges[nEdge].mRight = Face; } else { mEdges[nEdge].mLeft = Face; } return nEdge; } //////////////////////////////////////////////////////////////////////////////////// // Create A New Face A->B->C, And Fix Up The Edges & Neighboring Faces //////////////////////////////////////////////////////////////////////////////////// int add_face(int A, int B, int C) { int Temp = 0; int nFace = mFaces.alloc(); // First, Make Sure Node A.x Is Greater Than B and C. If Not, Swap With B or C //------------------------------------------------------------------------------ if (mGraph.get_node(B)[0]>mGraph.get_node(A)[0]) { Temp = A; A = B; B = Temp; } if (mGraph.get_node(C)[0]>mGraph.get_node(A)[0]) { Temp = A; A = C; C = Temp; } // Similarly, Make Sure Node B.y Is Greater Than Node C.y //-------------------------------------------------------- if (mGraph.get_node(C).LRTest(mGraph.get_node(A), mGraph.get_node(B))==Side_Left) { Temp = C; C = B; B = Temp; } // DEBUG ASSERTS //==================================================================================== // IF YOU HIT THESE ASSERTS, CHANCES ARE THAT YOU ARE TRYING TO TRIANGULATE OVER A SET // WITH MORE THAN 2 COLINEAR POINTS ON THE SAME FACE. INSERT HULL WILL FAIL IN THIS // FACE. INSERT HULL WILL FAIL IN THIS SITUATION assert(mGraph.get_node(C).LRTest(mGraph.get_node(A), mGraph.get_node(B))==Side_Right); assert(mGraph.get_node(A).LRTest(mGraph.get_node(B), mGraph.get_node(C))==Side_Right); assert(mGraph.get_node(B).LRTest(mGraph.get_node(C), mGraph.get_node(A))==Side_Right); //==================================================================================== mFaces[nFace].mA = A; mFaces[nFace].mB = B; mFaces[nFace].mC = C; mFaces[nFace].mRight = add_edge(C, A, nFace); mFaces[nFace].mBottom = add_edge(A, B, nFace); mFaces[nFace].mLeft = add_edge(B, C, nFace); mFaces[nFace].mFlips = 0; return nFace; } //////////////////////////////////////////////////////////////////////////////////// // Insertion Hull Triangulation // // This algorithm works by scanning the outer convex hull of the set of points that // have already been triangulated. When encountering a hull edge which evaluates // LEFT in a left right test (remember, the triangles always have clockwise orientation) // it adds a face to the triangulation including the edge as one side of the triangle // and two new edges to the node handle. It's very important to traverse the convex // hull in counter clockwise order (backwards). // // In the example below, we assume the convex hull starts at the edge (CA). (nodeHandle) is // RIGHT of (C->A), so it skips that edge and moves on to (D->C). (nodeHandle) is in fact // LEFT of (D->C), so we would add a new face that would go (D->nodeHandle->C), and we remove // (D->C) from the hull. // // // // (C)-------------(A) // / \ __/ \ // (nodeHandle) / \ __/ \ // / \ / \ // (D)----____(B)_ \ // \ | \ __ // \ | \__ // \ | \ // //////////////////////////////////////////////////////////////////////////////////// void insert_point(int nodeHandle) { // Iterate Over The Existing Convex Hull //--------------------------------------- for (mHullIter = mHull.begin(); mHullIter!=mHull.end(); mHullIter++) { edge& curEdge = mEdges[*mHullIter]; // Can This Edge "See" The node Handle We Have Passed In? //--------------------------------------------------------- if ( mGraph.get_node(nodeHandle).LRTest(mGraph.get_node(curEdge.mA), mGraph.get_node(curEdge.mB))==Side_Left ) { // Then Add The Face And Remove This Edge From The Hull //------------------------------------------------------ add_face(curEdge.mA, curEdge.mB, nodeHandle); } } } //////////////////////////////////////////////////////////////////////////////////// // Edge Flip Function // // This function scans the edge list for any edge that is "bad" (defined as not // fitting within the circumscribed circle of either adjoining face). When it // encounters one, it "flips" the edge in question and fixes up the adjoining faces // which were altered. // // // The Flip Edge (PtA->PtB): // // // // BEFORE AFTER // // (PtR) (PtA) // / \ / | \ // / \ / | \ // / (FaceR) \ / V \ // / \ / | \ // (PtB)-<---------<-(PtA) (PtR) | (PtL) // \ / \ | / // \ (FaceL) / \ V / // \ / \ | / // \ / \ | / // (PtL) (PtB) // //////////////////////////////////////////////////////////////////////////////////// int flip() { int Flipped = 0; int EdgeHandle; int PtR, PtL, PtA, PtB; int EdgeRL, EdgeRR, EdgeLL, EdgeLR; // Iterate Through All The Edges Looking For Potential NON-Delauney Edges //------------------------------------------------------------------------ for (TEdgesIter CurEdge=mEdges.begin(); CurEdge!=mEdges.end(); CurEdge++) { // If It Is On The Hull, We Don't Even Need To Look At It //-------------------------------------------------------- if (!(*CurEdge).mOnHull) { edge& EdgeAt = *CurEdge; face& FaceR = mFaces[EdgeAt.mRight]; face& FaceL = mFaces[EdgeAt.mLeft]; EdgeHandle = mEdges.index_to_handle(CurEdge.index()); PtA = EdgeAt.mA; PtB = EdgeAt.mB; PtR = FaceR.opposing_node(PtA, PtB); PtL = FaceL.opposing_node(PtA, PtB); assert(EdgeAt.mRight!=EdgeAt.mLeft); assert(PtA!=PtB); assert(PtR!=PtL); assert(PtA!=PtR && PtA!=PtL); assert(PtB!=PtR && PtB!=PtL); // Is This Edge Invalid For Delaunay? //------------------------------------- if (!mGraph.get_node(PtB).InCircle(mGraph.get_node(PtR), mGraph.get_node(PtL), mGraph.get_node(PtA)) && !mGraph.get_node(PtA).InCircle(mGraph.get_node(PtR), mGraph.get_node(PtB), mGraph.get_node(PtL)) ) { // Change The Link: Remove The Old, Add The New //---------------------------------------------- mLinks.get(mGraph.node_index(PtA), mGraph.node_index(PtB)) = 0; mLinks.get(mGraph.node_index(PtB), mGraph.node_index(PtA)) = 0; mLinks.get(mGraph.node_index(PtR), mGraph.node_index(PtL)) = EdgeHandle; mLinks.get(mGraph.node_index(PtL), mGraph.node_index(PtR)) = EdgeHandle; Flipped++; EdgeAt.mFlips++; FaceL.mFlips++; FaceR.mFlips++; // Flip The Edge We Found //------------------------ EdgeAt.mA = PtR; EdgeAt.mB = PtL; // Calculate Relatave Edges And Points Assuming (EdgeAt) Were mBottom For The Two Faces //-------------------------------------------------------------------------------------- EdgeRL = FaceR.relative_left(EdgeHandle); EdgeRR = FaceR.relative_right(EdgeHandle); EdgeLL = FaceL.relative_left(EdgeHandle); EdgeLR = FaceL.relative_right(EdgeHandle); // Fix Edges Which Had Been Rotated To New Faces //----------------------------------------------- mEdges[EdgeLR].flip_face(EdgeAt.mLeft, EdgeAt.mRight); mEdges[EdgeRR].flip_face(EdgeAt.mRight, EdgeAt.mLeft); // Rotate The Edges Clockwise //---------------------------- FaceR.mLeft = EdgeLR; FaceR.mRight = EdgeRL; FaceR.mBottom = EdgeHandle; FaceL.mLeft = EdgeRR; FaceL.mRight = EdgeLL; FaceL.mBottom = EdgeHandle; FaceR.mA = PtR; FaceR.mB = PtL; FaceR.mC = PtB; FaceL.mA = PtR; FaceL.mB = PtL; FaceL.mC = PtA; // DEBUG VERIFICATION //======================================================================== #ifdef _DEBUG mEdges[FaceR.mLeft ].verify(FaceR.mA, FaceR.mB, FaceR.mC, EdgeAt.mRight); mEdges[FaceR.mRight ].verify(FaceR.mA, FaceR.mB, FaceR.mC, EdgeAt.mRight); mEdges[FaceR.mBottom].verify(FaceR.mA, FaceR.mB, EdgeAt.mRight); mEdges[FaceL.mLeft ].verify(FaceL.mA, FaceL.mB, FaceL.mC, EdgeAt.mLeft); mEdges[FaceL.mRight ].verify(FaceL.mA, FaceL.mB, FaceL.mC, EdgeAt.mLeft); mEdges[FaceL.mBottom].verify(FaceL.mA, FaceL.mB, EdgeAt.mLeft); #endif assert(EdgeAt.mRight!=EdgeAt.mLeft); assert(PtA!=PtB); assert(PtR!=PtL); //======================================================================== } } } return Flipped; } }; } #endif