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1 
#include <queue>
 1 
#include <queue>
2 
#include <iostream>
 2 
#include <iostream>
3 
#include "quadric_simplify.h"
 3 
#include "quadric_simplify.h"
4 
#include "smooth.h"
 4 
#include "smooth.h"
- 
 
 5 
#include "Util/BinaryHeap.h"
5 
#include "HMesh/VertexCirculator.h"
 6 
#include "HMesh/VertexCirculator.h"
6 
#include "Geometry/QEM.h"
 7 
#include "Geometry/QEM.h"
7 
 
 8 
 
8 
 
 9 
 
9 
namespace HMesh
 10 
namespace HMesh
10 
{
 11 
{
11 
  using namespace CGLA;
 12 
		using namespace CGLA;
12 
  using namespace std;
 13 
		using namespace std;
13 
	using namespace GEO;
 14 
		using namespace GEO;
14 
	using namespace HMesh;
 15 
		using namespace HMesh;
15 
 
 - 
 
16 
	namespace
 - 
 
17 
	{
 - 
 
18 
		struct HalfEdgeRec
 - 
 
19 
		{
 - 
 
20 
			HalfEdgeIter he;
 - 
 
21 
			int time_stamp;
 - 
 
22 
			void halfedge_removed() {time_stamp = -1;}
 - 
 
23 
			HalfEdgeRec(): time_stamp(0) {}
 - 
 
24 
		};
 - 
 
25 
 
 16 
 
26 
		struct SimplifyRec
 17 
		namespace
27 
		{
 18 
		{
- 
 
 19 
				/* We create a record for each halfedge where we can keep its time
- 
 
 20 
					 stamp. If the time stamp on the halfedge record is bigger than
- 
 
 21 
					 the stamp on the simplification record, we cannot use the
- 
 
 22 
					 simplification record (see below). */
- 
 
 23 
				struct HalfEdgeRec
- 
 
 24 
				{
28 
			Vec3f opt_pos;
 25 
						HalfEdgeIter he;
29 
			int he_index;
 26 
						int time_stamp;
- 
 
 27 
						void halfedge_removed() {time_stamp = -1;}
- 
 
 28 
						HalfEdgeRec(): time_stamp(0) {}
30 
			float err;
 29 
				};
- 
 
 30 
 
- 
 
 31 
				/* The simpliciation record contains information about a potential
- 
 
 32 
					 edge contraction */
31 
			int time_stamp;
 33 
				struct SimplifyRec
- 
 
 34 
				{
- 
 
 35 
						Vec3d opt_pos;  // optimal vertex position
- 
 
 36 
						int he_index;   // Index (into HalfEdgeRec vector) of edge
- 
 
 37 
						                // we want to contract
- 
 
 38 
						float err;      // Error associated with contraction
- 
 
 39 
						int time_stamp; // Time stamp (see comment on HalfEdgeRec)
- 
 
 40 
						int visits;     // Visits (number of times we considered this
- 
 
 41 
						                // record).
32 
		};
 42 
				};
33 
 
 43 
 
34 
		bool operator<(const SimplifyRec& s1, const SimplifyRec& s2)
 44 
				bool operator<(const SimplifyRec& s1, const SimplifyRec& s2)
35 
		{
 45 
				{
36 
			return s1.err > s2.err;
 46 
						return s1.err > s2.err;
37 
		}
 47 
				}
38 
 
 48 
 
39 
		class QuadricSimplifier
 49 
				class QuadricSimplifier
40 
		{
 50 
				{
41 
			typedef priority_queue<SimplifyRec> SimplifyQueue;
 51 
						typedef priority_queue<SimplifyRec> SimplifyQueue;
42 
			typedef vector<QEM> QEMVec;
 52 
						typedef vector<QEM> QEMVec;
43 
			typedef vector<HalfEdgeRec> HalfEdgeVec;
 53 
						typedef vector<HalfEdgeRec> HalfEdgeVec;
44 
 
 54 
 
45 
			Manifold& m;
 55 
						Manifold& m;
46 
			HalfEdgeVec halfedge_vec;
 56 
						HalfEdgeVec halfedge_vec;
47 
			QEMVec qem_vec;
 57 
						QEMVec qem_vec;
48 
			SimplifyQueue sim_queue;
 58 
						SimplifyQueue sim_queue;
49 
 
 59 
 
- 
 
 60 
						/* Compute the error associated with contraction of he and the
- 
 
 61 
							 optimal position of resulting vertex. */
50 
			void push_simplify_rec(HalfEdgeIter he);
 62 
						void push_simplify_rec(HalfEdgeIter he);
- 
 
 63 
 
- 
 
 64 
						/* Check whether the contraction is valid. See below for details*/
- 
 
 65 
						bool check_consistency(HalfEdgeIter he, const Vec3d& opt_pos);
- 
 
 66 
 
- 
 
 67 
						/* Update the time stamp of a halfedge. A halfedge and its opp edge
- 
 
 68 
							 may have different stamps. We choose a stamp that is greater
- 
 
 69 
							 than either and assign to both.*/
- 
 
 70 
						void update_time_stamp(HalfEdgeIter he)
- 
 
 71 
								{
- 
 
 72 
										int time_stamp = s_max(halfedge_vec[he->touched].time_stamp,
- 
 
 73 
																					 halfedge_vec[he->opp->touched].time_stamp);
- 
 
 74 
										time_stamp++;
- 
 
 75 
										halfedge_vec[he->touched].time_stamp = time_stamp;
- 
 
 76 
										halfedge_vec[he->opp->touched].time_stamp = time_stamp;
- 
 
 77 
								}
51 
 
 78 
 
- 
 
 79 
						/* Update time stamps for all halfedges in one ring of vi */
52 
			void put_onering_in_queue(VertexIter vi);
 80 
						void update_onering_timestamp(VertexIter vi);
53 
 
 81 
 
- 
 
 82 
						/* Perform a collapse - if conditions are met. Returns 1 or 0
- 
 
 83 
							 accordingly. */
54 
			int collapse(const SimplifyRec& simplify_rec);
 84 
						int collapse(SimplifyRec& simplify_rec);
55 
 
 85 
 
56 
		public:
 86 
				public:
57 
 
 87 
 
- 
 
 88 
						/* Create a simplifier for a manifold */
58 
			QuadricSimplifier(Manifold& _m):
89 
						QuadricSimplifier(Manifold& _m):
59 
				m(_m),
90 
								m(_m),
60 
				halfedge_vec(m.no_halfedges()),
91 
								halfedge_vec(m.no_halfedges()),
61 
				qem_vec(m.no_vertices())
92 
								qem_vec(m.no_vertices())
62 
			{
 93 
								{
63 
				// Enumerate vertices
 94 
										// Enumerate vertices
64 
				m.enumerate_vertices();
 95 
										m.enumerate_vertices();
65
96
66 
				// Enumerate halfedges
 97 
										// Enumerate halfedges
67 
				m.enumerate_halfedges();
 98 
										m.enumerate_halfedges();
68 
			}
 99 
								}
69
100
- 
 
 101 
						/* Simplify doing at most max_work contractions */
70 
			void reduce(int max_work);
 102 
						void reduce(int max_work);
71 
		};
 103 
				};
72 
 
 104 
 
73 
		void QuadricSimplifier::push_simplify_rec(HalfEdgeIter he)
 105 
				bool QuadricSimplifier::check_consistency(HalfEdgeIter he,
- 
 
 106 
																									const Vec3d& opt_pos)
74 
		{
 107 
				{
75 
			// Update time_stamp
 108 
						VertexIter v0 = he->vert;
76 
			assert(halfedge_vec[he->touched].time_stamp >=0);
 109 
						VertexIter v1 = he->opp->vert;
- 
 
 110 
						Vec3d p0(v0->pos);
- 
 
 111 
 
- 
 
 112 
						/* This test is inspired by Garland's Ph.D. thesis. We try
77 
			assert(halfedge_vec[he->opp->touched].time_stamp>=0);
 113 
							 to detect whether flipped triangles will occur by sort of
78 
			int time_stamp = s_max(halfedge_vec[he->touched].time_stamp,
 114 
							 ensuring that the new vertex is in the hull of the one rings
79 
														 halfedge_vec[he->opp->touched].time_stamp);
 115 
							 of the vertices at either end of the edge being contracted */
- 
 
 116
- 
 
 117 
						for(VertexCirculator vc(v0); !vc.end(); ++vc)
80 
			time_stamp++;
 118 
						{
81 
			halfedge_vec[he->touched].time_stamp = time_stamp;
 119 
								HalfEdgeIter h = vc.get_halfedge();
82 
			halfedge_vec[he->opp->touched].time_stamp = time_stamp;
 120 
								if(h->vert != v1 && h->next->vert != v1)
- 
 
 121 
								{
83 
			// Get QEM for both end points
 122 
										Vec3d pa(h->vert->pos);
84 
			const QEM& Q1 = qem_vec[he->vert->touched];
 123 
										Vec3d pb(h->next->vert->pos);
- 
 
 124
85 
			const QEM& Q2 = qem_vec[he->opp->vert->touched];
 125 
										Vec3d dir = normalize(pb-pa);
86 
 
 126 
 
87 
			QEM q = Q1;
 127 
										Vec3d n = p0 - pa;
88 
			q += Q2;
 128 
										n = n - dir * dot(dir,n);
89 
 
 129 
 
- 
 
 130 
										if(dot(n,opt_pos - pa) <= 0)
- 
 
 131 
												return false;
90 
			float err;
 132 
								}
91 
			Vec3f opt_pos(0);
 133 
						}
92 
 
 134 
 
93 
			//cout << q.determinant() << endl;
 135 
						/* Since the test above is not really enough, we also make sure
- 
 
 136 
							 that we do not introduce vertices of very high (>=10) or low
- 
 
 137 
							 (<=3) valency. Flipped faces seem to be always associated with
- 
 
 138 
							 very irregular valencies. It seems to get rid of most problems
94 
			if (q.determinant()>= 1e-8)
 139 
							 not fixed by the check above. */
95 
				{
 140
96 
					opt_pos = q.opt_pos(0.001);
 141 
						if(valency(he->next->vert)<5)
- 
 
 142 
								return false;
- 
 
 143 
 
- 
 
 144 
						if((valency(he->vert) + valency(he->opp->vert) ) > 12)
97 
					err = q.error(opt_pos);
 145 
								return false;
- 
 
 146 
 
- 
 
 147 
						return true;
98 
				}
 148 
				}
- 
 
 149 
 
99 
			else
 150 
 
- 
 
 151 
				void QuadricSimplifier::push_simplify_rec(HalfEdgeIter he)
100 
				{
 152 
				{
101 
					// To see the effectivenes of the scheme, we can create
153 
						// Get QEM for both end points
102 
					// Random errors for comparison. Uncomment to use:
 154 
						const QEM& Q1 = qem_vec[he->vert->touched];
103 
					// 			float e0 = time_stamp + rand()/float(RAND_MAX);//q.error(v0);
 - 
 
104 
					// 			float e1 = time_stamp + rand()/float(RAND_MAX);//q.error(v1);
 155 
						const QEM& Q2 = qem_vec[he->opp->vert->touched];
105 
 
 156 
 
106 
					Vec3f v0 = he->vert->pos;
 157 
						QEM q = Q1;
107 
					Vec3f v1 = he->opp->vert->pos;
 158 
						q += Q2;
- 
 
 159 
 
108 
					float e0 = q.error(v0);
 160 
						float err;
109 
					float e1 = q.error(v1);
 161 
						Vec3d opt_pos(0);
110
162 
 
- 
 
 163 
						//cout << q.determinant() << endl;
111 
					if(e0 < e1)
 164 
						if (q.determinant()>= 1e-5)
112 
						{
 165 
						{
113 
							err = e0;
 166 
								opt_pos = q.opt_pos(1e-5);
114 
							opt_pos = v0;
 167 
								err = q.error(opt_pos);
115 
						}
 168 
						}
116 
					else
 169 
						else
117 
						{
 170 
						{
- 
 
 171 
								// To see the effectivenes of the scheme, we can create
- 
 
 172 
								// Random errors for comparison. Uncomment to use:
- 
 
 173 
								// 			float e0 = time_stamp + rand()/float(RAND_MAX);//q.error(v0);
- 
 
 174 
								// 			float e1 = time_stamp + rand()/float(RAND_MAX);//q.error(v1);
- 
 
 175 
 
- 
 
 176 
								Vec3d v0(he->vert->pos);
- 
 
 177 
								Vec3d v1(he->opp->vert->pos);
118 
							err = e1;
 178 
								float e0 = q.error(v0);
119 
							opt_pos = v1;
 179 
								float e1 = q.error(v1);
120 
						}
 180
- 
 
 181 
								if(e0 < e1)
121 
				}
182 
								{
122 
 
 - 
 
123 
			// Create SimplifyRec
 183 
										err = e0;
124 
			int he_index = he->touched;
 184 
										opt_pos = v0;
- 
 
 185 
								}
125 
			SimplifyRec simplify_rec;
 186 
								else
126 
			simplify_rec.opt_pos = opt_pos;
 187 
								{
127 
			simplify_rec.err = err;
 188 
										err = e1;
128 
			simplify_rec.he_index = he_index;
 189 
										opt_pos = v1;
- 
 
 190 
								}
129 
			simplify_rec.time_stamp = time_stamp;
 191 
						}
130 
 
 192 
 
- 
 
 193 
						// Create SimplifyRec
- 
 
 194 
						int he_index = he->touched;
- 
 
 195 
						SimplifyRec simplify_rec;
- 
 
 196 
						simplify_rec.opt_pos = opt_pos;
- 
 
 197 
						simplify_rec.err = err;
- 
 
 198 
						simplify_rec.he_index = he_index;
- 
 
 199 
						simplify_rec.time_stamp = halfedge_vec[he->touched].time_stamp;
- 
 
 200 
						simplify_rec.visits = 0;
131 
			// push it.
 201 
						// push it.
132 
			sim_queue.push(simplify_rec);
 202 
						sim_queue.push(simplify_rec);
- 
 
 203
133 
		}
 204 
				}
134
205
135 
 
 206 
 
136 
		void QuadricSimplifier::put_onering_in_queue(VertexIter vi)
 207 
				void QuadricSimplifier::update_onering_timestamp(VertexIter vi)
137 
		{
 - 
 
138 
			// For all emanating edges he
 - 
 
139 
			for(VertexCirculator vc(vi);
 - 
 
140 
					!vc.end(); ++vc)
 - 
 
141 
				{
 208 
				{
- 
 
 209 
						// For all emanating edges he
- 
 
 210 
						for(VertexCirculator vc(vi);
- 
 
 211 
								!vc.end(); ++vc)
- 
 
 212 
						{
142 
					HalfEdgeIter he = vc.get_halfedge();
 213 
								HalfEdgeIter he = vc.get_halfedge();
143 
					push_simplify_rec(he);
 214 
								update_time_stamp(he);
- 
 
 215 
						}
144 
				}
 216 
				}
145 
		}
 - 
 
146 
 
 - 
 
147 
		int QuadricSimplifier::collapse(const SimplifyRec& simplify_rec)
 - 
 
148 
		{
 - 
 
149 
			int he_index = simplify_rec.he_index;
 - 
 
150 
 
 217 
 
151 
			// Check the time stamp to verify that the simplification
- 
 
152 
			// record is the newest. If the halfedge has been removed
 - 
 
153 
			// the time stamp is -1 and the comparison will also fail.
 - 
 
154 
			if(halfedge_vec[he_index].time_stamp == simplify_rec.time_stamp)
 218 
				int QuadricSimplifier::collapse(SimplifyRec& simplify_rec)
155 
				{
 219 
				{
156 
					HalfEdgeIter he = halfedge_vec[he_index].he;
 220 
						int he_index = simplify_rec.he_index;
157 
					VertexIter v = he->opp->vert;
 221 
						HalfEdgeIter he = halfedge_vec[he_index].he;
158 
					VertexIter n = he->vert;
 - 
 
159 
 
 222 
 
- 
 
 223 
						// Check the time stamp to verify that the simplification
- 
 
 224 
						// record is the newest. If the halfedge has been removed
160 
					// If the edge is, in fact, collapsible
 225 
						// the time stamp is -1 and the comparison will also fail.
161 
					if(m.collapse_precond(he))
 226 
						if(halfedge_vec[he_index].time_stamp == simplify_rec.time_stamp)
162 
						{
 227 
						{
163 
							//cout << simplify_rec.err << " " << &(*he->vert) << endl;
 - 
 
164 
							// Get QEM for both end points
 - 
 
165 
							const QEM& Q1 = qem_vec[he->vert->touched];
 - 
 
166 
							const QEM& Q2 = qem_vec[he->opp->vert->touched];
 228 
								VertexIter v = he->opp->vert;
167 
 
 - 
 
168 
							// Compute Q_new = Q_1 + Q_2
 229 
								VertexIter n = he->vert;
169 
							QEM q = Q1;
 - 
 
170 
							q += Q2;
 - 
 
171 
 
 230 
 
172 
							// Mark all halfedges that will be removed as dead
 231 
								// If the edge is, in fact, collapsible
173 
							halfedge_vec[he->touched].halfedge_removed();
 - 
 
174 
							halfedge_vec[he->opp->touched].halfedge_removed();
 - 
 
175
- 
 
176 
							if(he->next->next->next == he)
 232 
								if(m.collapse_precond(he))
177 
								{
 233 
								{
- 
 
 234 
										// If our consistency checks pass, we are relatively
- 
 
 235 
										// sure that the contraction does not lead to a face flip.
- 
 
 236 
										if(check_consistency(he, simplify_rec.opt_pos) &&
- 
 
 237 
											 check_consistency(he->opp, simplify_rec.opt_pos))
- 
 
 238 
										{
- 
 
 239 
 
- 
 
 240 
												//cout << simplify_rec.err << " " << &(*he->vert) << endl;
- 
 
 241 
												// Get QEM for both end points
- 
 
 242 
												const QEM& Q1 = qem_vec[he->vert->touched];
- 
 
 243 
												const QEM& Q2 = qem_vec[he->opp->vert->touched];
- 
 
 244
- 
 
 245 
												// Compute Q_new = Q_1 + Q_2
- 
 
 246 
												QEM q = Q1;
- 
 
 247 
												q += Q2;
- 
 
 248
- 
 
 249 
												// Mark all halfedges that will be removed as dead
- 
 
 250 
												halfedge_vec[he->touched].halfedge_removed();
- 
 
 251 
												halfedge_vec[he->opp->touched].halfedge_removed();
- 
 
 252
- 
 
 253 
												if(he->next->next->next == he)
- 
 
 254 
												{
178 
									halfedge_vec[he->next->touched].halfedge_removed();
 255 
														halfedge_vec[he->next->touched].halfedge_removed();
179 
									halfedge_vec[he->next->next->touched].halfedge_removed();
 256 
														halfedge_vec[he->next->next->touched].halfedge_removed();
- 
 
 257 
												}
- 
 
 258 
												if(he->opp->next->next->next == he->opp)
- 
 
 259 
												{
- 
 
 260 
														halfedge_vec[he->opp->next->touched].halfedge_removed();
- 
 
 261 
														halfedge_vec[he->opp->next->next->touched].halfedge_removed();
- 
 
 262 
												}
- 
 
 263
- 
 
 264 
												// Do collapse
- 
 
 265 
												m.collapse_halfedge(he,false);
- 
 
 266 
												n->pos = Vec3f(simplify_rec.opt_pos);
- 
 
 267 
												qem_vec[n->touched] = q;
- 
 
 268
- 
 
 269 
												update_onering_timestamp(n);
- 
 
 270 
												return 1;
- 
 
 271 
										}
180 
								}
 272 
								}
- 
 
 273 
								// If we are here, the collapse was not allowed. If we have
- 
 
 274 
								// seen this simplify record less than 100 times, we try to
- 
 
 275 
								// increase the error and store the record again. Maybe some
- 
 
 276 
								// other contractions will make it more digestible later.
181 
							if(he->opp->next->next->next == he->opp)
 277 
								if(simplify_rec.visits < 10)
182 
								{
 278 
								{
183 
									halfedge_vec[he->opp->next->touched].halfedge_removed();
 279 
										simplify_rec.err += 5*simplify_rec.err + 1e-10;
- 
 
 280 
										++simplify_rec.visits;
184 
									halfedge_vec[he->opp->next->next->touched].halfedge_removed();
 281 
										sim_queue.push(simplify_rec);
185 
								}
 282 
								}
186 
 
 - 
 
187 
							// Do collapse
 - 
 
188 
							m.collapse_halfedge(he,false);
 - 
 
189 
							n->pos = simplify_rec.opt_pos;
 - 
 
190 
							qem_vec[n->touched] = q;
 - 
 
191
- 
 
192 
							put_onering_in_queue(n);
 - 
 
193 
							return 1;
 - 
 
194 
						}
 283 
						}
- 
 
 284 
						// Ok the time stamp did not match. Create a new record.
- 
 
 285 
						else if(halfedge_vec[he_index].time_stamp != -1)
- 
 
 286 
								push_simplify_rec(he);
- 
 
 287 
 
- 
 
 288 
						return 0;
195 
				}
 289 
				}
196 
			return 0;
 - 
 
197 
		}
 - 
 
198 
 
 290 
 
199 
		void QuadricSimplifier::reduce(int max_work)
 291 
				void QuadricSimplifier::reduce(int max_work)
200 
		{
 292 
				{
- 
 
 293 
						// Set t = 0 for all halfedges
- 
 
 294 
						int i=0;
- 
 
 295 
						for(HalfEdgeIter he = m.halfedges_begin();
- 
 
 296 
								he != m.halfedges_end(); ++he, ++i)
- 
 
 297 
								halfedge_vec[i].he = he;
201 
 
 298 
 
202 
			// Set t = 0 for all halfedges
 - 
 
203 
			int i=0;
 - 
 
204 
			for(HalfEdgeIter he = m.halfedges_begin();
 - 
 
205 
					he != m.halfedges_end(); ++he, ++i)
 299 
						cout << "Computing quadrics" << endl;
206 
				halfedge_vec[i].he = he;
 - 
 
207
300
208 
			// For all vertices, compute quadric and store in qem_vec
 301 
						// For all vertices, compute quadric and store in qem_vec
209 
			for(VertexIter vi=m.vertices_begin(); vi != m.vertices_end(); ++vi)
 302 
						for(VertexIter vi=m.vertices_begin(); vi != m.vertices_end(); ++vi)
210 
				{
 - 
 
211 
					Vec3d p(vi->pos);
 - 
 
212 
					QEM q;
 - 
 
213 
					for(VertexCirculator vc(vi); !vc.end(); ++vc)
 - 
 
214 
						{
 303 
						{
215 
							FaceIter f = vc.get_face();
 304 
								Vec3d p(vi->pos);
216 
							if(f != NULL_FACE_ITER)
 305 
								QEM q;
- 
 
 306 
								for(VertexCirculator vc(vi); !vc.end(); ++vc)
217 
								{
 307 
								{
- 
 
 308 
										FaceIter f = vc.get_face();
- 
 
 309 
										if(f != NULL_FACE_ITER)
- 
 
 310 
										{
218 
									Vec3d n(normal(f));
 311 
												Vec3d n(normal(f));
219 
									double a = area(f);
 312 
												double a = area(f);
220 
									q += QEM(p, n, a / 3.0);
 313 
												q += QEM(p, n, a / 3.0);
- 
 
 314 
										}
221 
								}
 315 
								}
- 
 
 316 
								qem_vec[vi->touched] = q;
222 
						}
 317 
						}
223 
					qem_vec[vi->touched] = q;
 318 
						cout << "Pushing initial halfedges" << endl;
224 
				}
 - 
 
225 
 
 319 
 
226 
			for(HalfEdgeIter he = m.halfedges_begin();
 320 
						for(HalfEdgeIter he = m.halfedges_begin();
227 
					he != m.halfedges_end(); ++he)
 321 
								he != m.halfedges_end(); ++he)
228 
				// For all halfedges,
322 
								// For all halfedges,
229 
				{
 323 
						{
230 
					if(halfedge_vec[he->touched].time_stamp == 0)
 324 
								if(halfedge_vec[he->touched].time_stamp == 0)
- 
 
 325 
								{
- 
 
 326 
										update_time_stamp(he);
231 
						push_simplify_rec(he);
 327 
										push_simplify_rec(he);
- 
 
 328 
								}
232 
				}
 329 
						}
233 
 
 330 
 
- 
 
 331 
						cout << "Simplify" << endl;
234 
 
 332 
 
235 
			int work = 0;
 333 
						int work = 0;
236 
			while(!sim_queue.empty() && work < max_work)
 334 
						while(!sim_queue.empty() && work < max_work)
237 
				{
 - 
 
238 
					int dwork = collapse(sim_queue.top());
 - 
 
239 
					if(dwork>0)
 - 
 
240 
						{
 335 
						{
- 
 
 336 
								SimplifyRec simplify_record = sim_queue.top();
241 
							work += dwork;
 337 
								sim_queue.pop();
- 
 
 338 
 
- 
 
 339 
								work += collapse(simplify_record);
242 
							if((work % 100) == 0)
 340 
								if((work % 100) == 0)
- 
 
 341 
								{
243 
								cout << "work = " << work << endl;
 342 
										cout << "work = " << work << endl;
- 
 
 343 
										cout << "sim Q size = " << sim_queue.size() << endl;
- 
 
 344 
								}
244 
						}
 345 
						}
245 
					sim_queue.pop();
 - 
 
246 
				}
 346 
				}
247 
		}
 347 
		}
248 
	}
 - 
 
249 
 
 348 
 
250 
	void quadric_simplify(Manifold& m, int max_work)
 349 
		void quadric_simplify(Manifold& m, int max_work)
251 
	{
 350 
		{
252 
		srand(1210);
 351 
				srand(1210);
253 
		QuadricSimplifier qsim(m);
 352 
				QuadricSimplifier qsim(m);
254 
		qsim.reduce(max_work);
 353 
				qsim.reduce(max_work);
255 
	}
 354 
		}
256 
 
 355 
 
257 
}
 356 
}