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2* *
3* Author : Angus Johnson *
4* Version : 6.4.0 *
5* Date : 2 July 2015 *
6* Website : http://www.angusj.com *
7* Copyright : Angus Johnson 2010-2015 *
8* *
9* License: *
10* Use, modification & distribution is subject to Boost Software License Ver 1. *
11* http://www.boost.org/LICENSE_1_0.txt *
12* *
13* Attributions: *
14* The code in this library is an extension of Bala Vatti's clipping algorithm: *
15* "A generic solution to polygon clipping" *
16* Communications of the ACM, Vol 35, Issue 7 (July 1992) pp 56-63. *
17* http://portal.acm.org/citation.cfm?id=129906 *
18* *
19* Computer graphics and geometric modeling: implementation and algorithms *
20* By Max K. Agoston *
21* Springer; 1 edition (January 4, 2005) *
22* http://books.google.com/books?q=vatti+clipping+agoston *
23* *
24* See also: *
25* "Polygon Offsetting by Computing Winding Numbers" *
26* Paper no. DETC2005-85513 pp. 565-575 *
27* ASME 2005 International Design Engineering Technical Conferences *
28* and Computers and Information in Engineering Conference (IDETC/CIE2005) *
29* September 24-28, 2005 , Long Beach, California, USA *
30* http://www.me.berkeley.edu/~mcmains/pubs/DAC05OffsetPolygon.pdf *
31* *
34#ifndef clipper_hpp
35#define clipper_hpp
37#define CLIPPER_VERSION "6.2.6"
39//use_int32: When enabled 32bit ints are used instead of 64bit ints. This
40//improve performance but coordinate values are limited to the range +/- 46340
41//#define use_int32
43//use_xyz: adds a Z member to IntPoint. Adds a minor cost to perfomance.
44//#define use_xyz
46//use_lines: Enables line clipping. Adds a very minor cost to performance.
47#define use_lines
49//use_deprecated: Enables temporary support for the obsolete functions
50//#define use_deprecated
52#include <vector>
53#include <list>
54#include <set>
55#include <stdexcept>
56#include <cstring>
57#include <cstdlib>
58#include <ostream>
59#include <functional>
60#include <queue>
62namespace ClipperLib {
66//By far the most widely used winding rules for polygon filling are
67//EvenOdd & NonZero (GDI, GDI+, XLib, OpenGL, Cairo, AGG, Quartz, SVG, Gr32)
68//Others rules include Positive, Negative and ABS_GTR_EQ_TWO (only in OpenGL)
69//see http://glprogramming.com/red/chapter11.html
72#ifdef use_int32
73 typedef int cInt;
74 static cInt const loRange = 0x7FFF;
75 static cInt const hiRange = 0x7FFF;
77 typedef signed long long cInt;
78 static cInt const loRange = 0x3FFFFFFF;
79 static cInt const hiRange = 0x3FFFFFFFFFFFFFFFLL;
80 typedef signed long long long64; //used by Int128 class
81 typedef unsigned long long ulong64;
85struct IntPoint {
88#ifdef use_xyz
89 cInt Z;
90 IntPoint(cInt x = 0, cInt y = 0, cInt z = 0): X(x), Y(y), Z(z) {};
92 IntPoint(cInt x = 0, cInt y = 0): X(x), Y(y) {};
95 friend inline bool operator== (const IntPoint& a, const IntPoint& b)
96 {
97 return a.X == b.X && a.Y == b.Y;
98 }
99 friend inline bool operator!= (const IntPoint& a, const IntPoint& b)
100 {
101 return a.X != b.X || a.Y != b.Y;
102 }
106typedef std::vector< IntPoint > Path;
107typedef std::vector< Path > Paths;
109inline Path& operator <<(Path& poly, const IntPoint& p) {poly.push_back(p); return poly;}
110inline Paths& operator <<(Paths& polys, const Path& p) {polys.push_back(p); return polys;}
112std::ostream& operator <<(std::ostream &s, const IntPoint &p);
113std::ostream& operator <<(std::ostream &s, const Path &p);
114std::ostream& operator <<(std::ostream &s, const Paths &p);
118 double X;
119 double Y;
120 DoublePoint(double x = 0, double y = 0) : X(x), Y(y) {}
121 DoublePoint(IntPoint ip) : X((double)ip.X), Y((double)ip.Y) {}
125#ifdef use_xyz
126typedef void (*ZFillCallback)(IntPoint& e1bot, IntPoint& e1top, IntPoint& e2bot, IntPoint& e2top, IntPoint& pt);
133class PolyNode;
134typedef std::vector< PolyNode* > PolyNodes;
139 PolyNode();
140 virtual ~PolyNode(){};
144 PolyNode* GetNext() const;
145 bool IsHole() const;
146 bool IsOpen() const;
147 int ChildCount() const;
149 unsigned Index; //node index in Parent.Childs
153 PolyNode* GetNextSiblingUp() const;
154 void AddChild(PolyNode& child);
155 friend class Clipper; //to access Index
156 friend class ClipperOffset;
159class PolyTree: public PolyNode
163 PolyNode* GetFirst() const;
164 void Clear();
165 int Total() const;
168 friend class Clipper; //to access AllNodes
171bool Orientation(const Path &poly);
172double Area(const Path &poly);
173int PointInPolygon(const IntPoint &pt, const Path &path);
175void SimplifyPolygon(const Path &in_poly, Paths &out_polys, PolyFillType fillType = pftEvenOdd);
176void SimplifyPolygons(const Paths &in_polys, Paths &out_polys, PolyFillType fillType = pftEvenOdd);
177void SimplifyPolygons(Paths &polys, PolyFillType fillType = pftEvenOdd);
179void CleanPolygon(const Path& in_poly, Path& out_poly, double distance = 1.415);
180void CleanPolygon(Path& poly, double distance = 1.415);
181void CleanPolygons(const Paths& in_polys, Paths& out_polys, double distance = 1.415);
182void CleanPolygons(Paths& polys, double distance = 1.415);
184void MinkowskiSum(const Path& pattern, const Path& path, Paths& solution, bool pathIsClosed);
185void MinkowskiSum(const Path& pattern, const Paths& paths, Paths& solution, bool pathIsClosed);
186void MinkowskiDiff(const Path& poly1, const Path& poly2, Paths& solution);
188void PolyTreeToPaths(const PolyTree& polytree, Paths& paths);
189void ClosedPathsFromPolyTree(const PolyTree& polytree, Paths& paths);
190void OpenPathsFromPolyTree(PolyTree& polytree, Paths& paths);
192void ReversePath(Path& p);
193void ReversePaths(Paths& p);
197//enums that are used internally ...
198enum EdgeSide { esLeft = 1, esRight = 2};
200//forward declarations (for stuff used internally) ...
201struct TEdge;
202struct IntersectNode;
203struct LocalMinimum;
204struct OutPt;
205struct OutRec;
206struct Join;
208typedef std::vector < OutRec* > PolyOutList;
209typedef std::vector < TEdge* > EdgeList;
210typedef std::vector < Join* > JoinList;
211typedef std::vector < IntersectNode* > IntersectList;
215//ClipperBase is the ancestor to the Clipper class. It should not be
216//instantiated directly. This class simply abstracts the conversion of sets of
217//polygon coordinates into edge objects that are stored in a LocalMinima list.
221 ClipperBase();
222 virtual ~ClipperBase();
223 virtual bool AddPath(const Path &pg, PolyType PolyTyp, bool Closed);
224 bool AddPaths(const Paths &ppg, PolyType PolyTyp, bool Closed);
225 virtual void Clear();
228 void PreserveCollinear(bool value) {m_PreserveCollinear = value;};
231 TEdge* AddBoundsToLML(TEdge *e, bool IsClosed);
232 virtual void Reset();
233 TEdge* ProcessBound(TEdge* E, bool IsClockwise);
234 void InsertScanbeam(const cInt Y);
235 bool PopScanbeam(cInt &Y);
236 bool LocalMinimaPending();
237 bool PopLocalMinima(cInt Y, const LocalMinimum *&locMin);
239 void DisposeAllOutRecs();
240 void DisposeOutRec(PolyOutList::size_type index);
241 void SwapPositionsInAEL(TEdge *edge1, TEdge *edge2);
242 void DeleteFromAEL(TEdge *e);
243 void UpdateEdgeIntoAEL(TEdge *&e);
245 typedef std::vector<LocalMinimum> MinimaList;
246 MinimaList::iterator m_CurrentLM;
256 typedef std::priority_queue<cInt> ScanbeamList;
261class Clipper : public virtual ClipperBase
264 Clipper(int initOptions = 0);
265 bool Execute(ClipType clipType,
266 Paths &solution,
267 PolyFillType fillType = pftEvenOdd);
268 bool Execute(ClipType clipType,
269 Paths &solution,
270 PolyFillType subjFillType,
271 PolyFillType clipFillType);
272 bool Execute(ClipType clipType,
273 PolyTree &polytree,
274 PolyFillType fillType = pftEvenOdd);
275 bool Execute(ClipType clipType,
276 PolyTree &polytree,
277 PolyFillType subjFillType,
278 PolyFillType clipFillType);
280 void ReverseSolution(bool value) {m_ReverseOutput = value;};
282 void StrictlySimple(bool value) {m_StrictSimple = value;};
283 //set the callback function for z value filling on intersections (otherwise Z is 0)
284#ifdef use_xyz
285 void ZFillFunction(ZFillCallback zFillFunc);
288 virtual bool ExecuteInternal();
294 typedef std::list<cInt> MaximaList;
303#ifdef use_xyz
304 ZFillCallback m_ZFill; //custom callback
306 void SetWindingCount(TEdge& edge);
307 bool IsEvenOddFillType(const TEdge& edge) const;
308 bool IsEvenOddAltFillType(const TEdge& edge) const;
309 void InsertLocalMinimaIntoAEL(const cInt botY);
310 void InsertEdgeIntoAEL(TEdge *edge, TEdge* startEdge);
311 void AddEdgeToSEL(TEdge *edge);
312 bool PopEdgeFromSEL(TEdge *&edge);
313 void CopyAELToSEL();
314 void DeleteFromSEL(TEdge *e);
315 void SwapPositionsInSEL(TEdge *edge1, TEdge *edge2);
316 bool IsContributing(const TEdge& edge) const;
317 bool IsTopHorz(const cInt XPos);
318 void DoMaxima(TEdge *e);
319 void ProcessHorizontals();
320 void ProcessHorizontal(TEdge *horzEdge);
321 void AddLocalMaxPoly(TEdge *e1, TEdge *e2, const IntPoint &pt);
322 OutPt* AddLocalMinPoly(TEdge *e1, TEdge *e2, const IntPoint &pt);
323 OutRec* GetOutRec(int idx);
324 void AppendPolygon(TEdge *e1, TEdge *e2);
325 void IntersectEdges(TEdge *e1, TEdge *e2, IntPoint &pt);
326 OutPt* AddOutPt(TEdge *e, const IntPoint &pt);
328 bool ProcessIntersections(const cInt topY);
329 void BuildIntersectList(const cInt topY);
331 void ProcessEdgesAtTopOfScanbeam(const cInt topY);
332 void BuildResult(Paths& polys);
333 void BuildResult2(PolyTree& polytree);
334 void SetHoleState(TEdge *e, OutRec *outrec);
337 void FixupOutPolygon(OutRec &outrec);
338 void FixupOutPolyline(OutRec &outrec);
339 bool IsHole(TEdge *e);
340 bool FindOwnerFromSplitRecs(OutRec &outRec, OutRec *&currOrfl);
341 void FixHoleLinkage(OutRec &outrec);
342 void AddJoin(OutPt *op1, OutPt *op2, const IntPoint offPt);
343 void ClearJoins();
344 void ClearGhostJoins();
345 void AddGhostJoin(OutPt *op, const IntPoint offPt);
346 bool JoinPoints(Join *j, OutRec* outRec1, OutRec* outRec2);
347 void JoinCommonEdges();
348 void DoSimplePolygons();
349 void FixupFirstLefts1(OutRec* OldOutRec, OutRec* NewOutRec);
350 void FixupFirstLefts2(OutRec* InnerOutRec, OutRec* OuterOutRec);
351 void FixupFirstLefts3(OutRec* OldOutRec, OutRec* NewOutRec);
352#ifdef use_xyz
353 void SetZ(IntPoint& pt, TEdge& e1, TEdge& e2);
361 ClipperOffset(double miterLimit = 2.0, double roundPrecision = 0.25);
363 void AddPath(const Path& path, JoinType joinType, EndType endType);
364 void AddPaths(const Paths& paths, JoinType joinType, EndType endType);
365 void Execute(Paths& solution, double delta);
366 void Execute(PolyTree& solution, double delta);
367 void Clear();
374 std::vector<DoublePoint> m_normals;
380 void FixOrientations();
381 void DoOffset(double delta);
382 void OffsetPoint(int j, int& k, JoinType jointype);
383 void DoSquare(int j, int k);
384 void DoMiter(int j, int k, double r);
385 void DoRound(int j, int k);
389class clipperException : public std::exception
391 public:
392 clipperException(const char* description): m_descr(description) {}
393 virtual ~clipperException() throw() {}
394 virtual const char* what() const throw() {return m_descr.c_str();}
395 private:
396 std::string m_descr;
400} //ClipperLib namespace
402#endif //clipper_hpp
static Index< 'p', 3 > p
constexpr double a
virtual void Reset()
Definition: clipper.cpp:1247
bool AddPaths(const Paths &ppg, PolyType PolyTyp, bool Closed)
Definition: clipper.cpp:1224
TEdge * ProcessBound(TEdge *E, bool IsClockwise)
Definition: clipper.cpp:928
void UpdateEdgeIntoAEL(TEdge *&e)
Definition: clipper.cpp:1442
std::priority_queue< cInt > ScanbeamList
Definition: clipper.hpp:256
virtual void Clear()
Definition: clipper.cpp:1233
TEdge * AddBoundsToLML(TEdge *e, bool IsClosed)
ScanbeamList m_Scanbeam
Definition: clipper.hpp:257
virtual bool AddPath(const Path &pg, PolyType PolyTyp, bool Closed)
Definition: clipper.cpp:1045
void DeleteFromAEL(TEdge *e)
Definition: clipper.cpp:1367
MinimaList m_MinimaList
Definition: clipper.hpp:247
void PreserveCollinear(bool value)
Definition: clipper.hpp:228
void SwapPositionsInAEL(TEdge *edge1, TEdge *edge2)
Definition: clipper.cpp:1395
MinimaList::iterator m_CurrentLM
Definition: clipper.hpp:246
void InsertScanbeam(const cInt Y)
Definition: clipper.cpp:1335
bool PopScanbeam(cInt &Y)
Definition: clipper.cpp:1341
std::vector< LocalMinimum > MinimaList
Definition: clipper.hpp:245
PolyOutList m_PolyOuts
Definition: clipper.hpp:253
void DisposeOutRec(PolyOutList::size_type index)
Definition: clipper.cpp:1358
bool PopLocalMinima(cInt Y, const LocalMinimum *&locMin)
Definition: clipper.cpp:1286
bool FixupIntersectionOrder()
Definition: clipper.cpp:2930
void ProcessHorizontal(TEdge *horzEdge)
Definition: clipper.cpp:2636
void AddJoin(OutPt *op1, OutPt *op2, const IntPoint offPt)
Definition: clipper.cpp:1942
void InsertEdgeIntoAEL(TEdge *edge, TEdge *startEdge)
Definition: clipper.cpp:3312
bool FindOwnerFromSplitRecs(OutRec &outRec, OutRec *&currOrfl)
void SetWindingCount(TEdge &edge)
Definition: clipper.cpp:1624
void InsertLocalMinimaIntoAEL(const cInt botY)
Definition: clipper.cpp:1978
void ProcessIntersectList()
Definition: clipper.cpp:2902
void BuildResult(Paths &polys)
Definition: clipper.cpp:3192
bool IsContributing(const TEdge &edge) const
Definition: clipper.cpp:1741
OutPt * AddLocalMinPoly(TEdge *e1, TEdge *e2, const IntPoint &pt)
Definition: clipper.cpp:1841
void BuildIntersectList(const cInt topY)
Definition: clipper.cpp:2852
bool JoinPoints(Join *j, OutRec *outRec1, OutRec *outRec2)
Definition: clipper.cpp:3451
bool Execute(ClipType clipType, Paths &solution, PolyFillType fillType=pftEvenOdd)
Definition: clipper.cpp:1496
void AddEdgeToSEL(TEdge *edge)
Definition: clipper.cpp:1900
void AppendPolygon(TEdge *e1, TEdge *e2)
Definition: clipper.cpp:2367
MaximaList m_Maxima
Definition: clipper.hpp:295
virtual bool ExecuteInternal()
Definition: clipper.cpp:1560
void ReverseSolution(bool value)
Definition: clipper.hpp:280
std::list< cInt > MaximaList
Definition: clipper.hpp:294
OutPt * AddOutPt(TEdge *e, const IntPoint &pt)
Definition: clipper.cpp:2463
bool IsTopHorz(const cInt XPos)
void SetHoleState(TEdge *e, OutRec *outrec)
Definition: clipper.cpp:2301
ClipType m_ClipType
Definition: clipper.hpp:293
void IntersectEdges(TEdge *e1, TEdge *e2, IntPoint &pt)
Definition: clipper.cpp:2106
OutRec * GetOutRec(int idx)
Definition: clipper.cpp:2358
void AddLocalMaxPoly(TEdge *e1, TEdge *e2, const IntPoint &pt)
Definition: clipper.cpp:1884
void BuildResult2(PolyTree &polytree)
Definition: clipper.cpp:3213
void ProcessHorizontals()
Definition: clipper.cpp:2512
void FixupFirstLefts3(OutRec *OldOutRec, OutRec *NewOutRec)
Definition: clipper.cpp:3659
bool IsEvenOddAltFillType(const TEdge &edge) const
Definition: clipper.cpp:1733
void StrictlySimple(bool value)
Definition: clipper.hpp:282
void FixupFirstLefts2(OutRec *InnerOutRec, OutRec *OuterOutRec)
Definition: clipper.cpp:3634
PolyFillType m_SubjFillType
Definition: clipper.hpp:299
void ProcessEdgesAtTopOfScanbeam(const cInt topY)
Definition: clipper.cpp:3005
void DoMaxima(TEdge *e)
Definition: clipper.cpp:2953
bool IsEvenOddFillType(const TEdge &edge) const
Definition: clipper.cpp:1725
void AddGhostJoin(OutPt *op, const IntPoint offPt)
Definition: clipper.cpp:1968
IntersectList m_IntersectList
Definition: clipper.hpp:292
void FixupFirstLefts1(OutRec *OldOutRec, OutRec *NewOutRec)
Definition: clipper.cpp:3618
bool ProcessIntersections(const cInt topY)
Definition: clipper.cpp:2823
TEdge * m_SortedEdges
Definition: clipper.hpp:296
PolyFillType m_ClipFillType
Definition: clipper.hpp:298
OutPt * GetLastOutPt(TEdge *e)
Definition: clipper.cpp:2502
bool IsHole(TEdge *e)
bool ReverseSolution()
Definition: clipper.hpp:279
void SwapPositionsInSEL(TEdge *edge1, TEdge *edge2)
Definition: clipper.cpp:2558
void FixHoleLinkage(OutRec &outrec)
Definition: clipper.cpp:1545
void DeleteFromSEL(TEdge *e)
Definition: clipper.cpp:2080
JoinList m_GhostJoins
Definition: clipper.hpp:291
bool PopEdgeFromSEL(TEdge *&edge)
Definition: clipper.cpp:1920
void FixupOutPolyline(OutRec &outrec)
Definition: clipper.cpp:3109
void FixupOutPolygon(OutRec &outrec)
Definition: clipper.cpp:3136
void DisposeIntersectNodes()
Definition: clipper.cpp:2844
void AddPath(const Path &path, JoinType joinType, EndType endType)
Definition: clipper.cpp:3802
void AddPaths(const Paths &paths, JoinType joinType, EndType endType)
Definition: clipper.cpp:3847
void DoSquare(int j, int k)
Definition: clipper.cpp:4168
void DoOffset(double delta)
Definition: clipper.cpp:3951
void DoRound(int j, int k)
Definition: clipper.cpp:4189
std::vector< DoublePoint > m_normals
Definition: clipper.hpp:374
void OffsetPoint(int j, int &k, JoinType jointype)
Definition: clipper.cpp:4124
void Execute(Paths &solution, double delta)
Definition: clipper.cpp:3880
void DoMiter(int j, int k, double r)
Definition: clipper.cpp:4181
bool IsHole() const
Definition: clipper.cpp:222
int ChildCount() const
Definition: clipper.cpp:187
void AddChild(PolyNode &child)
Definition: clipper.cpp:193
PolyNode * Parent
Definition: clipper.hpp:143
virtual ~PolyNode()
Definition: clipper.hpp:140
bool IsOpen() const
Definition: clipper.cpp:235
PolyNode * GetNext() const
Definition: clipper.cpp:202
PolyNode * GetNextSiblingUp() const
Definition: clipper.cpp:211
PolyNodes AllNodes
Definition: clipper.hpp:167
PolyNode * GetFirst() const
Definition: clipper.cpp:161
int Total() const
Definition: clipper.cpp:170
virtual const char * what() const
Definition: clipper.hpp:394
clipperException(const char *description)
Definition: clipper.hpp:392
FTensor::Index< 'j', 3 > j
FTensor::Index< 'k', 3 > k
unsigned long long ulong64
Definition: clipper.hpp:81
@ ioReverseSolution
Definition: clipper.hpp:129
@ ioPreserveCollinear
Definition: clipper.hpp:129
@ ioStrictlySimple
Definition: clipper.hpp:129
void SimplifyPolygon(const Path &in_poly, Paths &out_polys, PolyFillType fillType=pftEvenOdd)
Definition: clipper.cpp:4289
void PolyTreeToPaths(const PolyTree &polytree, Paths &paths)
Definition: clipper.cpp:4568
@ ctIntersection
Definition: clipper.hpp:64
@ ctDifference
Definition: clipper.hpp:64
double Area(const Path &poly)
Definition: clipper.cpp:391
std::vector< Path > Paths
Definition: clipper.hpp:107
void CleanPolygons(const Paths &in_polys, Paths &out_polys, double distance=1.415)
Definition: clipper.cpp:4449
static cInt const hiRange
Definition: clipper.hpp:79
signed long long cInt
Definition: clipper.hpp:77
void MinkowskiDiff(const Path &poly1, const Path &poly2, Paths &solution)
Definition: clipper.cpp:4544
std::vector< Join * > JoinList
Definition: clipper.hpp:210
signed long long long64
Definition: clipper.hpp:80
bool Orientation(const Path &poly)
Definition: clipper.cpp:385
void ClosedPathsFromPolyTree(const PolyTree &polytree, Paths &paths)
Definition: clipper.cpp:4576
std::vector< TEdge * > EdgeList
Definition: clipper.hpp:209
std::vector< OutRec * > PolyOutList
Definition: clipper.hpp:208
@ pftNegative
Definition: clipper.hpp:70
@ pftPositive
Definition: clipper.hpp:70
@ pftEvenOdd
Definition: clipper.hpp:70
@ pftNonZero
Definition: clipper.hpp:70
std::vector< IntersectNode * > IntersectList
Definition: clipper.hpp:211
void OpenPathsFromPolyTree(PolyTree &polytree, Paths &paths)
Definition: clipper.cpp:4584
void SimplifyPolygons(const Paths &in_polys, Paths &out_polys, PolyFillType fillType=pftEvenOdd)
Definition: clipper.cpp:4298
void ReversePath(Path &p)
Definition: clipper.cpp:4276
static cInt const loRange
Definition: clipper.hpp:78
@ etClosedLine
Definition: clipper.hpp:131
@ etClosedPolygon
Definition: clipper.hpp:131
@ etOpenSquare
Definition: clipper.hpp:131
int PointInPolygon(const IntPoint &pt, const Path &path)
Definition: clipper.cpp:440
std::vector< PolyNode * > PolyNodes
Definition: clipper.hpp:134
void MinkowskiSum(const Path &pattern, const Path &path, Paths &solution, bool pathIsClosed)
Definition: clipper.cpp:4507
void ReversePaths(Paths &p)
Definition: clipper.cpp:4282
void CleanPolygon(const Path &in_poly, Path &out_poly, double distance=1.415)
Definition: clipper.cpp:4383
std::vector< IntPoint > Path
Definition: clipper.hpp:106
static constexpr double delta
DoublePoint(double x=0, double y=0)
Definition: clipper.hpp:120
DoublePoint(IntPoint ip)
Definition: clipper.hpp:121
friend bool operator==(const IntPoint &a, const IntPoint &b)
Definition: clipper.hpp:95
IntPoint(cInt x=0, cInt y=0)
Definition: clipper.hpp:92
friend bool operator!=(const IntPoint &a, const IntPoint &b)
Definition: clipper.hpp:99