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clipper.pas
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unit clipper;
(*******************************************************************************
* *
* Author : Angus Johnson *
* Version : 6.2.1 *
* Date : 31 October 2014 *
* Website : http://www.angusj.com *
* Copyright : Angus Johnson 2010-2014 *
* *
* License: *
* Use, modification & distribution is subject to Boost Software License Ver 1. *
* http://www.boost.org/LICENSE_1_0.txt *
* *
* Attributions: *
* The code in this library is an extension of Bala Vatti's clipping algorithm: *
* "A generic solution to polygon clipping" *
* Communications of the ACM, Vol 35, Issue 7 (July 1992) PP 56-63. *
* http://portal.acm.org/citation.cfm?id=129906 *
* *
* Computer graphics and geometric modeling: implementation and algorithms *
* By Max K. Agoston *
* Springer; 1 edition (January 4, 2005) *
* http://books.google.com/books?q=vatti+clipping+agoston *
* *
* See also: *
* "Polygon Offsetting by Computing Winding Numbers" *
* Paper no. DETC2005-85513 PP. 565-575 *
* ASME 2005 International Design Engineering Technical Conferences *
* and Computers and Information in Engineering Conference (IDETC/CIE2005) *
* September 24-28, 2005 , Long Beach, California, USA *
* http://www.me.berkeley.edu/~mcmains/pubs/DAC05OffsetPolygon.pdf *
* *
*******************************************************************************)
//use_int32: When enabled 32bit ints are used instead of 64bit ints. This
//improve performance but coordinate values are limited to the range +/- 46340
//{$DEFINE use_int32}
//use_xyz: adds a Z member to IntPoint (with only a minor cost to performance)
{$DEFINE use_xyz}
//use_lines: Enables open path clipping (with a very minor cost to performance)
{$DEFINE use_lines}
//use_deprecated: Enables temporary support for the obsolete functions
//{$DEFINE use_deprecated}
// enable LEGACYIFEND for Delphi XE4+
{$IF CompilerVersion >= 25.0}
{$LEGACYIFEND ON}
{$IFEND}
// use generic lists for NextGen compiler
{$IFDEF NEXTGEN}
{$DEFINE USEGENERICS}
{$ENDIF}
{$IFDEF FPC}
{$DEFINE INLINING}
{$DEFINE UInt64Support}
{$ELSE}
{$IFDEF ConditionalExpressions}
{$IF CompilerVersion >= 15} //Delphi 7
{$DEFINE UInt64Support} //nb: Delphi7 only marginally supports UInt64.
{$IFEND}
{$IF CompilerVersion >= 18} //Delphi 2007
//Inline has been supported since D2005.
//However D2005 and D2006 have an Inline codegen bug (QC41166).
//http://www.thedelphigeek.com/2007/02/nasty-inline-codegen-bug-in-bds-2006.html
{$DEFINE INLINING}
{$IFEND}
{$ENDIF}
{$ENDIF}
interface
uses
SysUtils, Types, Classes,
{$IFDEF USEGENERICS}
Generics.Collections, Generics.Defaults,
{$ENDIF}
Math;
const
def_arc_tolerance = 0.25;
type
{$IFDEF use_int32}
{$IF CompilerVersion < 20} //Delphi 2009
cInt = Integer; //Int32 supported since D2009.
{$ELSE}
cInt = Int32;
{$IFEND}
{$ELSE}
cInt = Int64;
{$ENDIF}
PIntPoint = ^TIntPoint;
{$IFDEF use_xyz}
TIntPoint = record X, Y, Z: cInt; end;
{$ELSE}
TIntPoint = record X, Y: cInt; end;
{$ENDIF}
TIntRect = record Left, Top, Right, Bottom: cInt; end;
TDoublePoint = record X, Y: Double; end;
TArrayOfDoublePoint = array of TDoublePoint;
{$IFDEF use_xyz}
TZFillCallback =
procedure (const E1Bot, E1Top, E2Bot, E2Top: TIntPoint; var Pt: TIntPoint);
{$ENDIF}
TInitOption = (ioReverseSolution, ioStrictlySimple, ioPreserveCollinear);
TInitOptions = set of TInitOption;
TClipType = (ctIntersection, ctUnion, ctDifference, ctXor);
TPolyType = (ptSubject, ptClip);
//By far the most widely used winding rules for polygon filling are
//EvenOdd & NonZero (GDI, GDI+, XLib, OpenGL, Cairo, AGG, Quartz, SVG, Gr32)
//Others rules include Positive, Negative and ABS_GTR_EQ_TWO (only in OpenGL)
//see http://glprogramming.com/red/chapter11.html
TPolyFillType = (pftEvenOdd, pftNonZero, pftPositive, pftNegative);
//TJoinType & TEndType are used by OffsetPaths()
TJoinType = (jtSquare, jtRound, jtMiter);
TEndType = (etClosedPolygon, etClosedLine,
etOpenButt, etOpenSquare, etOpenRound); //and etSingle still to come
TPath = array of TIntPoint;
TPaths = array of TPath;
TPolyNode = class;
TArrayOfPolyNode = array of TPolyNode;
TPolyNode = class
private
FPath : TPath;
FParent : TPolyNode;
FIndex : Integer;
FCount : Integer;
FBuffLen : Integer;
FIsOpen : Boolean;
FChilds : TArrayOfPolyNode;
FJoinType: TJoinType; //used by ClipperOffset only
FEndType : TEndType; //used by ClipperOffset only
function GetChild(Index: Integer): TPolyNode;
function IsHoleNode: boolean;
procedure AddChild(PolyNode: TPolyNode);
function GetNextSiblingUp: TPolyNode;
public
function GetNext: TPolyNode;
property ChildCount: Integer read FCount;
property Childs[index: Integer]: TPolyNode read GetChild;
property Parent: TPolyNode read FParent;
property IsHole: Boolean read IsHoleNode;
property IsOpen: Boolean read FIsOpen;
property Contour: TPath read FPath;
end;
TPolyTree = class(TPolyNode)
private
FAllNodes: TArrayOfPolyNode; //container for ALL PolyNodes
function GetTotal: Integer;
public
procedure Clear;
function GetFirst: TPolyNode;
destructor Destroy; override;
property Total: Integer read GetTotal;
end;
//the definitions below are used internally ...
TEdgeSide = (esLeft, esRight);
TDirection = (dRightToLeft, dLeftToRight);
POutPt = ^TOutPt;
PEdge = ^TEdge;
TEdge = record
Bot : TIntPoint; //bottom
Curr : TIntPoint; //current (ie relative to bottom of current scanbeam)
Top : TIntPoint; //top
Delta: TIntPoint;
Dx : Double; //inverse of slope
PolyType : TPolyType;
Side : TEdgeSide;
WindDelta: Integer; //1 or -1 depending on winding direction
WindCnt : Integer;
WindCnt2 : Integer; //winding count of the opposite PolyType
OutIdx : Integer;
Next : PEdge;
Prev : PEdge;
NextInLML: PEdge;
PrevInAEL: PEdge;
NextInAEL: PEdge;
PrevInSEL: PEdge;
NextInSEL: PEdge;
end;
PEdgeArray = ^TEdgeArray;
TEdgeArray = array[0.. MaxInt div sizeof(TEdge) -1] of TEdge;
PScanbeam = ^TScanbeam;
TScanbeam = record
Y : cInt;
Next: PScanbeam;
end;
PIntersectNode = ^TIntersectNode;
TIntersectNode = record
Edge1: PEdge;
Edge2: PEdge;
Pt : TIntPoint;
end;
PLocalMinimum = ^TLocalMinimum;
TLocalMinimum = record
Y : cInt;
LeftBound : PEdge;
RightBound: PEdge;
end;
POutRec = ^TOutRec;
TOutRec = record
Idx : Integer;
BottomPt : POutPt;
IsHole : Boolean;
IsOpen : Boolean;
//The 'FirstLeft' field points to the OutRec representing the polygon
//immediately to the left of the current OutRec's polygon. When a polygon is
//contained within another polygon, the polygon immediately to its left will
//either be its outer polygon or a sibling also contained by the same outer
//polygon. By storing this field, it's easy to sort polygons into a tree
//structure which reflects the parent/child relationships of all polygons.
FirstLeft : POutRec;
Pts : POutPt;
PolyNode : TPolyNode;
end;
TOutPt = record
Idx : Integer;
Pt : TIntPoint;
Next : POutPt;
Prev : POutPt;
end;
PJoin = ^TJoin;
TJoin = record
OutPt1 : POutPt;
OutPt2 : POutPt;
OffPt : TIntPoint; //offset point (provides slope of common edges)
end;
{$IFDEF USEGENERICS}
TEgdeList = TList<PEdgeArray>;
TLocMinList = TList<PLocalMinimum>;
{$ELSE}
TEgdeList = TList;
TLocMinList = TList;
{$ENDIF}
TClipperBase = class
private
FEdgeList : TEgdeList;
FUse64BitRange : Boolean; //see LoRange and HiRange consts notes below
FHasOpenPaths : Boolean;
procedure DisposeLocalMinimaList;
procedure DisposePolyPts(PP: POutPt);
function ProcessBound(E: PEdge; NextIsForward: Boolean): PEdge;
protected
FLocMinList : TLocMinList;
FCurrentLocMinIdx : Integer;
FPreserveCollinear : Boolean;
procedure Reset; virtual;
property HasOpenPaths: Boolean read FHasOpenPaths;
public
constructor Create; virtual;
destructor Destroy; override;
procedure Clear; virtual;
function AddPath(const Path: TPath; PolyType: TPolyType; Closed: Boolean): Boolean;
function AddPaths(const Paths: TPaths; PolyType: TPolyType; Closed: Boolean): Boolean;
//PreserveCollinear: Prevents removal of 'inner' vertices when three or
//more vertices are collinear in solution polygons.
property PreserveCollinear: Boolean
read FPreserveCollinear write FPreserveCollinear;
end;
{$IFDEF USEGENERICS}
TPolyOutList = TList<POutRec>;
TJoinList = TList<PJoin>;
TIntersecList = TList<PIntersectNode>;
{$ELSE}
TPolyOutList = TList;
TJoinList = TList;
TIntersecList = TList;
{$ENDIF}
TClipper = class(TClipperBase)
private
FPolyOutList : TPolyOutList;
FJoinList : TJoinList;
FGhostJoinList : TJoinList;
FIntersectList : TIntersecList;
FClipType : TClipType;
FScanbeam : PScanbeam; //scanbeam list
FActiveEdges : PEdge; //active Edge list
FSortedEdges : PEdge; //used for temporary sorting
FClipFillType : TPolyFillType;
FSubjFillType : TPolyFillType;
FExecuteLocked : Boolean;
FReverseOutput : Boolean;
FStrictSimple : Boolean;
FUsingPolyTree : Boolean;
{$IFDEF use_xyz}
FZFillCallback : TZFillCallback;
{$ENDIF}
procedure DisposeScanbeamList;
procedure InsertScanbeam(const Y: cInt);
function PopScanbeam: cInt;
procedure SetWindingCount(Edge: PEdge);
function IsEvenOddFillType(Edge: PEdge): Boolean;
function IsEvenOddAltFillType(Edge: PEdge): Boolean;
procedure AddEdgeToSEL(Edge: PEdge);
procedure CopyAELToSEL;
procedure InsertLocalMinimaIntoAEL(const BotY: cInt);
procedure SwapPositionsInAEL(E1, E2: PEdge);
procedure SwapPositionsInSEL(E1, E2: PEdge);
procedure ProcessHorizontal(HorzEdge: PEdge; IsTopOfScanbeam: Boolean);
procedure ProcessHorizontals(IsTopOfScanbeam: Boolean);
function ProcessIntersections(const TopY: cInt): Boolean;
procedure BuildIntersectList(const TopY: cInt);
procedure ProcessIntersectList;
procedure DeleteFromAEL(E: PEdge);
procedure DeleteFromSEL(E: PEdge);
procedure IntersectEdges(E1,E2: PEdge; Pt: TIntPoint);
procedure DoMaxima(E: PEdge);
procedure UpdateEdgeIntoAEL(var E: PEdge);
function FixupIntersectionOrder: Boolean;
procedure ProcessEdgesAtTopOfScanbeam(const TopY: cInt);
function IsContributing(Edge: PEdge): Boolean;
function CreateOutRec: POutRec;
function AddOutPt(E: PEdge; const Pt: TIntPoint): POutPt;
procedure AddLocalMaxPoly(E1, E2: PEdge; const Pt: TIntPoint);
function AddLocalMinPoly(E1, E2: PEdge; const Pt: TIntPoint): POutPt;
function GetOutRec(Idx: integer): POutRec;
procedure AppendPolygon(E1, E2: PEdge);
procedure DisposeAllOutRecs;
procedure DisposeOutRec(Index: Integer);
procedure DisposeIntersectNodes;
function BuildResult: TPaths;
function BuildResult2(PolyTree: TPolyTree): Boolean;
procedure FixupOutPolygon(OutRec: POutRec);
procedure SetHoleState(E: PEdge; OutRec: POutRec);
procedure AddJoin(Op1, Op2: POutPt; const OffPt: TIntPoint);
procedure ClearJoins;
procedure AddGhostJoin(OutPt: POutPt; const OffPt: TIntPoint);
procedure ClearGhostJoins;
function JoinPoints(Jr: PJoin; OutRec1, OutRec2: POutRec): Boolean;
procedure FixupFirstLefts1(OldOutRec, NewOutRec: POutRec);
procedure FixupFirstLefts2(OldOutRec, NewOutRec: POutRec);
procedure DoSimplePolygons;
procedure JoinCommonEdges;
procedure FixHoleLinkage(OutRec: POutRec);
protected
procedure Reset; override;
function ExecuteInternal: Boolean; virtual;
public
function Execute(clipType: TClipType;
out solution: TPaths;
subjFillType: TPolyFillType = pftEvenOdd;
clipFillType: TPolyFillType = pftEvenOdd): Boolean; overload;
function Execute(clipType: TClipType;
out PolyTree: TPolyTree;
subjFillType: TPolyFillType = pftEvenOdd;
clipFillType: TPolyFillType = pftEvenOdd): Boolean; overload;
constructor Create(InitOptions: TInitOptions = []); reintroduce; overload;
destructor Destroy; override;
//ReverseSolution: reverses the default orientation
property ReverseSolution: Boolean read FReverseOutput write FReverseOutput;
//StrictlySimple: when false (the default) solutions are 'weakly' simple
property StrictlySimple: Boolean read FStrictSimple write FStrictSimple;
{$IFDEF use_xyz}
property ZFillFunction: TZFillCallback read FZFillCallback write FZFillCallback;
{$ENDIF}
end;
TClipperOffset = class
private
FDelta: Double;
FSinA, FSin, FCos: Extended;
FMiterLim, FStepsPerRad: Double;
FNorms: TArrayOfDoublePoint;
FSolution: TPaths;
FOutPos: Integer;
FInP: TPath;
FOutP: TPath;
FLowest: TIntPoint; //X = Path index, Y = Path offset (to lowest point)
FPolyNodes: TPolyNode;
FMiterLimit: Double;
FArcTolerance: Double;
procedure AddPoint(const Pt: TIntPoint);
procedure DoSquare(J, K: Integer);
procedure DoMiter(J, K: Integer; R: Double);
procedure DoRound(J, K: Integer);
procedure OffsetPoint(J: Integer;
var K: Integer; JoinType: TJoinType);
procedure FixOrientations;
procedure DoOffset(Delta: Double);
public
constructor Create(MiterLimit: Double = 2; ArcTolerance: Double = def_arc_tolerance);
destructor Destroy; override;
procedure AddPath(const Path: TPath; JoinType: TJoinType; EndType: TEndType);
procedure AddPaths(const Paths: TPaths; JoinType: TJoinType; EndType: TEndType);
procedure Clear;
procedure Execute(out solution: TPaths; Delta: Double); overload;
procedure Execute(out solution: TPolyTree; Delta: Double); overload;
property MiterLimit: double read FMiterLimit write FMiterLimit;
property ArcTolerance: double read FArcTolerance write FArcTolerance;
end;
function Orientation(const Pts: TPath): Boolean; overload;
function Area(const Pts: TPath): Double; overload;
function PointInPolygon (const pt: TIntPoint; const poly: TPath): Integer; overload;
function GetBounds(const polys: TPaths): TIntRect;
{$IFDEF use_xyz}
function IntPoint(const X, Y: Int64; Z: Int64 = 0): TIntPoint; overload;
function IntPoint(const X, Y: Double; Z: Double = 0): TIntPoint; overload;
{$ELSE}
function IntPoint(const X, Y: cInt): TIntPoint; overload;
function IntPoint(const X, Y: Double): TIntPoint; overload;
{$ENDIF}
function DoublePoint(const X, Y: Double): TDoublePoint; overload;
function DoublePoint(const Ip: TIntPoint): TDoublePoint; overload;
function ReversePath(const Pts: TPath): TPath;
function ReversePaths(const Pts: TPaths): TPaths;
//SimplifyPolygon converts a self-intersecting polygon into a simple polygon.
function SimplifyPolygon(const Poly: TPath; FillType: TPolyFillType = pftEvenOdd): TPaths;
function SimplifyPolygons(const Polys: TPaths; FillType: TPolyFillType = pftEvenOdd): TPaths;
//CleanPolygon removes adjacent vertices closer than the specified distance.
function CleanPolygon(const Poly: TPath; Distance: double = 1.415): TPath;
function CleanPolygons(const Polys: TPaths; Distance: double = 1.415): TPaths;
function MinkowskiSum(const Pattern, Path: TPath; PathIsClosed: Boolean): TPaths; overload;
function MinkowskiSum(const Pattern: TPath; const Paths: TPaths;
PathFillType: TPolyFillType; PathIsClosed: Boolean): TPaths; overload;
function MinkowskiDiff(const Poly1, Poly2: TPath): TPaths;
function PolyTreeToPaths(PolyTree: TPolyTree): TPaths;
function ClosedPathsFromPolyTree(PolyTree: TPolyTree): TPaths;
function OpenPathsFromPolyTree(PolyTree: TPolyTree): TPaths;
const
//The SlopesEqual function places the most limits on coordinate values
//So, to avoid overflow errors, they must not exceed the following values...
//Also, if all coordinates are within +/-LoRange, then calculations will be
//faster. Otherwise using Int128 math will render the library ~10-15% slower.
{$IFDEF use_int32}
LoRange: cInt = 46340;
HiRange: cInt = 46340;
{$ELSE}
LoRange: cInt = $B504F333; //3.0e+9
HiRange: cInt = $3FFFFFFFFFFFFFFF; //9.2e+18
{$ENDIF}
implementation
//NOTE: The Clipper library has been developed with software that uses an
//inverted Y axis display. Therefore 'above' and 'below' in the code's comments
//will reflect this. For example: given coord A (0,20) and coord B (0,10),
//A.Y would be considered BELOW B.Y to correctly understand the comments.
const
Horizontal: Double = -3.4e+38;
Unassigned : Integer = -1;
Skip : Integer = -2; //flag for the edge that closes an open path
Tolerance : double = 1.0E-15;
Two_Pi : double = 2 * PI;
resourcestring
rsDoMaxima = 'DoMaxima error';
rsUpdateEdgeIntoAEL = 'UpdateEdgeIntoAEL error';
rsHorizontal = 'ProcessHorizontal error';
rsInvalidInt = 'Coordinate exceeds range bounds';
rsIntersect = 'Intersection error';
rsOpenPath = 'AddPath: Open paths must be subject.';
rsOpenPath2 = 'AddPath: Open paths have been disabled.';
rsOpenPath3 = 'Error: TPolyTree struct is need for open path clipping.';
rsPolylines = 'Error intersecting polylines';
rsClipperOffset = 'Error: No PolyTree assigned';
//------------------------------------------------------------------------------
// TPolyNode methods ...
//------------------------------------------------------------------------------
function TPolyNode.GetChild(Index: Integer): TPolyNode;
begin
if (Index < 0) or (Index >= FCount) then
raise Exception.Create('TPolyNode range error: ' + inttostr(Index));
Result := FChilds[Index];
end;
//------------------------------------------------------------------------------
procedure TPolyNode.AddChild(PolyNode: TPolyNode);
begin
if FCount = FBuffLen then
begin
Inc(FBuffLen, 16);
SetLength(FChilds, FBuffLen);
end;
PolyNode.FParent := self;
PolyNode.FIndex := FCount;
FChilds[FCount] := PolyNode;
Inc(FCount);
end;
//------------------------------------------------------------------------------
function TPolyNode.IsHoleNode: boolean;
var
Node: TPolyNode;
begin
Result := True;
Node := FParent;
while Assigned(Node) do
begin
Result := not Result;
Node := Node.FParent;
end;
end;
//------------------------------------------------------------------------------
function TPolyNode.GetNext: TPolyNode;
begin
if FCount > 0 then
Result := FChilds[0] else
Result := GetNextSiblingUp;
end;
//------------------------------------------------------------------------------
function TPolyNode.GetNextSiblingUp: TPolyNode;
begin
if not Assigned(FParent) then //protects against TPolyTree.GetNextSiblingUp()
Result := nil
else if FIndex = FParent.FCount -1 then
Result := FParent.GetNextSiblingUp
else
Result := FParent.Childs[FIndex +1];
end;
//------------------------------------------------------------------------------
// TPolyTree methods ...
//------------------------------------------------------------------------------
destructor TPolyTree.Destroy;
begin
Clear;
inherited;
end;
//------------------------------------------------------------------------------
procedure TPolyTree.Clear;
var
I: Integer;
begin
for I := 0 to high(FAllNodes) do FAllNodes[I].Free;
FAllNodes := nil;
FBuffLen := 16;
SetLength(FChilds, FBuffLen);
FCount := 0;
end;
//------------------------------------------------------------------------------
function TPolyTree.GetFirst: TPolyNode;
begin
if FCount > 0 then
Result := FChilds[0] else
Result := nil;
end;
//------------------------------------------------------------------------------
function TPolyTree.GetTotal: Integer;
begin
Result := length(FAllNodes);
//with negative offsets, ignore the hidden outer polygon ...
if (Result > 0) and (FAllNodes[0] <> FChilds[0]) then dec(Result);
end;
{$IFNDEF use_int32}
//------------------------------------------------------------------------------
// UInt64 math support for Delphi 6
//------------------------------------------------------------------------------
{$OVERFLOWCHECKS OFF}
{$IFNDEF UInt64Support}
function CompareUInt64(const i, j: Int64): Integer;
begin
if Int64Rec(i).Hi < Int64Rec(j).Hi then
Result := -1
else if Int64Rec(i).Hi > Int64Rec(j).Hi then
Result := 1
else if Int64Rec(i).Lo < Int64Rec(j).Lo then
Result := -1
else if Int64Rec(i).Lo > Int64Rec(j).Lo then
Result := 1
else
Result := 0;
end;
{$ENDIF}
function UInt64LT(const i, j: Int64): Boolean; {$IFDEF INLINING} inline; {$ENDIF}
begin
{$IFDEF UInt64Support}
Result := UInt64(i) < UInt64(j);
{$ELSE}
Result := CompareUInt64(i, j) = -1;
{$ENDIF}
end;
function UInt64GT(const i, j: Int64): Boolean; {$IFDEF INLINING} inline; {$ENDIF}
begin
{$IFDEF UInt64Support}
Result := UInt64(i) > UInt64(j);
{$ELSE}
Result := CompareUInt64(i, j) = 1;
{$ENDIF}
end;
{$OVERFLOWCHECKS ON}
//------------------------------------------------------------------------------
// Int128 Functions ...
//------------------------------------------------------------------------------
const
Mask32Bits = $FFFFFFFF;
type
//nb: TInt128.Lo is typed Int64 instead of UInt64 to provide Delphi 7
//compatability. However while UInt64 isn't a recognised type in
//Delphi 7, it can still be used in typecasts.
TInt128 = record
Hi : Int64;
Lo : Int64;
end;
{$OVERFLOWCHECKS OFF}
procedure Int128Negate(var Val: TInt128);
begin
if Val.Lo = 0 then
begin
Val.Hi := -Val.Hi;
end else
begin
Val.Lo := -Val.Lo;
Val.Hi := not Val.Hi;
end;
end;
//------------------------------------------------------------------------------
function Int128(const val: Int64): TInt128; overload;
begin
Result.Lo := val;
if val < 0 then
Result.Hi := -1 else
Result.Hi := 0;
end;
//------------------------------------------------------------------------------
function Int128Equal(const Int1, Int2: TInt128): Boolean;
begin
Result := (Int1.Lo = Int2.Lo) and (Int1.Hi = Int2.Hi);
end;
//------------------------------------------------------------------------------
function Int128LessThan(const Int1, Int2: TInt128): Boolean;
begin
if (Int1.Hi <> Int2.Hi) then Result := Int1.Hi < Int2.Hi
else Result := UInt64LT(Int1.Lo, Int2.Lo);
end;
//------------------------------------------------------------------------------
function Int128Add(const Int1, Int2: TInt128): TInt128;
begin
Result.Lo := Int1.Lo + Int2.Lo;
Result.Hi := Int1.Hi + Int2.Hi;
if UInt64LT(Result.Lo, Int1.Lo) then Inc(Result.Hi);
end;
//------------------------------------------------------------------------------
function Int128Sub(const Int1, Int2: TInt128): TInt128;
begin
Result.Hi := Int1.Hi - Int2.Hi;
Result.Lo := Int1.Lo - Int2.Lo;
if UInt64GT(Result.Lo, Int1.Lo) then Dec(Result.Hi);
end;
//------------------------------------------------------------------------------
function Int128Mul(Int1, Int2: Int64): TInt128;
var
A, B, C: Int64;
Int1Hi, Int1Lo, Int2Hi, Int2Lo: Int64;
Negate: Boolean;
begin
//save the Result's sign before clearing both sign bits ...
Negate := (Int1 < 0) <> (Int2 < 0);
if Int1 < 0 then Int1 := -Int1;
if Int2 < 0 then Int2 := -Int2;
Int1Hi := Int1 shr 32;
Int1Lo := Int1 and Mask32Bits;
Int2Hi := Int2 shr 32;
Int2Lo := Int2 and Mask32Bits;
A := Int1Hi * Int2Hi;
B := Int1Lo * Int2Lo;
//because the high (sign) bits in both int1Hi & int2Hi have been zeroed,
//there's no risk of 64 bit overflow in the following assignment
//(ie: $7FFFFFFF*$FFFFFFFF + $7FFFFFFF*$FFFFFFFF < 64bits)
C := Int1Hi*Int2Lo + Int2Hi*Int1Lo;
//Result = A shl 64 + C shl 32 + B ...
Result.Hi := A + (C shr 32);
A := C shl 32;
Result.Lo := A + B;
if UInt64LT(Result.Lo, A) then
Inc(Result.Hi);
if Negate then Int128Negate(Result);
end;
//------------------------------------------------------------------------------
function Int128Div(Dividend, Divisor: TInt128{; out Remainder: TInt128}): TInt128;
var
Cntr: TInt128;
Negate: Boolean;
begin
if (Divisor.Lo = 0) and (Divisor.Hi = 0) then
raise Exception.create('int128Div error: divide by zero');
Negate := (Divisor.Hi < 0) <> (Dividend.Hi < 0);
if Dividend.Hi < 0 then Int128Negate(Dividend);
if Divisor.Hi < 0 then Int128Negate(Divisor);
if Int128LessThan(Divisor, Dividend) then
begin
Result.Hi := 0;
Result.Lo := 0;
Cntr.Lo := 1;
Cntr.Hi := 0;
//while (Dividend >= Divisor) do
while not Int128LessThan(Dividend, Divisor) do
begin
//divisor := divisor shl 1;
Divisor.Hi := Divisor.Hi shl 1;
if Divisor.Lo < 0 then Inc(Divisor.Hi);
Divisor.Lo := Divisor.Lo shl 1;
//Cntr := Cntr shl 1;
Cntr.Hi := Cntr.Hi shl 1;
if Cntr.Lo < 0 then Inc(Cntr.Hi);
Cntr.Lo := Cntr.Lo shl 1;
end;
//Divisor := Divisor shr 1;
Divisor.Lo := Divisor.Lo shr 1;
if Divisor.Hi and $1 = $1 then
Int64Rec(Divisor.Lo).Hi := Cardinal(Int64Rec(Divisor.Lo).Hi) or $80000000;
Divisor.Hi := Divisor.Hi shr 1;
//Cntr := Cntr shr 1;
Cntr.Lo := Cntr.Lo shr 1;
if Cntr.Hi and $1 = $1 then
Int64Rec(Cntr.Lo).Hi := Cardinal(Int64Rec(Cntr.Lo).Hi) or $80000000;
Cntr.Hi := Cntr.Hi shr 1;
//while (Cntr > 0) do
while not ((Cntr.Hi = 0) and (Cntr.Lo = 0)) do
begin
//if ( Dividend >= Divisor) then
if not Int128LessThan(Dividend, Divisor) then
begin
//Dividend := Dividend - Divisor;
Dividend := Int128Sub(Dividend, Divisor);
//Result := Result or Cntr;
Result.Hi := Result.Hi or Cntr.Hi;
Result.Lo := Result.Lo or Cntr.Lo;
end;
//Divisor := Divisor shr 1;
Divisor.Lo := Divisor.Lo shr 1;
if Divisor.Hi and $1 = $1 then
Int64Rec(Divisor.Lo).Hi := Cardinal(Int64Rec(Divisor.Lo).Hi) or $80000000;
Divisor.Hi := Divisor.Hi shr 1;
//Cntr := Cntr shr 1;
Cntr.Lo := Cntr.Lo shr 1;
if Cntr.Hi and $1 = $1 then
Int64Rec(Cntr.Lo).Hi := Cardinal(Int64Rec(Cntr.Lo).Hi) or $80000000;
Cntr.Hi := Cntr.Hi shr 1;
end;
if Negate then Int128Negate(Result);
//Remainder := Dividend;
end
else if (Divisor.Hi = Dividend.Hi) and (Divisor.Lo = Dividend.Lo) then
begin
if Negate then Result := Int128(-1) else Result := Int128(1);
end else
begin
Result := Int128(0);
end;
end;
//------------------------------------------------------------------------------
function Int128AsDouble(val: TInt128): Double;
const
shift64: Double = 18446744073709551616.0;
var
lo: Int64;
begin
if (val.Hi < 0) then
begin
lo := -val.Lo;
if lo = 0 then
Result := val.Hi * shift64 else
Result := -(not val.Hi * shift64 + UInt64(lo));
end else
Result := val.Hi * shift64 + UInt64(val.Lo);
end;
//------------------------------------------------------------------------------
{$OVERFLOWCHECKS ON}
{$ENDIF}
//------------------------------------------------------------------------------
// Miscellaneous Functions ...
//------------------------------------------------------------------------------
function PointCount(Pts: POutPt): Integer;
var
P: POutPt;
begin
Result := 0;
if not Assigned(Pts) then Exit;
P := Pts;
repeat
Inc(Result);
P := P.Next;
until P = Pts;
end;
//------------------------------------------------------------------------------
function PointsEqual(const P1, P2: TIntPoint): Boolean; {$IFDEF INLINING} inline; {$ENDIF}
begin
Result := (P1.X = P2.X) and (P1.Y = P2.Y);
end;
//------------------------------------------------------------------------------
{$IFDEF use_xyz}
function IntPoint(const X, Y: Int64; Z: Int64 = 0): TIntPoint;
begin
Result.X := X;
Result.Y := Y;
Result.Z := Z;
end;
//------------------------------------------------------------------------------
function IntPoint(const X, Y: Double; Z: Double = 0): TIntPoint;
begin
Result.X := Round(X);
Result.Y := Round(Y);
Result.Z := Round(Z);
end;
//------------------------------------------------------------------------------
{$ELSE}
function IntPoint(const X, Y: cInt): TIntPoint;
begin
Result.X := X;
Result.Y := Y;
end;
//------------------------------------------------------------------------------
function IntPoint(const X, Y: Double): TIntPoint;
begin
Result.X := Round(X);
Result.Y := Round(Y);
end;
{$ENDIF}
//------------------------------------------------------------------------------
function DoublePoint(const X, Y: Double): TDoublePoint;
begin
Result.X := X;
Result.Y := Y;
end;
//------------------------------------------------------------------------------
function DoublePoint(const Ip: TIntPoint): TDoublePoint;
begin
Result.X := Ip.X;
Result.Y := Ip.Y;
end;
//------------------------------------------------------------------------------
function Area(const Pts: TPath): Double;
var
I, J, Cnt: Integer;
D: Double;
begin
Result := 0.0;
Cnt := Length(Pts);
if (Cnt < 3) then Exit;
J := cnt - 1;
for I := 0 to Cnt -1 do
begin
D := (Pts[j].X + Pts[i].X);
Result := Result + D * (Pts[j].Y - Pts[i].Y);
J := I;
end;
Result := -Result * 0.5;
end;
//------------------------------------------------------------------------------
function Area(OutRec: POutRec): Double; overload;
var
Op: POutPt;
D, D2: Double;
begin
D := 0;
Op := OutRec.Pts;
if Assigned(Op) then
repeat
D2 := Op.Prev.Pt.X + Op.Pt.X;
D := D + D2 * (Op.Prev.Pt.Y - Op.Pt.Y);
Op := Op.Next;
until Op = OutRec.Pts;
Result := D * 0.5;
end;
//------------------------------------------------------------------------------
function Orientation(const Pts: TPath): Boolean;
begin
Result := Area(Pts) >= 0;
end;
//------------------------------------------------------------------------------
function ReversePath(const Pts: TPath): TPath;
var
I, HighI: Integer;
begin
HighI := high(Pts);
SetLength(Result, HighI +1);
for I := 0 to HighI do
Result[I] := Pts[HighI - I];
end;
//------------------------------------------------------------------------------
function ReversePaths(const Pts: TPaths): TPaths;
var
I, J, highJ: Integer;
begin
I := length(Pts);
SetLength(Result, I);
for I := 0 to I -1 do
begin
highJ := high(Pts[I]);
SetLength(Result[I], highJ+1);
for J := 0 to highJ do
Result[I][J] := Pts[I][highJ - J];
end;
end;
//------------------------------------------------------------------------------
function GetBounds(const polys: TPaths): TIntRect;
var
I,J,Len: Integer;
begin
Len := Length(polys);
I := 0;
while (I < Len) and (Length(polys[I]) = 0) do inc(I);
if (I = Len) then
begin
with Result do begin Left := 0; Top := 0; Right := 0; Bottom := 0; end;
Exit;