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bgrapath.pas
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bgrapath.pas
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{ ***************************************************************************
* *
* This file is part of BGRABitmap library which is distributed under the *
* modified LGPL. *
* *
* See the file COPYING.modifiedLGPL.txt, included in this distribution, *
* for details about the copyright. *
* *
* 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. *
* *
************************* BGRABitmap library ******************************
- Drawing routines with transparency and antialiasing with Lazarus.
Offers also various transforms.
- These routines allow to manipulate 32bit images in BGRA format or RGBA
format (depending on the platform).
- This code is under modified LGPL (see COPYING.modifiedLGPL.txt).
This means that you can link this library inside your programs for any purpose.
Only the included part of the code must remain LGPL.
- If you make some improvements to this library, please notify here:
http://www.lazarus.freepascal.org/index.php/topic,12037.0.html
********************* Contact : Circular at operamail.com *******************
******************************* CONTRIBUTOR(S) ******************************
- Edivando S. Santos Brasil | [email protected]
(Compatibility with FPC ($Mode objfpc/delphi) and delphi VCL 11/2018)
***************************** END CONTRIBUTOR(S) *****************************}
Unit BGRAPath;
{$i bgrabitmap.inc}{$H+}
{.$POINTERMATH ON}
interface
//todo: tangent interpolation
{ There are different conventions for angles.
First is about the unit. It can be one of the following:
- degrees (0..360)
- radian (0..2*Pi)
- tenth of degrees (0..3600)
- from 0 to 65536
Second is about the origin. It can be one of the following:
- right-most position (this is the default origin for radian and 65536)
- top-most position (this is the default origin for degrees)
Third is about the sign. It can be one of the following:
- positive is clockwise (this is the default for degrees)
- positive is counterclockwise (this is the default for radian and 65536)
TBGRAPath and TBGRACanvas2D follow HTML5 convention which is:
(radian, right-most, clockwise) that can be shortened to (radian, clockwise)
because right-most is the default for radian. This is abbreviated as "radCW".
When radian are CCW, it is also specified in order to make it clear, even
if it is the default convention in mathematics.
In order to make things easier, there are some functions that accept angles
in degrees. The convention used here is the usual degree convention:
(degrees, top-most, clockwise) that can be shortened to (degree)
because top-most and clockwise is the default for degrees.
}
uses
Classes, BGRATypes, BGRABitmapTypes, {$IFNDEF FPC}GraphType,{$ENDIF} BGRAGraphics, BGRATransform;
type
TBGRAPathElementType = (peNone, peMoveTo, peLineTo, peCloseSubPath,
peQuadraticBezierTo, peCubicBezierTo, peArc, peOpenedSpline,
peClosedSpline);
TBGRAPathDrawProc = procedure(const APoints: array of TPointF; AClosed: boolean; AData: Pointer) of object;
TBGRAPathFillProc = procedure(const APoints: array of TPointF; AData: pointer) of object;
TBGRAPath = class;
{ TBGRAPathCursor }
TBGRAPathCursor = class(TBGRACustomPathCursor)
protected
FPath: TBGRAPath;
FDataPos: BGRAPtrInt;
FAcceptedDeviation: single;
FPathLength: single;
FPathLengthComputed: boolean;
FBounds: TRectF;
FBoundsComputed: boolean;
FArcPos: Single;
FStartCoordinate: TPointF;
FEndCoordinate: TPointF;
FLoopClosedShapes,FLoopPath: boolean;
FCurrentElementType: TBGRAPathElementType;
FCurrentElement: Pointer;
FCurrentElementArcPos,
FCurrentElementArcPosScale: single;
FCurrentElementStartCoord,
FCurrentElementEndCoord: TPointF;
FCurrentElementLength: single;
FCurrentElementPoints: ArrayOfTPointF;
FCurrentSegment: BGRANativeInt;
FCurrentSegmentPos: single;
function GoToNextElement(ACanJump: boolean): boolean;
function GoToPreviousElement(ACanJump: boolean): boolean;
procedure MoveToEndOfElement;
procedure MoveForwardInElement(ADistance: single);
procedure MoveBackwardInElement(ADistance: single);
function NeedPolygonalApprox: boolean;
procedure OnPathFree; virtual;
function GetLoopClosedShapes: boolean; override;
function GetLoopPath: boolean; override;
function GetStartCoordinate: TPointF; override;
procedure SetLoopClosedShapes(AValue: boolean); override;
procedure SetLoopPath(AValue: boolean); override;
function GetArcPos: single; override;
function GetCurrentTangent: TPointF; override;
procedure SetArcPos(AValue: single); override;
function GetBounds: TRectF; override;
function GetPathLength: single; override;
procedure PrepareCurrentElement; virtual;
function GetCurrentCoord: TPointF; override;
function GetPath: TBGRAPath; virtual;
public
constructor Create(APath: TBGRAPath; AAcceptedDeviation: single = 0.1);
function MoveForward(ADistance: single; ACanJump: boolean = true): single; override;
function MoveBackward(ADistance: single; ACanJump: boolean = true): single; override;
destructor Destroy; override;
property CurrentCoordinate: TPointF read GetCurrentCoord;
property CurrentTangent: TPointF read GetCurrentTangent;
property Position: single read GetArcPos write SetArcPos;
property PathLength: single read GetPathLength;
property Path: TBGRAPath read GetPath;
property Bounds: TRectF read GetBounds;
property StartCoordinate: TPointF read GetStartCoordinate;
property LoopClosedShapes: boolean read GetLoopClosedShapes write SetLoopClosedShapes;
property LoopPath: boolean read GetLoopPath write SetLoopPath;
property AcceptedDeviation: single read FAcceptedDeviation;
end;
{ TBGRAPath }
TBGRAPath = class(TObject, IBGRAPath)
protected
FData: PByte;
FDataCapacity: BGRAPtrInt;
FDataPos: BGRAPtrInt;
FLastSubPathElementType, FLastStoredElementType: TBGRAPathElementType;
FLastMoveToDataPos: BGRAPtrInt;
FLastCoord,FLastTransformedCoord,
FSubPathStartCoord, FSubPathTransformedStartCoord: TPointF;
FExpectedTransformedControlPoint: TPointF;
FMatrix: TAffineMatrix; //this matrix must have a base of vectors
//orthogonal, of same length and with positive
//orientation in order to preserve arcs
FScale,FAngleRadCW: single;
FCursors: array of TBGRAPathCursor;
FInternalDrawOffset: TPointF;
procedure OnModify;
procedure OnMatrixChange;
procedure NeedSpace(count: integer);
function AllocateElement(AElementType: TBGRAPathElementType;
AExtraBytes: BGRAPtrInt = 0): Pointer;
procedure Init;
procedure DoClear;
function CheckElementType(AElementType: TBGRAPathElementType): boolean;
function GoToNextElement(var APos: BGRAPtrInt): boolean;
function GoToPreviousElement(var APos: BGRAPtrInt): boolean;
function PeekNextElement(APos: BGRAPtrInt): TBGRAPathElementType;
function GetElementStartCoord(APos: BGRAPtrInt): TPointF;
function GetElementEndCoord(APos: BGRAPtrInt): TPointF;
function GetElementLength(APos: BGRAPtrInt; AAcceptedDeviation: single): single;
procedure GetElementAt(APos: BGRAPtrInt;
out AElementType: TBGRAPathElementType; out AElement: pointer);
function GetSvgString: string; virtual;
procedure SetSvgString(const AValue: string); virtual;
procedure RegisterCursor(ACursor: TBGRAPathCursor);
procedure UnregisterCursor(ACursor: TBGRAPathCursor);
function SetLastCoord(ACoord: TPointF): TPointF; {$ifdef inline}inline;{$endif}
procedure ClearLastCoord;
procedure BezierCurveFromTransformed(tcp1, cp2, pt:TPointF);
procedure QuadraticCurveFromTransformed(tcp, pt: TPointF);
function LastCoordDefined: boolean; {$ifdef inline}inline;{$endif}
function GetPolygonalApprox(APos: BGRAPtrInt; AAcceptedDeviation: single; AIncludeFirstPoint: boolean): ArrayOfTPointF;
function getPoints: ArrayOfTPointF; overload;
function getPoints(AMatrix: TAffineMatrix): ArrayOfTPointF; overload;
function getCursor: TBGRACustomPathCursor;
procedure InternalDraw(ADrawProc: TBGRAPathDrawProc; const AMatrix: TAffineMatrix; AAcceptedDeviation: single; AData: pointer);
procedure BitmapDrawSubPathProc(const APoints: array of TPointF; AClosed: boolean; AData: pointer);
function CorrectAcceptedDeviation(AAcceptedDeviation: single; const AMatrix: TAffineMatrix): single;
public
constructor Create; overload;
constructor Create(ASvgString: string); overload;
constructor Create(const APoints: ArrayOfTPointF); overload;
constructor Create(APath: IBGRAPath); overload;
destructor Destroy; override;
procedure beginPath;
procedure beginSubPath;
procedure closePath;
procedure translate(x,y: single);
procedure resetTransform;
procedure rotate(angleRadCW: single); overload;
procedure rotateDeg(angleDeg: single); overload;
procedure rotate(angleRadCW: single; center: TPointF); overload;
procedure rotateDeg(angleDeg: single; center: TPointF); overload;
procedure scale(factor: single);
procedure moveTo(x,y: single); overload;
procedure lineTo(x,y: single); overload;
procedure moveTo(const pt: TPointF); overload;
procedure lineTo(const pt: TPointF); overload;
procedure polyline(const pts: array of TPointF);
procedure polylineTo(const pts: array of TPointF);
procedure polygon(const pts: array of TPointF);
procedure quadraticCurveTo(cpx,cpy,x,y: single); overload;
procedure quadraticCurveTo(const cp,pt: TPointF); overload;
procedure quadraticCurve(const curve: TQuadraticBezierCurve); overload;
procedure quadraticCurve(p1,cp,p2: TPointF); overload;
procedure smoothQuadraticCurveTo(x,y: single); overload;
procedure smoothQuadraticCurveTo(const pt: TPointF); overload;
procedure bezierCurveTo(cp1x,cp1y,cp2x,cp2y,x,y: single); overload;
procedure bezierCurveTo(const cp1,cp2,pt: TPointF); overload;
procedure bezierCurve(const curve: TCubicBezierCurve); overload;
procedure bezierCurve(p1,cp1,cp2,p2: TPointF); overload;
procedure smoothBezierCurveTo(cp2x,cp2y,x,y: single); overload;
procedure smoothBezierCurveTo(const cp2,pt: TPointF); overload;
procedure rect(x,y,w,h: single);
procedure roundRect(x,y,w,h,radius: single);
procedure arc(cx, cy, radius, startAngleRadCW, endAngleRadCW: single; anticlockwise: boolean); overload;
procedure arc(cx, cy, radius, startAngleRadCW, endAngleRadCW: single); overload;
procedure arcDeg(cx, cy, radius, startAngleDeg, endAngleDeg: single; anticlockwise: boolean); overload;
procedure arcDeg(cx, cy, radius, startAngleDeg, endAngleDeg: single); overload;
procedure arcTo(x1, y1, x2, y2, radius: single); overload;
procedure arcTo(const p1,p2: TPointF; radius: single); overload;
procedure arc(const arcDef: TArcDef); overload;
procedure arc(cx, cy, rx,ry: single; xAngleRadCW, startAngleRadCW, endAngleRadCW: single); overload;
procedure arc(cx, cy, rx,ry, xAngleRadCW, startAngleRadCW, endAngleRadCW: single; anticlockwise: boolean); overload;
procedure arcTo(rx,ry, xAngleRadCW: single; largeArc, anticlockwise: boolean; x,y:single); overload;
procedure copyTo(dest: IBGRAPath);
procedure addPath(const AValue: string); overload;
procedure addPath(source: IBGRAPath); overload;
procedure openedSpline(const pts: array of TPointF; style: TSplineStyle);
procedure closedSpline(const pts: array of TPointF; style: TSplineStyle);
property SvgString: string read GetSvgString write SetSvgString;
function ComputeLength(AAcceptedDeviation: single = 0.1): single;
function ToPoints(AAcceptedDeviation: single = 0.1): ArrayOfTPointF; overload;
function ToPoints(AMatrix: TAffineMatrix; AAcceptedDeviation: single = 0.1): ArrayOfTPointF; overload;
function IsEmpty: boolean;
function GetBounds(AAcceptedDeviation: single = 0.1): TRectF;
procedure SetPoints(const APoints: ArrayOfTPointF);
procedure stroke(ABitmap: TBGRACustomBitmap; AColor: TBGRAPixel; AWidth: single; AAcceptedDeviation: single = 0.1); overload;
procedure stroke(ABitmap: TBGRACustomBitmap; ATexture: IBGRAScanner; AWidth: single; AAcceptedDeviation: single = 0.1); overload;
procedure stroke(ABitmap: TBGRACustomBitmap; x,y: single; AColor: TBGRAPixel; AWidth: single; AAcceptedDeviation: single = 0.1); overload;
procedure stroke(ABitmap: TBGRACustomBitmap; x,y: single; ATexture: IBGRAScanner; AWidth: single; AAcceptedDeviation: single = 0.1); overload;
procedure stroke(ABitmap: TBGRACustomBitmap; const AMatrix: TAffineMatrix; AColor: TBGRAPixel; AWidth: single; AAcceptedDeviation: single = 0.1); overload;
procedure stroke(ABitmap: TBGRACustomBitmap; const AMatrix: TAffineMatrix; ATexture: IBGRAScanner; AWidth: single; AAcceptedDeviation: single = 0.1); overload;
procedure stroke(ADrawProc: TBGRAPathDrawProc; const AMatrix: TAffineMatrix; AAcceptedDeviation: single = 0.1; AData: pointer = nil); overload;
procedure fill(ABitmap: TBGRACustomBitmap; AColor: TBGRAPixel; AAcceptedDeviation: single = 0.1); overload;
procedure fill(ABitmap: TBGRACustomBitmap; ATexture: IBGRAScanner; AAcceptedDeviation: single = 0.1); overload;
procedure fill(ABitmap: TBGRACustomBitmap; x,y: single; AColor: TBGRAPixel; AAcceptedDeviation: single = 0.1); overload;
procedure fill(ABitmap: TBGRACustomBitmap; x,y: single; ATexture: IBGRAScanner; AAcceptedDeviation: single = 0.1); overload;
procedure fill(ABitmap: TBGRACustomBitmap; const AMatrix: TAffineMatrix; AColor: TBGRAPixel; AAcceptedDeviation: single = 0.1); overload;
procedure fill(ABitmap: TBGRACustomBitmap; const AMatrix: TAffineMatrix; ATexture: IBGRAScanner; AAcceptedDeviation: single = 0.1); overload;
procedure fill(AFillProc: TBGRAPathFillProc; const AMatrix: TAffineMatrix; AAcceptedDeviation: single = 0.1; AData: pointer = nil); overload;
function CreateCursor(AAcceptedDeviation: single = 0.1): TBGRAPathCursor;
procedure Fit(ARect: TRectF; AAcceptedDeviation: single = 0.1);
procedure FitInto(ADest: TBGRAPath; ARect: TRectF; AAcceptedDeviation: single = 0.1);
protected
{$IFNDEF FPC}
function QueryInterface(const IID: TGUID; out Obj): HResult; stdcall;
function _AddRef: Integer; stdcall;
function _Release: Integer; stdcall;
{$ELSE}
function QueryInterface({$IFDEF FPC_HAS_CONSTREF}constref{$ELSE}const{$ENDIF} IID: TGUID; out Obj): HResult; {$IF (not defined(WINDOWS)) AND (not defined(FPC20501))}cdecl{$ELSE}stdcall{$IFEND};
function _AddRef: Integer; {$IF (not defined(WINDOWS)) AND (not defined(FPC20501))}cdecl{$ELSE}stdcall{$IFEND};
function _Release: Integer; {$IF (not defined(WINDOWS)) AND (not defined(FPC20501))}cdecl{$ELSE}stdcall{$IFEND};
{$ENDIF}
end;
{----------------------- Spline ------------------}
function SplineVertexToSide(y0, y1, y2, y3: single; t: single): single;
function ComputeBezierCurve(const curve: TCubicBezierCurve; AAcceptedDeviation: single = 0.1): ArrayOfTPointF; overload;
function ComputeBezierCurve(const curve: TQuadraticBezierCurve; AAcceptedDeviation: single = 0.1): ArrayOfTPointF; overload;
function ComputeBezierSpline(const spline: array of TCubicBezierCurve; AAcceptedDeviation: single = 0.1): ArrayOfTPointF; overload;
function ComputeBezierSpline(const spline: array of TQuadraticBezierCurve; AAcceptedDeviation: single = 0.1): ArrayOfTPointF; overload;
function ComputeClosedSpline(const points: array of TPointF; Style: TSplineStyle; AAcceptedDeviation: single = 0.1): ArrayOfTPointF;
function ComputeOpenedSpline(const points: array of TPointF; Style: TSplineStyle; EndCoeff: single = 0.25; AAcceptedDeviation: single = 0.1): ArrayOfTPointF;
function ClosedSplineStartPoint(const points: array of TPointF; Style: TSplineStyle): TPointF;
{ Compute points to draw an antialiased ellipse }
function ComputeEllipse(x,y,rx,ry: single; quality: single = 1): ArrayOfTPointF;
function ComputeArc65536(x, y, rx, ry: single; start65536,end65536: BGRAWord; quality: single = 1): ArrayOfTPointF;
function ComputeArcRad(x, y, rx, ry: single; startRadCCW,endRadCCW: single; quality: single = 1): ArrayOfTPointF;
function ComputeArc(const arc: TArcDef; quality: single = 1): ArrayOfTPointF;
function ComputeRoundRect(x1,y1,x2,y2,rx,ry: single; quality: single = 1): ArrayOfTPointF; overload;
function ComputeRoundRect(x1,y1,x2,y2,rx,ry: single; options: TRoundRectangleOptions; quality: single = 1): ArrayOfTPointF; overload;
function Html5ArcTo(const p0, p1, p2: TPointF; radius: single): TArcDef;
function SvgArcTo(const p0: TPointF; rx, ry, xAngleRadCW: single; largeArc,
anticlockwise: boolean; const p1: TPointF): TArcDef;
function ArcStartPoint(const arc: TArcDef): TPointF;
function ArcEndPoint(const arc: TArcDef): TPointF;
function IsLargeArc(const arc: TArcDef): boolean;
implementation
uses Math, BGRAResample, SysUtils;
type
TStrokeData = record
Bitmap: TBGRACustomBitmap;
Texture: IBGRAScanner;
Color: TBGRAPixel;
Width: Single;
end;
PPathElementHeader = ^TPathElementHeader;
TPathElementHeader = record
ElementType: TBGRAPathElementType;
PreviousElementType: TBGRAPathElementType;
end;
PMoveToElement = ^TMoveToElement;
TMoveToElement = record
StartCoordinate: TPointF;
LoopDataPos: BGRAPtrInt; //if the path is closed
end;
PClosePathElement = ^TClosePathElement;
TClosePathElement = type TMoveToElement;
PQuadraticBezierToElement = ^TQuadraticBezierToElement;
TQuadraticBezierToElement = record
ControlPoint, Destination: TPointF;
end;
PCubicBezierToElement = ^TCubicBezierToElement;
TCubicBezierToElement = record
ControlPoint1, ControlPoint2, Destination: TPointF;
end;
PArcElement = ^TArcElement;
TArcElement = TArcDef;
PSplineElement = ^TSplineElement;
TSplineElement = record
SplineStyle: TSplineStyle;
NbControlPoints: integer;
end;
const
PathElementSize : array[TBGRAPathElementType] of BGRAPtrInt =
(0, Sizeof(TMoveToElement), Sizeof(TClosePathElement), sizeof(TPointF),
sizeof(TQuadraticBezierToElement), sizeof(TCubicBezierToElement),
sizeof(TArcElement), sizeof(TSplineElement)+sizeof(integer),
sizeof(TSplineElement)+sizeof(integer));
function SplineVertexToSide(y0, y1, y2, y3: single; t: single): single;
var
a0, a1, a2, a3: single;
t2: single;
begin
t2 := t * t;
a0 := y3 - y2 - y0 + y1;
a1 := y0 - y1 - a0;
a2 := y2 - y0;
a3 := y1;
Result := a0 * t * t2 + a1 * t2 + a2 * t + a3;
end;
function ComputeCurvePartPrecision(pt1, pt2, pt3, pt4: TPointF; AAcceptedDeviation: single = 0.1): integer;
var
len: single;
begin
len := sqr(pt1.x - pt2.x) + sqr(pt1.y - pt2.y);
len := max(len, sqr(pt3.x - pt2.x) + sqr(pt3.y - pt2.y));
len := max(len, sqr(pt3.x - pt4.x) + sqr(pt3.y - pt4.y));
Result := round(sqrt(sqrt(len)/AAcceptedDeviation) * 0.9);
if Result<=0 then Result:=1;
end;
function ComputeBezierCurve(const curve: TCubicBezierCurve; AAcceptedDeviation: single = 0.1): ArrayOfTPointF; overload;
begin
result := curve.ToPoints(AAcceptedDeviation);
end;
function ComputeBezierCurve(const curve: TQuadraticBezierCurve; AAcceptedDeviation: single = 0.1): ArrayOfTPointF; overload;
begin
result := curve.ToPoints(AAcceptedDeviation);
end;
function ComputeBezierSpline(const spline: array of TCubicBezierCurve; AAcceptedDeviation: single = 0.1): ArrayOfTPointF;
var
curves: array of ArrayOfTPointF;
nb: integer;
lastPt: TPointF;
i: Integer;
j: Integer;
procedure AddPt(pt: TPointF); //@{$ifdef inline}inline;{$endif}
begin
result[nb]:= pt;
inc(nb);
lastPt := pt;
end;
function EqLast(pt: TPointF): boolean;
begin
result := (pt.x = lastPt.x) and (pt.y = lastPt.y);
end;
begin
if length(spline)= 0 then
begin
setlength(result,0);
exit;
end;
setlength(curves, length(spline));
for i := 0 to high(spline) do
curves[i] := ComputeBezierCurve(spline[i],AAcceptedDeviation);
nb := length(curves[0]);
lastPt := curves[0][high(curves[0])];
for i := 1 to high(curves) do
begin
inc(nb,length(curves[i]));
if EqLast(curves[i][0]) then dec(nb);
lastPt := curves[i][high(curves[i])];
end;
setlength(result,nb);
nb := 0;
for j := 0 to high(curves[0]) do
AddPt(curves[0][j]);
for i := 1 to high(curves) do
begin
if not EqLast(curves[i][0]) then AddPt(curves[i][0]);
for j := 1 to high(curves[i]) do
AddPt(curves[i][j]);
end;
end;
function ComputeBezierSpline(const spline: array of TQuadraticBezierCurve;
AAcceptedDeviation: single = 0.1): ArrayOfTPointF;
var
curves: array of ArrayOfTPointF;
nb: integer;
lastPt: TPointF;
i: Integer;
j: Integer;
procedure AddPt(pt: TPointF); //@{$ifdef inline}inline;{$endif}
begin
result[nb]:= pt;
inc(nb);
lastPt := pt;
end;
function EqLast(pt: TPointF): boolean;
begin
result := (pt.x = lastPt.x) and (pt.y = lastPt.y);
end;
begin
if length(spline)= 0 then
begin
setlength(result,0);
exit;
end;
setlength(curves, length(spline));
for i := 0 to high(spline) do
curves[i] := ComputeBezierCurve(spline[i],AAcceptedDeviation);
nb := length(curves[0]);
lastPt := curves[0][high(curves[0])];
for i := 1 to high(curves) do
begin
inc(nb,length(curves[i]));
if EqLast(curves[i][0]) then dec(nb);
lastPt := curves[i][high(curves[i])];
end;
setlength(result,nb);
nb := 0;
for j := 0 to high(curves[0]) do
AddPt(curves[0][j]);
for i := 1 to high(curves) do
begin
if not EqLast(curves[i][0]) then AddPt(curves[i][0]);
for j := 1 to high(curves[i]) do
AddPt(curves[i][j]);
end;
end;
function ComputeClosedSpline(const points: array of TPointF; Style: TSplineStyle; AAcceptedDeviation: single = 0.1): ArrayOfTPointF;
var
i, j, nb, idx, pre: integer;
ptPrev, ptPrev2, ptNext, ptNext2: TPointF;
t: single;
kernel: TWideKernelFilter;
begin
if length(points) <= 2 then
begin
setlength(result,length(points));
for i := 0 to high(result) do
result[i] := points[i];
exit;
end;
nb := 1;
for i := 0 to high(points) do
begin
ptPrev2 := points[(i + length(points) - 1) mod length(points)];
ptPrev := points[i];
ptNext := points[(i + 1) mod length(points)];
ptNext2 := points[(i + 2) mod length(points)];
nb := nb +ComputeCurvePartPrecision(ptPrev2, ptPrev, ptNext, ptNext2, AAcceptedDeviation);
end;
kernel := CreateInterpolator(style);
setlength(Result, nb);
idx := 0;
for i := 0 to high(points) do
begin
ptPrev2 := points[(i + length(points) - 1) mod length(points)];
ptPrev := points[i];
ptNext := points[(i + 1) mod length(points)];
ptNext2 := points[(i + 2) mod length(points)];
pre := ComputeCurvePartPrecision(ptPrev2, ptPrev, ptNext, ptNext2, AAcceptedDeviation);
if i=0 then
j := 0
else
j := 1;
while j <= pre do
begin
t := j/pre;
result[idx] := ptPrev2*kernel.Interpolation(t+1) + ptPrev*kernel.Interpolation(t) +
ptNext*kernel.Interpolation(t-1) + ptNext2*kernel.Interpolation(t-2);
Inc(idx);
inc(j);
end;
end;
kernel.Free;
end;
function ComputeOpenedSpline(const points: array of TPointF; Style: TSplineStyle; EndCoeff: single; AAcceptedDeviation: single): ArrayOfTPointF;
var
i, j, nb, idx, pre: integer;
ptPrev, ptPrev2, ptNext, ptNext2: TPointF;
t: single;
kernel: TWideKernelFilter;
begin
if length(points) <= 2 then
begin
setlength(result,length(points));
for i := 0 to high(result) do
result[i] := points[i];
exit;
end;
if style in[ssInsideWithEnds,ssCrossingWithEnds] then EndCoeff := 0;
if EndCoeff < -0.3 then EndCoeff := -0.3;
nb := 1;
for i := 0 to high(points) - 1 do
begin
ptPrev := points[i];
ptNext := points[i + 1];
if i=0 then
ptPrev2 := (ptPrev+(ptNext+points[i + 2])*EndCoeff)*(1/(1+2*EndCoeff))
else
ptPrev2 := points[i - 1];
if i = high(points)-1 then
ptNext2 := (ptNext+(ptPrev+points[i - 1])*EndCoeff)*(1/(1+2*EndCoeff))
else
ptNext2 := points[i + 2];
nb := nb +ComputeCurvePartPrecision(ptPrev2, ptPrev, ptNext, ptNext2, AAcceptedDeviation);
end;
kernel := CreateInterpolator(style);
if Style in[ssInsideWithEnds,ssCrossingWithEnds] then
begin
inc(nb,2);
setlength(Result, nb);
result[0] := points[0];
idx := 1;
end else
begin
idx := 0;
setlength(Result, nb);
end;
for i := 0 to high(points) - 1 do
begin
ptPrev := points[i];
ptNext := points[i + 1];
if i=0 then
ptPrev2 := (ptPrev+(ptNext+points[i + 2])*EndCoeff)*(1/(1+2*EndCoeff))
else
ptPrev2 := points[i - 1];
if i = high(points)-1 then
ptNext2 := (ptNext+(ptPrev+points[i - 1])*EndCoeff)*(1/(1+2*EndCoeff))
else
ptNext2 := points[i + 2];
pre := ComputeCurvePartPrecision(ptPrev2, ptPrev, ptNext, ptNext2, AAcceptedDeviation);
if i=0 then
begin
j := 0;
end else j := 1;
while j <= pre do
begin
t := j/pre;
result[idx] := ptPrev2*kernel.Interpolation(t+1) + ptPrev*kernel.Interpolation(t) +
ptNext*kernel.Interpolation(t-1) + ptNext2*kernel.Interpolation(t-2);
Inc(idx);
inc(j);
end;
end;
kernel.Free;
if Style in[ssInsideWithEnds,ssCrossingWithEnds] then
result[idx] := points[high(points)];
end;
function ClosedSplineStartPoint(const points: array of TPointF;
Style: TSplineStyle): TPointF;
var
kernel: TWideKernelFilter;
ptPrev2: TPointF;
ptPrev: TPointF;
ptNext: TPointF;
ptNext2: TPointF;
begin
if length(points) = 0 then
result := EmptyPointF
else
if length(points)<=2 then
result := points[0]
else
begin
kernel := CreateInterpolator(style);
ptPrev2 := points[high(points)];
ptPrev := points[0];
ptNext := points[1];
ptNext2 := points[2];
result := ptPrev2*kernel.Interpolation(1) + ptPrev*kernel.Interpolation(0) +
ptNext*kernel.Interpolation(-1) + ptNext2*kernel.Interpolation(-2);
kernel.free;
end;
end;
function ComputeArc65536(x, y, rx, ry: single; start65536,end65536: BGRAWord; quality: single): ArrayOfTPointF;
var i,nb: integer;
arclen: integer;
pos: BGRAWord;
begin
if end65536 > start65536 then
arclen := end65536-start65536 else
arclen := 65536-(start65536-end65536);
if quality < 0 then quality := 0;
nb := round(((rx+ry)*2*quality+8)*arclen/65536) and not 3;
if arclen <= 16384 then
begin
if nb < 2 then nb := 2;
end else
if arclen <= 32768 then
begin
if nb < 3 then nb := 3;
end else
if arclen <= 32768+16384 then
begin
if nb < 4 then nb := 4;
end else
if nb < 5 then nb := 5;
if nb > arclen+1 then nb := arclen+1;
setlength(result,nb);
for i := 0 to nb-1 do
begin
{.$PUSH}{$R-}
pos := start65536+BGRAInt64(i)*arclen div (BGRAInt64(nb)-1);
{.$POP}
result[i] := PointF(x+rx*(Cos65536(pos)-32768)/32768,
y-ry*(Sin65536(pos)-32768)/32768);
end;
end;
function ComputeEllipse(x, y, rx, ry: single; quality: single): ArrayOfTPointF;
begin
result := ComputeArc65536(x,y,rx,ry,0,0,quality);
end;
function ComputeArcRad(x, y, rx, ry: single; startRadCCW, endRadCCW: single;
quality: single): ArrayOfTPointF;
begin
result := ComputeArc65536(x,y,rx,ry,round(startRadCCW*32768/Pi) and $ffff,round(endRadCCW*32768/Pi) and $ffff,quality);
result[0] := PointF(x+cos(startRadCCW)*rx,y-sin(startRadCCW)*ry);
result[high(result)] := PointF(x+cos(endRadCCW)*rx,y-sin(endRadCCW)*ry);
end;
function ComputeArc(const arc: TArcDef; quality: single): ArrayOfTPointF;
var startAngle,endAngle: single;
i,n: integer;
temp: TPointF;
m: TAffineMatrix;
begin
startAngle := -arc.startAngleRadCW;
endAngle:= -arc.endAngleRadCW;
if not arc.anticlockwise then
begin
result := ComputeArcRad(arc.center.x,arc.center.y,arc.radius.x,arc.radius.y,endAngle,startAngle,quality);
n := length(result);
if n>1 then
for i := 0 to (n-2) div 2 do
begin
temp := result[i];
result[i] := result[n-1-i];
result[n-1-i] := temp;
end;
end else
result := ComputeArcRad(arc.center.x,arc.center.y,arc.radius.x,arc.radius.y,startAngle,endAngle,quality);
if arc.xAngleRadCW <> 0 then
begin
m := AffMatrixMult(AffMatrixMult(AffineMatrixTranslation(arc.center.x,arc.center.y),AffineMatrixRotationRad(-arc.xAngleRadCW)),AffineMatrixTranslation(-arc.center.x,-arc.center.y));
for i := 0 to high(result) do
result[i] := AffMatrixMult(m,result[i]);
end;
end;
function ComputeRoundRect(x1,y1,x2,y2,rx,ry: single; quality: single): ArrayOfTPointF;
begin
result := ComputeRoundRect(x1,y1,x2,y2,rx,ry,[],quality);
end;
function ComputeRoundRect(x1, y1, x2, y2, rx, ry: single;
options: TRoundRectangleOptions; quality: single): ArrayOfTPointF;
var q0,q1,q2,q3,q4: ArrayOfTPointF;
temp: Single;
begin
if x1 > x2 then
begin
temp := x1;
x1 := x2;
x2 := temp;
end;
if y1 > y2 then
begin
temp := y1;
y1 := y2;
y2 := temp;
end;
rx := abs(rx);
ry := abs(ry);
if 2*rx > x2-x1 then
rx := (x2-x1)/2;
if 2*ry > y2-y1 then
ry := (y2-y1)/2;
q0 := PointsF([PointF(x2,(y1+y2)/2)]);
if rrTopRightBevel in options then
q1 := PointsF([PointF(x2,y1+ry),PointF(x2-rx,y1)]) else
if rrTopRightSquare in options then
q1 := PointsF([PointF(x2,y1)])
else
q1 := ComputeArc65536(x2-rx,y1+ry,rx,ry,0,16384,quality);
if rrTopLeftBevel in options then
q2 := PointsF([PointF(x1+rx,y1),PointF(x1,y1+ry)]) else
if rrTopLeftSquare in options then
q2 := PointsF([PointF(x1,y1)])
else
q2 := ComputeArc65536(x1+rx,y1+ry,rx,ry,16384,32768,quality);
if rrBottomLeftBevel in options then
q3 := PointsF([PointF(x1,y2-ry),PointF(x1+rx,y2)]) else
if rrBottomLeftSquare in options then
q3 := PointsF([PointF(x1,y2)])
else
q3 := ComputeArc65536(x1+rx,y2-ry,rx,ry,32768,32768+16384,quality);
if rrBottomRightBevel in options then
q4 := PointsF([PointF(x2-rx,y2),PointF(x2,y2-ry)]) else
if rrBottomRightSquare in options then
q4 := PointsF([PointF(x2,y2)])
else
q4 := ComputeArc65536(x2-rx,y2-ry,rx,ry,32768+16384,0,quality);
result := ConcatPointsF([q0,q1,q2,q3,q4]);
end;
function Html5ArcTo(const p0, p1, p2: TPointF; radius: single
): TArcDef;
var p3,p4,an,bn,cn,c: TPointF;
dir, a2, b2, c2, cosx, sinx, d: single;
anticlockwise: boolean;
begin
result.center := p1;
result.radius := PointF(0,0);
result.xAngleRadCW:= 0;
result.startAngleRadCW := 0;
result.endAngleRadCW:= 0;
result.anticlockwise:= false;
radius := abs(radius);
if (p0 = p1) or (p1 = p2) or (radius = 0) then exit;
dir := (p2.x-p1.x)*(p0.y-p1.y) + (p2.y-p1.y)*(p1.x-p0.x);
if dir = 0 then exit;
a2 := (p0.x-p1.x)*(p0.x-p1.x) + (p0.y-p1.y)*(p0.y-p1.y);
b2 := (p1.x-p2.x)*(p1.x-p2.x) + (p1.y-p2.y)*(p1.y-p2.y);
c2 := (p0.x-p2.x)*(p0.x-p2.x) + (p0.y-p2.y)*(p0.y-p2.y);
cosx := (a2+b2-c2)/(2*sqrt(a2*b2));
sinx := sqrt(1 - cosx*cosx);
if (sinx = 0) or (cosx = 1) then exit;
d := radius / ((1 - cosx) / sinx);
an := (p1-p0)*(1/sqrt(a2));
bn := (p1-p2)*(1/sqrt(b2));
p3 := p1 - an*d;
p4 := p1 - bn*d;
anticlockwise := (dir < 0);
cn := PointF(an.y,-an.x)*radius;
if not anticlockwise then cn := -cn;
c := p3 + cn;
result.center := c;
result.radius:= PointF(radius,radius);
result.startAngleRadCW := arctan2((p3.y-c.y), (p3.x-c.x));
result.endAngleRadCW := arctan2((p4.y-c.y), (p4.x-c.x));
result.anticlockwise:= anticlockwise;
end;
function SvgArcTo(const p0: TPointF; rx, ry, xAngleRadCW: single; largeArc,
anticlockwise: boolean; const p1: TPointF): TArcDef;
var
p0p,cp: TPointF;
cross1,cross2,lambda: single;
begin
if (rx=0) or (ry=0) or (p0 = p1) then
begin
result.radius := PointF(0,0);
result.xAngleRadCW:= 0;
result.anticlockwise := false;
result.endAngleRadCW := 0;
result.startAngleRadCW:= 0;
result.center := p1;
exit;
end;
result.xAngleRadCW := xAngleRadCW;
result.anticlockwise := anticlockwise;
p0p := AffMatrixMult(AffineMatrixRotationRad(xAngleRadCW),( (p0-p1)*0.5 ));
//ensure radius is big enough
lambda := sqr(p0p.x/rx) + sqr(p0p.y/ry);
if lambda > 1 then
begin
lambda := sqrt(lambda);
rx := rx *lambda;
ry := ry *lambda;
end;
result.radius := PointF(rx,ry);
//compute center
cross2 := sqr(rx*p0p.y) + sqr(ry*p0p.x);
cross1 := sqr(rx*ry);
if cross1 <= cross2 then
cp := PointF(0,0)
else
cp := sqrt((cross1-cross2)/cross2)*
PointF(rx*p0p.y/ry, -ry*p0p.x/rx);
if largeArc <> anticlockwise then cp := -cp;
result.center := AffMatrixMult(AffineMatrixRotationRad(-xAngleRadCW),cp) +
(p0+p1)*0.5;
result.startAngleRadCW := arctan2((p0p.y-cp.y)/ry,(p0p.x-cp.x)/rx);
result.endAngleRadCW := arctan2((-p0p.y-cp.y)/ry,(-p0p.x-cp.x)/rx);
end;
function ArcStartPoint(const arc: TArcDef): TPointF;
begin
result := AffMatrixMult(AffineMatrixRotationRad(-arc.xAngleRadCW),PointF(cos(arc.startAngleRadCW)*arc.radius.x,
sin(arc.startAngleRadCW)*arc.radius.y)) + arc.center;
end;
function ArcEndPoint(const arc: TArcDef): TPointF;
begin
result := AffMatrixMult(AffineMatrixRotationRad(-arc.xAngleRadCW),PointF(cos(arc.endAngleRadCW)*arc.radius.x,
sin(arc.endAngleRadCW)*arc.radius.y)) + arc.center;
end;
function IsLargeArc(const arc: TArcDef): boolean;
var diff,a1,a2: single;
begin
a1 := arc.startAngleRadCW - floor(arc.startAngleRadCW/(2*Pi))*(2*Pi);
a2 := arc.endAngleRadCW - floor(arc.endAngleRadCW/(2*Pi))*(2*Pi);
if not arc.anticlockwise then
diff := a2 - a1
else
diff := a1 - a2;
result := (diff < 0) or (diff >= Pi);
end;
{ TBGRAPathCursor }
function TBGRAPathCursor.GetCurrentCoord: TPointF;
begin
case FCurrentElementType of
peNone: result := EmptyPointF;
peMoveTo,peLineTo,peCloseSubPath:
if FCurrentElementLength <= 0 then
result := FCurrentElementStartCoord
else
result := FCurrentElementStartCoord + (FCurrentElementEndCoord-FCurrentElementStartCoord)*(FCurrentElementArcPos/FCurrentElementLength);
peCubicBezierTo,peQuadraticBezierTo,peArc,peOpenedSpline,peClosedSpline:
begin
NeedPolygonalApprox;
if FCurrentSegment >= high(FCurrentElementPoints) then
result := FCurrentElementEndCoord
else
result := FCurrentElementPoints[FCurrentSegment]+
(FCurrentElementPoints[FCurrentSegment+1]-
FCurrentElementPoints[FCurrentSegment])*FCurrentSegmentPos;
end;
else
raise Exception.Create('Unknown element type');
end;
end;
function TBGRAPathCursor.GetPath: TBGRAPath;
begin
if not Assigned(FPath) then
raise exception.Create('Path does not exist');
result := FPath;
end;
procedure TBGRAPathCursor.MoveToEndOfElement;
begin
FCurrentElementArcPos := FCurrentElementLength;
if not NeedPolygonalApprox then exit;
if length(FCurrentElementPoints) > 1 then
begin
FCurrentSegment := high(FCurrentElementPoints)-1;
FCurrentSegmentPos := 1;
end else
begin
FCurrentSegment := high(FCurrentElementPoints);
FCurrentSegmentPos := 0;
end;
end;
procedure TBGRAPathCursor.MoveForwardInElement(ADistance: single);
var segLen,rightSpace,remaining: single;
begin
if not NeedPolygonalApprox then exit;
ADistance := ADistance *FCurrentElementArcPosScale;
remaining := ADistance;
while remaining > 0 do
begin
if FCurrentSegment < high(FCurrentElementPoints) then
segLen := VectLen(FCurrentElementPoints[FCurrentSegment+1]-FCurrentElementPoints[FCurrentSegment])
else
segLen := 0;
rightSpace := segLen*(1-FCurrentSegmentPos);
if (segLen > 0) and (remaining <= rightSpace) then
begin
FCurrentSegmentPos := FCurrentSegmentPos +(remaining/segLen);
exit;
end else
begin
remaining := remaining -rightSpace;
if FCurrentSegment < high(FCurrentElementPoints)-1 then
begin
inc(FCurrentSegment);
FCurrentSegmentPos := 0;
end else
begin
FCurrentSegmentPos := 1;
exit;
end;
end;
end;
end;
procedure TBGRAPathCursor.MoveBackwardInElement(ADistance: single);
var
segLen,leftSpace,remaining: Single;
begin
if not NeedPolygonalApprox then exit;
ADistance := ADistance *FCurrentElementArcPosScale;
remaining := ADistance;
while remaining > 0 do