BGRABitmap Geometry types

Here are all the basic geometry types used in BGRABitmap library. They are provided by BGRABitmapTypes unit.

Geometry types

2D points

TPoint = BGRAClasses.TPoint;

Represents a point with X and Y integer coordinates

const EmptyPoint : TPoint = (X: -2147483648; Y: -2147483648);

A constant representing an empty point (with minimum possible integer values for X and Y) that can be used as a separator in a list of TPoint

function IsEmptyPoint(const APoint: TPoint): boolean;

Checks if the given point is equivalent to EmptyPoint

const EmptySingle = single(-3.402823e38);

Value indicating that there is nothing in the single-precision floating point value. It is also used as a separator in lists

PPointF = ^BGRAClasses.TPointF;

Pointer to a TPointF structure

TPointF = BGRAClasses.TPointF;

Contains a point with single-precision floating point coordinates

const EmptyPointF: TPointF = (x: -3.402823e38; y: -3.402823e38);

Value indicating that there is an empty TPointF structure. It is also used as a separator in lists of points

function PointF(x, y: single): TPointF; overload;

Creates a new structure with values x and y

function PointF(pt: TPoint): TPointF; overload;

Creates a new structure converting integer values to single-precision floating-point coordinates

function isEmptyPointF(const pt: TPointF): boolean;

Checks if the structure is empty (equal to EmptyPointF)

operator = (const pt1, pt2: TPointF): boolean; inline;

Checks if both x and y are equal

operator + (const pt1, pt2: TPointF): TPointF; inline;

Adds x and y components separately. It is like adding vectors

operator - (const pt1, pt2: TPointF): TPointF; inline;

Subtract x and y components separately. It is like subtracting vectors

operator - (const pt2: TPointF): TPointF; inline;

Returns a point with opposite values for x and y components

operator * (const pt1, pt2: TPointF): single; inline;

Scalar product (deprecated): multiplies x and y components and returns the sum

operator ** (const pt1, pt2: TPointF): single; inline;

Scalar product: multiplies x and y components and returns the sum

operator * (const pt1: TPointF; factor: single): TPointF; inline;

Multiplies both x and y by factor. It scales the vector represented by (x, y)

operator * (factor: single; const pt1: TPointF): TPointF; inline;

Multiplies both x and y by factor. It scales the vector represented by (x, y)

function VectLen(const dx,dy: single): single; overload; inline;

Returns the length of the vector (dx, dy)

function VectLen(const v: TPointF): single; overload;

Returns the length of the vector represented by (x, y)

function VectDet(const v1,v2: TPointF): double; inline;

Computes the determinant of the two vectors (equal to the determinant of the square matrix with those vectors as columns)

TPointFHelper = record helper for TPointF

Helper for TPointF structure providing additional functionality for point manipulation

procedure Offset(const apt: TPointF); overload;

Offsets the point by another point (TPointF)

procedure Offset(const apt: TPoint); overload;

Offsets the point by another point (TPoint)

procedure Offset(dx, dy: longint); overload;

Offsets the point by specified distances in the X (dx) and Y (dy) directions (integer values)

procedure Offset(dx, dy: single); overload;

Offsets the point by specified distances in the X (dx) and Y (dy) directions (single values)

procedure Scale(AScale: single);

Scales the point as a vector from the origin) by a specified factor

procedure Normalize;

Normalizes the point (modifies it to a unit length)

function Ceiling: TPoint;

Rounds the coordinates of the point to the nearest integer towards positive infinity

function Truncate: TPoint;

Truncates the coordinates of the point, discarding fractional part

function Floor: TPoint;

Rounds the coordinates of the point to the nearest integer towards negative infinity

function Round: TPoint;

Rounds the coordinates of the point to the nearest integer

function Length: Single;

Calculates the length (magnitude) of the point from the origin

function IsEmpty: boolean;

Determines if the point is empty (has special coordinates EmptyPointF)

ArrayOfTPointF = array of TPointF;

Contains an array of points with single-precision floating point coordinates

function PointsF(const pts: array of TPointF): ArrayOfTPointF;

Creates an array of TPointF

function ConcatPointsF(const APolylines: array of ArrayOfTPointF; AInsertEmptyPointInBetween: boolean = false): ArrayOfTPointF;

Concatenates arrays of TPointF

function PolylineLen(const pts: array of TPointF; AClosed: boolean = false): single;

Compute the length of the polyline contained in the array. AClosed specifies if the last point is to be joined to the first one

TAffineMatrix = array[1..2,1..3] of single;

An affine matrix contains three 2D vectors: the image of x, the image of y and the translation

3D points

PPoint3D = ^TPoint3D;

Pointer to a TPoint3D structure

TPoint3D = record

Point in 3D with single-precision floating point coordinates

procedure Offset(const point3D: TPoint3D);

Offsets the point by the given 3D vector

procedure Scale(AScale: single);

Scale the point (as a vector from the origin)

function Point3D(x,y,z: single): TPoint3D;

Creates a new structure with values (x, y, z)

operator = (const v1,v2: TPoint3D): boolean; inline;

Checks if all components x, y and z are equal

operator + (const v1,v2: TPoint3D): TPoint3D; inline;

Adds components separately. It is like adding vectors

operator - (const v1,v2: TPoint3D): TPoint3D; inline;

Subtract components separately. It is like subtracting vectors

operator - (const v: TPoint3D): TPoint3D; inline;

Returns a point with opposite values for all components

operator * (const v1,v2: TPoint3D): single; inline;

Scalar product: multiplies components and returns the sum

operator * (const v1: TPoint3D; const factor: single): TPoint3D; inline;

Multiplies components by factor. It scales the vector represented by (x, y, z)

operator * (const factor: single; const v1: TPoint3D): TPoint3D; inline;

Multiplies components by factor. It scales the vector represented by (x, y, z)

procedure VectProduct3D(u,v: TPoint3D; out w: TPoint3D);

Computes the vectorial product w. It is perpendicular to both u and v

procedure Normalize3D(var v: TPoint3D); inline;

Normalize the vector, i.e. scale it so that its length be 1

function VectLen3D(const v: TPoint3D): single;

Computes the length of the vector from the origin to the point

TFaceCulling = (

Enumerates the modes of face culling in 3D rendering. Face culling is a technique used to determine which faces of a polygon are visible and should be rendered

fcNone,

No face culling is applied. All faces of the polygon are rendered

fcKeepCW,

Keeps only the faces that are clockwise (CW) from the viewer's perspective. Typically used to remove back faces when the convention is that CW is for front faces

fcKeepCCW);

Keeps only the faces that are counter-clockwise (CCW) from the viewer's perspective. Typically used to remove back faces when the convention is that CCW is for front faces

Rectangles

TRectF = BGRAClasses.TRectF;

Represents a rectangle with single-precision floating point coordinates

const EmptyRectF : TRectF = (left:0; top:0; right:0; bottom: 0);

A constant representing an empty rectangle with all coordinates set to 0

function RectF(Left, Top, Right, Bottom: Single): TRectF;

Creates a TRectF structure with specified left, top, right, and bottom coordinates

function RectF(const ATopLeft,ABottomRight: TPointF): TRectF;

Creates a TRectF structure from two TPointF points representing the top-left and bottom-right corners

function RectF(const ARect: TRect): TRectF;

Creates a TRectF structure from a TRect structure (integer coordinates converted to single precision)

function RectWithSizeF(left,top,width,height: Single): TRectF;

Creates a TRectF structure with a specified position (left, top) and size (width, height)

function IsEmptyRectF(const ARect:TRectF): boolean;

Checks if the given TRectF structure is empty (of zero size)

const EmptyRect : TRect = (left:0; top:0; right:0; bottom: 0);

A value for an empty rectangle with integer coordinates

function PtInRect(const pt: TPoint; r: TRect): boolean; overload;

Checks if a point is in a rectangle with integer coordinates. This follows usual convention that r.Right and r.Bottom are not considered to be included in the rectangle.

function RectWithSize(left,top,width,height: integer): TRect;

Creates a rectangle with integer coordinates with the specified width and height

TRectHelper = record helper for TRect

Helper for TRect structure providing additional functionality to manipulate rectangles

function GetHeight: integer;

Gets the height of the rectangle

function GetIsEmpty: boolean;

Determines if the rectangle is empty (of zero size)

function GetWidth: integer;

Gets the width of the rectangle

procedure SetHeight(AValue: integer);

Sets the height of the rectangle

procedure SetWidth(AValue: integer);

Sets the width of the rectangle

constructor Create(Origin: TPoint; AWidth, AHeight: Longint); overload;

Creates a rectangle with specified origin, width, and height

constructor Create(ALeft, ATop, ARight, ABottom: Longint); overload;

Creates a rectangle with specified left, top, right, and bottom coordinates

procedure Intersect(R: TRect);

Modifies the rectangle to be the intersection of itself and another rectangle

class function Intersect(R1: TRect; R2: TRect): TRect; static;

Returns the intersection of two given rectangles

function IntersectsWith(R: TRect): Boolean;

Checks if the rectangle intersects with another rectangle

class function Union(R1, R2: TRect): TRect; static;

Returns the smallest rectangle that contains both of the given rectangles

procedure Union(R: TRect);

Modifies the rectangle to be the union of itself and another rectangle

procedure Offset(DX, DY: Longint);

Offsets the rectangle by the given distances in the X and Y directions

procedure Inflate(DX, DY: Longint);

Expands or contracts the rectangle by the specified amounts in both directions

function Contains(const APoint: TPoint): boolean; overload;

Checks if the rectangle contains a specified point

function Contains(const ARect: TRect): boolean; overload;

Checks if the rectangle completely contains another rectangle

property Width: integer read GetWidth write SetWidth;

Property to get or set the width of the rectangle

property Height: integer read GetHeight write SetHeight;

Property to get or set the height of the rectangle

property IsEmpty: boolean read GetIsEmpty;

Property to check if the rectangle is empty

TSize = BGRAClasses.TSize;

Constains a size with integer with and height

TSizeHelper = record helper for TSize

Helper to access a size

function GetHeight: integer;

Gets the height of the size

function GetWidth: integer;

Gets the width of the size

property Width: integer read GetWidth;

Property to get the width

property Height: integer read GetHeight;

Property to get the height

PRectF = ^TRectF;

Pointer to a TRectF structure

TRectFHelper = record helper for TRectF

Helper for TRectF structure providing additional functionality for rectangle manipulation

class function Intersect(const R1: TRectF; const R2: TRectF): TRectF; overload; static;

Returns the intersection of two given rectangles

class function Union(const R1: TRectF; const R2: TRectF): TRectF; overload; static;

Returns the union of two given rectangles

class function Union(const R1: TRectF; const R2: TRectF; ADiscardEmpty: boolean): TRectF; overload; static;

Returns the union of two given rectangles, with an option to ignore empty rectangles

function Union(const r: TRectF): TRectF; overload;

Returns the union of itself and another rectangle

function Union(const r: TRectF; ADiscardEmpty: boolean): TRectF; overload;

Returns the union of itself and another rectangle, with an option to ignore empty rectangles

procedure Include(const APoint: TPointF);

Expands the rectangle to include a specified point (empty points are ignored)

function Contains(const APoint: TPointF; AIncludeBottomRight: boolean = false): boolean;

Checks if the rectangle contains a specified point, with an option to include or exclude the bottom-right boundary

function IntersectsWith(const r: TRectF): boolean;

Checks if the rectangle intersects with another rectangle

function IsEmpty: boolean;

Determines if the rectangle is empty (of zero size)

TAffineBox = object

Object representing an affine box, defined by three corner points (top-left, top-tight, bottom-left)

function GetAsPolygon: ArrayOfTPointF;

Retrieves the affine box as an array of points (polygon representation)

function GetBottomRight: TPointF;

Gets the bottom-right corner of the affine box

function GetCenter: TPointF;

Calculates the center point of the affine box

function GetHeight: single;

Calculates the height of the affine box

function GetIsEmpty: boolean;

Determines if the affine box is empty (one of the point being empty, not just of zero size)

function GetRectBounds: TRect;

Gets the bounding rectangle of the affine box as TRect

function GetRectBoundsF: TRectF;

Gets the bounding rectangle of the affine box as TRectF

function GetSurface: single;

Calculates the surface area of the affine box

function GetWidth: single;

Calculates the width of the affine box

TopLeft,

Top-left corner of the affine box

TopRight,

Top-right corner of the affine box

BottomLeft: TPointF;

Bottom-left corner of the affine box

class function EmptyBox: TAffineBox; static;

Creates an empty affine box

class function AffineBox(ATopLeft, ATopRight, ABottomLeft: TPointF): TAffineBox; overload; static;

Creates an affine box defined by three corner points

class function AffineBox(ARectF: TRectF): TAffineBox; overload; static;

Creates an affine box from a TRectF structure

procedure Offset(AOfsX, AOfsY: single); overload;

Offsets the affine box by specified X and Y amounts

procedure Offset(AOfs: TPointF); overload;

Offsets the affine box by a specified point

procedure Inflate(AHoriz, AVert: single);

Inflates the affine box along its axes by specified horizontal and vertical amounts

function Contains(APoint: TPointF): boolean;

Checks if a point is contained within the affine box

property RectBounds: TRect read GetRectBounds;

Bounding rectangle as TRect

property RectBoundsF: TRectF read GetRectBoundsF;

Bounding rectangle as TRectF

property BottomRight: TPointF read GetBottomRight;

Bottom-right corner of the affine box

property IsEmpty: boolean read GetIsEmpty;

Check if the affine box is empty (containing empty points, not just of zero size)

property AsPolygon: ArrayOfTPointF read GetAsPolygon;

Affine box as an array of points (polygon)

property Width: single read GetWidth;

Width of the affine box along its axes

property Height: single read GetHeight;

Height of the affine box along its axes

property Surface: single read GetSurface;

Surface area of the affine box

property Center: TPointF read GetCenter;

Center point of the affine box

TRoundRectangleOption = (

Possible options for a round rectangle

rrTopLeftSquare,rrTopRightSquare,rrBottomRightSquare,rrBottomLeftSquare,

specify that a corner is a square (not rounded)

rrTopLeftBevel,rrTopRightBevel,rrBottomRightBevel,rrBottomLeftBevel,

specify that a corner is a bevel (cut)

rrDefault);

default option, does nothing particular

TRoundRectangleOptions = set of TRoundRectangleOption;

A set of options for a round rectangle

Paths

TBGRAPenStyle = array of Single;

A pen style can be dashed, dotted, etc. It is defined as a list of floating point number. The first number is the length of the first dash, the second number is the length of the first gap, the third number is the length of the second dash... It must have an even number of values. This is used as a complement TPenStyle.

function BGRAPenStyle(dash1, space1: single; dash2: single=0; space2: single = 0; dash3: single=0; space3: single = 0; dash4 : single = 0; space4 : single = 0): TBGRAPenStyle;

Creates a pen style with the specified length for the dashes and the spaces

TSplineStyle = (

Different types of spline. A spline is a series of points that are used as control points to draw a curve. The first point and last point may or may not be the starting and ending point

ssInside,

The curve is drawn inside the polygonal envelope without reaching the starting and ending points

ssInsideWithEnds,

The curve is drawn inside the polygonal envelope and the starting and ending points are reached

ssCrossing,

The curve crosses the polygonal envelope without reaching the starting and ending points

ssCrossingWithEnds,

The curve crosses the polygonal envelope and the starting and ending points are reached

ssOutside,

The curve is outside the polygonal envelope (starting and ending points are reached)

ssRoundOutside,

The curve expands outside the polygonal envelope (starting and ending points are reached)

ssVertexToSide,

The curve is outside the polygonal envelope and there is a tangeant at vertices (starting and ending points are reached)

ssEasyBezier);

The curve is rounded using Bezier curves when the angle is less than or equal to 45°

PArcDef = ^TArcDef;

Pointer to an arc definition

TArcDef = record

Definition of an arc of an ellipse

center: TPointF;

Center of the ellipse

radius: TPointF;

Horizontal and vertical of the ellipse before rotation

xAngleRadCW: single;

Rotation of the ellipse

startAngleRadCW, endAngleRadCW: single;

Start and end angle, in radian and clockwise. See angle convention in BGRAPath

anticlockwise: boolean

Specifies if the arc goes anticlockwise

function ArcDef(cx, cy, rx,ry, xAngleRadCW, startAngleRadCW, endAngleRadCW: single; anticlockwise: boolean) : TArcDef;

Creates a structure for an arc definition

TArcOption = (

Possible options for drawing an arc of an ellipse (used in BGRACanvas)

aoClosePath,

Close the path by joining the ending and starting point together

aoPie,

Draw a pie shape by joining the ending and starting point to the center of the ellipse

aoFillPath);

Fills the shape

TArcOptions = set of TArcOption;

Set of options for drawing an arc

TLineDef = record

Defition of a line in the euclidian plane

origin: TPointF;

Some point in the line

dir: TPointF;

Vector indicating the direction

function IntersectLine(line1, line2: TLineDef): TPointF; overload;

Computes the intersection of two lines. If they are parallel, returns the middle of the segment between the two origins

function IntersectLine(line1, line2: TLineDef; out parallel: boolean): TPointF; overload;

Computes the intersection of two lines. If they are parallel, returns the middle of the segment between the two origins. The value parallel is set to indicate if the lines were parallel

function IsConvex(const pts: array of TPointF; IgnoreAlign: boolean = true): boolean;

Checks if the polygon formed by the given points is convex. IgnoreAlign specifies that if the points are aligned, it should still be considered as convex

function IsClockwise(const pts: array of TPointF): boolean;

Checks if the points follow a clockwise curve

function IsMostlyClockwise(const pts: array of TPointF): boolean;

Checks if the curve is clockwise on the whole but accepting some counter-clockwise points

function DoesQuadIntersect(pt1,pt2,pt3,pt4: TPointF): boolean;

Checks if the quad formed by the 4 given points intersects itself

function DoesSegmentIntersect(pt1,pt2,pt3,pt4: TPointF): boolean;

Checks if two segment intersect

TBGRAPathDrawProc = procedure(const APoints: array of TPointF; AClosed: boolean; AData: Pointer) of object;

Callback function when rendering a stroke

TBGRAPathFillProc = procedure(const APoints: array of TPointF; AData: pointer) of object;

Callback function when filling a shape

IBGRAPath = interface

A path is the ability to define a contour with moveTo, lineTo... Even if it is an interface, it must not implement reference counting.

procedure closePath;

Closes the current path with a line to the starting point

procedure moveTo(constref pt: TPointF);

Moves to a location, disconnected from previous points

procedure lineTo(constref pt: TPointF);

Adds a line from the current point

procedure polylineTo(const pts: array of TPointF);

Adds a polyline from the current point

procedure quadraticCurveTo(constref cp,pt: TPointF);

Adds a quadratic Bézier curve from the current point

procedure bezierCurveTo(constref cp1,cp2,pt: TPointF);

Adds a cubic Bézier curve from the current point

procedure arc(constref arcDef: TArcDef);

Adds an arc. If there is a current point, it is connected to the beginning of the arc

procedure openedSpline(const pts: array of TPointF; style: TSplineStyle);

Adds an opened spline. If there is a current point, it is connected to the beginning of the spline

procedure closedSpline(const pts: array of TPointF; style: TSplineStyle);

Adds an closed spline. If there is a current point, it is connected to the beginning of the spline

procedure copyTo(dest: IBGRAPath);

Copy the content of this path to the specified destination

function getPoints: ArrayOfTPointF; overload;

Returns the content of the path as an array of points

function getPoints(AMatrix: TAffineMatrix): ArrayOfTPointF; overload;

Returns the content of the path as an array of points with the transformation specified by AMatrix

procedure stroke(ADrawProc: TBGRAPathDrawProc; AData: pointer); overload;

Calls a given draw procedure for each sub path with computed coordinates for rendering

procedure stroke(ADrawProc: TBGRAPathDrawProc; const AMatrix: TAffineMatrix; AData: pointer); overload;

Calls a given draw procedure for each sub path with computed coordinates using given AMatrix transformation

procedure fill(AFillProc: TBGRAPathFillProc; AData: pointer); overload;

Calls a given fill procedure for each sub path with computed coordinates for rendering

procedure fill(AFillProc: TBGRAPathFillProc; const AMatrix: TAffineMatrix; AData: pointer); overload;

Calls a given fill procedure for each sub path with computed coordinates using given AMatrix transformation

function getCursor: TBGRACustomPathCursor;

Returns a cursor to go through the path. The cursor must be freed by calling Free.

TBGRACustomPath = class(IBGRAPath)

Generic class representing a path, providing methods for creation, exploration and rendering

constructor Create; virtual; abstract;

Constructor to create a custom path. Must be overridden in subclasses

procedure beginPath; virtual; abstract;

Begins a new path

procedure closePath; virtual; abstract;

Closes the current path

procedure moveTo(constref pt: TPointF); virtual; abstract;

Moves the current point to a specified location, starting a new sub-path

procedure lineTo(constref pt: TPointF); virtual; abstract;

Adds a line from the current point to a specified point

procedure polylineTo(const pts: array of TPointF); virtual; abstract;

Adds a series of lines to the path based on an array of points

procedure quadraticCurveTo(constref cp, pt: TPointF); virtual; abstract;

Adds a quadratic Bézier curve to the path

procedure bezierCurveTo(constref cp1, cp2, pt: TPointF); virtual; abstract;

Adds a cubic Bézier curve to the path

procedure arc(constref arcDef: TArcDef); virtual; abstract;

Adds an arc to the path based on an arc definition

procedure openedSpline(const pts: array of TPointF; style: TSplineStyle); virtual; abstract;

Adds an open spline to the path based on a series of points and a spline style

procedure closedSpline(const pts: array of TPointF; style: TSplineStyle); virtual; abstract;

Adds a closed spline to the path based on a series of points and a spline style

procedure copyTo(dest: IBGRAPath); virtual; abstract;

Copies the path to another path object

function getPoints: ArrayOfTPointF; overload; virtual; abstract;

Retrieves the points of the path

function getPoints(AMatrix: TAffineMatrix): ArrayOfTPointF; overload; virtual; abstract;

Retrieves the points of the path, transformed by a specified matrix

procedure stroke(ADrawProc: TBGRAPathDrawProc; AData: pointer); overload; virtual; abstract;

Strokes the path with a specified drawing procedure

procedure stroke(ADrawProc: TBGRAPathDrawProc; const AMatrix: TAffineMatrix; AData: pointer); overload; virtual; abstract;

Strokes the path with a specified drawing procedure and transformation matrix

procedure fill(AFillProc: TBGRAPathFillProc; AData: pointer); overload; virtual; abstract;

Fills the path with a specified filling procedure

procedure fill(AFillProc: TBGRAPathFillProc; const AMatrix: TAffineMatrix; AData: pointer); overload; virtual; abstract;

Fills the path with a specified filling procedure and transformation matrix

function getLength: single; virtual; abstract;

Retrieves the length of the path

function getCursor: TBGRACustomPathCursor; virtual; abstract;

Retrieves a cursor for navigating the path

TBGRAPathAny = class of TBGRACustomPath;

Type for specifying any derived class of TBGRACustomPath

TBGRACustomPathCursor = class

Class that contains a cursor to browse an existing path

function GetArcPos: single; virtual; abstract;

Retrieves the current position from the start

function GetCurrentCoord: TPointF; virtual; abstract;

Returns the current coordinate in the path

function GetCurrentTangent: TPointF; virtual; abstract;

Returns the tangent vector to the current position

function GetLoopClosedShapes: boolean; virtual; abstract;

Retrieves if the cursor loops when there is a closed shape

function GetLoopPath: boolean; virtual; abstract;

Retrieves if the cursor loops at the end of the whole path

function GetPathLength: single; virtual; abstract;

Retreive the full arc length of the path

function GetBounds: TRectF; virtual; abstract;

Compute the bounds of the path

function GetStartCoordinate: TPointF; virtual; abstract;

Starting coordinate of the path

procedure SetArcPos(AValue: single); virtual; abstract;

Sets the current position from the start

procedure SetLoopClosedShapes(AValue: boolean); virtual; abstract;

Sets if the cursor loops when there is a closed shape

procedure SetLoopPath(AValue: boolean); virtual; abstract;

Sets if the cursor loops at the end of the whole path

function MoveForward(ADistance: single; ACanJump: boolean = true): single; virtual; abstract;

Go forward in the path, increasing the value of Position. If ADistance is negative, then it goes backward instead. ACanJump specifies if the cursor can jump from one shape to another without a line or an arc. Otherwise, the cursor is stuck, and the return value is less than the value ADistance provided. If all the way has been travelled, the return value is equal to ADistance

function MoveBackward(ADistance: single; ACanJump: boolean = true): single; virtual; abstract;

Go backward, decreasing the value of Position. If ADistance is negative, then it goes forward instead. ACanJump specifies if the cursor can jump from one shape to another without a line or an arc. Otherwise, the cursor is stuck, and the return value is less than the value ADistance provided. If all the way has been travelled, the return value is equal to ADistance

property CurrentCoordinate: TPointF read GetCurrentCoord;

Returns the current coordinate in the path

property CurrentTangent: TPointF read GetCurrentTangent;

Returns the tangent vector. It is a vector of length one that is parallel to the curve at the current point. A normal vector is easily deduced as PointF(y,-x)

property Position: single read GetArcPos write SetArcPos;

Current position in the path, as a distance along the arc from the starting point of the path

property PathLength: single read GetPathLength;

Full arc length of the path

property StartCoordinate: TPointF read GetStartCoordinate;

Starting coordinate of the path

property LoopClosedShapes: boolean read GetLoopClosedShapes write SetLoopClosedShapes;

Specifies if the cursor loops when there is a closed shape

property LoopPath: boolean read GetLoopPath write SetLoopPath;

Specifies if the cursor loops at the end of the path. Note that if it needs to jump to go to the beginning, it will be only possible if the parameter ACanJump is set to True when moving along the path

BGRAPathFactory: TBGRAPathAny;

Factory provided to create a TBGRAPath object

Polygon filling

TPolygonOrder = (

Order of polygons when rendered using TBGRAMultiShapeFiller (in unit BGRAPolygon)

poNone,

No order, colors are mixed together

poFirstOnTop,

First polygon is on top

poLastOnTop);

Last polygon is on top

TIntersectionInfo = class

Contains an intersection between an horizontal line and any shape. It is used when filling shapes

interX: single;

Horizontal position of the intersection

winding: integer;

Winding count

numSegment: integer;

Number identifying the current segment where the intersection was found

procedure SetValues(AInterX: Single; AWinding, ANumSegment: integer);

Sets the position and other information about the intersection

ArrayOfTIntersectionInfo = array of TIntersectionInfo;

An array of intersections between an horizontal line and any shape

TBGRACustomFillInfo = class

Abstract class defining any shape that can be filled

function SegmentsCurved: boolean; virtual; abstract;

Returns true if one segment number can represent a curve and thus cannot be considered exactly straight

function GetBounds: TRect; virtual; abstract;

Returns integer bounds for the shape

function IsPointInside(x,y: single; windingMode: boolean): boolean; virtual; abstract;

Check if the point is inside the shape

function CreateIntersectionArray: ArrayOfTIntersectionInfo; virtual; abstract;

Create an array that will contain computed intersections. To augment that array, use CreateIntersectionInfo for new items

function CreateIntersectionInfo: TIntersectionInfo; virtual; abstract;

Create a structure to define one single intersection

procedure FreeIntersectionArray(var inter: ArrayOfTIntersectionInfo); virtual; abstract;

Free an array of intersections

procedure ComputeAndSort(cury: single; var inter: ArrayOfTIntersectionInfo; out nbInter: integer; windingMode: boolean); virtual; abstract;

Fill an array inter with actual intersections with the shape at the y coordinate cury. nbInter receives the number of computed intersections. windingMode specifies if the winding method must be used to determine what is inside of the shape

function GetSliceIndex: integer; virtual; abstract;

Returns the index of the current slice (horizontal stripe)

Arrows

TBGRAArrowStyle = (

Enumerates different styles of arrows that can be used in graphic rendering. Each style represents a unique visual appearance for arrowheads or tails

asNone,

No arrow style. This option indicates that no arrowhead or tail is to be rendered

asNormal,

A normal arrow style, representing a standard arrowhead with an angle

asCut,

A cut arrow style, where the edge of the arrow are cut instead of using the pen end cap

asTriangle,

A triangle arrow style, forming a simple triangular arrowhead

asHollowTriangle,

A hollow triangle arrow style, similar to asTriangle but with an unfilled center

asFlipped,

A flipped arrow style, where the arrowhead points in the opposite direction to the normal style

asFlippedCut,

A flipped cut arrow style, combining the aspects of asFlipped and asCut

asTail,

A small tail, typically used to depict the starting point of an arrow

asTailRepeat);

A tail repeat arrow style, depicting a series of repeated patterns typically used for the starting point of an arrow

TBGRACustomArrow = class

Generic class configuring and rendering an arrow

function GetEndOffsetX: single; virtual; abstract;

Retrieves the X-offset for the end of the arrow

function GetEndRepeatCount: integer; virtual; abstract;

Retrieves the repeat count for the end symbol

function GetEndSizeFactor: TPointF; virtual; abstract;

Retrieves the size factor for the end of the arrow

function GetIsEndDefined: boolean; virtual; abstract;

Determines if the end of the arrow is defined

function GetIsStartDefined: boolean; virtual; abstract;

Determines if the start of the arrow is defined

function GetStartOffsetX: single; virtual; abstract;

Retrieves the X-offset for the start of the arrow

function GetStartRepeatCount: integer; virtual; abstract;

Retrieves the repeat count for the start symbol

function GetStartSizeFactor: TPointF; virtual; abstract;

Retrieves the size factor for the start of the arrow

procedure SetEndOffsetX(AValue: single); virtual; abstract;

Sets the X-offset for the end of the arrow

procedure SetEndRepeatCount(AValue: integer); virtual; abstract;

Sets the repeat count for the end symbol

procedure SetEndSizeFactor(AValue: TPointF); virtual; abstract;

Sets the size factor for the end of the arrow

procedure SetStartOffsetX(AValue: single); virtual; abstract;

Sets the X-offset for the start of the arrow

procedure SetStartRepeatCount(AValue: integer); virtual; abstract;

Sets the repeat count for the start symbol

procedure SetStartSizeFactor(AValue: TPointF); virtual; abstract;

Sets the size factor for the start of the arrow

function GetLineCap: TPenEndCap; virtual; abstract;

Retrieves the line cap style for the classic arrow

procedure SetLineCap(AValue: TPenEndCap); virtual; abstract;

Sets the line cap style for the classic arrow

function ComputeStartAt(const APosition, ADirection: TPointF; const AWidth, ACurrentPos: single): ArrayOfTPointF; virtual; abstract;

Computes the start of the arrow at a given position and direction

function ComputeEndAt(const APosition, ADirection: TPointF; const AWidth, ACurrentPos: single): ArrayOfTPointF; virtual; abstract;

Computes the end of the arrow at a given position and direction

procedure StartAsNone; virtual; abstract;

Sets the start of the arrow to no style

procedure StartAsClassic(AFlipped: boolean = false; ACut: boolean = false; ARelativePenWidth: single = 1); virtual; abstract;

Sets the start of the arrow to a classic style

procedure StartAsTriangle(ABackOffset: single = 0; ARounded: boolean = false; AHollow: boolean = false; AHollowPenWidth: single = 0.5); virtual; abstract;

Sets the start of the arrow to a triangle style

procedure StartAsTail; virtual; abstract;

Sets the start of the arrow to a tail style

procedure EndAsNone; virtual; abstract;

Sets the end of the arrow to no style

procedure EndAsClassic(AFlipped: boolean = false; ACut: boolean = false; ARelativePenWidth: single = 1); virtual; abstract;

Sets the end of the arrow to a classic style

procedure EndAsTriangle(ABackOffset: single = 0; ARounded: boolean = false; AHollow: boolean = false; AHollowPenWidth: single = 0.5); virtual; abstract;

Sets the end of the arrow to a triangle style

procedure EndAsTail; virtual; abstract;

Sets the end of the arrow to a tail style

property IsStartDefined: boolean read GetIsStartDefined;

Check if the start of the arrow is defined

property IsEndDefined: boolean read GetIsEndDefined;

Check if the end of the arrow is defined

property StartOffsetX: single read GetStartOffsetX write SetStartOffsetX;

X-offset for the start of the arrow

property EndOffsetX: single read GetEndOffsetX write SetEndOffsetX;

X-offset for the end of the arrow

property LineCap: TPenEndCap read GetLineCap write SetLineCap;

Line cap style

property StartSize: TPointF read GetStartSizeFactor write SetStartSizeFactor;

Size factor for the start of the arrow

property EndSize: TPointF read GetEndSizeFactor write SetEndSizeFactor;

Size factor for the end of the arrow

property StartRepeatCount: integer read GetStartRepeatCount write SetStartRepeatCount;

Repeat count for the start symbol

property EndRepeatCount: integer read GetEndRepeatCount write SetEndRepeatCount;

Repeat count for the end symbol

TBGRACustomPenStroker = class

Generic class representing a pen stroker, used for drawing and styling lines with various attributes

function GetArrow: TBGRACustomArrow; virtual; abstract;

Retrieves the arrow style used at both ends of strokes

function GetArrowOwned: boolean; virtual; abstract;

Determines if the arrow is owned (managed) by the pen stroker

function GetCustomPenStyle: TBGRAPenStyle; virtual; abstract;

Gets the custom pen style

function GetJoinStyle: TPenJoinStyle; virtual; abstract;

Retrieves the style of line joins (e.g., bevel, miter)

function GetLineCap: TPenEndCap; virtual; abstract;

Retrieves the line cap style (e.g., butt, round)

function GetMiterLimit: single; virtual; abstract;

Gets the miter limit for line joins

function GetPenStyle: TPenStyle; virtual; abstract;

Retrieves the standard pen style

function GetStrokeMatrix: TAffineMatrix; virtual; abstract;

Gets the stroke transformation matrix (applied only to stroke and not to path points)

procedure SetArrow(AValue: TBGRACustomArrow); virtual; abstract;

Sets the arrow style used at both ends of strokes

procedure SetArrowOwned(AValue: boolean); virtual; abstract;

Sets whether the arrow is owned by the pen stroker

procedure SetCustomPenStyle(AValue: TBGRAPenStyle); virtual; abstract;

Sets the custom pen style

procedure SetJoinStyle(AValue: TPenJoinStyle); virtual; abstract;

Sets the style of line joins

procedure SetLineCap(AValue: TPenEndCap); virtual; abstract;

Sets the line cap style

procedure SetMiterLimit(AValue: single); virtual; abstract;

Sets the miter limit for line joins

procedure SetPenStyle(AValue: TPenStyle); virtual; abstract;

Sets the standard pen style

procedure SetStrokeMatrix(const AValue: TAffineMatrix); virtual; abstract;

Sets the stroke transformation matrix (applied only to stroke and not to path points)

function ComputePolyline(const APoints: array of TPointF; AWidth: single; AClosedCap: boolean = true): ArrayOfTPointF; overload; virtual; abstract;

Computes a polyline with the given points and width, optionally closing the cap

function ComputePolyline(const APoints: array of TPointF; AWidth: single; APenColor: TBGRAPixel; AClosedCap: boolean = true): ArrayOfTPointF; overload; virtual; abstract;

Computes a polyline with the given points, width, and pen color, optionally closing the cap

function ComputePolylineAutoCycle(const APoints: array of TPointF; AWidth: single): ArrayOfTPointF; virtual; abstract;

Computes a polyline with automatic cycling of points and given width

function ComputePolygon(const APoints: array of TPointF; AWidth: single): ArrayOfTPointF; virtual; abstract;

Computes a polygon with the given points and width

property Style: TPenStyle read GetPenStyle write SetPenStyle;

Standard pen style

property CustomPenStyle: TBGRAPenStyle read GetCustomPenStyle write SetCustomPenStyle;

Custom pen style (with given dash and gap lengths)

property Arrow: TBGRACustomArrow read GetArrow write SetArrow;

Arrow style at both ends of strokes

property ArrowOwned: boolean read GetArrowOwned write SetArrowOwned;

Is the arrow is owned by the pen stroker

property StrokeMatrix: TAffineMatrix read GetStrokeMatrix write SetStrokeMatrix;

Stroke transformation matrix (applied only to stroke and not to path points)

property LineCap: TPenEndCap read GetLineCap write SetLineCap;

Line cap style

property JoinStyle: TPenJoinStyle read GetJoinStyle write SetJoinStyle;

Join style of lines

property MiterLimit: single read GetMiterLimit write SetMiterLimit;

Miter limit for line joins

Gradients

TGradientType = (

Shape of a gradient

gtLinear,

The color changes along a certain vector and does not change along its perpendicular direction

gtReflected,

The color changes like in gtLinear however it is symmetrical to a specified direction

gtDiamond,

The color changes along a diamond shape

gtRadial,

The color changes in a radial way from a given center

gtAngular);

The color changes according to the angle relative to a given center

const GradientTypeStr : array[TGradientType] of string

List of string to represent gradient types

function StrToGradientType(str: string): TGradientType;

Returns the gradient type represented by the given string

TBGRAGradientGetColorAtFunc = function(position: integer): TBGRAPixel of object;

Function type to get the the color at a given integer position

TBGRAGradientGetColorAtFloatFunc = function(position: single): TBGRAPixel of object;

Function type to get the the color at a given single-precision floating type position

TBGRAGradientGetExpandedColorAtFunc = function(position: integer): TExpandedPixel of object;

Function type to get the the expanded color at a given integer position

TBGRAGradientGetExpandedColorAtFloatFunc = function(position: single): TExpandedPixel of object;

Function type to get the the expanded color at a given single-precision floating type position

TBGRACustomGradient = class

Defines a gradient of color, not specifying its shape but only the series of colors

function GetColorAt(position: integer): TBGRAPixel; virtual; abstract;

Returns the color at a given position. The reference range is from 0 to 65535, however values beyond are possible as well

function GetExpandedColorAt(position: integer): TExpandedPixel; virtual;

Returns the expanded color at a given position. The reference range is from 0 to 65535, however values beyond are possible as well

function GetColorAtF(position: single): TBGRAPixel; virtual;

Returns the color at a given position. The reference range is from 0 to 1, however values beyond are possible as well

function GetExpandedColorAtF(position: single): TExpandedPixel; virtual;

Returns the expanded color at a given position. The reference range is from 0 to 1, however values beyond are possible as well

function GetAverageColor: TBGRAPixel; virtual; abstract;

Returns the average color of the gradient

function GetAverageExpandedColor: TExpandedPixel; virtual;

Returns the average expanded color of the gradient

function GetMonochrome: boolean; virtual; abstract;

Returns whether the gradient has only one color

property Monochrome: boolean read GetMonochrome;

If the gradient contains only one color and thus is not really a gradient

Bézier curves

TCubicBezierCurve = object

Definition of a Bézier curve of order 3. It has two control points c1 and c2. Those are not reached by the curve in general.

function SimpleComputePoints(AAcceptedDeviation: single = 0.1; AIncludeFirstPoint: boolean = true): ArrayOfTPointF;

Compute the points using the simple approach of computing for each time value

p1: TPointF;

Starting point (reached)

c1: TPointF;

First control point (not reached by the curve)

c2: TPointF;

Second control point (not reached by the curve)

p2: TPointF;

Ending point (reached)

function ComputePointAt(t: single): TPointF;

Computes the point at time t, varying from 0 to 1

procedure Split(out ALeft, ARight: TCubicBezierCurve);

Split the curve in two such that ALeft.p2 = ARight.p1

function ComputeLength(AAcceptedDeviation: single = 0.1): single;

Compute an approximation of the length of the curve. AAcceptedDeviation indicates the maximum orthogonal distance that is ignored and approximated by a straight line.

function ToPoints(AAcceptedDeviation: single = 0.1; AIncludeFirstPoint: boolean = true): ArrayOfTPointF;

Computes a polygonal approximation of the curve. AAcceptedDeviation indicates the maximum orthogonal distance that is ignored and approximated by a straight line. AIncludeFirstPoint indicates if the first point must be included in the array

procedure CopyToPath(ADest: IBGRAPath);

Copy the curve to the given path

function GetBounds: TRectF;

Computes the rectangular bounds

function BezierCurve(origin, control1, control2, destination: TPointF) : TCubicBezierCurve; overload;

Creates a structure for a cubic Bézier curve

TQuadraticBezierCurve = object

Definition of a Bézier curve of order 2. It has one control point

function SimpleComputePoints(AAcceptedDeviation: single = 0.1; AIncludeFirstPoint: boolean = true): ArrayOfTPointF;

Compute the points using the simple approach of computing for each time value

function ComputeExtremumPositionOutsideSegment: single;

Computes the position where the curve has its extremum

p1: TPointF;

Starting point (reached)

c: TPointF;

Control point (not reached by the curve)

p2: TPointF;

Ending point (reached)

function ComputePointAt(t: single): TPointF;

Computes the point at time t, varying from 0 to 1

procedure Split(out ALeft, ARight: TQuadraticBezierCurve);

Split the curve in two such that ALeft.p2 = ARight.p1

function ComputeLength: single;

Compute the exact length of the curve

function ToPoints(AAcceptedDeviation: single = 0.1; AIncludeFirstPoint: boolean = true): ArrayOfTPointF;

procedure CopyToPath(ADest: IBGRAPath);

Copy the curve to the given path

function GetBounds: TRectF;

Computes the rectangular bounds

function BezierCurve(origin, control, destination: TPointF) : TQuadraticBezierCurve; overload;

Creates a structure for a quadratic Bézier curve

function BezierCurve(origin, destination: TPointF) : TQuadraticBezierCurve; overload;

Creates a structure for a quadratic Bézier curve without curvature

ArrayOfSingle = array of single;

Array of single-precision floating point values

TRationalQuadraticBezierCurve = object

Quasi-standard rational quadratic Bezier curve, defined by three points and a number:

p1: starting point
c: control point
p2: ending point
weight: weight for the control point

The curve is defined with the function (t in [0; 1]):

f: t → ((1-t)2 * p1 + 2 * t * (1-t) * weight * c + t2*p2) / (1-t)2 + 2 * t * (1-t) * weight + t2)

The curve is an arc of:

ellipse when weight in ]-1; 1[
parabola when weight = 1 (classical quadratic Bezier curve)
hyperbola when weight > 1

A negative weight give the complementary curve for its positive counterpart. So when weight ≤ -1 the curve is discontinuous:

infinite branches of parabola when weight = -1
infinite branches of hyperbola and symetric hyperbola when weight < -1

To transform a rational quadratic Bezier curve with an affin transformation, you only have to transform the three points and leave the weight as it is.

p1, c, p2 : TPointF;

Starting, control and ending points

weight : single;

Weight of control point

function GetIsInfinite: boolean;

Checks whether the curve is infinitely long

function InternalComputePoints(AInfiniteBounds: TRectF; AAcceptedDeviation: single = 0.1; AIncludeFirstPoint: boolean = true): ArrayOfTPointF;

Compute points in the general case

function GetBoundingPositions(AIncludeFirstAndLast: boolean; ASorted: boolean): ArrayOfSingle;

Computes the points relevant to compute bounds

function ComputePointAt(t: single): TPointF;

Compute a point at the specified time

function ComputeLength(AAcceptedDeviation: single = 0.1): single;

Compute the length

function ToPoints(AAcceptedDeviation: single = 0.1; AIncludeFirstPoint: boolean = true): ArrayOfTPointF; overload;

Computes the points of the curve

function ToPoints(AInfiniteBounds: TRectF; AAcceptedDeviation: single = 0.1; AIncludeFirstPoint: boolean = true): ArrayOfTPointF; overload;

Computes the points of the curve by providing where the infinite curve can stop

function GetBounds: TRectF;

Compute the rectangular bounds

procedure Split(out ALeft, ARight: TRationalQuadraticBezierCurve);

Split into two curves

property IsInfinite: boolean read GetIsInfinite;

Is the curve infinitely long

function BezierCurve(origin, control, destination: TPointF; Aweight:single) : TRationalQuadraticBezierCurve; overload;

Creates a rational Bézier curve

TEasyBezierCurveMode = (

Enumerates modes for handling curves in a Bezier curve sequence

cmAuto,

Automatically determines whether to curve or form an angle based on the points' positions

cmCurve,

Forces a curve at the point

cmAngle

Forces an angle at the point, meaning the point is reached and forms an angle instead of a curve

TEasyBezierPointTransformFunc = function(APoint: PPointF; AData: Pointer): TPointF of object;

Function type for transforming Bezier curve points

TEasyBezierCurve = object

Object representing an easy-to-use Bezier curve, with configurable curve modes and transformation functions

function GetCurveMode(AIndex: integer): TEasyBezierCurveMode;

Retrieves the curve mode for a specified point index

function GetCurveStartPoint: TPointF;

Gets the starting point of the curve

function GetPoint(AIndex: integer): TPointF;

Retrieves the point at a specified index

function GetPointCount: integer;

Gets the total number of points in the curve

procedure SetClosed(AValue: boolean);

Sets whether the curve is closed

procedure SetCurveMode(AIndex: integer; AValue: TEasyBezierCurveMode);

Sets the curve mode for a specified point index

procedure SetMinimumDotProduct(AValue: single);

Sets the minimum dot product to form a curve instead of an angle

procedure SetPoint(AIndex: integer; AValue: TPointF);

Sets the point at a specified index

FCurves: array of record

Computed Bézier control points

FInvalidated: boolean;

Whether the curve need to be recomputed

FPoints: array of record

Definition of the curve by the user

FMinimumDotProduct: single;

Minimum dot product to form a curve instead of an angle

FClosed: boolean;

Is the curve is closed

function MaybeCurve(start1, end1, start2, end2: integer): boolean;

Checks whether two vectors have the minimum dot product to suggest a curve. start1 and end1 are the indices for the first vector. start2 and end2 for the second vector.

procedure ComputeQuadraticCurves;

Computes the control points for the classical quadratic curve

function PointTransformNone(APoint: PPointF; AData: Pointer): TPointF;

Fonction to apply no transformation

function PointTransformOffset(APoint: PPointF; AData: Pointer): TPointF;

Fonction to apply an offset

procedure Init;

Initializes the Bezier curve object

procedure Clear;

Clears all points and resets the curve

procedure SetPoints(APoints: array of TPointF; ACurveMode: TEasyBezierCurveMode); overload;

Sets the points and curve mode for the entire curve

procedure SetPoints(APoints: array of TPointF; ACurveMode: array of TEasyBezierCurveMode); overload;

Sets the points and individual curve modes for each point

procedure SetPoints(APoints: array of TPointF; ACurveMode: TEasyBezierCurveMode; AStart, ACount: integer); overload;

Sets a subset of points and a single curve mode for these points

procedure SetPoints(APoints: array of TPointF; ACurveMode: array of TEasyBezierCurveMode; AStart, ACount: integer); overload;

Sets a subset of points and individual curve modes for each of these points

procedure CopyToPath(ADest: IBGRAPath); overload;

Copies the Bezier curve to a path object

procedure CopyToPath(ADest: IBGRAPath; AOffset: TPointF; AReverse: boolean = false); overload;

Copies the Bezier curve to a path object with an offset and optional reversal

procedure CopyToPath(ADest: IBGRAPath; ATransformFunc: TEasyBezierPointTransformFunc; ATransformData: Pointer; AReverse: boolean = false); overload;

Copies the Bezier curve to a path object with a custom transformation

property Point[AIndex: integer]: TPointF read GetPoint write SetPoint;

Coordinates of the points

property CurveMode[AIndex: integer]: TEasyBezierCurveMode read GetCurveMode write SetCurveMode;

Mode to use for each point

property PointCount: integer read GetPointCount;

Number of points

property MinimumDotProduct: single read FMinimumDotProduct write SetMinimumDotProduct;

Minimum dot product to form a curve rather than an angle when using cmAuto mode

property Closed: boolean read FClosed write SetClosed;

Gets or sets whether to close the curve

property CurveStartPoint: TPointF read GetCurveStartPoint;

Coordinates of the starting point

function ToPoints: ArrayOfTPointF;

Converts the Bezier curve into an array of points

function ComputeLength: single;

Computes the total length of the Bezier curve

const EasyBezierDefaultMinimumDotProduct = 0.707;

Minimum dot product, corresponding to approximately 45 degrees, to form a curve instead of an angle

function EasyBezierCurve(APoints: array of TPointF; AClosed: boolean; ACurveMode: TEasyBezierCurveMode;

Create a TEasyBezierCurve object with only one curve mode

function EasyBezierCurve(APoints: array of TPointF; AClosed: boolean; ACurveMode: array of TEasyBezierCurveMode;

Create a TEasyBezierCurve object with a curve mode for each point

function EasyBezierCurve(APoints: array of TPointF; AStart, ACount: integer; AClosed: boolean; ACurveMode: TEasyBezierCurveMode;

Create a TEasyBezierCurve object with a subsection of the array of points, with only one curve mode

function EasyBezierCurve(APoints: array of TPointF; AStart, ACount: integer; AClosed: boolean; ACurveMode: array of TEasyBezierCurveMode;

Create a TEasyBezierCurve object with a subsection of the array of points, with a curve mode for each point

From the Free Pascal wiki, page "BGRABitmap Geometry types", as it stood on 2023-12-16 after a change by Circular, out of the wiki's dump of 2024-05-26. Copyright stays with the author who wrote it, according to the old wiki's Licensing page. If you have concerns about this material, message the admin.

Revision 2, last changed by WikiArchive 11-4-2026.

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