TBLMatrix2D

2D matrix represents an affine transformation matrix that can be used to transform geometry and images.

Definition

type TBLMatrix2D = record ... end;

Fields

Name	Description
M

Properties

Name	Description
Kind	The matrix kind.
M00	Element [0, 0]. Contains X scaling.
M01	Element [0, 1]. Contains rotation and skewing.
M10	Element [1, 0]. Contains rotation and skewing.
M11	Element [1, 1]. Contains Y scaling.
M20	Element [2, 0]. Contains X translation.
M21	Element [2, 1]. Contains Y translation.

Constructors

Name	Description
Create

Operators

Name	Description
Equal
NotEqual

Methods

Name	Description
Determinant	Calculates the matrix determinant.
Equals
Invert(TBLMatrix2D, TBLMatrix2D)	Inverts `ASrc` matrix and stores the result in `ADst`. Returns True if the matrix has been inverted successfully.
Invert	Inverts the matrix. Returns True if the matrix has been inverted successfully.
MakeIdentity	Creates a new matrix initialized to identity.
MakeRotation(Double, TBLPoint)
MakeRotation(Double, Double, Double)
MakeRotation(Double)	Creates a new matrix initialized to rotation.
MakeScaling(TBLPointI)
MakeScaling(TBLPoint)
MakeScaling(Double, Double)
MakeScaling(Double)	Creates a new matrix initialized to scaling.
MakeSinCos(Double, Double, TBLPoint)
MakeSinCos(Double, Double, Double, Double)
MakeSkewing(TBLPoint)
MakeSkewing(Double, Double)	Create a new skewing matrix.
MakeTranslation(TBLPointI)
MakeTranslation(TBLPoint)
MakeTranslation(Double, Double)	Creates a new matrix initialized to translation.
MapPoint(TBLPoint)
MapPoint(Double, Double)
MapVector(TBLPoint)
MapVector(Double, Double)
PostRotate(Double, TBLPointI)
PostRotate(Double, TBLPoint)
PostRotate(Double, Double, Double)
PostRotate(Double)
PostScale(TBLPointI)
PostScale(TBLPoint)
PostScale(Double, Double)
PostScale(Double)
PostSkew(TBLPoint)
PostSkew(Double, Double)
PostTransform
PostTranslate(TBLPointI)
PostTranslate(TBLPoint)
PostTranslate(Double, Double)
Reset(Double, Double, Double, Double, Double, Double)	Resets matrix to `[AM00, AM01, AM10, AM11, AM20, AM21]`.
Reset(TBLMatrix2D)	Resets matrix to `AOther` (copy its content to this matrix).
Reset	Resets matrix to identity.
ResetToRotation(Double, TBLPoint)	Resets matrix to rotation around a point `p`.
ResetToRotation(Double, Double, Double)	Resets matrix to rotation around a point `[X, Y]`.
ResetToRotation(Double)	Resets matrix to rotation.
ResetToScaling(TBLPointI)	Resets matrix to scaling.
ResetToScaling(TBLPoint)	Resets matrix to scaling.
ResetToScaling(Double, Double)	Resets matrix to scaling.
ResetToScaling(Double)	Resets matrix to scaling.
ResetToSinCos(Double, Double, TBLPoint)	Resets matrix to rotation specified by `ASin` and `ACos` and translation `AP`.
ResetToSinCos(Double, Double, Double, Double)	Resets matrix to rotation specified by `ASin` and `ACos` and optional translation `ATX` and `ATY`.
ResetToSkewing(TBLPoint)	Resets matrix to skewing.
ResetToSkewing(Double, Double)	Resets matrix to skewing.
ResetToTranslation(TBLPointI)	Resets matrix to translation.
ResetToTranslation(TBLPoint)	Resets matrix to translation.
ResetToTranslation(Double, Double)	Resets matrix to translation.
Rotate(Double, TBLPointI)
Rotate(Double, TBLPoint)
Rotate(Double, Double, Double)
Rotate(Double)
Scale(TBLPointI)
Scale(TBLPoint)
Scale(Double, Double)
Scale(Double)
Skew(TBLPoint)
Skew(Double, Double)
Transform
Translate(TBLPointI)
Translate(TBLPoint)
Translate(Double, Double)

Field Descriptions

M

var M: array [0..5] of Double

Type: array [0..5] of Double

Property Descriptions

Kind

The matrix kind.

property Kind: TBLTransformKind read GetKind

Type: TBLTransformKind

M00

Element [0, 0]. Contains X scaling.

property M00: Double read M[0] write M[0]

Type: Double

M01

Element [0, 1]. Contains rotation and skewing.

property M01: Double read M[1] write M[1]

Type: Double

M10

Element [1, 0]. Contains rotation and skewing.

property M10: Double read M[2] write M[2]

Type: Double

M11

Element [1, 1]. Contains Y scaling.

property M11: Double read M[3] write M[3]

Type: Double

M20

Element [2, 0]. Contains X translation.

property M20: Double read M[4] write M[4]

Type: Double

M21

Element [2, 1]. Contains Y translation.

property M21: Double read M[5] write M[5]

Type: Double

Constructor Descriptions

`Create`

constructor Create(const AM00, AM01, AM10, AM11, AM20, AM21: Double)

Parameters

AM00: Double

AM01: Double

AM10: Double

AM11: Double

AM20: Double

AM21: Double

Operator Descriptions

Equal(TBLMatrix2D, TBLMatrix2D)

class operator Equal(const ALeft, ARight: TBLMatrix2D): Boolean; inline; static

Parameters

ALeft: TBLMatrix2D

ARight: TBLMatrix2D

Returns

Boolean

NotEqual(TBLMatrix2D, TBLMatrix2D)

class operator NotEqual(const ALeft, ARight: TBLMatrix2D): Boolean; inline; static

Parameters

ALeft: TBLMatrix2D

ARight: TBLMatrix2D

Returns

Boolean

Method Descriptions

Determinant

Calculates the matrix determinant.

function Determinant: Double; inline

Returns

Double

Equals(TBLMatrix2D)

function Equals(const AOther: TBLMatrix2D): Boolean; inline

Parameters

AOther: TBLMatrix2D

Returns

Boolean

Invert(TBLMatrix2D, TBLMatrix2D)

Inverts ASrc matrix and stores the result in ADst. Returns True if the matrix has been inverted successfully.

class function Invert(const ASrc: TBLMatrix2D; out ADst: TBLMatrix2D): Boolean; overload; inline; static

Parameters

ASrc: TBLMatrix2D

ADst: TBLMatrix2D

Returns

Boolean

Invert

Inverts the matrix. Returns True if the matrix has been inverted successfully.

function Invert: Boolean; overload; inline

Returns

Boolean

MakeIdentity

Creates a new matrix initialized to identity.

class function MakeIdentity: TBLMatrix2D; inline; static

Returns

TBLMatrix2D

MakeRotation(Double, TBLPoint)

class function MakeRotation(const AAngle: Double; const AOrigin: TBLPoint): TBLMatrix2D; overload; inline; static

Parameters

AAngle: Double

AOrigin: TBLPoint

Returns

TBLMatrix2D

MakeRotation(Double, Double, Double)

class function MakeRotation(const AAngle, AX, AY: Double): TBLMatrix2D; overload; inline; static

Parameters

AAngle: Double

AX: Double

AY: Double

Returns

TBLMatrix2D

MakeRotation(Double)

Creates a new matrix initialized to rotation.

class function MakeRotation(const AAngle: Double): TBLMatrix2D; overload; inline; static

Parameters

AAngle: Double

Returns

TBLMatrix2D

MakeScaling(TBLPointI)

class function MakeScaling(const AP: TBLPointI): TBLMatrix2D; overload; inline; static

Parameters

AP: TBLPointI

Returns

TBLMatrix2D

MakeScaling(TBLPoint)

class function MakeScaling(const AP: TBLPoint): TBLMatrix2D; overload; inline; static

Parameters

AP: TBLPoint

Returns

TBLMatrix2D

MakeScaling(Double, Double)

class function MakeScaling(const AX, AY: Double): TBLMatrix2D; overload; inline; static

Parameters

AX: Double

AY: Double

Returns

TBLMatrix2D

MakeScaling(Double)

Creates a new matrix initialized to scaling.

class function MakeScaling(const AXY: Double): TBLMatrix2D; overload; inline; static

Parameters

AXY: Double

Returns

TBLMatrix2D

MakeSinCos(Double, Double, TBLPoint)

class function MakeSinCos(const ASin, ACos: Double; const AP: TBLPoint): TBLMatrix2D; overload; inline; static

Parameters

ASin: Double

ACos: Double

AP: TBLPoint

Returns

TBLMatrix2D

MakeSinCos(Double, Double, Double, Double)

class function MakeSinCos(const ASin, ACos: Double; const ATX: Double = 0; const ATY: Double = 0): TBLMatrix2D; overload; inline; static

Parameters

ASin: Double

ACos: Double

ATX: Double = 0

ATY: Double = 0

Returns

TBLMatrix2D

MakeSkewing(TBLPoint)

class function MakeSkewing(const AOrigin: TBLPoint): TBLMatrix2D; overload; inline; static

Parameters

AOrigin: TBLPoint

Returns

TBLMatrix2D

MakeSkewing(Double, Double)

Create a new skewing matrix.

class function MakeSkewing(const AX, AY: Double): TBLMatrix2D; overload; inline; static

Parameters

AX: Double

AY: Double

Returns

TBLMatrix2D

MakeTranslation(TBLPointI)

class function MakeTranslation(const AP: TBLPointI): TBLMatrix2D; overload; inline; static

Parameters

AP: TBLPointI

Returns

TBLMatrix2D

MakeTranslation(TBLPoint)

class function MakeTranslation(const AP: TBLPoint): TBLMatrix2D; overload; inline; static

Parameters

AP: TBLPoint

Returns

TBLMatrix2D

MakeTranslation(Double, Double)

Creates a new matrix initialized to translation.

class function MakeTranslation(const AX, AY: Double): TBLMatrix2D; overload; inline; static

Parameters

AX: Double

AY: Double

Returns

TBLMatrix2D

MapPoint(TBLPoint)

function MapPoint(const AP: TBLPoint): TBLPoint; overload; inline

Parameters

AP: TBLPoint

Returns

TBLPoint

MapPoint(Double, Double)

function MapPoint(const AX, AY: Double): TBLPoint; overload; inline

Parameters

AX: Double

AY: Double

Returns

TBLPoint

MapVector(TBLPoint)

function MapVector(const AP: TBLPoint): TBLPoint; overload; inline

Parameters

AP: TBLPoint

Returns

TBLPoint

MapVector(Double, Double)

function MapVector(const AX, AY: Double): TBLPoint; overload; inline

Parameters

AX: Double

AY: Double

Returns

TBLPoint

PostRotate(Double, TBLPointI)

procedure PostRotate(const AAngle: Double; const AP: TBLPointI); overload; inline

Parameters

AAngle: Double

AP: TBLPointI

PostRotate(Double, TBLPoint)

procedure PostRotate(const AAngle: Double; const AP: TBLPoint); overload; inline

Parameters

AAngle: Double

AP: TBLPoint

PostRotate(Double, Double, Double)

procedure PostRotate(const AAngle, AX, AY: Double); overload; inline

Parameters

AAngle: Double

AX: Double

AY: Double

PostRotate(Double)

procedure PostRotate(const AAngle: Double); overload; inline

Parameters

AAngle: Double

PostScale(TBLPointI)

procedure PostScale(const AP: TBLPointI); overload; inline

Parameters

AP: TBLPointI

PostScale(TBLPoint)

procedure PostScale(const AP: TBLPoint); overload; inline

Parameters

AP: TBLPoint

PostScale(Double, Double)

procedure PostScale(const AX, AY: Double); overload; inline

Parameters

AX: Double

AY: Double

PostScale(Double)

procedure PostScale(const AXY: Double); overload; inline

Parameters

AXY: Double

PostSkew(TBLPoint)

procedure PostSkew(const AP: TBLPoint); overload; inline

Parameters

AP: TBLPoint

PostSkew(Double, Double)

procedure PostSkew(const AX, AY: Double); overload; inline

Parameters

AX: Double

AY: Double

PostTransform(TBLMatrix2D)

procedure PostTransform(const AM: TBLMatrix2D); inline

Parameters

AM: TBLMatrix2D

PostTranslate(TBLPointI)

procedure PostTranslate(const AP: TBLPointI); overload; inline

Parameters

AP: TBLPointI

PostTranslate(TBLPoint)

procedure PostTranslate(const AP: TBLPoint); overload; inline

Parameters

AP: TBLPoint

PostTranslate(Double, Double)

procedure PostTranslate(const AX, AY: Double); overload; inline

Parameters

AX: Double

AY: Double

Reset(Double, Double, Double, Double, Double, Double)

Resets matrix to [AM00, AM01, AM10, AM11, AM20, AM21].

procedure Reset(const AM00, AM01, AM10, AM11, AM20, AM21: Double); overload; inline

Parameters

AM00: Double

AM01: Double

AM10: Double

AM11: Double

AM20: Double

AM21: Double

Reset(TBLMatrix2D)

Resets matrix to AOther (copy its content to this matrix).

procedure Reset(const AOther: TBLMatrix2D); overload; inline

Parameters

AOther: TBLMatrix2D

Reset

Resets matrix to identity.

procedure Reset; overload; inline

ResetToRotation(Double, TBLPoint)

Resets matrix to rotation around a point p.

procedure ResetToRotation(const AAngle: Double; const AOrigin: TBLPoint); overload; inline

Parameters

AAngle: Double

AOrigin: TBLPoint

ResetToRotation(Double, Double, Double)

Resets matrix to rotation around a point [X, Y].

procedure ResetToRotation(const AAngle, AX, AY: Double); overload; inline

Parameters

AAngle: Double

AX: Double

AY: Double

ResetToRotation(Double)

Resets matrix to rotation.

procedure ResetToRotation(const AAngle: Double); overload; inline

Parameters

AAngle: Double

ResetToScaling(TBLPointI)

Resets matrix to scaling.

procedure ResetToScaling(const AP: TBLPointI); overload; inline

Parameters

AP: TBLPointI

ResetToScaling(TBLPoint)

Resets matrix to scaling.

procedure ResetToScaling(const AP: TBLPoint); overload; inline

Parameters

AP: TBLPoint

ResetToScaling(Double, Double)

Resets matrix to scaling.

procedure ResetToScaling(const AX, AY: Double); overload; inline

Parameters

AX: Double

AY: Double

ResetToScaling(Double)

Resets matrix to scaling.

procedure ResetToScaling(const AXY: Double); overload; inline

Parameters

AXY: Double

ResetToSinCos(Double, Double, TBLPoint)

Resets matrix to rotation specified by ASin and ACos and translation AP.

procedure ResetToSinCos(const ASin, ACos: Double; const AP: TBLPoint); overload; inline

Parameters

ASin: Double

ACos: Double

AP: TBLPoint

ResetToSinCos(Double, Double, Double, Double)

Resets matrix to rotation specified by ASin and ACos and optional translation ATX and ATY.

procedure ResetToSinCos(const ASin, ACos: Double; const ATX: Double = 0; const ATY: Double = 0); overload; inline

Parameters

ASin: Double

ACos: Double

ATX: Double = 0

ATY: Double = 0

ResetToSkewing(TBLPoint)

Resets matrix to skewing.

procedure ResetToSkewing(const AP: TBLPoint); overload; inline

Parameters

AP: TBLPoint

ResetToSkewing(Double, Double)

Resets matrix to skewing.

procedure ResetToSkewing(const AX, AY: Double); overload; inline

Parameters

AX: Double

AY: Double

ResetToTranslation(TBLPointI)

Resets matrix to translation.

procedure ResetToTranslation(const AP: TBLPointI); overload; inline

Parameters

AP: TBLPointI

ResetToTranslation(TBLPoint)

Resets matrix to translation.

procedure ResetToTranslation(const AP: TBLPoint); overload; inline

Parameters

AP: TBLPoint

ResetToTranslation(Double, Double)

Resets matrix to translation.

procedure ResetToTranslation(const AX, AY: Double); overload; inline

Parameters

AX: Double

AY: Double

Rotate(Double, TBLPointI)

procedure Rotate(const AAngle: Double; const AP: TBLPointI); overload; inline

Parameters

AAngle: Double

AP: TBLPointI

Rotate(Double, TBLPoint)

procedure Rotate(const AAngle: Double; const AP: TBLPoint); overload; inline

Parameters

AAngle: Double

AP: TBLPoint

Rotate(Double, Double, Double)

procedure Rotate(const AAngle, AX, AY: Double); overload; inline

Parameters

AAngle: Double

AX: Double

AY: Double

Rotate(Double)

procedure Rotate(const AAngle: Double); overload; inline

Parameters

AAngle: Double

Scale(TBLPointI)

procedure Scale(const AP: TBLPointI); overload; inline

Parameters

AP: TBLPointI

Scale(TBLPoint)

procedure Scale(const AP: TBLPoint); overload; inline

Parameters

AP: TBLPoint

Scale(Double, Double)

procedure Scale(const AX, AY: Double); overload; inline

Parameters

AX: Double

AY: Double

Scale(Double)

procedure Scale(const AXY: Double); overload; inline

Parameters

AXY: Double

Skew(TBLPoint)

procedure Skew(const AP: TBLPoint); overload; inline

Parameters

AP: TBLPoint

Skew(Double, Double)

procedure Skew(const AX, AY: Double); overload; inline

Parameters

AX: Double

AY: Double

Transform(TBLMatrix2D)

procedure Transform(const AM: TBLMatrix2D); inline

Parameters

AM: TBLMatrix2D

Translate(TBLPointI)

procedure Translate(const AP: TBLPointI); overload; inline

Parameters

AP: TBLPointI

Translate(TBLPoint)

procedure Translate(const AP: TBLPoint); overload; inline

Parameters

AP: TBLPoint

Translate(Double, Double)

procedure Translate(const AX, AY: Double); overload; inline

Parameters

AX: Double

AY: Double