Matrix Class Reference

Represents a mathematical transformation matrix. Transformation matrices can transform the coordinate pairs of one coordinate space into another coordinate space. Matrices are used in Camelot for the rendering process in various ways. These include coordinate conversion, scaling, rotation and translation. More...

#include <matrix.h>

Inheritance diagram for Matrix:

List of all members.

Public Member Functions
	Matrix ()
	Default initialisation - sets up the identity matrix.
	Matrix (const FIXED16 &, const FIXED16 &)
	Default initialisation - sets up the scale matrix.
	Matrix (const ANGLE &theta)
	Default initialisation - sets up the rotation matrix.
	Matrix (const Coord &)
	Default initialisation - Sets up a translate matrix.
	Matrix (const Coord &, const ANGLE &)
	Creates a Matrix transform object that will perform a rotation about the given point by the given number of degrees.
	Matrix (const INT32, const INT32)
	Default initialisation - Sets up a translate matrix.
	Matrix (const FIXED16 &, const FIXED16 &, const FIXED16 &, const FIXED16 &, const INT32, const INT32)
	Initialise a while matrix.
	Matrix (const DocRect &, const DocRect &)
	Matrix constructor taking two document rectangles. Creates a matrix which can be used to transform coordinates within the source rectangle into coordinates in the second rectangle.
void	transform (Coord *) const
	Transforms a single point.
void	transform (Coord[], UINT32 count) const
	Transforms a list of points.
void	transform (Coord[], const Coord[], UINT32) const
	Transforms a list of points.
void	translate (const INT32 TransX, const INT32 TransY)
	QUICKLY add a translation to a matrix!
BOOL	TransformBounds (DocRect *pRect) const
	Given a rect, find its bounds when transformed.
BOOL	Decompose (FIXED16 *pScale=NULL, FIXED16 *pAspect=NULL, ANGLE *pRotation=NULL, ANGLE *pShear=NULL, Coord *pTranslate=NULL, FIXED16 *pScaleY=NULL)
	Decompose a matrix into its component transforms.
BOOL	Compose (FIXED16 Scale=1.0, FIXED16 Aspect=1.0, ANGLE Rotation=0, ANGLE Shear=0, Coord Translation=Coord(0, 0))
	Compose a matrix from its components.
BOOL	IsRotation (const double epsilon=0.0) const
	Determine whether this matrix is a rotation matrix or not.
BOOL	IsReflection (const double epsilon=0.0) const
	Determine whether this matrix is a reflection matrix or not.
BOOL	IsTranslation (const double epsilon=0.0) const
	Examine this matrix and determin whether it is a translation matrix or not. This function is needed as within the code there are areas where complex matricees are built which are really translation matricees. The function will return immediately with TRUE if the matrix type is Translation otherwise the function will actually check the matrix values for translation type See also: IsRotation(), IsReflection().
BOOL	IsIdentity () const
	Support function for IsIsometric Determines whether two values are near enough to each other to be considered equal. Notes: This is a templated function with <class t>="">Determines whether or not this matrix is an identity matrix. Used by the MOA interface, XMOAFhMtx::FHIMtxIsUnity.
Matrix &	operator= (const Matrix &)
	Matrix assignment.
BOOL	operator== (const Matrix &) const
	Test for Matrix equality.
Matrix &	operator *= (const Matrix &)
	optimized *= operator for matrices Note: e,f are not optimised as MatrixCalc() has different round from explicit operations however, it does have optimisations for 0 an 1
Matrix	Inverse () const
	Inverts the 'this' matrix and returns the result. 'this' matrix is not effected.
void	GetComponents (FIXED16 *, INT32 *) const
	Allows code to get to the elements in the matrix without having to be a friend of the class. Should be used very sparingly indeed.
void	GetTranslation (DocCoord &) const
void	GetTranslation (INT32 &, INT32 &) const
void	SetTranslation (const DocCoord &)
void	SetTranslation (const INT32 &, const INT32 &)
double	Trace () const
double	Det () const
void	RatioMatrix (const double ratio)
Matrix	Interpolate (const Matrix &op, const double ratio) const
	Interpolate between this and another matrix.
Matrix	PostRotate (DocCoord dcCentre, const ANGLE &Angle) const
	Allows you to transform an object, then rotate it about some point relative to its original self, which has now been transformed.
Static Public Member Functions
static Matrix	CreateTransMatrix (const Coord &dcTrans)
	Factory method - maps directly onto the translation Matrix constructor.
static Matrix	CreateScaleMatrix (const double &xScale, const double &yScale)
	Factory method - maps directly onto the scaling Matrix constructor.
static Matrix	CreateScaleMatrix (const double &ScaleFactor)
	Factory method - maps directly onto the scaling Matrix constructor.
static Matrix	CreateShearMatrix (const double &ShearAngle)
	Factory method - maps directly onto the 'complex' Matrix constructor.
static Matrix	CreateRotateMatrix (const double &RotateAngle)
	Factory method - maps directly onto the rotation Matrix constructor.
Public Attributes
TransformType	Type
ANGLE	Angle
Private Attributes
FIXED16	a
FIXED16	b
FIXED16	c
FIXED16	d
INT32	e
INT32	f
Friends
class	OSRenderRegion
class	XMatrix
Matrix	operator * (const Matrix &, const Matrix &)
	Matrix multiplication.

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Detailed Description

Represents a mathematical transformation matrix. Transformation matrices can transform the coordinate pairs of one coordinate space into another coordinate space. Matrices are used in Camelot for the rendering process in various ways. These include coordinate conversion, scaling, rotation and translation.

Author:

Mario_Shamtani (Xara Group Ltd) <camelotdev@xara.com> (extended by Rik)

Date:

13/5/1993 (extended 19/10/93)

Depending on the constructor applied it is possible to specify any of the above types of matrix. MonoOn eg. Matrix(); //creates the identity matrix Matrix(ANGLE(90)); //creates a rotation matrix by 90 deg Matrix(ScaleX, ScaleY); //creates a scaling matrix Matrix(xOffset, yOffset); //creates a translation matrix MonoOff The Matrix also contains a couple of Public vars that may or may not be of any use to anyone. These are as follows :- MonoOn TransformType Type; // The type of transformation this matrix represents ANGLE Angle; // The angle of rotation for a rotation matrix MonoOff

See also:

TransformType

Definition at line 170 of file matrix.h.

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Constructor & Destructor Documentation

Matrix::Matrix (   )

Default initialisation - sets up the identity matrix. Author: Mario_Shamtani (Xara Group Ltd) <camelotdev@xara.com> Date: 14/5/93 Parameters: None  [INPUTS] None  [OUTPUTS] Returns: None. Errors: None. Definition at line 133 of file matrix.cpp. { a = (FIXED16)1; b = (FIXED16)0; c = (FIXED16)0; d = (FIXED16)1; e = 0; f = 0; Type = TRANS_IDENTITY; Angle = (ANGLE)0; }

Matrix::Matrix (  const FIXED16 &  xScale, const FIXED16 &  yScale )

Default initialisation - sets up the scale matrix. Author: Mario_Shamtani (Xara Group Ltd) <camelotdev@xara.com> Date: 14/5/93 Parameters: Two  fixed16s representing the x and y scale factors. [INPUTS] None  [OUTPUTS] Returns: None. Errors: None. Definition at line 164 of file matrix.cpp. { a = xScale; b = (FIXED16)0; c = (FIXED16)0; d = yScale; e = 0; f = 0; Type = TRANS_SCALE; Angle = (ANGLE)0; }

Matrix::Matrix (  const ANGLE &  theta  )

Default initialisation - sets up the rotation matrix. Author: Mario_Shamtani (Xara Group Ltd) <camelotdev@xara.com> Date: 14/5/93 Parameters: An  angle representing the degree of rotation. [INPUTS] None  [OUTPUTS] Returns: None. Errors: None. Definition at line 195 of file matrix.cpp. { #if 0 a = b = c = d = theta; a.Cos(); b.Sin(); c = -(c.Sin()); d.Cos(); #else double thetaradians = TORADIANS(theta.MakeDouble()); FIXED16 costheta = cos(thetaradians); FIXED16 sintheta = sin(thetaradians); a = d = costheta; b = sintheta; c = -sintheta; #endif e = 0; f = 0; Type = TRANS_ROTATION; Angle = theta; }

Matrix::Matrix (  const Coord &  disp  )

Default initialisation - Sets up a translate matrix. Author: Mario_Shamtani (Xara Group Ltd) <camelotdev@xara.com> Date: 14/5/93 Parameters: Displacement  of translation. [INPUTS] None  [OUTPUTS] Returns: None. Errors: None. Definition at line 240 of file matrix.cpp. { a = (FIXED16)1; b = (FIXED16)0; c = (FIXED16)0; d = (FIXED16)1; e = disp.x; f = disp.y; Type = TRANS_TRANSLATION; Angle = (ANGLE)0; }

Matrix::Matrix (  const Coord &  CentreOfRotation, const ANGLE &  Rotation )

Creates a Matrix transform object that will perform a rotation about the given point by the given number of degrees. Author: Rik_Heywood (Xara Group Ltd) <camelotdev@xara.com> Date: 7/3/94 Parameters: CentreOfRot  - The centre of rotation [INPUTS] RotateBy - The angle of the rotation that this transform object will perform Definition at line 1031 of file matrix.cpp. { // need to translate the centre of rotation to the origin *this = Matrix(-CentreOfRotation.x, -CentreOfRotation.y); // rotate about the origin *this *= Matrix(Rotation); // translate back to the centre of rotation this->translate(CentreOfRotation.x, CentreOfRotation.y); Type = TRANS_COMPLEX; Angle = (ANGLE)0; }

Matrix::Matrix (  const INT32  x, const INT32  y )

Default initialisation - Sets up a translate matrix. Author: Andy_Pennell (Xara Group Ltd) <camelotdev@xara.com> Date: 30/5/93 Parameters: Displacement  of translation. [INPUTS] None  [OUTPUTS] Returns: None. Errors: None. Definition at line 272 of file matrix.cpp. { a = (FIXED16)1; b = (FIXED16)0; c = (FIXED16)0; d = (FIXED16)1; e = x; f = y; Type = TRANS_TRANSLATION; Angle = (ANGLE)0; }

Matrix::Matrix (  const FIXED16 &  ca, const FIXED16 &  cb, const FIXED16 &  cc, const FIXED16 &  cd, const INT32  ce, const INT32  cf )

Initialise a while matrix. Author: Phil_Martin (Xara Group Ltd) <camelotdev@xara.com> Date: 21/7/93 Parameters: All  six parameters which make up a matrix [INPUTS] None  [OUTPUTS] Returns: None. Errors: None. Definition at line 305 of file matrix.cpp. { a = ca; b = cb; c = cc; d = cd; e = ce; f = cf; Type = TRANS_COMPLEX; Angle = (ANGLE)0; }

Matrix::Matrix (  const DocRect &  Source, const DocRect &  Destin )

Matrix constructor taking two document rectangles. Creates a matrix which can be used to transform coordinates within the source rectangle into coordinates in the second rectangle. Author: Mike_Kenny (Xara Group Ltd) <camelotdev@xara.com> Date: 13/12/93 Parameters: Source  = source rectangle [INPUTS] Destin = destination rectangle Returns: a matrix whose domain is the source rectangle and range is the destination rectangle. Definition at line 341 of file matrix.cpp. { double Sx0 = Source.lo.x; double Sy0 = Source.lo.y; double Sx1 = Source.hi.x; double Sy1 = Source.hi.y; double Dx0 = Destin.lo.x; double Dy0 = Destin.lo.y; double Dx1 = Destin.hi.x; double Dy1 = Destin.hi.y; double t0,t1; (Sx1==Sx0) ? t0=1 : t0=(Dx1-Dx0)/(Sx1-Sx0); (Sy1==Sy0) ? t1=1 : t1=(Dy1-Dy0)/(Sy1-Sy0); a = (FIXED16)t0; b = (FIXED16)0; c = (FIXED16)0; d = (FIXED16)t1; e = (INT32)(Dx0-Sx0*t0); f = (INT32)(Dy0-Sy0*t1); Type = TRANS_COMPLEX; Angle = (ANGLE)0; }

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Member Function Documentation

BOOL Matrix::Compose (  FIXED16  Scale = 1.0, FIXED16  Aspect = 1.0, ANGLE  Rotation = 0, ANGLE  Shear = 0, Coord  Translation = Coord(0,0) )

Compose a matrix from its components. Author: Ed_Cornes (Xara Group Ltd) <camelotdev@xara.com> Date: 7/4/95 Parameters: Scale  - [INPUTS] Aspect - Rotation - Shear - Translation - Returns: FALSE if falis Definition at line 970 of file matrix.cpp. { // do scale, aspect and shear FIXED16 AbsScale = (Scale<0) ? -Scale : Scale; *this=Matrix(AbsScale*Aspect,0,Scale*tan(Shear.MakeDouble()),Scale,0,0); // do rotate *this*=Matrix((Rotation*180)/PI); // god damned amatuers using degrees! // translate this->translate(Translation.x,Translation.y); return TRUE; }

Matrix Matrix::CreateRotateMatrix (  const double &  RotateAngle  )  [static]

Factory method - maps directly onto the rotation Matrix constructor. Author: Karim_MacDonald (Xara Group Ltd) <camelotdev@xara.com> Date: 23-07-2000 Parameters: RotateAngle  the angle to rotate anti-clockwise by, in radians. [INPUTS] Returns: A rotation matrix. Notes: Karim 06/09/2001 Method now in use & fixed bug so input is processed as radians, not degrees. Definition at line 1381 of file matrix.cpp. { return Matrix(FIXED16(DDegrees(RotateAngle))); }

Matrix Matrix::CreateScaleMatrix (  const double &  ScaleFactor  )  [static]

Factory method - maps directly onto the scaling Matrix constructor. Author: Karim_MacDonald (Xara Group Ltd) <camelotdev@xara.com> Date: 23-07-2000 Parameters: ScaleFactor  the uniform scaling to perform. [INPUTS] Returns: A scaling matrix. Definition at line 1337 of file matrix.cpp. { return Matrix(FIXED16(ScaleFactor), FIXED16(ScaleFactor)); }

Matrix Matrix::CreateScaleMatrix (  const double &  xScale, const double &  yScale )  [static]

Factory method - maps directly onto the scaling Matrix constructor. Author: Karim_MacDonald (Xara Group Ltd) <camelotdev@xara.com> Date: 23-07-2000 Parameters: xScale  the x-scaling to perform. [INPUTS] yScale the y-scaling to perform. Returns: A scaling matrix. Definition at line 1319 of file matrix.cpp. { return Matrix(FIXED16(xScale), FIXED16(yScale)); }

Matrix Matrix::CreateShearMatrix (  const double &  ShearAngle  )  [static]

Factory method - maps directly onto the 'complex' Matrix constructor. Author: Karim_MacDonald (Xara Group Ltd) <camelotdev@xara.com> Date: 23-07-2000 Parameters: ShearAngle  the angle clockwise from vertical to shear by, in radians. [INPUTS] Returns: A shearing matrix. Definition at line 1355 of file matrix.cpp. { FIXED16 one = FIXED16(1); FIXED16 zero = FIXED16(0); FIXED16 shear = FIXED16(tan(ShearAngle)); return Matrix( one, zero, shear, one, 0, 0 ); }

Matrix Matrix::CreateTransMatrix (  const Coord &  dcTrans  )  [static]

Factory method - maps directly onto the translation Matrix constructor. Author: Karim_MacDonald (Xara Group Ltd) <camelotdev@xara.com> Date: 23-07-2000 Parameters: dcTrans  the translation to perform. [INPUTS] Returns: A translation matrix. Definition at line 1300 of file matrix.cpp. { return Matrix(dcTrans); }

BOOL Matrix::Decompose (  FIXED16 *  pScale = NULL, FIXED16 *  pAspect = NULL, ANGLE *  pRotation = NULL, ANGLE *  pShear = NULL, Coord *  pTranslate = NULL, FIXED16 *  pScaleY = NULL )

Decompose a matrix into its component transforms. Author: Ed_Cornes (Xara Group Ltd) <camelotdev@xara.com> Date: 7/4/95 Parameters: pScale  - if not NULL, outputs scale (-ve indicates mirror Y) [OUTPUTS] pAspect - if not NULL, outputs aspect pRotation - if not NULL, outputs rotation (-PI..PI) pShear - if not NULL, outputs sheer (-PI/2..PI/2) pTranslate - if not NULL, outputs translation Returns: FALSE if falis Definition at line 897 of file matrix.cpp. { // unit square decomposition of matrix ... // A={a,c}, B={b,d}, Q=angle between vectors (ie PI/2-shear angle)! // |A|=sqrt(aa+cc) // |B|=sqrt(bb+dd) // AxB=|A||B|sinQ=ad-bc=(new area of unit square) // A.B=|A||B|cosQ=ab+cd // so ... // ScaleX = |A| // ScaleY = |B| // Scale = ScaleY*cos(PI/2-Q) = ScaleY*sinQ = AxB/|A| // AbsScale = abs(Scale) // effectively remove any mirror // Aspect = ScaleX/abs(Scale) // Shear = PI/2-Q = PI/2-acos((A.B)/(|A||B|)) // Rotate = RotateX = atan2(c,a) double a=this->a.MakeDouble(); double b=this->c.MakeDouble(); // 'cos I think of coords as column vectors not rows! double c=this->b.MakeDouble(); double d=this->d.MakeDouble(); // get cross product (determinant), modulus (length) of A and scale double AxB = a*d-b*c; double ModA = sqrt(a*a+c*c); double ModB = sqrt(b*b+d*d); double Scale = AxB/ModA; // set output values where required if (pTranslate) *pTranslate = Coord(this->e,this->f); if (pScale) *pScale = Scale; if (pAspect) if (Scale==0) *pAspect = (FIXED16)1; else *pAspect = ModA/fabs(Scale); if (pRotation) *pRotation = (ANGLE)atan2(c,a); if (pShear) { double AdotB = a*b+c*d; *pShear = (ANGLE)(PI/2-acos(AdotB/(ModB*ModA))); } if (pScaleY) *pScaleY = ModB; // TRACE( _T("\n")); // TRACE( _T("Scale = %f\n"),Scale); // TRACE( _T("Aspect = %f\n"),ModA/fabs(Scale)); // TRACE( _T("Rotate = %f\n"),atan2(c,a)/PI*180); // double AdotB = a*b+c*d; // double ModB = sqrt(b*b+d*d); // TRACE( _T("Shear = %f\n"),(PI/2-acos(AdotB/(ModB*ModA)))/PI*180); return TRUE; }

double Matrix::Det (   )  const

Author: Karim_MacDonald (Xara Group Ltd) <camelotdev@xara.com> Date: 04 September 2000 Returns: The determinant of this matrix: (ad - bc) if matrix is ((a b),(c d)). Notes: Det(Matrix) = area scale factor on application of the matrix. Definition at line 1418 of file matrix.cpp. { return ( (a.MakeDouble() * d.MakeDouble()) - (b.MakeDouble() * c.MakeDouble()) ); }

void Matrix::GetComponents (  FIXED16 *  abcd, INT32 *  ef )  const

Allows code to get to the elements in the matrix without having to be a friend of the class. Should be used very sparingly indeed. Author: Andy_Pennell (Xara Group Ltd) <camelotdev@xara.com> Date: 24/5/94 Parameters: -  [INPUTS] abcd  should point to FIXED16[4] which will get loaded with the a,b,c,d [OUTPUTS] values from the matrix. Similarly ef should point to INT32[2] which will get loaded with the e and f values. If either pointer is NULL then nothing will get written for that type. Returns: - Definition at line 802 of file matrix.cpp. { if (abcd) { abcd[0] = a; abcd[1] = b; abcd[2] = c; abcd[3] = d; } if (ef) { ef[0] = e; ef[1] = f; } }

void Matrix::GetTranslation (  INT32 &  , INT32 &  )  const

Definition at line 854 of file matrix.cpp. { xlate=e; ylate=f; }

void Matrix::GetTranslation (  DocCoord &   )  const

Definition at line 848 of file matrix.cpp. { coord.x = e; coord.y = f; }

Matrix Matrix::Interpolate (  const Matrix &  op, const double  ratio )  const

Interpolate between this and another matrix. Author: Karim_MacDonald (Xara Group Ltd) <camelotdev@xara.com> Date: 25/09/2001 Parameters: op  other matrix to interpolate to. [INPUTS] ratio interpolation ratio. Returns: Interpolated matrix. Definition at line 1466 of file matrix.cpp. { // Essential: 0 <= ratio <= 1. if (ratio < 0 || ratio > 1 || Type == TRANS_ROTATION || op.Type == TRANS_ROTATION) { ERROR3("Interpolate() requires 0 <= ratio <= 1 and no rotation matrices."); return Matrix(); } else if (ratio == 0) return *this; else if (ratio == 1) return op; else { const FIXED16 f16Ratio (ratio); const FIXED16 f16InvRatio (1 - ratio); Matrix temp; temp.a = a * f16InvRatio + op.a * f16Ratio; temp.b = b * f16InvRatio + op.b * f16Ratio; temp.c = c * f16InvRatio + op.c * f16Ratio; temp.d = d * f16InvRatio + op.d * f16Ratio; temp.e = e * (INT32)((1 - ratio) + op.e * ratio); temp.f = f * (INT32)((1 - ratio) + op.f * ratio); temp.Type = TRANS_COMPLEX; temp.Angle = 0; return temp; } }

Matrix Matrix::Inverse (   )  const

Inverts the 'this' matrix and returns the result. 'this' matrix is not effected. Author: Rik_Heywood (Xara Group Ltd) <camelotdev@xara.com> Date: 2/11/93 Returns: The Inverse of this matrix Definition at line 659 of file matrix.cpp. { Matrix Temp; // Inverting a general matrix is quite an expensive operation, so we will try and // avoid having to do all the maths (esp as it can fail - some matrices do not have // an inverse! eg Scale by a factor of zero) switch ( Type ) { case TRANS_IDENTITY: // Inverse is the same as this ENSURE(a==FIXED16(1), "Matrix inconsistency!"); ENSURE(b==FIXED16(0), "Matrix inconsistency!"); ENSURE(c==FIXED16(0), "Matrix inconsistency!"); ENSURE(d==FIXED16(1), "Matrix inconsistency!"); ENSURE(e==0, "Matrix inconsistency!"); ENSURE(f==0, "Matrix inconsistency!"); return Temp; break; case TRANS_TRANSLATION : // Translation matrix - The inverse of this requires negating the x and y // components of the translation ENSURE(a==FIXED16(1), "Matrix inconsistency!"); ENSURE(b==FIXED16(0), "Matrix inconsistency!"); ENSURE(c==FIXED16(0), "Matrix inconsistency!"); ENSURE(d==FIXED16(1), "Matrix inconsistency!"); Temp.a = this->a; Temp.b = this->b; Temp.c = this->c; Temp.d = this->d; Temp.e = -this->e; Temp.f = -this->f; Temp.Type = this->Type; Temp.Angle = this->Angle; break; case TRANS_ROTATION: // The inverse of a rotation matrix is the Transpose of this matrix // ie components b and c are swapped ENSURE(e==0, "Matrix inconsistency!"); ENSURE(f==0, "Matrix inconsistency!"); Temp.a = this->a; Temp.b = this->c; Temp.c = this->b; Temp.d = this->d; Temp.e = this->e; Temp.f = this->f; Temp.Type = this->Type; Temp.Angle = -this->Angle; break; case TRANS_SCALE: // This can fail if one of the scale factors is 0. This will cause an ENSURE to fail // The inverse of a scale involves finding the inverse of the scale factors // ENSURE( this->a != 0, "Matrix Inversion failed - X scale factor was zero!" ); // ENSURE( this->d != 0, "Matrix Inversion failed - Y scale factor was zero!" ); if ((this->a==0) || (this->d==0)) { TRACE( _T("Matrix Inversion failed!\n")); // There is no inversion of this matrix // return the identity matrix return Temp; } ENSURE(e==0, "Matrix inconsistency!"); ENSURE(f==0, "Matrix inconsistency!"); Temp.a = 1/this->a; Temp.b = this->b; Temp.c = this->c; Temp.d = 1/this->d; Temp.e = this->e; Temp.f = this->f; Temp.Type = this->Type; Temp.Angle = this->Angle; break; case TRANS_SHEAR: case TRANS_COMPLEX: default: // This is the general case. It may be possible for this to fail. // I got the general idea for this from Graphics Gems page 766. // It did take 4 pages of c code in there, but it was a slightly // more complex solution. // Find the determinent of the Adjoint matrix - Luckily we can calculate // this before we calculate the Adjoint matrix as we know that the // right hand edge of the matrix is 0 0 1 double Det = a.MakeDouble()*d.MakeDouble() - b.MakeDouble()*c.MakeDouble(); if (Det==0.0) { // There is no inversion of this matrix // return the identity matrix // ENSURE( FALSE, "Matrix Inversion Failed - Tried to Invert a non-invertable matrix" ); TRACE( _T("Matrix Inversion failed!\n")); return Temp; } // this section calculates the inverse of the matrix. As it takes into // account that our 3x3 matrix always has 0,0,1 down its right hand side // it has been greatly simplified. The operations combine the calculation // of the adjoint matrix and scaling it by the Determinent with a matrix // transpose (the inverse is the transpose of the adjoint scaled by the // determinent) Temp.a = (FIXED16)(d.MakeDouble() / Det); Temp.b = (FIXED16)(-b.MakeDouble() / Det); Temp.c = (FIXED16)(-c.MakeDouble() / Det); Temp.d = (FIXED16)(a.MakeDouble() / Det); Temp.e = (INT32)( ((c.MakeDouble()*f)-(e*d.MakeDouble()))/Det ); Temp.f = (INT32)( -(((a.MakeDouble()*f) - (e*b.MakeDouble()))/Det)); Temp.Type = TRANS_COMPLEX; Temp.Angle = 0; break; } // return the inverted matrix back return Temp; }

BOOL Matrix::IsIdentity (   )  const

Support function for IsIsometric Determines whether two values are near enough to each other to be considered equal. Notes: This is a templated function with <class t>="">Determines whether or not this matrix is an identity matrix. Used by the MOA interface, XMOAFhMtx::FHIMtxIsUnity. Author: Colin_Barfoot (Xara Group Ltd) <camelotdev@xara.com> Date: 26/01/97 Returns: TRUE if this matrix is an identity matrix FALSE if not Definition at line 1253 of file matrix.cpp. { BOOL bIsIdentity = FALSE; if (Type == TRANS_IDENTITY) { bIsIdentity = TRUE; } if (Type != TRANS_IDENTITY) // && epsilon == 0.0) { const FIXED16 c0 = FIXED16(0); const FIXED16 c1 = FIXED16(1); bIsIdentity = ( (a == c1) && (b == c0) && (c == c0) && (d == c1) && (e == 0) && (f == 0)); } /* if (Type != TRANS_IDENTITY && epsilon != 0.0) { const double ca = a.MakeDouble(); const double cb = b.MakeDouble(); const double cc = c.MakeDouble(); const double cd = d.MakeDouble(); const double ce = e.MakeDouble(); const double cf = f.MakeDouble(); bIsIdentity = ( IsNear(ca, 1.0, epsilon) && IsNear(cb, 1.0, epsilon) && IsNear(cc, 1.0, epsilon) && IsNear(cd, 1.0, epsilon) && IsNear(ce, 1.0, epsilon) && IsNear(cf, 1.0, epsilon)) }*/ return bIsIdentity; }

BOOL Matrix::IsReflection (  const double  epsilon = 0.0  )  const

Determine whether this matrix is a reflection matrix or not. Author: Karim_MacDonald (Xara Group Ltd) <camelotdev@xara.com> Date: 16/11/2000 Parameters: epsilon  optional error threshold to use in our calculations. [INPUTS] Returns: TRUE if we're a reflection matrix, FALSE otherwise. Notes: In the interests of speed, this test is INCOMPLETE - we're *only* testing for x- or y- axis reflections (no, not both together either). Feel free to modify this method to test for all reflections, but first make sure you won't break any code which uses it (at time of writing, you're ok). See also: IsTranslation(), IsRotation(). Definition at line 1179 of file matrix.cpp. { // A Camelot matrix of the form: (a c) , is an x- or y- reflection if: // (b d) // 1. b = c = 0. // 2. a = -d. // 3. |a| = 1. if (epsilon == 0.0) { if (b == c && c == FIXED16(0) && a == -d && (a == FIXED16(1) || a == FIXED16(-1)) ) return TRUE; } else { double c0,c1,c2,c3; c0 = a.MakeDouble(); c1 = b.MakeDouble(); c2 = c.MakeDouble(); c3 = d.MakeDouble(); if (fabs(c1) < epsilon && fabs(c2) < epsilon && fabs(c0 + c3) < epsilon && (fabs(c0 - 1.0) < epsilon || fabs(c0 + 1.0) < epsilon) ) return TRUE; } return FALSE; }

BOOL Matrix::IsRotation (  const double  epsilon = 0.0  )  const

Determine whether this matrix is a rotation matrix or not. Author: Karim_MacDonald (Xara Group Ltd) <camelotdev@xara.com> Date: 16/11/2000 Parameters: epsilon  optional error threshold to use in our calculations. [INPUTS] Returns: TRUE if we're a rotation matrix, FALSE otherwise. See also: IsTranslation(), IsReflection(). Definition at line 1108 of file matrix.cpp. { if (Type == TRANS_ROTATION) return TRUE; // Note: Camelot matrices swap the b & c components, so the form is: // // (a c) , instead of the more familiar (a b) . // (b d) (c d) // // So tests for rotation are: // 1. a = d // 2. b = -c // 3. |(a b)| = |(c d)| = 1. if (epsilon == 0.0) { if (a == d && b == -c) { FIXED16 aa = (a * a); FIXED16 bb = (b * b); FIXED16 ab = aa + bb; if (ab == FIXED16(1)) return TRUE; } } else { double c0,c1,c2,c3; c0 = a.MakeDouble(); c1 = b.MakeDouble(); c2 = c.MakeDouble(); c3 = d.MakeDouble(); if (fabs(c0 - c3) < epsilon && fabs(c1 + c2) < epsilon) { double ab = (c0 * c0) + (c1 * c1); if (fabs(ab - 1.0) < epsilon) return TRUE; } } return FALSE; }

BOOL Matrix::IsTranslation (  const double  epsilon = 0.0  )  const

Examine this matrix and determin whether it is a translation matrix or not. This function is needed as within the code there are areas where complex matricees are built which are really translation matricees. The function will return immediately with TRUE if the matrix type is Translation otherwise the function will actually check the matrix values for translation type See also: IsRotation(), IsReflection(). Author: Mike_Kenny (Xara Group Ltd) <camelotdev@xara.com> Date: 11/01/96 Parameters: epsilon  - an error threshold to use against the scaling components [INPUTS] Returns: TRUE if this matrix is a translation matrix FALSE if not Definition at line 1065 of file matrix.cpp. { if (Type==TRANS_TRANSLATION) return TRUE; if (epsilon==0.0) { FIXED16 c0,c1,c2,c3; c0 = (FIXED16)1; c1 = (FIXED16)0; c2 = (FIXED16)0; c3 = (FIXED16)1; return ((a==c0) && (b==c1) && (c==c2) && (d==c3)); } double c0,c1,c2,c3; c0=a.MakeDouble(); c1=b.MakeDouble(); c2=c.MakeDouble(); c3=d.MakeDouble(); return ( (fabs(c0-1.0)<epsilon) && (fabs(c1-0.0)<epsilon) && (fabs(c2-0.0)<epsilon) && (fabs(c3-1.0)<epsilon) ); }

Matrix & Matrix::operator *= (  const Matrix &  op  )

optimized *= operator for matrices Note: e,f are not optimised as MatrixCalc() has different round from explicit operations however, it does have optimisations for 0 an 1 Author: Ed_Cornes (Xara Group Ltd) <camelotdev@xara.com> Date: 5/2/96 Parameters: Matrix  to be multiplied by. [INPUTS] Returns: result of multiplication. Definition at line 604 of file matrix.cpp. { if (op.b==0 && op.c==0) { // it's just an x or y scaling ... if (op.a!=1) { a *= op.a; c *= op.a; } if (op.d!=1) { b *= op.d; d *= op.d; } } else { // it's the complex case ... FIXED16 t; t = a*op.a + b*op.c; b = a*op.b + b*op.d; a = t; t = c*op.a + d*op.c; d = c*op.b + d*op.d; c = t; } // either case requires these bits INT32 u; u = MatrixCalc(op.a, e, op.c, f) + op.e; f = MatrixCalc(op.b, e, op.d, f) + op.f; e = u; Type = TRANS_COMPLEX; Angle = (ANGLE)0; return *this; }

Matrix & Matrix::operator= (  const Matrix &  rhs  )

Matrix assignment. Author: Mario_Shamtani (Xara Group Ltd) <camelotdev@xara.com> Date: 14/5/93 Parameters: rhs  - matrix to be assigned. [INPUTS] None.  [OUTPUTS] Returns: None. Errors: None. Definition at line 537 of file matrix.cpp. { this->a = rhs.a; this->b = rhs.b; this->c = rhs.c; this->d = rhs.d; this->e = rhs.e; this->f = rhs.f; this->Type = rhs.Type; this->Angle = rhs.Angle; return *this; }

BOOL Matrix::operator== (  const Matrix &  rhs  )  const

Test for Matrix equality. Author: Colin_Barfoot (Xara Group Ltd) <camelotdev@xara.com> Date: 26/01/97 Parameters: rhs,:  The right-hand side of the equality. [INPUTS] Returns: TRUE if this Matrix is equal to rhs Definition at line 564 of file matrix.cpp. { return (a == rhs.a && b == rhs.b && c == rhs.c && d == rhs.d && e == rhs.e && f == rhs.f); }

Matrix Matrix::PostRotate (  DocCoord  dcCentre, const ANGLE &  Angle )  const

Allows you to transform an object, then rotate it about some point relative to its original self, which has now been transformed. Author: Karim_MacDonald (Xara Group Ltd) <camelotdev@xara.com> Date: 04/10/2001 Parameters: dcCentre  centre of rotation *before* it is transformed by this matrix. [INPUTS] Angle angle of rotation, anti-clockwise in degrees. Returns: A matrix which will apply this transformation followed by a rotation of Angle around the transformed centre. eg: squash an object, then rotate it around its centre. You can't rotate-then-squash, as you will lose the right-angles. Nor should you rotate about its new centre, as this may be different to the transformed version of its old centre. Definition at line 1528 of file matrix.cpp. { transform(&dcCentre); return (*this) * Matrix(dcCentre, Angle); }

void Matrix::RatioMatrix (  const double  ratio  )

Author: Chris_Snook (Xara Group Ltd) <camelotdev@xara.com> Date: ???? Returns: This routine ratios *this* matrix. For example, if we have a scaling matrix and ratio is 0.5, then we get a scaling matrix that has half the effect of the original matrix. Do NOT go changing this routine !!!!!! It is fundamental to the entire animation system - and an error will break everything !!!!!!! You should get CGS to change this routine if needs be .... This routine cannot be used to ratio a rotation matrix. This is because the elements in a rotation matrix are cos & sin of the quantity which must be interpolated (the angle), and these are non-linear functions. Definition at line 1443 of file matrix.cpp. { static Matrix Identity; *this = Identity.Interpolate(*this, ratio); }

void Matrix::SetTranslation (  const INT32 &  , const INT32 &  )

Definition at line 869 of file matrix.cpp. { e = xlate; f = ylate; if (Type!=TRANS_TRANSLATION) Type = TRANS_COMPLEX; }

void Matrix::SetTranslation (  const DocCoord &   )

Definition at line 860 of file matrix.cpp. { e = coord.x; f = coord.y; if (Type!=TRANS_TRANSLATION) Type = TRANS_COMPLEX; }

double Matrix::Trace (   )  const

Author: Karim_MacDonald (Xara Group Ltd) <camelotdev@xara.com> Date: 04 September 2000 Returns: The trace of this matrix (the sum of the elements on its leading diagonal). Notes: Trace(Rotation matrix) = 2cos(theta), where theta is the angle of rotation. (Usually 1+2cos(theta), but these are 3x2 matrices). Definition at line 1400 of file matrix.cpp. { return (a.MakeDouble() + d.MakeDouble()); }

void Matrix::transform (  Coord  pts[], const Coord  input[], UINT32  count )  const

Transforms a list of points. Author: Mario_Shamtani (Xara Group Ltd) <camelotdev@xara.com> Date: 14/5/93 Parameters: input  - points to be translated. [INPUTS] count - number of points. result  points translated. [OUTPUTS] Returns: None. Errors: None. Definition at line 450 of file matrix.cpp. { if ( Type == TRANS_TRANSLATION ) { for (UINT32 i = 0; i < count; i++) { pts[i].x = input[i].x + e; pts[i].y = input[i].y + f; } } else { #ifdef OLD_MATRIX_TRANSFORMATIONS for (UINT32 i = 0; i < count; i++) { pts[i].x = MatrixCalc(a, input[i].x, c, input[i].y); pts[i].x += e; pts[i].y = MatrixCalc(b, input[i].x, d, input[i].y); pts[i].y += f; } #else // We use GDraw to transform the path // Alex asserts it is unimportant to switch contexts here as path transformations are not context // dependent; thus we call GDraw directly GMATRIX gmat; gmat.AX = a.GetShifted16(); gmat.AY = b.GetShifted16(); gmat.BX = c.GetShifted16(); gmat.BY = d.GetShifted16(); gmat.CX.SetHighLow(e>>16, e<<16); gmat.CY.SetHighLow(f>>16, f<<16); // Alex promises we don't need a context to do this op // XaDrawOld_TransformPath( (LPPOINT)input, (LPPOINT)pts, count, &gmat ); GRenderRegion::GetStaticDrawContext()->TransformPath( (LPPOINT)input, (LPPOINT)pts, count, &gmat ); #endif } }

void Matrix::transform (  Coord  pts[], UINT32  count )  const

Transforms a list of points. Author: Mario_Shamtani (Xara Group Ltd) <camelotdev@xara.com> Date: 14/5/93 Parameters: result  - points to be translated. [INPUTS] count - number of points. None  [OUTPUTS] Returns: None. Errors: None. Definition at line 390 of file matrix.cpp. { if ( Type == TRANS_TRANSLATION ) { for (UINT32 i = 0; i < count; i++) { pts[i].x += e; pts[i].y += f; } } else { #ifdef OLD_MATRIX_TRANSFORMATIONS INT32 tx; // Holds INPUT value of pts[i].x for use in second MatrixCalc for (UINT32 i = 0; i < count; i++) { tx = pts[i].x; pts[i].x = MatrixCalc(a, tx, c, pts[i].y) + e; pts[i].y = MatrixCalc(b, tx, d, pts[i].y) + f; } #else // We use GDraw to transform the path // Alex asserts it is unimportant to switch contexts here as path transformations are not context // dependent; thus we call GDraw directly GMATRIX gmat; gmat.AX = a.GetShifted16(); gmat.AY = b.GetShifted16(); gmat.BX = c.GetShifted16(); gmat.BY = d.GetShifted16(); gmat.CX.SetHighLow(e>>16, e<<16); gmat.CY.SetHighLow(f>>16, f<<16); // Alex promises we don't need a context to do this op // XaDrawOld_TransformPath( (LPPOINT)pts, (LPPOINT)pts, count, &gmat ); GRenderRegion::GetStaticDrawContext()->TransformPath( (LPPOINT)pts, (LPPOINT)pts, count, &gmat ); #endif } }

void Matrix::transform (  Coord *  pt  )  const

Transforms a single point. Author: Mario_Shamtani (Xara Group Ltd) <camelotdev@xara.com> Date: 19/5/93 Parameters: Coordinate  to be transformed. [INPUTS] Coordinate  is overwritten with new values [OUTPUTS] Returns: None. Errors: None. Definition at line 507 of file matrix.cpp. { INT32 tx; // Holds INPUT value of pt.x for use in second MatrixCalc! if ( Type == TRANS_TRANSLATION ) { pt->x += e; pt->y += f; } else { tx = pt->x; pt->x = MatrixCalc(a, tx, c, pt->y) + e; pt->y = MatrixCalc(b, tx, d, pt->y) + f; } }

BOOL Matrix::TransformBounds (  DocRect *  pRect  )  const

Given a rect, find its bounds when transformed. Author: Ed_Cornes (Xara Group Ltd) <camelotdev@xara.com> Date: 23/4/95 Parameters: pRect  - rect to transform [INPUTS] pRect  - transformed rect [OUTPUTS] Returns: FALSE if fails Definition at line 997 of file matrix.cpp. { ERROR2IF(pRect==NULL,FALSE,"Matrix::Transform() - pRect==NULL"); static DocCoord coords[4]; coords[0] = pRect->lo; coords[1] = DocCoord(pRect->hi.x,pRect->lo.y); coords[2] = pRect->hi; coords[3] = DocCoord(pRect->lo.x,pRect->hi.y); this->transform((Coord*)&coords,4); *pRect = DocRect(coords[0],coords[0]); pRect->IncludePoint(coords[1]); pRect->IncludePoint(coords[2]); pRect->IncludePoint(coords[3]); return TRUE; }

void Matrix::translate (  const INT32  TransX, const INT32  TransY )

QUICKLY add a translation to a matrix! Author: Ed_Cornes (Xara Group Ltd) <camelotdev@xara.com> Date: 17/4/95 Parameters: TransX,TransY  - translations to apply [INPUTS] Definition at line 841 of file matrix.cpp. { e+=TransX; f+=TransY; }

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Friends And Related Function Documentation

Matrix operator * (  const Matrix &  op1, const Matrix &  op2 )  [friend]

Matrix multiplication. Author: Ed_Cornes (Xara Group Ltd) <camelotdev@xara.com> Date: 5/2/96 Parameters: Two  matrices to be multiplied. [INPUTS] Returns: result of multiplication. Definition at line 581 of file matrix.cpp. { static Matrix t; t = op1; t *= op2; // no point in duplicating code, just call *= operator return t; }

friend class OSRenderRegion [friend]

Definition at line 172 of file matrix.h.

friend class XMatrix [friend]

Definition at line 173 of file matrix.h.

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Member Data Documentation

FIXED16 Matrix::a [private]

Definition at line 176 of file matrix.h.

ANGLE Matrix::Angle

Definition at line 185 of file matrix.h.

FIXED16 Matrix::b [private]

Definition at line 177 of file matrix.h.

FIXED16 Matrix::c [private]

Definition at line 178 of file matrix.h.

FIXED16 Matrix::d [private]

Definition at line 179 of file matrix.h.

INT32 Matrix::e [private]

Definition at line 180 of file matrix.h.

INT32 Matrix::f [private]

Definition at line 181 of file matrix.h.

TransformType Matrix::Type

Definition at line 184 of file matrix.h.

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The documentation for this class was generated from the following files:

• Kernel/matrix.h (r1785/r1285)
• Kernel/matrix.cpp (r1785/r1282)

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