Matrix3 Class Reference

#include <matrix3.h>

Class Description

See also

Class Point3, Matrix Representations of 3D Transformations, Class Quat, Class AngAxis, Structure AffineParts, Class BigMatrix.

Description:

This class implements a 4x3 3D transformation matrix object. Methods are provided to zero the matrix, set it to the identity, compute its inverse, apply incremental translation, rotation and scaling, and build new X, Y and Z rotation matrices. Operators are provided for matrix addition, subtraction, and multiplication. All methods are implemented by the system.

Note: In 3ds Max, all vectors are assumed to be row vectors. Under this assumption, multiplication of a vector with a matrix can be written either way (Matrix*Vector or Vector*Matrix), for ease of use, and the result is the same – the (row) vector transformed by the matrix.

Data Members:

private:

float m[4][3];

Matrix storage.

DWORD flags;

Matrix Identity Flags.

POS_IDENT

Indicates the translation row of the matrix is the identity.

ROT_IDENT

Indicates the rotation elements of the matrix are the identity.

SCL_IDENT

Indicates the scale elements of the matrix are the identity.

MAT_IDENT

Indicates the matrix is the identity matrix. This is equivalent to (POS_IDENT|ROT_IDENT|SCL_IDENT).

Inheritance diagram for Matrix3:

Public Member Functions
const Point3 &	operator[] (int i) const
void	SetNotIdent ()
void	SetIdentFlags (DWORD f)
DWORD	GetIdentFlags () const
void	ClearIdentFlag (DWORD f)
BOOL	IsIdentity () const
void	ValidateFlags ()
MRow *	GetAddr ()
const MRow *	GetAddr () const
	Matrix3 ()
	Matrix3 (BOOL init)
	Matrix3 (float(*fp)[3])
	Matrix3 (const Point3 &U, const Point3 &V, const Point3 &N, const Point3 &T)
Matrix3 &	Set (const Point3 &U, const Point3 &V, const Point3 &N, const Point3 &T)
int	operator== (const Matrix3 &M) const
bool	operator!= (const Matrix3 &M) const
int	Equals (const Matrix3 &M, float epsilon=1E-6f) const
Matrix3 &	operator-= (const Matrix3 &M)
Matrix3 &	operator+= (const Matrix3 &M)
Matrix3 &	operator*= (const Matrix3 &M)
	Multiply this matrix on the right by Matrix m. More...
Matrix3 &	operator*= (float a)
void	IdentityMatrix ()
void	Zero ()
Point3	GetRow (int i) const
void	SetRow (int i, Point3 p)
Point4	GetColumn (int i) const
void	SetColumn (int i, Point4 col)
Point3	GetColumn3 (int i) const
void	NoTrans ()
void	NoRot ()
void	NoScale ()
void	Orthogonalize ()
	Ortho-normalize the matrix. More...
void	SetTrans (const Point3 &p)
void	SetTrans (int i, float v)
const Point3 &	GetTrans () const
void	Translate (const Point3 &p)
void	RotateX (float angle)
void	RotateY (float angle)
void	RotateZ (float angle)
void	Scale (const Point3 &s, BOOL trans=FALSE)
void	PreTranslate (const Point3 &p)
void	PreRotateX (float angle)
void	PreRotateY (float angle)
void	PreRotateZ (float angle)
void	PreScale (const Point3 &s, BOOL trans=FALSE)
void	SetTranslate (const Point3 &p)
void	SetRotateX (float angle)
void	SetRotateY (float angle)
void	SetRotateZ (float angle)
void	SetRotate (const Quat &q)
void	SetRotate (const AngAxis &aa)
void	SetRotate (float yaw, float pitch, float roll)
void	SetAngleAxis (const Point3 &axis, float angle)
void	SetScale (const Point3 &s)
void	SetFromToUp (const Point3 &from, const Point3 &to, const Point3 &up)
void	Invert ()
Matrix3	operator* (const Matrix3 &) const
Matrix3	operator+ (const Matrix3 &) const
Matrix3	operator- (const Matrix3 &) const
Point3	PointTransform (const Point3 &p) const
Point3	VectorTransform (const Point3 &p) const
void	TransformPoints (Point3 *array, int n, int stride=sizeof(Point3))
void	TransformPoints (const Point3 *array, Point3 *to, int n, int stride=sizeof(Point3), int strideTo=sizeof(Point3))
void	TransformVectors (Point3 *array, int n, int stride=sizeof(Point3))
void	TransformVectors (const Point3 *array, Point3 *to, int n, int stride=sizeof(Point3), int strideTo=sizeof(Point3))
void	GetYawPitchRoll (float *yaw, float *pitch, float *roll)
IOResult	Save (ISave *isave)
	Save this Matrix3 to disk. More...
IOResult	Load (ILoad *iload)
	Load the data for this Matrix3. More...
BOOL	Parity () const

Static Public Attributes
static const Matrix3	Identity
	An global instance of Matrix3 set to the identity. More...

Friends
class	Quat
Matrix3	RotateXMatrix (float angle)
Matrix3	RotateYMatrix (float angle)
Matrix3	RotateZMatrix (float angle)
Matrix3	TransMatrix (const Point3 &p)
Matrix3	ScaleMatrix (const Point3 &s)
Matrix3	RotateYPRMatrix (float Yaw, float Pitch, float Roll)
Matrix3	RotAngleAxisMatrix (Point3 &axis, float angle)
Matrix3	Inverse (const Matrix3 &M)
Matrix3	PseudoInverse (const Matrix3 &m)
Matrix3	InverseHighPrecision (const Matrix3 &M)
Matrix3	AffineTranspose (const Matrix3 &M)
Point3	operator* (const Matrix3 &A, const Point3 &V)
Point3	operator* (const Point3 &V, const Matrix3 &A)
Point3	VectorTransform (const Matrix3 &M, const Point3 &V)
Matrix3	XFormMat (const Matrix3 &xm, const Matrix3 &m)
Point3	VectorTransform (const Point3 &V, const Matrix3 &M)
void	MatrixMultiply (Matrix3 &outMatrix, const Matrix3 &matrixA, const Matrix3 &matrixB)
void	Inverse (Matrix3 &outMatrix, const Matrix3 &M)
void	AffineTranspose (Matrix3 &outMatrix, const Matrix3 &M)

Additional Inherited Members
Static Public Member Functions inherited from MaxHeapOperators
static UtilExport void *	operator new (size_t size)
	Standard new operator used to allocate objects If there is insufficient memory, an exception will be thrown. More...
static UtilExport void *	operator new (size_t size, const std::nothrow_t &e)
	Standard new operator used to allocate objects if there is insufficient memory, NULL will be returned. More...
static UtilExport void *	operator new (size_t size, const char *filename, int line)
	New operator used to allocate objects that takes the filename and line number where the new was called If there is insufficient memory, an exception will be thrown. More...
static UtilExport void *	operator new (size_t size, int block_type, const char *filename, int line)
	New operator used to allocate objects that takes the type of memory, filename and line number where the new was called If there is insufficient memory, an exception will be thrown. More...
static UtilExport void *	operator new (size_t size, const std::nothrow_t &e, const char *filename, int line)
	New operator used to allocate objects that takes the filename and line number where the new was called If there is insufficient memory, NULL will be returned. More...
static UtilExport void *	operator new (size_t size, unsigned long flags)
	New operator used to allocate objects that takes extra flags to specify special operations If there is insufficient memory, an exception will be thrown. More...
static UtilExport void *	operator new (size_t size, const std::nothrow_t &e, unsigned long flags)
	New operator used to allocate objects that takes extra flags to specify special operations If there is insufficient memory, NULL will be returned. More...
static UtilExport void *	operator new[] (size_t size)
	New operator used to allocate arrays of objects If there is insufficient memory, an exception will be thrown. More...
static UtilExport void *	operator new[] (size_t size, const std::nothrow_t &e)
	New operator used to allocate arrays of objects If there is insufficient memory, NULL will be returned. More...
static UtilExport void *	operator new[] (size_t size, const char *filename, int line)
	New operator used to allocate arrays of objects If there is insufficient memory, an exception will be thrown. More...
static UtilExport void *	operator new[] (size_t size, int block_type, const char *filename, int line)
	New operator used to allocate arrays of objects. More...
static UtilExport void *	operator new[] (size_t size, const std::nothrow_t &e, const char *filename, int line)
	New operator used to allocate arrays of objects If there is insufficient memory, NULL will be returned. More...
static UtilExport void *	operator new[] (size_t size, unsigned long flags)
	New operator used to allocate arrays of objects If there is insufficient memory, an exception will be thrown. More...
static UtilExport void *	operator new[] (size_t size, const std::nothrow_t &e, unsigned long flags)
	New operator used to allocate arrays of objects If there is insufficient memory, NULL will be returned. More...
static UtilExport void	operator delete (void *ptr)
	Standard delete operator used to deallocate an object If the pointer is invalid, an exception will be thrown. More...
static UtilExport void	operator delete (void *ptr, const std::nothrow_t &e)
	Standard delete operator used to deallocate an object If the pointer is invalid, nothing will happen. More...
static UtilExport void	operator delete (void *ptr, const char *filename, int line)
	Delete operator used to deallocate an object that takes the filename and line number where the delete was called If the pointer is invalid, an exception will be thrown. More...
static UtilExport void	operator delete (void *ptr, int block_type, const char *filename, int line)
	Delete operator used to deallocate an object that takes the type of memory, filename and line number where the delete was called If the pointer is invalid, an exception will be thrown. More...
static UtilExport void	operator delete (void *ptr, const std::nothrow_t &e, const char *filename, int line)
	Delete operator used to deallocate an object that takes the filename and line number where the delete was called If the pointer is invalid, nothing will happen. More...
static UtilExport void	operator delete (void *ptr, unsigned long flags)
	Delete operator used to deallocate an object that takes extra flags to specify special operations If the pointer is invalid, an exception will be thrown. More...
static UtilExport void	operator delete (void *ptr, const std::nothrow_t &e, unsigned long flags)
	Delete operator used to deallocate an object that takes extra flags to specify special operations If the pointer is invalid, nothing will happen. More...
static UtilExport void	operator delete[] (void *ptr)
	Standard delete operator used to deallocate an array of objects If the pointer is invalid, an exception will be thrown. More...
static UtilExport void	operator delete[] (void *ptr, const std::nothrow_t &e)
	Standard delete operator used to deallocate an array of objects If the pointer is invalid, nothing will happen. More...
static UtilExport void	operator delete[] (void *ptr, const char *filename, int line)
	Delete operator used to deallocate an array of objects that takes the filename and line number where the delete was called If the pointer is invalid, an exception will be thrown. More...
static UtilExport void	operator delete[] (void *ptr, int block_type, const char *filename, int line)
	Delete operator used to deallocate an array of objects that takes the type of memory, filename and line number where the delete was called If the pointer is invalid, an exception will be thrown. More...
static UtilExport void	operator delete[] (void *ptr, const std::nothrow_t &e, const char *filename, int line)
	Delete operator used to deallocate an array of objects that takes the filename and line number where the delete was called If the pointer is invalid, nothing will happen. More...
static UtilExport void	operator delete[] (void *ptr, unsigned long flags)
	Delete operator used to deallocate an array of objects that takes extra flags to specify special operations If the pointer is invalid, an exception will be thrown. More...
static UtilExport void	operator delete[] (void *ptr, const std::nothrow_t &e, unsigned long flags)
	Delete operator used to deallocate an array of objects that takes extra flags to specify special operations If the pointer is invalid, an exception will be thrown. More...
static UtilExport void *	operator new (size_t size, void *placement_ptr)
	Placement new operator. More...
static UtilExport void	operator delete (void *ptr, void *placement_ptr)
	Placement delete operator. More...
static UtilExport void *	aligned_malloc (size_t size, size_t alignment)
	Allocates memory on a specified alignment boundary. More...
static UtilExport void *	aligned_realloc (void *ptr, size_t size, size_t alignment)
	Reallocates memory on a specified alignment boundary. More...
static UtilExport void	aligned_free (void *ptr)
	Frees a block of memory that was allocated with aligned_malloc/aligned_realloc. More...

Constructor & Destructor Documentation

Matrix3 ( )

inline

Remarks

Constructor. Note that no initialization is done. Use Zero() or Identity(), or the constructors below.

{ flags = 0; }

Matrix3 ( BOOL  init )

inline

Remarks

Constructor. The matrix is set to the identity.

Parameters

init

Unused.

{UNREFERENCED_PARAMETER(init); flags=0; IdentityMatrix();}

Matrix3

(

float(*)

fp[3]

)

Remarks

Constructor. The matrix is initialized to fp.

Parameters

fp	Specifies the initial values for the matrix.

Matrix3 ( const Point3 &  U, const Point3 &  V, const Point3 &  N, const Point3 &  T  )

inline

Remarks

Constructor. Initializes the matrix with the row data passed and validates the matrix flags.

Parameters

U	The data for row 0.
V	The data for row 1.
N	The data for row 2.
T	The data for row 3.

{ Set(U, V, N, T); }

Member Function Documentation

const Point3& operator[] ( int  i ) const

inline

Remarks

Returns a reference to the 'i-th' Point3 of the matrix.

{ return((Point3&)(*m[i])); }

void SetNotIdent ( )

inline

Remarks

This clears the MAT_IDENT flag to indicate the matrix is not the identity. If any changes are made to components directly via GetAddr(), this method must be called.

{ flags &= ~MAT_IDENT; }

void SetIdentFlags ( DWORD  f )

inline

Remarks

This sets the specified identity flag(s).

Parameters

f	Specifies the identity flag bit(s) to set. See Matrix Identity Flags above.

{ flags &= ~MAT_IDENT; flags |= f; }

DWORD GetIdentFlags ( ) const

inline

Remarks

Returns the identity flags.

{ return flags; }

void ClearIdentFlag ( DWORD  f )

inline

Remarks

Clears the specified identity flag(s). See Matrix Identity Flags above.

Parameters

f	Specifies the identity flag bit(s) to clear.

{ flags &= ~f; }

BOOL IsIdentity ( ) const

inline

Remarks

Returns TRUE if the matrix is the identity matrix (based on the flags); otherwise FALSE.

{ return ((flags&MAT_IDENT)==MAT_IDENT); }

void ValidateFlags

(

)

Remarks

This method may be used to recompute the *_IDENT flags for this matrix. For instance, if you call a method, such as INode::GetObjTMAfterWSM(), and it returns a matrix, you cannot use the IsIdentity() method to check if the matrix is indeed the identity. This is because the flags that method checks are not initialized by the INode method. What you can do however is call this method first. This will validate the flags in the matrix so they accuratly reflect the properties of the matrix. If after calling this method, and then calling IsIdentity(), the proper result would be returned.

MRow* GetAddr ( )

inline

Remarks

Returns the address of this Matrix3.

The Matrix3 class keeps flags indicating identity for rotation, scale, position, and the matrix as a whole, and thus the direct access via the [] operator is restricted to prevent developers from modifying the matrix without updating the flags. This method, GetAddr(), still lets you get at the matrix itself and then you can use the [] operator on the result. Note: If you change the matrix via this pointer, you MUST clear the proper IDENT flags!

Also Note: typedef float MRow[3];

Returns

The address of the Matrix3.

{ return (MRow *)(m); }   

const MRow* GetAddr ( ) const

inline

Remarks

Returns the address of this Matrix3.

The Matrix3 class keeps flags indicating identity for rotation, scale, position, and the matrix as a whole, and thus the direct access via the [] operator is restricted to prevent developers from modifying the matrix without updating the flags. This method, GetAddr(), still lets you get at the matrix itself and then you can use the [] operator on the result. Note: If you change the matrix via this pointer, you MUST clear the proper IDENT flags!

Also Note: typedef float MRow[3];

{ return (MRow *)(m); }

Matrix3& Set ( const Point3 &  U, const Point3 &  V, const Point3 &  N, const Point3 &  T  )

inline

Remarks

Initializes the matrix with the row data passed and validates the matrix flags.

Parameters

U	The data for row 0.
V	The data for row 1.
N	The data for row 2.
T	The data for row 3.

Returns

A reference to this matrix.

                                                                                     {
        flags = 0; SetRow(kXAxis, U); SetRow(kYAxis, V); SetRow(kZAxis, N); SetRow(kTrans, T); 
        ValidateFlags(); return *this; }

int operator==

(

const Matrix3 &

M

)

const

Remarks

Compares the elements of this matrix and the one specified element by element for exact equality. Returns nonzero if they are equal; otherwise zero.

Parameters

M	The matrix to compare against.

bool operator!= ( const Matrix3 &  M ) const

inline

Remarks

Compares the elements of this matrix and the one specified element by element for inequality. Returns false iff they are unequal.

Parameters

M	The matrix to compare against.

{ return (operator==(M) == 0); }

int Equals	(	const Matrix3 &	M,
		float	epsilon = 1E-6f
	)		const

Remarks

Compares the elements of this matrix and the one specified element by element for equality within the specified tolerance epsilon. Returns nonzero if they are 'equal'; otherwise zero.

Parameters

M	The matrix to compare against.
epsilon	The tolerance for comparison. If the values in the matrix are within this value (+ epsilon or - epsilon) they are considered equal.

Matrix3& operator-=

(

const Matrix3 &

M

)

Remarks

Subtracts a Matrix3 from this Matrix3.

Matrix3& operator+=

(

const Matrix3 &

M

)

Remarks

Adds a Matrix3 to this Matrix3.

Matrix3& operator*=

(

const Matrix3 &

M

)

Multiply this matrix on the right by Matrix m.

Remarks

Multiplies this Matrix3 by the specified Matrix3 (*this = (*this)*M;).

Matrix3 tm1, tm2;
Matrix3 tm3 = tm1 * tm2;    // Is equivalent to the below
tm1 *= tm2;                 // tm1 now equals tm3

Parameters

M	The matrix multiplied to the right of this matrix

Returns

A reference to this matrix

Matrix3& operator*=

(

float

a

)

Remarks

Multiplies each element of this Matrix3 by a float.

Matrix3 tm1(1), tm2(2);
tm1 *= 0.7f;    // This multiplies all elements by 0.7f
tm2.Scale(Point3(0.7f, 0.7f, 0.7f), TRUE); // This multiplies all elements by 0.7f
tm1 == tm2; // is true

Parameters

a	The scale to apply to each element of this matrix

Returns

a reference to this matrix

void IdentityMatrix

(

)

Remarks

Set this matrix to the Identity Matrix.

void Zero

(

)

Remarks

This method sets all elements of the matrix to 0.0f

Point3 GetRow ( int  i ) const

inline

Remarks

Returns the specified row of this matrix.

Parameters

i	Specifies the row to retrieve.

{ return (*this)[i]; }

void SetRow	(	int	i,
		Point3	p
	)

Remarks

Sets the specified row of this matrix to the specified values.

Parameters

i	Specifies the row to set.
p	The values to set.

Point4 GetColumn

(

int

i

)

const

Remarks

Returns the 'i-th' column of this matrix.

Parameters

i	Specifies the column to get (0-2).

void SetColumn	(	int	i,
		Point4	col
	)

Remarks

Sets the 'i-th' column of this matrix to the specified values.

Parameters

i	Specifies the column to set (0-2).
col	The values to set.

Point3 GetColumn3

(

int

i

)

const

Remarks

Returns the upper three entries in the specified column.

Parameters

i	Specifies the partial column to get (0-2).

void NoTrans

(

)

Remarks

This method zeros the translation portion of this matrix.

void NoRot

(

)

Remarks

This method zeros the rotation and scale portion of this matrix.

void NoScale

(

)

Remarks

This method zeros the scale portion of this matrix without orthogonalization. If the matrix was sheared (skewed) then this method is not able to remove the scale component completely. In that case, use the Orthogonalize() method instead to remove the scale component entirely. Read the SCL_IDENT flag to check whether the NoScale() method was enough to make the matrix to be orthogonal (with perpendicular axes of unit length).

void Orthogonalize

(

)

Ortho-normalize the matrix.

This ensures that each axis of the basis is of length 1 and at right angles to the other. This is an "unbiased" orthogonalization, which means that no single axis is used as the basis for the other axis, and all axis will be modified equally.

Note

This is an iterative process, and should not be used in high-performance situations. It seems to take a maximum of 4 iterations to converge.

void SetTrans ( const Point3 &  p )

inline

Remarks

Sets the translation row of this matrix to the specified values. The POS_IDENT flag is cleared.

Parameters

p	Specifies the values for the translation row.

{ (*this)[kTrans] = p;  flags &= ~POS_IDENT; }

void SetTrans ( int  i, float  v  )

inline

Remarks

Sets the specified component of the translation row of this matrix to the specified value. The POS_IDENT flag is cleared.

Parameters

i	Specifies the component of the translation row of this matrix to set.
v	The value to set.

{ (*this)[kTrans][i] = v; flags &= ~POS_IDENT; }

const Point3& GetTrans ( ) const

inline

Remarks

Returns the translation row of this matrix.

Returns

The translation row of this matrix.

{ return (*this)[kTrans]; }

void Translate

(

const Point3 &

p

)

Remarks

Apply an incremental translation transformation to this matrix. This is equivalent to multiplying on the RIGHT by the transform.

Parameters

p	Specifies the translation.

void RotateX

(

float

angle

)

Remarks

Apply an incremental X rotation transformation to this matrix. This is equivalent to multiplying on the RIGHT by the transform.

Parameters

angle

Specifies the X rotation in radians.

void RotateY

(

float

angle

)

Remarks

Apply an incremental Y rotation transformation to this matrix. This is equivalent to multiplying on the RIGHT by the transform.

Parameters

angle

Specifies the Y rotation in radians.

void RotateZ

(

float

angle

)

Remarks

Apply an incremental Z rotation transformation to this matrix. This is equivalent to multiplying on the RIGHT by the transform.

Parameters

angle

Specifies the Z rotation in radians.

void Scale	(	const Point3 &	s,
		BOOL	trans = FALSE
	)

Remarks

Apply an incremental scaling transformation to this matrix. This is equivalent to multiplying on the RIGHT by the transform.

Parameters

s

The scale values.

trans

If set to TRUE, the translation component is scaled. If trans = FALSE the translation component is unaffected. When 3ds Max was originally written there was a bug in the code for this method where the translation portion of the matrix was not being scaled. This meant that when a matrix was scaled the bottom row was not scaled. Thus it would always scale about the local origin of the object, but it would scale the world axes. When this bug was discovered, dependencies existed in the code upon this bug. Thus it could not simply be fixed because it would break the existing code that depended upon it working the incorrect way. To correct this the trans parameter was added. If this is set to TRUE, the translation component will be scaled correctly. The existing plug-ins don't use this parameter, it defaults to FALSE, and the code behaves the old way.

void PreTranslate

(

const Point3 &

p

)

Remarks

Apply an incremental translation transformation to this matrix. This is equivalent to multiplying on the LEFT by the transform. param p Specifies the translation distance.

void PreRotateX

(

float

angle

)

Remarks

Apply an incremental X rotation transformation to this matrix. This is equivalent to multiplying on the LEFT by the transform.

Parameters

angle

Specifies the X rotation in radians.

void PreRotateY

(

float

angle

)

Remarks

Apply an incremental Y rotation transformation to this matrix. This is equivalent to multiplying on the LEFT by the transform.

Parameters

angle

Specifies the Y rotation in radians.

void PreRotateZ

(

float

angle

)

Remarks

Apply an incremental Z rotation transformation to this matrix. This is equivalent to multiplying on the LEFT by the transform.

Parameters

angle

Specifies the Z rotation in radians.

void PreScale	(	const Point3 &	s,
		BOOL	trans = FALSE
	)

Remarks

Apply an incremental scaling transformation to this matrix. This is equivalent to multiplying on the LEFT by the transform.

Parameters

s	The scale values.
trans	= FALSE If trans = FALSE the translation component is unaffected.

void SetTranslate

(

const Point3 &

p

)

Remarks

Sets this matrix to the identity and the translation components to the specified values.

Parameters

p	The translation values to store.

void SetRotateX

(

float

angle

)

Remarks

Sets this matrix to the identity and the rotation components to the specified X rotation.

Parameters

angle

The angle for X rotation (in radians).

void SetRotateY

(

float

angle

)

Remarks

Sets this matrix to the identity and the rotation components to the specified Y rotation.

Parameters

angle

The angle for Y rotation (in radians).

void SetRotateZ

(

float

angle

)

Remarks

Sets this matrix to the identity and the rotation components to the specified Z rotation.

Parameters

angle

The angle for Z rotation (in radians).

void SetRotate

(

const Quat &

q

)

Remarks

Sets the rotation components of the matrix as specified by the quaternion. The translation and scale components will match the identity matrix.

Parameters

q	Specifies the rotation to use for the matrix.

void SetRotate

(

const AngAxis &

aa

)

Remarks

Sets the rotation components of the matrix as specified by the AngAxis. The translation and scale components will match the identity matrix.

Parameters

aa	Specifies the rotation to use for the matrix.

void SetRotate	(	float	yaw,
		float	pitch,
		float	roll
	)

Remarks

Sets the rotation components of this matrix using yaw, pitch and roll angles. There are many different conventions for specifying a rotation by means of three Euler angles. This function uses the convention of rotating around the world Z axis, then the X axis, then the Y axis; the three arguments are given in the order Y, X, Z.

This one is equivalent to:

M.IdentityMatrix();

M.RotateZ(roll);

M.RotateX(pitch);

M.RotateY(yaw);

–Which presupposes Y is vertical, X is sideways, Z is forward

Parameters

yaw	The yaw angle in radians.
pitch	The pitch angle in radians.
roll	The roll angle in radians.

void SetAngleAxis	(	const Point3 &	axis,
		float	angle
	)

Remarks

Sets the rotation portion of the matrix to the rotation specified by the angle and axis and sets the translation portion to zeros.

Parameters

axis	The axis of rotation.
angle	The angle of rotation about the axis in radians.

void SetScale

(

const Point3 &

s

)

Remarks

Sets the scale components of this matrix to the specified values. The other components to this matrix will match the identity.

Parameters

s	The scale factors for the matrix.

void SetFromToUp	(	const Point3 &	from,
		const Point3 &	to,
		const Point3 &	up
	)

Remarks

This creates a matrix describing a viewpoint which is at the 'from' location, looking toward the 'to' location; the viewpoint is tilted so that the 'up' vector points to the top of the view.

Parameters

from	This specifies the viewpoint source location.
to	This vector specifies the direction of view.
up	This vector points to the top of the view.

void Invert

(

)

Remarks

This method performs an in-place inversion on this matrix. An inverted matrix, when multiplied by the original, yields the identity.

Matrix3 operator*

(

const Matrix3 &

)

const

Remarks

Perform matrix multiplication.

Matrix3 operator+

(

const Matrix3 &

)

const

Remarks

Perform matrix addition.

Matrix3 operator-

(

const Matrix3 &

)

const

Remarks

Perform matrix subtraction.

Point3 PointTransform

(

const Point3 &

p

)

const

Remarks

Returns the specified point transformed by this matrix.

Parameters

p	The point to transform by this matrix.

Point3 VectorTransform

(

const Point3 &

p

)

const

Remarks

Returns the specified vector transformed by this matrix.

Parameters

p	The vector to transform by this matrix.

void TransformPoints	(	Point3 *	array,
		int	n,
		int	stride = sizeof(Point3)
	)

Remarks

Transforms the specified list of points with this matrix.

Parameters

array	The array of points to transform with this matrix.
n	The number of points in the array.
stride	The size of the increment used when moving to the next point. If you wish to transform an array of data objects which contain x, y, and z coordinates in order (such as a Point4, or a structure containing a Point3 as a member) you can specify a 'stride' value (for instance sizeof(data_object)).

void TransformPoints	(	const Point3 *	array,
		Point3 *	to,
		int	n,
		int	stride = sizeof(Point3),
		int	strideTo = sizeof(Point3)
	)

Remarks

Transforms the specified list of points with this matrix and stores the resulting transformed points in the storage passed.

Parameters

array	The array of points to transform (the source).
to	The array to store the transformed points (the destination).
n	The number of points in the source array.
stride	The size increment used when moving to the next source location.
strideTo	The size increment used when moving to the next storage location.

void TransformVectors	(	Point3 *	array,
		int	n,
		int	stride = sizeof(Point3)
	)

Remarks

Transforms the specified list of vectors with this matrix.

Parameters

array	The array of vectors to transform with this matrix.
n	The number of vectors in the array.
stride	The size of the increment used when moving to the next vector. If you wish to transform an array of data objects which contain x, y, and z coordinates in order (such as a Point4, or a structure containing a Point3 as a member) you can specify a 'stride' value (for instance sizeof(data_object)).

void TransformVectors	(	const Point3 *	array,
		Point3 *	to,
		int	n,
		int	stride = sizeof(Point3),
		int	strideTo = sizeof(Point3)
	)

Remarks

Transforms the specified list of vectors with this matrix and stores the resulting transformed vectors in the storage passed.

Parameters

array	The array of vectors to transform (the source).
to	The array to store the transformed vectors (the destination).
n	The number of vectors in the source array.
stride	The size increment used when moving to the next source location.
strideTo	The size increment used when moving to the next storage location.

void GetYawPitchRoll	(	float *	yaw,
		float *	pitch,
		float *	roll
	)

Remarks

Retrieves the yaw, pitch and roll angles represented by the rotation in this matrix.

Parameters

yaw	The yaw rotation angle is stored here (in radians).
pitch	The pitch rotation angle is stored here (in radians).
roll	The roll rotation angle is stored here (in radians).

IOResult Save

(

ISave *

isave

)

Save this Matrix3 to disk.

Parameters

isave

The interface responsible for actually saving the data

Returns

IO_OK on success, or a failure code

IOResult Load

(

ILoad *

iload

)

Load the data for this Matrix3.

Parameters

iload

The interface responsible for actually loading the data

Returns

IO_OK on success, or a failure code

BOOL Parity

(

)

const

Remarks

Returns the 'parity' of the matrix. Scaling one axis of the matrix negatively switches the 'parity'. However if you scale two axis the parity will flip back. Scaling three axis switches the parity again.

When rendering a mesh, if you scale something along one axis, it turns 'inside out'. That is the direction when the normals are reversed. This method may be used to detect that case and then reverse the normals. The 3ds Max renderer does this – if this method returns TRUE it flips all the normals so it won't turn inside out.

Friends And Related Function Documentation

friend class Quat

friend

Matrix3 RotateXMatrix ( float  angle )

friend

Remarks

Builds a new matrix for use as a X rotation transformation.

Parameters

angle

Specifies the angle of rotation in radians.

Returns

A new X rotation Matrix3.

Matrix3 RotateYMatrix ( float  angle )

friend

Remarks

Builds a new matrix for use as a Y rotation transformation.

Parameters

angle

Specifies the angle of rotation in radians.

Returns

A new Y rotation Matrix3.

Matrix3 RotateZMatrix ( float  angle )

friend

Remarks

Builds a new matrix for use as a Z rotation transformation.

Parameters

angle

Specifies the angle of rotation in radians.

Returns

A new Z rotation Matrix3.

Matrix3 TransMatrix ( const Point3 &  p )

friend

Remarks

Builds a new matrix for use as a translation transformation.

Parameters

p	Specifies the translation values.

Returns

A new translation Matrix3.

Matrix3 ScaleMatrix ( const Point3 &  s )

friend

Remarks

Builds a new matrix for use as a scale transformation.

Parameters

s	Specifies the scale values.

Returns

A new scale Matrix3.

Matrix3 RotateYPRMatrix ( float  Yaw, float  Pitch, float  Roll  )

friend

Remarks

Builds a new matrix for use as a rotation transformation by specifying yaw, pitch and roll angles.

This definition will depend on what our coordinate system is. This one is equivalent to:

M.IdentityMatrix();

M.RotateZ(roll);

M.RotateX(pitch);

M.RotateY(yaw);

Which presupposes Y is vertical, X is sideways, Z is forward

Parameters

Yaw	Specifies the yaw angle in radians.
Pitch	Specifies the pitch angle in radians.
Roll	Specifies the roll angle in radians.

Returns

A new rotation Matrix3.

Matrix3 RotAngleAxisMatrix ( Point3 &  axis, float  angle  )

friend

Remarks

Builds a new matrix for use as a rotation transformation by specifying an angle and axis.

Parameters

axis	Specifies the axis of rotation. Note that this angle is expected to be normalized.
angle	Specifies the angle of rotation. Note: The direction of the angle in this method is opposite of that in AngAxisFromQ().

Returns

A new rotation Matrix3.

Matrix3 Inverse ( const Matrix3 &  M )

friend

Remarks

Return the inverse of the matrix

Parameters

M	The matrix to compute the inverse of.

Matrix3 PseudoInverse ( const Matrix3 &  m )

friend

Remarks

Return the pseudoinverse of an affine symmetric matrix, meaning that if the matrix is degenerate (projects into a plane, line or point; eg. has both row 1 and column 1 zero) this will still produce a matrix that inverts the nonzero parts of the transform.

Parameters

m	The matrix to compute the pseudoinverse of.

Matrix3 InverseHighPrecision ( const Matrix3 &  M )

friend

Remarks

Return the inverse of the matrix using doubles for the intermediary results

Parameters

M	The matrix to compute the inverse of.

Matrix3 AffineTranspose ( const Matrix3 &  M )

friend

Remarks

Transposes the affine portion of the matrix. Since Matrix3 does not have a 4th column you cannot transpose the entire 4x4 matrix, so this method only transposes the 3x3 matrix representing rotations, scale and skew.

Parameters

M	The matrix to compute the affine transpose of.

Point3 operator* ( const Matrix3 &  A, const Point3 &  V  )

friend

Remarks

These transform a Point3 with a Matrix3. These two versions of transforming a point with a matrix do the same thing, regardless of the order of operands (linear algebra rules notwithstanding).

Parameters

A	The matrix to transform the point with.
V	The point to transform.

Returns

The transformed Point3.

Point3 operator* ( const Point3 &  V, const Matrix3 &  A  )

friend

Remarks

These transform a Point3 with a Matrix3. These two versions of transforming a point with a matrix do the same thing, regardless of the order of operands (linear algebra rules notwithstanding).

Parameters

V	The point to transform.
A	The matrix to transform the point with.

Returns

The transformed Point3.

Point3 VectorTransform ( const Matrix3 &  M, const Point3 &  V  )

friend

Remarks

Transform the vector (Point3) with the specified matrix.

Parameters

M	The matrix to transform the vector with.
V	The vector to transform.

Returns

The transformed vector (as a Point3).

Matrix3 XFormMat ( const Matrix3 &  xm, const Matrix3 &  m  )

friend

Remarks

This method is used to build a matrix that constructs a transformation in a particular space. For example, say you have a rotation you want to apply, but you want to perform the rotation in another coordinate system. To do this, you typically transform into the space of the coordinate system, then apply the transformation, and then transform out of that coordinate system. This method constructs a matrix that does just this. It transforms matrix m so it is applied in the space of matrix xm. It returns a Matrix3 that is xm*m*Inverse(xm).

Parameters

xm	Specifies the coordinate system you want to work in.
m	Specifies the transformation matrix.

Returns

Returns a Matrix3 that is xm*m*Inverse(xm).

Point3 VectorTransform ( const Point3 &  V, const Matrix3 &  M  )

friend

void MatrixMultiply ( Matrix3 &  outMatrix, const Matrix3 &  matrixA, const Matrix3 &  matrixB  )

friend

Remarks

Same as Maxtrix3::operator[]. Perform matrix multiplication without additional matrix copy

Parameters

outMatrix	The result of matrixA * matrixB
matrixA	First matrix to multiply
matrixB	Second matrix to multiply

void Inverse ( Matrix3 &  outMatrix, const Matrix3 &  M  )

friend

Remarks

Same as Maxtrix3::Inverse. Compute the inverse of the matrix without additional matrix copy

Parameters

outMatrix	The inversed matrix.
M	The matrix to compute the inverse of.

void AffineTranspose ( Matrix3 &  outMatrix, const Matrix3 &  M  )

friend

Remarks

Same as Matrix3::AffineTranspose. Computes the affine transpose without additional matrix copy

Parameters

outMatrix	The inversed matrix.
M	The matrix to compute the affine transpose of.

Member Data Documentation

const Matrix3 Identity

static

An global instance of Matrix3 set to the identity.

An identity matrix has no rotation, scale or translation on it. In other words, it is a matrix that has no effect when multiplied with another matrix.
the structure of the Matrix is as follows:

[1, 0, 0]
[0, 1, 0]
[0, 0, 1]
[0, 0, 0]