Define an affine transformation. More...

#include <AffineXform.hpp>

Public Member Functions
	AffineXform ()
	AffineXform (const double three_by_three, const double translation)
	AffineXform (const Matrix3 &mat, const CartVect &off)
void	accumulate (const AffineXform &other)
void	xform_point (const double input, double output) const
void	xform_point (double *in_out) const
void	xform_vector (const double input, double output) const
void	xform_vector (double *in_out) const
AffineXform	inverse () const
const Matrix3 &	matrix () const
const CartVect &	offset () const
bool	reflection () const
bool	scale () const
Static Public Member Functions
static AffineXform	translation (const double *vector)
static AffineXform	rotation (double radians, const double *axis)
static AffineXform	rotation (const double from_vec, const double to_vec)
static AffineXform	reflection (const double *plane_normal)
static AffineXform	scale (double f)
static AffineXform	scale (const double *fractions)
static AffineXform	scale (double f, const double *point)
static AffineXform	scale (const double fractions, const double point)
static ErrorCode	get_tag (Tag &tag_handle_out, Interface moab, const char tagname=0)
Static Private Member Functions
static AffineXform	rotation (double cos_angle, double sin_angle, const CartVect &unit_axis)
Private Attributes
Matrix3	mMatrix
CartVect	mOffset

Detailed Description

Define an affine transformation.

Author:: Jason Kraftcheck ([email protected])

Date:: August, 2006

Definition at line 34 of file AffineXform.hpp.

Constructor & Destructor Documentation

AffineXform::AffineXform ( ) [inline]

Definition at line 127 of file AffineXform.hpp.

  : mMatrix(1.0), mOffset(0.0) 
  {}

AffineXform::AffineXform	(	const double *	three_by_three,
		const double *	translation
	)		`[inline]`

Definition at line 131 of file AffineXform.hpp.

 : mMatrix(three_by_three), mOffset(trans)
 {}

AffineXform::AffineXform	(	const Matrix3 &	mat,
		const CartVect &	off
	)		`[inline]`

Definition at line 136 of file AffineXform.hpp.

  : mMatrix(mat), mOffset(off)
  {}

Member Function Documentation

void AffineXform::accumulate ( const AffineXform & other ) [inline]

incorporate the passed transform into this one such that the resulting transform is the cumulative affect of this initial transform followed by the passed transform

Definition at line 198 of file AffineXform.hpp.

{
  mMatrix = other.mMatrix * mMatrix;
  other.xform_point( mOffset.array() );
}

ErrorCode AffineXform::get_tag	(	Tag &	tag_handle_out,
		Interface *	moab,
		const char *	tagname = `0`
	)		`[static]`

get a tag that can be used to store an instance of this class

Definition at line 36 of file AffineXform.cpp.

{
  assert( sizeof(AffineXform) == 12*sizeof(double) );
  
  if (!tagname)
    tagname = AFFINE_XFORM_TAG_NAME;
 
  return interface->tag_get_handle( tagname, 
                                    sizeof(AffineXform),
                                    MB_TYPE_DOUBLE,
                                    tag_out,
                                    MB_TAG_BYTES|MB_TAG_CREAT|MB_TAG_DENSE );
}

AffineXform AffineXform::inverse ( ) const [inline]

get transform that is the inverse of this transform

Definition at line 233 of file AffineXform.hpp.

{
  Matrix3 m = mMatrix.inverse();
  return AffineXform( m, m * -mOffset );
}

const Matrix3& moab::AffineXform::matrix ( ) const [inline]

get 3x3 matrix portion of transform

Definition at line 86 of file AffineXform.hpp.

{ return mMatrix; }

const CartVect& moab::AffineXform::offset ( ) const [inline]

get translation portion of transform

Definition at line 88 of file AffineXform.hpp.

{ return mOffset; }

AffineXform AffineXform::reflection ( const double * plane_normal ) [inline, static]

reflect about plane through origin

Definition at line 162 of file AffineXform.hpp.

{
  double i = plane_normal[0];
  double j = plane_normal[1];
  double k = plane_normal[2];
  Matrix3 m( j*j+k*k-i*i,    -2.0*i*j,    -2.0*i*k,
                  -2.0*i*j, i*i+k*k-j*j,    -2.0*j*k,
                  -2.0*i*k,    -2.0*j*k, i*i+j*j-k*k );
  m *= 1.0 / (i*i + j*j + k*k); //normalize
  return AffineXform( m, CartVect(0.0) );
}

bool AffineXform::reflection ( ) const [inline]

Is this transform a reflection

A relfecting transform will require the reversal of the order of edges in a loop, etc. because it produces a mirror-image of the input geometry. This method tests if this is such a transform. A reflection may be created with by an explicit transform, scaling with a negative scale factor, etc. If multiple transforms are combined such that the transform is no longer a reflection (e.g. two reflections that are effectively a rotation), this method will return false.

Definition at line 239 of file AffineXform.hpp.

{
  return mMatrix.determinant() < 0.0;
}

AffineXform AffineXform::rotation	(	double	radians,
		const double *	axis
	)		`[inline, static]`

rotate about axis through origin

Definition at line 145 of file AffineXform.hpp.

{
  CartVect a(axis);
  a.normalize();
  return AffineXform::rotation( std::cos(angle), std::sin(angle), a );
}

AffineXform AffineXform::rotation	(	const double *	from_vec,
		const double *	to_vec
	)		`[static]`

define rotation such that if applied to from_vec the result aligned with to_vec

Definition at line 54 of file AffineXform.cpp.

{
  CartVect from(from_vec);
  CartVect to(to_vec);
  CartVect a = from * to;
  double len = a.length();
  
  // If input vectors are not parallel (the normal case)
  if (len >= std::numeric_limits<double>::epsilon()) {
    from.normalize();
    to.normalize();
    return rotation( from % to, (from * to).length(), a/len );
  }
  
  // Vectors are parallel:
  //
  // If vectors are in same direction then rotation is identity (no transform)
  if (from % to >= 0.0)
    return AffineXform(); 
    
  // Parallel vectors in opposite directions:
  //
  // NOTE:  This case is ill-defined.  There are infinitely
  // many rotations that can align the two vectors.  The angle
  // of rotation is 180 degrees, but the axis of rotation may 
  // be any unit vector orthogonal to the input vectors.
  //
  from.normalize();
  double lenxy = std::sqrt( from[0]*from[0] + from[1]*from[1] );
  CartVect axis( -from[0]*from[2]/lenxy, 
                 -from[1]*from[2]/lenxy,
                                  lenxy );
  return rotation( -1, 0, axis );
}

AffineXform AffineXform::rotation	(	double	cos_angle,
		double	sin_angle,
		const CartVect &	unit_axis
	)		`[inline, static, private]`

Definition at line 152 of file AffineXform.hpp.

{
  const Matrix3 m1(    c,   -a[2]*s, a[1]*s,
                     a[2]*s,   c,   -a[0]*s,
                    -a[1]*s, a[0]*s,   c    );
  return AffineXform( m1 + (1.0-c)*outer_product( a, a ), CartVect(0.0) );
}

AffineXform AffineXform::scale ( double f ) [inline, static]

scale about origin

Definition at line 179 of file AffineXform.hpp.

{
  return AffineXform( Matrix3( CartVect(f) ), CartVect( 0.0 ) );
}

AffineXform AffineXform::scale ( const double * fractions ) [inline, static]

scale about origin

Definition at line 174 of file AffineXform.hpp.

{
  return AffineXform( Matrix3( CartVect(f) ), CartVect( 0.0 ) );
}

AffineXform AffineXform::scale	(	double	f,
		const double *	point
	)		`[inline, static]`

scale about a point

Definition at line 184 of file AffineXform.hpp.

{
  double fs[] = { f, f, f };
  return AffineXform::scale( fs, point );
}

AffineXform AffineXform::scale	(	const double *	fractions,
		const double *	point
	)		`[inline, static]`

scale about a point

Definition at line 190 of file AffineXform.hpp.

{
  double offset[] = { p[0] * (1 - f[0]), 
                      p[1] * (1 - f[1]),
                      p[2] * (1 - f[2]) };
  return AffineXform( Matrix3( CartVect(f) ), CartVect(offset) );
}

bool AffineXform::scale ( ) const [inline]

Does this transform do any scaling

Definition at line 244 of file AffineXform.hpp.

{
  return fabs(fabs(mMatrix.determinant()) - 1) > std::numeric_limits<double>::epsilon();
}

AffineXform AffineXform::translation ( const double * vector ) [inline, static]

move

Definition at line 140 of file AffineXform.hpp.

{
  return AffineXform( Matrix3(1.0), CartVect(vector) );
}

void AffineXform::xform_point	(	const double *	input,
		double *	output
	)		const `[inline]`

apply transform to a point

Definition at line 204 of file AffineXform.hpp.

{
  xform_vector( input, output );
  output[0] += mOffset[0];
  output[1] += mOffset[1];
  output[2] += mOffset[2];
}

void AffineXform::xform_point ( double * in_out ) const [inline]

apply transform to a point

Definition at line 212 of file AffineXform.hpp.

{
  xform_vector( in_out );
  in_out[0] += mOffset[0];
  in_out[1] += mOffset[1];
  in_out[2] += mOffset[2];
}

void AffineXform::xform_vector	(	const double *	input,
		double *	output
	)		const `[inline]`

apply transform to a vector

Definition at line 220 of file AffineXform.hpp.

{
  output[0] = input[0]*mMatrix[0][0] + input[1]*mMatrix[0][1] + input[2]*mMatrix[0][2];
  output[1] = input[0]*mMatrix[1][0] + input[1]*mMatrix[1][1] + input[2]*mMatrix[1][2];
  output[2] = input[0]*mMatrix[2][0] + input[1]*mMatrix[2][1] + input[2]*mMatrix[2][2];
}

void AffineXform::xform_vector ( double * in_out ) const [inline]

apply transform to a vector

Definition at line 227 of file AffineXform.hpp.

{
  double input[] = { in_out[0], in_out[1], in_out[2] };
  xform_vector( input, in_out );
}

Member Data Documentation

Matrix3 moab::AffineXform::mMatrix [private]

Definition at line 113 of file AffineXform.hpp.

CartVect moab::AffineXform::mOffset [private]

Definition at line 114 of file AffineXform.hpp.

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

Public Member Functions

Static Public Member Functions

Static Private Member Functions

Private Attributes

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation