DGtalTools  0.9.4
DGtal::functions::dec Namespace Reference

## Functions

template<typename Calculus , DGtal::Dimension dim, DGtal::Duality duality>
DGtal::LinearOperator< Calculus, dim, duality, dim, duality > diagonal (const DGtal::KForm< Calculus, dim, duality > &kform)

template<typename Calculus , DGtal::Dimension dim, DGtal::Duality duality>
void squares (DGtal::KForm< Calculus, dim, duality > &kform)

template<typename Calculus , DGtal::Dimension dim, DGtal::Duality duality>
DGtal::LinearOperator< Calculus, dim, duality, dim, duality > squaredDiagonal (const DGtal::KForm< Calculus, dim, duality > &kform)

template<typename Image >
void writePixel (Image &image, typename Image::Point pt, typename Image::Value val, int pixel_size=1)

template<typename Image >
void writePrimalLinel (Image &image, typename Image::Point pt, typename Image::Value val, int pixel_size=1)

template<typename Image >
void writeDualLinel (Image &image, typename Image::Point pt, typename Image::Value val, int pixel_size=1)

template<typename Calculus , typename AnyForm2 , typename Image , typename Function >
void form2ToImage (const Calculus &calculus, const AnyForm2 &u, Image &image, const Function &functor, double cut_low=0.0, double cut_up=1.0, int pixel_size=1)

template<typename Calculus , typename Form1 , typename Image , typename Function , typename Predicate >
void form1ToImage (const Calculus &calculus, const Form1 &v, bool primal, Image &image, const Function &functor, const Predicate &predicate, double cut_low=0.0, double cut_up=1.0, int pixel_size=1)

template<typename Calculus , typename Image , typename Function , typename Predicate >
void dualForm1ToImage (const Calculus &calculus, const typename Calculus::DualForm1 &v, Image &image, const Function &functor, const Predicate &predicate, double cut_low=0.0, double cut_up=1.0, int pixel_size=1)

template<typename Calculus , typename Image , typename Function , typename Predicate >
void primalForm1ToImage (const Calculus &calculus, const typename Calculus::PrimalForm1 &v, Image &image, const Function &functor, const Predicate &predicate, double cut_low=0.0, double cut_up=1.0, int pixel_size=1)

template<typename Calculus , typename AnyForm2 , typename Image , typename Function >
void threeForms2ToImage (const Calculus &calculus, const AnyForm2 &u0, const AnyForm2 &u1, const AnyForm2 &u2, Image &image, const Function &functor, double cut_low=0.0, double cut_up=1.0, int pixel_size=1)

template<typename Calculus , typename AnyForm2 , typename Image >
void form2ToGreyLevelImage (const Calculus &calculus, const AnyForm2 &u, Image &image, double cut_low=0.0, double cut_up=1.0, int pixel_size=1)

template<typename Calculus , typename Image >
void primalForm1ToGreyLevelImage (const Calculus &calculus, const typename Calculus::PrimalForm1 &v, Image &image, double cut_low=0.0, double cut_up=1.0, int pixel_size=1)

template<typename Calculus , typename Image >
void dualForm1ToGreyLevelImage (const Calculus &calculus, const typename Calculus::DualForm1 &v, Image &image, double cut_low=0.0, double cut_up=1.0, int pixel_size=1)

template<typename Calculus , typename Image >
void primalForm1ToRGBColorImage (const Calculus &calculus, const typename Calculus::PrimalForm1 &v, Image &image, Color color, double cut_low=0.0, double cut_up=1.0, int pixel_size=1)

template<typename Calculus , typename Image >
void dualForm1ToRGBColorImage (const Calculus &calculus, const typename Calculus::DualForm1 &v, Image &image, Color color, double cut_low=0.0, double cut_up=1.0, int pixel_size=1)

template<typename Calculus , typename AnyForm2 , typename Image >
void threeForms2ToRGBColorImage (const Calculus &calculus, const AnyForm2 &u0, const AnyForm2 &u1, const AnyForm2 &u2, Image &image, double cut_low=0.0, double cut_up=1.0, int pixel_size=1)

## Function Documentation

template<typename Calculus , DGtal::Dimension dim, DGtal::Duality duality>
 DGtal::LinearOperator DGtal::functions::dec::diagonal ( const DGtal::KForm< Calculus, dim, duality > & kform )

Builds a diagonal linear operator from a k-form. These operators arise naturally when differentiating with respect to another variable (e.g. d/dx (vx)^t (vx) = diag(v^2) x).

Parameters
 [in] kform any kform w.
Returns
the corresponding linear operator diag(w)
Template Parameters
 Calculus any discrete exterior calculus. dim the dimension of the form. duality either PRIMAL for a primal form or DUAL for a dual form.

Definition at line 72 of file DECImageHelpers.h.

Referenced by squaredDiagonal().

73  {
75  typedef typename Calculus::LinearAlgebraBackend::Triplet Triplet;
76  typedef typename Calculus::Index Index;
77  typedef std::vector<Triplet> Triplets;
78
79  Triplets triplets;
80  for (Index index=0; index<kform.length(); index++)
81  triplets.push_back(Triplet(index, index, kform.myContainer(index)));
82
83  Operator op( kform.myCalculus );
84  op.myContainer.setFromTriplets( triplets.begin(), triplets.end() );
85  return op;
86  }
Container myContainer
Index length() const
const Calculus * myCalculus
LinearAlgebraBackend::DenseVector::Index Index
template<typename Calculus , typename Image >
 void DGtal::functions::dec::dualForm1ToGreyLevelImage ( const Calculus & calculus, const typename Calculus::DualForm1 & v, Image & image, double cut_low = 0.0, double cut_up = 1.0, int pixel_size = 1 )

Standard method to output a dual 1-form into a grey-level image.

Displays the dual 1-form v in the given image. Scalar values of v are first cut up and low according to cut_low and cut_up, and then rescaled according to max and min value. If this value is belows 0.25, it is written in the image as a "line" of size pixel_size x 1 or 1 x pixel_size, depending on position.

Parameters
 calculus the discrete exterior calculus containing the 1-form v. v any dual 1-form defined in calculus. [in,out] image the image where v is written. cut_low every value of u below is set to cut_low. cut_up every value of u above is set to cut_up. pixel_size every value of a 1-form is mapped into image as pixel_size x 1 pixels or 1 x pixel_size pixels.
Template Parameters
 Calculus any discrete exterior calculus type. Image any image type (see concepts::CImage).

Definition at line 578 of file DECImageHelpers.h.

References dualForm1ToImage().

583  {
584  BOOST_CONCEPT_ASSERT(( concepts::CImage<Image> ));
585  // Threshold is 0.25 instead of 0.5 because an edge connecting
586  // two vertices with v=0 and v=1 should not belong to the
587  // discontinuity set.
588  dualForm1ToImage( calculus, v, image,
589  [] ( double x ) { return (unsigned char) ( round( x * 255.0 ) ); },
590  [] ( double x ) { return x < 0.25; },
591  cut_low, cut_up, pixel_size );
592  }
void dualForm1ToImage(const Calculus &calculus, const typename Calculus::DualForm1 &v, Image &image, const Function &functor, const Predicate &predicate, double cut_low=0.0, double cut_up=1.0, int pixel_size=1)
template<typename Calculus , typename Image , typename Function , typename Predicate >
 void DGtal::functions::dec::dualForm1ToImage ( const Calculus & calculus, const typename Calculus::DualForm1 & v, Image & image, const Function & functor, const Predicate & predicate, double cut_low = 0.0, double cut_up = 1.0, int pixel_size = 1 )

Displays the dual 1-form v in the given image. Scalar values of v are first cut up and low according to cut_low and cut_up, and then rescaled according to max and min value. Then these values are transformed to image values with the function functor. They are written in the image as "lines" of size pixel_size x 1 or 1 x pixel_size, depending on position and duality.

Parameters
 calculus the discrete exterior calculus containing the 1-form v. v any dual 1-form defined in calculus. [in,out] image the image where v is written. functor the function transforming scalar values to image values. predicate the predicate telling for a value if it must be displayed (returns true in this case). cut_low every value of u below is set to cut_low. cut_up every value of u above is set to cut_up. pixel_size every value of a 1-form is mapped into image as pixel_size x 1 pixels or 1 x pixel_size pixels.
Template Parameters
 Calculus any discrete exterior calculus type. Image any image type (see concepts::CImage). Function any function type (double) -> typename Image::Value to convert form value to Image value. Predicate any function type (double) -> bool to select 1-forms to display.

Definition at line 360 of file DECImageHelpers.h.

References form1ToImage().

Referenced by dualForm1ToGreyLevelImage(), and dualForm1ToRGBColorImage().

366  {
367  BOOST_CONCEPT_ASSERT(( concepts::CImage<Image> ));
368  form1ToImage( calculus, v, false, image, functor, predicate,
369  cut_low, cut_up, pixel_size );
370  }
void form1ToImage(const Calculus &calculus, const Form1 &v, bool primal, Image &image, const Function &functor, const Predicate &predicate, double cut_low=0.0, double cut_up=1.0, int pixel_size=1)
template<typename Calculus , typename Image >
 void DGtal::functions::dec::dualForm1ToRGBColorImage ( const Calculus & calculus, const typename Calculus::DualForm1 & v, Image & image, Color color, double cut_low = 0.0, double cut_up = 1.0, int pixel_size = 1 )

Standard method to output a dual 1-form into a color image.

Displays the dual 1-form v in the given image. Scalar values of v are first cut up and low according to cut_low and cut_up, and then rescaled according to max and min value. If this value is belows 0.25, it is written in the image as a "line" of size pixel_size x 1 or 1 x pixel_size, depending on position, and of color color.

Parameters
 calculus the discrete exterior calculus containing the 1-form v. v any dual 1-form defined in calculus. [in,out] image the image where v is written. color the color for displaying 1-forms below 0.25. cut_low every value of u below is set to cut_low. cut_up every value of u above is set to cut_up. pixel_size every value of a 1-form is mapped into image as pixel_size x 1 pixels or 1 x pixel_size pixels.
Template Parameters
 Calculus any discrete exterior calculus type. Image any image type (see concepts::CImage).

Definition at line 656 of file DECImageHelpers.h.

References dualForm1ToImage().

661  {
662  BOOST_CONCEPT_ASSERT(( concepts::CImage<Image> ));
663  // Threshold is 0.25 instead of 0.5 because an edge connecting
664  // two vertices with v=0 and v=1 should not belong to the
665  // discontinuity set.
666  dualForm1ToImage( calculus, v, image,
667  [color] ( double x ) { return color; },
668  [] ( double x ) { return x < 0.25; },
669  cut_low, cut_up, pixel_size );
670  }
void dualForm1ToImage(const Calculus &calculus, const typename Calculus::DualForm1 &v, Image &image, const Function &functor, const Predicate &predicate, double cut_low=0.0, double cut_up=1.0, int pixel_size=1)
template<typename Calculus , typename Form1 , typename Image , typename Function , typename Predicate >
 void DGtal::functions::dec::form1ToImage ( const Calculus & calculus, const Form1 & v, bool primal, Image & image, const Function & functor, const Predicate & predicate, double cut_low = 0.0, double cut_up = 1.0, int pixel_size = 1 )

Displays the primal or dual 1-form v in the given image. Scalar values of v are first cut up and low according to cut_low and cut_up, and then rescaled according to max and min value. Then these values are transformed to image values with the function functor. They are written in the image as "lines" of size pixel_size x 1 or 1 x pixel_size, depending on position and duality.

Parameters
 calculus the discrete exterior calculus containing the 1-form v. v any primal 1-form defined in calculus if primal is true, otherwise a dual 1-form. primal tells if v is a primal 1-form (true), or a dual 1-form (false). [in,out] image the image where v is written. functor the function transforming scalar values to image values. predicate the predicate telling for a value if it must be displayed (returns true in this case). cut_low every value of u below is set to cut_low. cut_up every value of u above is set to cut_up. pixel_size every value of a 1-form is mapped into image as pixel_size x 1 pixels or 1 x pixel_size pixels.
Template Parameters
 Calculus any discrete exterior calculus type. Form1 either a primal 1-form if primal is true, or dual 1-form is primal is false. Image any image type (see concepts::CImage). Function any function type (double) -> typename Image::Value to convert form value to Image value. Predicate any function type (double) -> bool to select 1-forms to display.

Definition at line 298 of file DECImageHelpers.h.

Referenced by dualForm1ToImage(), and primalForm1ToImage().

304  {
305  BOOST_CONCEPT_ASSERT(( concepts::CImage<Image> ));
306  typedef typename Calculus::Index Index;
307  typedef typename Calculus::SCell SCell;
308  typedef typename Calculus::Scalar Scalar;
309  typedef typename Calculus::KSpace KSpace;
310  typedef typename KSpace::Point Point;
311  typedef typename KSpace::Integer Integer;
312  double min_v = NumberTraits<Scalar>::castToDouble( v.myContainer[ 0 ] );
313  double max_v = min_v;
314  for ( Index index = 0; index < v.myContainer.rows(); index++)
315  {
316  double w = NumberTraits<Scalar>::castToDouble( v.myContainer[ index ] );
317  min_v = std::min( min_v, w );
318  max_v = std::max( max_v, w );
319  }
320  if ( min_v < cut_low ) min_v = cut_low;
321  if ( max_v > cut_up ) max_v = cut_up;
322  for ( Index index = 0; index < v.myContainer.rows(); index++)
323  {
324  SCell cell = v.getSCell( index );
325  double u = NumberTraits<Scalar>::castToDouble( v.myContainer[ index ] );
326  if ( ! predicate( u ) ) continue;
327  double w = std::min( cut_up, std::max( cut_low, u ) );
328  if ( min_v != max_v ) w = ( w - min_v ) / ( max_v - min_v );
329  Point kpt = calculus.myKSpace.sKCoords( cell );
330  if ( primal ) writePrimalLinel( image, kpt, functor( w ), pixel_size );
331  else writeDualLinel ( image, kpt, functor( w ), pixel_size );
332  }
333  }
DGtal::int32_t Integer
LinearAlgebraBackend::DenseVector::Scalar Scalar
const Point & sKCoords(const SCell &c) const
void writeDualLinel(Image &image, typename Image::Point pt, typename Image::Value val, int pixel_size=1)
void writePrimalLinel(Image &image, typename Image::Point pt, typename Image::Value val, int pixel_size=1)
typename Self::Point Point
LinearAlgebraBackend::DenseVector::Index Index
template<typename Calculus , typename AnyForm2 , typename Image >
 void DGtal::functions::dec::form2ToGreyLevelImage ( const Calculus & calculus, const AnyForm2 & u, Image & image, double cut_low = 0.0, double cut_up = 1.0, int pixel_size = 1 )

Standard method to output a 2-form into a grey-level image.

Displays the 2-form u in the given image. Scalar values of u are first cut up and low according to cut_low and cut_up, and then rescaled according to max and min value. They are written in the image as grey-level "pixels" of size pixel_size x pixel_size.

Parameters
 calculus the discrete exterior calculus containing the 2-form u. u any primal or dual 2-form defined in calculus. [in,out] image the image where u is written. cut_low every value of u below is set to cut_low. cut_up every value of u above is set to cut_up. pixel_size every value of a 2-form is mapped into image as pixel_size x pixel_size pixels.
Template Parameters
 Calculus any discrete exterior calculus type. AnyForm2 either a primal 2-form type or a dual 2-form type of the given Calculus. Image any image type (see concepts::CImage).

Definition at line 506 of file DECImageHelpers.h.

References form2ToImage().

511  {
512  BOOST_CONCEPT_ASSERT(( concepts::CImage<Image> ));
513  form2ToImage( calculus, u, image,
514  [] ( double x ) { return (unsigned char) ( round( x * 255.0 ) ); },
515  cut_low, cut_up, pixel_size );
516  }
void form2ToImage(const Calculus &calculus, const AnyForm2 &u, Image &image, const Function &functor, double cut_low=0.0, double cut_up=1.0, int pixel_size=1)
template<typename Calculus , typename AnyForm2 , typename Image , typename Function >
 void DGtal::functions::dec::form2ToImage ( const Calculus & calculus, const AnyForm2 & u, Image & image, const Function & functor, double cut_low = 0.0, double cut_up = 1.0, int pixel_size = 1 )

Displays the 2-form u in the given image. Scalar values of u are first cut up and low according to cut_low and cut_up, and then rescaled according to max and min value. Then these values are transformed to image values with the function functor. They are written in the image as "pixels" of size pixel_size x pixel_size.

Parameters
 calculus the discrete exterior calculus containing the 2-form u. u any primal or dual 2-form defined in calculus. [in,out] image the image where u is written. functor the function transforming scalar values to image values. cut_low every value of u below is set to cut_low. cut_up every value of u above is set to cut_up. pixel_size every value of a 2-form is mapped into image as pixel_size x pixel_size pixels.
Template Parameters
 Calculus any discrete exterior calculus type. AnyForm2 either a primal 2-form type or a dual 2-form type of the given Calculus. Image any image type (see concepts::CImage). Function any function type (double) -> typename Image::Value to convert form value to Image value.

Definition at line 238 of file DECImageHelpers.h.

Referenced by form2ToGreyLevelImage().

243  {
244  BOOST_CONCEPT_ASSERT(( concepts::CImage<Image> ));
245  typedef typename Calculus::Index Index;
246  typedef typename Calculus::SCell SCell;
247  typedef typename Calculus::Scalar Scalar;
248  typedef typename Calculus::KSpace KSpace;
249  typedef typename KSpace::Point Point;
250  typedef typename KSpace::Integer Integer;
251  double min_u = NumberTraits<Scalar>::castToDouble( u.myContainer[ 0 ] );
252  double max_u = min_u;
253  for ( Index index = 0; index < u.myContainer.rows(); index++)
254  {
255  double v = NumberTraits<Scalar>::castToDouble( u.myContainer[ index ] );
256  min_u = std::min( min_u, v );
257  max_u = std::max( max_u, v );
258  }
259  if ( min_u < cut_low ) min_u = cut_low;
260  if ( max_u > cut_up ) max_u = cut_up;
261  for ( Index index = 0; index < u.myContainer.rows(); index++)
262  {
263  SCell cell = u.getSCell( index );
264  double v = NumberTraits<Scalar>::castToDouble( u.myContainer[ index ] );
265  double w = std::min( cut_up, std::max( cut_low, v ) );
266  if ( min_u != max_u ) w = ( w - min_u ) / ( max_u - min_u );
267  writePixel( image, calculus.myKSpace.sCoords( cell ), functor( w ), pixel_size );
268  }
269  }
DGtal::int32_t Integer
LinearAlgebraBackend::DenseVector::Scalar Scalar
void writePixel(Image &image, typename Image::Point pt, typename Image::Value val, int pixel_size=1)
Point sCoords(const SCell &c) const
typename Self::Point Point
LinearAlgebraBackend::DenseVector::Index Index
template<typename Calculus , typename Image >
 void DGtal::functions::dec::primalForm1ToGreyLevelImage ( const Calculus & calculus, const typename Calculus::PrimalForm1 & v, Image & image, double cut_low = 0.0, double cut_up = 1.0, int pixel_size = 1 )

Standard method to output a primal 1-form into a grey-level image.

Displays the primal 1-form v in the given image. Scalar values of v are first cut up and low according to cut_low and cut_up, and then rescaled according to max and min value. If this value is belows 0.25, it is written in the image as a "line" of size pixel_size x 1 or 1 x pixel_size, depending on position.

Parameters
 calculus the discrete exterior calculus containing the 1-form v. v any primal 1-form defined in calculus. [in,out] image the image where v is written. cut_low every value of u below is set to cut_low. cut_up every value of u above is set to cut_up. pixel_size every value of a 1-form is mapped into image as pixel_size x 1 pixels or 1 x pixel_size pixels.
Template Parameters
 Calculus any discrete exterior calculus type. Image any image type (see concepts::CImage).

Definition at line 540 of file DECImageHelpers.h.

References primalForm1ToImage().

545  {
546  BOOST_CONCEPT_ASSERT(( concepts::CImage<Image> ));
547  // Threshold is 0.25 instead of 0.5 because an edge connecting
548  // two vertices with v=0 and v=1 should not belong to the
549  // discontinuity set.
550  primalForm1ToImage( calculus, v, image,
551  [] ( double x ) { return (unsigned char) ( round( x * 255.0 ) ); },
552  [] ( double x ) { return x < 0.25; },
553  cut_low, cut_up, pixel_size );
554  }
void primalForm1ToImage(const Calculus &calculus, const typename Calculus::PrimalForm1 &v, Image &image, const Function &functor, const Predicate &predicate, double cut_low=0.0, double cut_up=1.0, int pixel_size=1)
template<typename Calculus , typename Image , typename Function , typename Predicate >
 void DGtal::functions::dec::primalForm1ToImage ( const Calculus & calculus, const typename Calculus::PrimalForm1 & v, Image & image, const Function & functor, const Predicate & predicate, double cut_low = 0.0, double cut_up = 1.0, int pixel_size = 1 )

Displays the primal 1-form v in the given image. Scalar values of v are first cut up and low according to cut_low and cut_up, and then rescaled according to max and min value. Then these values are transformed to image values with the function functor. They are written in the image as "lines" of size pixel_size x 1 or 1 x pixel_size, depending on position and duality.

Parameters
 calculus the discrete exterior calculus containing the 1-form v. v any primal 1-form defined in calculus. [in,out] image the image where v is written. functor the function transforming scalar values to image values. predicate the predicate telling for a value if it must be displayed (returns true in this case). cut_low every value of u below is set to cut_low. cut_up every value of u above is set to cut_up. pixel_size every value of a 1-form is mapped into image as pixel_size x 1 pixels or 1 x pixel_size pixels.
Template Parameters
 Calculus any discrete exterior calculus type. Image any image type (see concepts::CImage). Function any function type (double) -> typename Image::Value to convert form value to Image value. Predicate any function type (double) -> bool to select 1-forms to display.

Definition at line 397 of file DECImageHelpers.h.

References form1ToImage().

Referenced by primalForm1ToGreyLevelImage(), and primalForm1ToRGBColorImage().

403  {
404  BOOST_CONCEPT_ASSERT(( concepts::CImage<Image> ));
405  form1ToImage( calculus, v, true, image, functor, predicate,
406  cut_low, cut_up, pixel_size );
407  }
void form1ToImage(const Calculus &calculus, const Form1 &v, bool primal, Image &image, const Function &functor, const Predicate &predicate, double cut_low=0.0, double cut_up=1.0, int pixel_size=1)
template<typename Calculus , typename Image >
 void DGtal::functions::dec::primalForm1ToRGBColorImage ( const Calculus & calculus, const typename Calculus::PrimalForm1 & v, Image & image, Color color, double cut_low = 0.0, double cut_up = 1.0, int pixel_size = 1 )

Standard method to output a primal 1-form into a color image.

Displays the primal 1-form v in the given image. Scalar values of v are first cut up and low according to cut_low and cut_up, and then rescaled according to max and min value. If this value is belows 0.25, it is written in the image as a "line" of size pixel_size x 1 or 1 x pixel_size, depending on position, and of color color.

Parameters
 calculus the discrete exterior calculus containing the 1-form v. v any primal 1-form defined in calculus. [in,out] image the image where v is written. color the color for displaying 1-forms below 0.25. cut_low every value of u below is set to cut_low. cut_up every value of u above is set to cut_up. pixel_size every value of a 1-form is mapped into image as pixel_size x 1 pixels or 1 x pixel_size pixels.
Template Parameters
 Calculus any discrete exterior calculus type. Image any image type (see concepts::CImage).

Definition at line 617 of file DECImageHelpers.h.

References primalForm1ToImage().

622  {
623  BOOST_CONCEPT_ASSERT(( concepts::CImage<Image> ));
624  // Threshold is 0.25 instead of 0.5 because an edge connecting
625  // two vertices with v=0 and v=1 should not belong to the
626  // discontinuity set.
627  primalForm1ToImage( calculus, v, image,
628  [color] ( double x ) { return color; },
629  [] ( double x ) { return x < 0.25; },
630  cut_low, cut_up, pixel_size );
631  }
void primalForm1ToImage(const Calculus &calculus, const typename Calculus::PrimalForm1 &v, Image &image, const Function &functor, const Predicate &predicate, double cut_low=0.0, double cut_up=1.0, int pixel_size=1)
template<typename Calculus , DGtal::Dimension dim, DGtal::Duality duality>
 DGtal::LinearOperator DGtal::functions::dec::squaredDiagonal ( const DGtal::KForm< Calculus, dim, duality > & kform )

Builds a diagonal linear operator from a k-form and squares it. These operators arise naturally when differentiating with respect to another variable (e.g. d/dx (vx)^t (vx) = diag(v^2) x).

Parameters
 [in] kform any kform v
Returns
the corresponding linear operator diag(v^2)
Template Parameters
 Calculus any discrete exterior calculus. dim the dimension of the form. duality either PRIMAL for a primal form or DUAL for a dual form.

Definition at line 118 of file DECImageHelpers.h.

References diagonal(), and squares().

119  {
120  auto v2 = kform;
121  squares( v2 );
122  return diagonal( v2 );
123  }
DGtal::LinearOperator< Calculus, dim, duality, dim, duality > diagonal(const DGtal::KForm< Calculus, dim, duality > &kform)
void squares(DGtal::KForm< Calculus, dim, duality > &kform)
template<typename Calculus , DGtal::Dimension dim, DGtal::Duality duality>
 void DGtal::functions::dec::squares ( DGtal::KForm< Calculus, dim, duality > & kform )

Squares the given k-form.

Parameters
 [in,out] kform any kform.
Template Parameters
 Calculus any discrete exterior calculus. dim the dimension of the form. duality either PRIMAL for a primal form or DUAL for a dual form.

Definition at line 99 of file DECImageHelpers.h.

Referenced by squaredDiagonal().

100  {
101  kform.myContainer.array() = kform.myContainer.array().square();
102  }
Container myContainer
template<typename Calculus , typename AnyForm2 , typename Image , typename Function >
 void DGtal::functions::dec::threeForms2ToImage ( const Calculus & calculus, const AnyForm2 & u0, const AnyForm2 & u1, const AnyForm2 & u2, Image & image, const Function & functor, double cut_low = 0.0, double cut_up = 1.0, int pixel_size = 1 )

Displays the three 2-forms u0, u1, u2 in the given image. Scalar values of u0, u1, u2 are first cut up and low according to cut_low and cut_up, and then rescaled according to max and min value. Then these values are transformed to image values with the function functor. They are written in the image as "pixels" of size pixel_size x pixel_size.

Parameters
 calculus the discrete exterior calculus containing the 2-forms u0, u1, u2. u0 any primal or dual 2-form defined in calculus. u1 any primal or dual 2-form defined in calculus. u2 any primal or dual 2-form defined in calculus. [in,out] image the image where u is written. functor the function transforming three scalar values to image values. cut_low every value of u0, u1, u2 below is set to cut_low. cut_up every value of u0, u1, u2 above is set to cut_up. pixel_size every value of 2-forms is mapped into image as pixel_size x pixel_size pixels.
Template Parameters
 Calculus any discrete exterior calculus type. AnyForm2 either a primal 2-form type or a dual 2-form type of the given Calculus. Image any image type (see concepts::CImage). Function any function type (double,double,double) -> typename Image::Value to convert form value to Image value.

Definition at line 434 of file DECImageHelpers.h.

Referenced by threeForms2ToRGBColorImage().

441  {
442  BOOST_CONCEPT_ASSERT(( concepts::CImage<Image> ));
443  typedef typename Calculus::Index Index;
444  typedef typename Calculus::SCell SCell;
445  typedef typename Calculus::Scalar Scalar;
446  double min_u = NumberTraits<Scalar>::castToDouble( u0.myContainer[ 0 ] );
447  double max_u = min_u;
448  for ( Index index = 0; index < u0.myContainer.rows(); index++)
449  {
450  double v = NumberTraits<Scalar>::castToDouble( u0.myContainer[ index ] );
451  min_u = std::min( min_u, v );
452  max_u = std::max( max_u, v );
453  }
454  for ( Index index = 0; index < u1.myContainer.rows(); index++)
455  {
456  double v = NumberTraits<Scalar>::castToDouble( u1.myContainer[ index ] );
457  min_u = std::min( min_u, v );
458  max_u = std::max( max_u, v );
459  }
460  for ( Index index = 0; index < u2.myContainer.rows(); index++)
461  {
462  double v = NumberTraits<Scalar>::castToDouble( u2.myContainer[ index ] );
463  min_u = std::min( min_u, v );
464  max_u = std::max( max_u, v );
465  }
466  if ( min_u < cut_low ) min_u = cut_low;
467  if ( max_u > cut_up ) max_u = cut_up;
468  for ( Index index = 0; index < u0.myContainer.rows(); index++)
469  {
470  SCell cell = u0.getSCell( index );
471  double v0 = NumberTraits<Scalar>::castToDouble( u0.myContainer[ index ] );
472  double w0 = std::min( cut_up, std::max( cut_low, v0 ) );
473  if ( min_u != max_u ) w0 = ( w0 - min_u ) / ( max_u - min_u );
474  double v1 = NumberTraits<Scalar>::castToDouble( u1.myContainer[ index ] );
475  double w1 = std::min( cut_up, std::max( cut_low, v1 ) );
476  if ( min_u != max_u ) w1 = ( w1 - min_u ) / ( max_u - min_u );
477  double v2 = NumberTraits<Scalar>::castToDouble( u2.myContainer[ index ] );
478  double w2 = std::min( cut_up, std::max( cut_low, v2 ) );
479  if ( min_u != max_u ) w2 = ( w2 - min_u ) / ( max_u - min_u );
480  writePixel( image, calculus.myKSpace.sCoords( cell ), functor( w0, w1, w2 ), pixel_size );
481  }
482  }
LinearAlgebraBackend::DenseVector::Scalar Scalar
void writePixel(Image &image, typename Image::Point pt, typename Image::Value val, int pixel_size=1)
Point sCoords(const SCell &c) const
LinearAlgebraBackend::DenseVector::Index Index
template<typename Calculus , typename AnyForm2 , typename Image >
 void DGtal::functions::dec::threeForms2ToRGBColorImage ( const Calculus & calculus, const AnyForm2 & u0, const AnyForm2 & u1, const AnyForm2 & u2, Image & image, double cut_low = 0.0, double cut_up = 1.0, int pixel_size = 1 )

Standard method to output three 2-forms into a RGB Color image.

Displays the three 2-forms u0, u1, u2 in the given image as RGB colors. Scalar values of u0, u1, u2 are first cut up and low according to cut_low and cut_up, and then rescaled according to max and min value. Then these values are transformed to RGB color image values (u0 defines the intensity of the red channel, u1 the green channel, u2, the blue channel). They are written in the image as "pixels" of size pixel_size x pixel_size.

Parameters
 calculus the discrete exterior calculus containing the 2-forms u0, u1, u2. u0 any primal or dual 2-form defined in calculus. u1 any primal or dual 2-form defined in calculus. u2 any primal or dual 2-form defined in calculus. [in,out] image the image where u is written. cut_low every value of u0, u1, u2 below is set to cut_low. cut_up every value of u0, u1, u2 above is set to cut_up. pixel_size every value of 2-forms is mapped into image as pixel_size x pixel_size pixels.
Template Parameters
 Calculus any discrete exterior calculus type. AnyForm2 either a primal 2-form type or a dual 2-form type of the given Calculus. Image any image type (see concepts::CImage).

Definition at line 699 of file DECImageHelpers.h.

References threeForms2ToImage().

706  {
707  BOOST_CONCEPT_ASSERT(( concepts::CImage<Image> ));
709  ( calculus, u0, u1, u2, image,
710  [] ( double r, double g, double b )
711  { return Color( (unsigned char) ( round( r * 255.0 ) ),
712  (unsigned char) ( round( g * 255.0 ) ),
713  (unsigned char) ( round( b * 255.0 ) ) ); },
714  cut_low, cut_up, pixel_size );
715  }
void threeForms2ToImage(const Calculus &calculus, const AnyForm2 &u0, const AnyForm2 &u1, const AnyForm2 &u2, Image &image, const Function &functor, double cut_low=0.0, double cut_up=1.0, int pixel_size=1)
template<typename Image >
 void DGtal::functions::dec::writeDualLinel ( Image & image, typename Image::Point pt, typename Image::Value val, int pixel_size = 1 )

Considers an image image to have pixels of size pixel_size x pixel_size, and writes the value val at the specified linel position pt.

Parameters
 [in,out] image any image of sufficient size. pt a linel Khalimsky coordinates. val the value to write in pixel_size x 1 pixels (if horizontal) or 1 x pixel_size pixels (if vertical). pixel_size the chosen pixel_size (when 1, this is the normal setValue of an image).
Template Parameters
 Image any image type (see concepts::CImage).

Definition at line 197 of file DECImageHelpers.h.

Referenced by form1ToImage().

199  {
200  BOOST_CONCEPT_ASSERT(( concepts::CImage<Image> ));
201  typedef typename Image::Point Point;
202  typedef typename Point::Coordinate Coordinate;
203  int pixel_size_x = NumberTraits<Coordinate>::even( pt[ 0 ] ) ? 0 : pixel_size-1;
204  int pixel_size_y = NumberTraits<Coordinate>::even( pt[ 1 ] ) ? 0 : pixel_size-1;
205  pt /= 2;
206  pt *= pixel_size;
207  for ( int y = pixel_size_y; y < pixel_size; y++ )
208  for ( int x = pixel_size_x; x < pixel_size; x++ )
209  {
210  Point q( (Coordinate) x, (Coordinate) y );
211  image.setValue( pt + q, val );
212  }
213  }
typename Self::Point Point
void setValue(const Point &aPoint, const Value &aValue)
template<typename Image >
 void DGtal::functions::dec::writePixel ( Image & image, typename Image::Point pt, typename Image::Value val, int pixel_size = 1 )

Considers an image image to have pixels of size pixel_size x pixel_size, and writes the value val at the specified pixel position pt.

Parameters
 [in,out] image any image of sufficient size. pt a pixel coordinate (which is multiplied by pixel_size within). val the value to write in pixel_size x pixel_size pixels. pixel_size the chosen pixel_size (when 1, this is the normal setValue of an image).
Template Parameters
 Image any image type (see concepts::CImage).

Definition at line 138 of file DECImageHelpers.h.

References DGtal::Image< class >::setValue().

Referenced by form2ToImage(), and threeForms2ToImage().

140  {
141  BOOST_CONCEPT_ASSERT(( concepts::CImage<Image> ));
142  typedef typename Image::Point Point;
143  typedef typename Point::Coordinate Coordinate;
144  pt *= pixel_size;
145  for ( int y = 0; y < pixel_size; y++ )
146  for ( int x = 0; x < pixel_size; x++ )
147  {
148  Point q( (Coordinate) x, (Coordinate) y );
149  image.setValue( pt + q, val );
150  }
151  }
typename Self::Point Point
void setValue(const Point &aPoint, const Value &aValue)
template<typename Image >
 void DGtal::functions::dec::writePrimalLinel ( Image & image, typename Image::Point pt, typename Image::Value val, int pixel_size = 1 )

Considers an image image to have pixels of size pixel_size x pixel_size, and writes the value val at the specified linel position pt.

Parameters
 [in,out] image any image of sufficient size. pt a linel Khalimsky coordinates. val the value to write in pixel_size x 1 pixels (if horizontal) or 1 x pixel_size pixels (if vertical). pixel_size the chosen pixel_size (when 1, this is the normal setValue of an image).
Template Parameters
 Image any image type (see concepts::CImage).

Definition at line 166 of file DECImageHelpers.h.

Referenced by form1ToImage().

168  {
169  BOOST_CONCEPT_ASSERT(( concepts::CImage<Image> ));
170  typedef typename Image::Point Point;
171  typedef typename Point::Coordinate Coordinate;
172  int pixel_size_x = NumberTraits<Coordinate>::even( pt[ 0 ] ) ? 1 : pixel_size;
173  int pixel_size_y = NumberTraits<Coordinate>::even( pt[ 1 ] ) ? 1 : pixel_size;
174  pt /= 2;
175  pt *= pixel_size;
176  for ( int y = 0; y < pixel_size_y; y++ )
177  for ( int x = 0; x < pixel_size_x; x++ )
178  {
179  Point q( (Coordinate) x, (Coordinate) y );
180  image.setValue( pt + q, val );
181  }
182  }
typename Self::Point Point
void setValue(const Point &aPoint, const Value &aValue)