CGAL 4.7 - Point Set Processing: VCMTraits Concept Reference

\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)

CGAL 4.7 - Point Set Processing

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VCMTraits Concept Reference
Concepts

## Definition

Concept providing functions to extract eigenvectors and eigenvalue from covariance matrices represented by an array `a` as follows:

\( \begin{bmatrix} a[0] & a[1] & a[2] \\ a[1] & a[3] & a[4] \\ a[2] & a[4] & a[5] \\ \end{bmatrix}\)

Has Models:
  `CGAL::Eigen_vcm_traits`

## Static Public Member Functions

static bool | diagonalize_selfadjoint_covariance_matrix (const cpp11::array< double, 6 > &cov, cpp11::array< double, 3 > &eigenvalues)
| fill `eigenvalues` with the eigenvalues of the covariance matrix represented by `cov`. More...
static bool | extract_largest_eigenvector_of_covariance_matrix (const cpp11::array< double, 6 > &cov, cpp11::array< double, 3 > &normal)
| Extract the eigenvector associated to the largest eigenvalue of the covariance matrix represented by `cov`. More...

## Member Function Documentation

static bool VCMTraits::diagonalize_selfadjoint_covariance_matrix | ( | const cpp11::array< double, 6 > & | cov,
|  | cpp11::array< double, 3 > & | eigenvalues
| ) |  |

static

fill `eigenvalues` with the eigenvalues of the covariance matrix represented by `cov`.

Eigenvalues are sorted by increasing order.

Returns
  `true` if the operation was successful and `false` otherwise.

static bool VCMTraits::extract_largest_eigenvector_of_covariance_matrix | ( | const cpp11::array< double, 6 > & | cov,
|  | cpp11::array< double, 3 > & | normal
| ) |  |

static

Extract the eigenvector associated to the largest eigenvalue of the covariance matrix represented by `cov`.

Returns
  `true` if the operation was successful and `false` otherwise.