.. _filters.normal:

filters.normal
===============================================================================

The **normal filter** returns the estimated normal and curvature for
a collection
of points. The algorithm first computes the eigenvalues and eigenvectors of the
collection of points, which is comprised of the k-nearest neighbors. The normal
is taken as the eigenvector corresponding to the smallest eigenvalue. The
curvature is computed as

.. math::

  curvature = \frac{\lambda_0}{\lambda_0 + \lambda_1 + \lambda_2}

where :math:`\lambda_i` are the eigenvalues sorted in ascending order.

The filter produces four new dimensions (``NormalX``, ``NormalY``, ``NormalZ``,
and ``Curvature``), which can be analyzed directly, or consumed by downstream
stages for more advanced filtering.

The eigenvalue decomposition is performed using Eigen's
`SelfAdjointEigenSolver <https://eigen.tuxfamily.org/dox/classEigen_1_1SelfAdjointEigenSolver.html>`_.

Normals will be automatically flipped towards positive Z, unless the always_up_
flag is set to `false`. Users can optionally set any of the XYZ coordinates to
specify a custom viewpoint_ or set them all to zero to effectively disable the
normal flipping.

.. note::

  By default, the Normal filter will invert normals such that they are always
  pointed "up" (positive Z). If the user provides a viewpoint_, normals will
  instead be inverted such that they are oriented towards the viewpoint,
  regardless of the always_up_ flag. To disable all normal flipping, do not
  provide a viewpoint_ and set `always_up`_ to false.

In addition to always_up_ and viewpoint_, users can run a refinement step (on
by default) that propagates normals using a minimum spanning tree. The
propagated normals can lead to much more consistent results across the dataset.

.. note::

  To disable normal propagation, users can set refine_ to `false`.

.. embed::

Example
-------

This pipeline demonstrates the calculation of the normal values (along with
curvature). The newly created dimensions are written out to BPF for further
inspection.

.. code-block:: json

  [
      "input.las",
      {
          "type":"filters.normal",
          "knn":8
      },
      {
          "type":"writers.bpf",
          "filename":"output.bpf",
          "output_dims":"X,Y,Z,NormalX,NormalY,NormalZ,Curvature"
      }
  ]

Options
-------------------------------------------------------------------------------

_`knn`
  The number of k-nearest neighbors. [Default: 8]

_`viewpoint`
  A single WKT or GeoJSON 3D point. Normals will be inverted such that they are
  all oriented towards the viewpoint.

_`always_up`
  A flag indicating whether or not normals should be inverted only when the Z
  component is negative. [Default: true]

_`refine`
  A flag indicating whether or not to reorient normals using minimum spanning
  tree propagation. [Default: true]
