points

The points module defines the Points base class, which bundles point coordinates, point weights, a local triangulation and a hull triangulation. The module provides several different implementations such as TensorPoints and SimplexGaussPoints that reflect the variety of elements in the nutils.element module.

class nutils.points.Points(npoints, ndims)

Bases: nutils.types.Singleton

Collection of points on an element.

The Points base class bundles point coordinates, point weights, a local triangulation and hull triangulation. Of these only the coordinates are mandatory, and should be provided by the derived class in the form of the coords attribute. Of the remaining properties only hull() has a functional base implementation that relies on the availability of tri.

coords

Coordinates of the points as a float array.

weights

Weights of the points as a float array.

Parameters
  • npoints (int) – Number of discrete points.

  • ndims (int) – Number of spatial dimensions.

tri

Triangulation of interior.

A two-dimensional integer array with ndims+1 columns, of which every row defines a simplex by mapping vertices into the list of points.

hull

Triangulation of the exterior hull.

A two-dimensional integer array with ndims columns, of which every row defines a simplex by mapping vertices into the list of points.

onhull

Boolean mask marking boundary points.

The array of length npoints is True where the corresponding point is part of the hull, and False where it is not.

__weakref__

list of weak references to the object (if defined)

class nutils.points.CoordsPoints(coords)

Bases: nutils.points.Points

Manually supplied points.

class nutils.points.CoordsWeightsPoints(coords, weights)

Bases: nutils.points.CoordsPoints

Manually supplied points and weights.

class nutils.points.CoordsUniformPoints(coords, volume)

Bases: nutils.points.CoordsPoints

Manually supplied points with uniform weights.

class nutils.points.TensorPoints(points1, points2)

Bases: nutils.points.Points

Tensor product of two Points instances.

class nutils.points.SimplexGaussPoints(ndims, degree)

Bases: nutils.points.CoordsWeightsPoints

Gauss quadrature points on a simplex.

class nutils.points.SimplexBezierPoints(ndims, n)

Bases: nutils.points.CoordsPoints

Bezier points on a simplex.

class nutils.points.TransformPoints(points, trans)

Bases: nutils.points.Points

Affinely transformed Points.

class nutils.points.ConcatPoints(allpoints, duplicates=frozenset())

Bases: nutils.points.Points

Concatenation of several Points objects.

An optional duplicates argument lists all points that are equal, triggering deduplication and resulting in a smaller total point count.

class nutils.points.ConePoints(edgepoints, edgeref, tip)

Bases: nutils.points.Points

Affinely transformed lower-dimensional points plus tip.

The point count is incremented by one regardless of the nature of the point set; no effort is made to introduce extra points between base plane and tip. Likewise, the simplex count stays equal, with all simplices obtaining an extra vertex in tip.

nutils.points.gauss1(degree)

Gauss quadrature for line.

nutils.points.gauss2

Gauss quadrature for triangle.

Reference: http://www.cs.rpi.edu/~flaherje/pdf/fea6.pdf

nutils.points.gauss3

Gauss quadrature for tetrahedron.

Reference http://www.cs.rpi.edu/~flaherje/pdf/fea6.pdf