discretize.utils.extend_surface_boundary

discretize.utils.extend_surface_boundary(xyz, max_miter=5.0)

Extend a triangulated surface outward from every node on its boundary.

A new point is added for every node along the boundary of the triangulation (not just the convex hull). Each new point starts at the same location as the node it comes from, and is offset horizontally along the outward bisector of the boundary edges adjacent to that node. The new points are triangulated with the original ones once, so extending the surface by a distance d (a nearest neighbor extrapolation of the surface) is just a scaling of the returned directions.

Parameters:

xyz(n_points, dim) array_like or tuple

Surface points, where dim is 2 or 3. The last column is the vertical coordinate. A point cloud is triangulated (Delaunay) along the horizontal dimensions (in 2D it is sorted along x and connected as a line). Alternatively supply your own connectivity as a tuple of (xyz, simplices), where simplices are line segments (2D) or triangles (3D) indexing xyz.

max_miterfloat, optional

Maximum length of the offset direction, which limits how far the extension of very sharp boundary corners can reach.

Returns:

xyz_ext(n_points + n_new, dim) numpy.ndarray

The original (sorted, in 2D) points followed by the new points, which have the vertical coordinate of the node they extend.

simplices_ext(n_simplices + n_new_simplices, dim) numpy.ndarray

The simplices connecting the original and new points.

directions(n_points + n_new, dim - 1) numpy.ndarray

Horizontal offset directions, which are zero for the original points. The extended surface for a distance d (a scalar, or one value per horizontal dimension) is xyz_ext[:, :-1] + d * directions. The directions are scaled such that boundary edges move out by a perpendicular distance d.

Raises:

ValueError

If xyz has 2 columns and all of its points have the same x location.

Notes

For surfaces with a non-convex boundary, the outward bisectors of different boundary nodes can intersect if the distance is large compared to the size of local features of the boundary (e.g. notches or concavities). The extended surface can then fold over itself and be unreliable.

Examples

>>> import numpy as np
>>> from discretize.utils import extend_surface_boundary
>>> x, y = np.mgrid[0:1:3j, 0:1:3j]
>>> xyz = np.stack([x, y, x + y], axis=-1).reshape(-1, 3)
>>> xyz_ext, simps, dirs = extend_surface_boundary(xyz)
>>> padded = xyz_ext[:, :-1] + 0.1 * dirs
>>> padded.shape
(17, 2)