Example 1 - Triangulation of arbitrary points

stripy provides a python interfact to TRIPACK and SRFPACK (Renka 1997c,d) as a triangulation class that would typically be used as follows:

import stripy
triangulation = stripy.Triangulation(x=vertices_x, y=vertices_y)
areas = triangulation.areas()

The methods of the Triangulation class include interpolation, smoothing and gradients (from SRFPACK), triangle areas, point location by simplex and nearest vertex, refinement operations by edge or centroid, and neighbourhood search / distance computations through a k-d tree algorithm suited to points on the surface of a unit sphere. stripy also includes template triangulated meshes with refinement operations.

In this notebook we introduce the Triangulation class itself.


  1. Renka, R. J. (1997), Algorithm 772: STRIPACK: Delaunay triangulation and Voronoi diagram on the surface of a sphere, ACM Transactions on Mathematical Software (TOMS).

  2. Renka, R. J. (1997), Algorithm 773: SSRFPACK: interpolation of scattered data on the surface of a sphere with a surface under tension, ACM Transactions on Mathematical Software (TOMS), 23(3), 435–442, doi:10.1145/275323.275330.

  3. Renka, R. J. (1996), Algorithm 751; TRIPACK: a constrained two-dimensional Delaunay triangulation package, ACM Transactions on Mathematical Software, 22(1), 1–8, doi:10.1145/225545.225546.

  4. Renka, R. J. (1996), Algorithm 752; SRFPACK: software for scattered data fitting with a constrained surface under tension, ACM Transactions on Mathematical Software, 22(1), 9–17, doi:10.1145/225545.225547.

The next example is Ex2-SphericalGrids

Triangulate the vertices of a square mesh

import stripy as stripy
import numpy as np

# Vertices of a square mesh

vertices_xy = np.array([[0.0,   0.0],
                        [1.0,   0.0],
                        [0.0,   1.0],
                        [1.0,   1.0]])

vertices_x = vertices_xy.T[0]
vertices_y = vertices_xy.T[1]

triangulation = stripy.Triangulation(x=vertices_x, y=vertices_y, permute=False)

This creates a triangulation object constructed using the wrapped fortran code of Renka (1997). The triangulation object has a number of useful methods and attached data which can be listed with

refined_triangulation = stripy.Triangulation(x=vertices_x, y=vertices_y, refinement_levels=4, permute=False)


Making a plot of the triangulation

We can make a plot of the two grids and the most straightforward way to display the information is through a standard map projection of the sphere to the plane.

(Here we superimpose the points on a global map of coastlines using the cartopy map library and use the Mollweide projection. Other projections to try include Robinson, Orthographic, PlateCarree)

%matplotlib inline

import matplotlib.pyplot as plt

fig, (ax1, ax2) = plt.subplots(1,2, figsize=(20, 10), facecolor="none", sharey=True)

## Plot the vertices and the edges for the original mesh
x = triangulation.x
y = triangulation.y
simplices = triangulation.simplices

ax1.triplot(x, y, simplices, linewidth=0.5, color='black')
ax1.scatter(x, y, color='Red', alpha=0.5, marker='o')

## Plot the vertices and the edges for the refined mesh
x = refined_triangulation.x
y = refined_triangulation.y
simplices = refined_triangulation.simplices

ax2.triplot(x, y, simplices, linewidth=0.5, color='black')
ax2.scatter(x, y, color='Red', alpha=0.5, marker='o')


Predefined meshes

One common use of stripy is in meshing x,y coordinates and, to this end, we provide pre-defined meshes for square and elliptical triangulations. A random mesh is included as a counterpoint to the regular meshes. The square mesh defined above can be created directly using:

triangulation         = stripy.cartesian_meshes.square_mesh(extent, spacingX, spacingY, refinement_levels=0)
refined_triangulation = stripy.cartesian_meshes.square_mesh(extent, spacingX, spacingY, refinement_levels=3)

This capability is shown in a companion notebook Ex2-CartesianGrids