TopographyMap

This class wraps a regular grid of elevation data, \(z_{ij}\), as function of \((x_j, y_i)\) coordinates at grid nodes. Elevation data are abstracted as a continuous function

\[z = f(x, y)\]

over the grid support by using a bilinear interpolation.

Warning

TopographyMap objects use indexing order. That is, coordinate (x[j], y[i]) corresponds to elevation z[i,j]. This differs from reading order used when storing topography data as images, where the \(y\)-axis is inverted.

Constructor

class TopographyMap(x, y, z=None)

The x and y arguments specify the support of the grid along \(x\) and \(y\) coordinates. Without additional arguments, an elevation of 0 is considered. For instance,

>>> zero = goupil.TopographyMap([-1e5, 1e5], [-1e5, 1e5])

represents zero elevation (\(f = 0\)) over the support \([-1,1]\times[-1,1]\) km². A z argument can also be provided, as a float or 2D numpy.ndarray, in order to initialise the elevation grid.

Note

If a grid node has no data, numpy.nan should be used.

Attributes

Note

TopographyMap attributes are read-only.

TopographyMap.x: numpy.ndarray

The grid of \(x_j\) values.

TopographyMap.y: numpy.ndarray

The grid of \(y_i\) values.

TopographyMap.z: numpy.ndarray

The grid of \(z_{ij}\) values.

TopographyMap.box: tuple

The map support (bounding-box) along \(x\) and \(y\)-axis.

Methods

TopographyMap.__call__(x, y, grid=None)

Returns interpolated elevation values at \((x, y)\) coordinates. The x and y arguments can be float or numpy.ndarray with consistent sizes. If grid is True, then a 2D grid of elevation values is returned over the outer product of x and y. For instance,

>>> z = topography(
...     numpy.linspace(xmin, xmax, 101),
...     numpy.linspace(ymin, ymax, 201),
...     grid=True
... )

returns a \(201 \times 101\) numpy.ndarray of elevation values computed over the grid delimited by \([x_\text{min}, x_\text{max}]\times[y_\text{min}, y_\text{max}]\).