Interpolation on Unstructured Grids

Interpolation on Unstructured Grids#

Interpolation of scattered points. Build a spatial index with RTree3D(), load the observations with its packing or insert methods, then interpolate with the functions of pyinterp.rtree listed below (inverse distance weighting, radial basis functions, kriging or window functions).

Spatial Index (R-Tree)#

RTree3D([spheroid, dtype, distance])

Spatial index for 3D point data with interpolation methods.

RTree3DFloat32(self[, spheroid, distance])

Spatial index for 3D point data with interpolation methods.

RTree3DFloat64(self[, spheroid, distance])

Spatial index for 3D point data with interpolation methods.

Algorithms#

Interpolation algorithms for unstructured data.

inverse_distance_weighting(tree, coordinates)

Inverse Distance Weighting interpolation.

radial_basis_function(tree, coordinates[, ...])

Radial Basis Function interpolation.

kriging(tree, coordinates[, config, k, ...])

Kriging interpolation.

window_function(tree, coordinates[, config, ...])

Window function interpolation.

query(tree, coordinates[, config, k, ...])

Query nearest neighbors.

Core RTree#

Base Class and Type Hints#

The RTree3DHolder is the generic base class used in type hints for R-Tree spatial indexes with support for different data types (float32 and float64). It is returned by the factory functions RTree3D(), RTree3DFloat32(), and RTree3DFloat64().

class pyinterp.core.RTree3DHolder(Generic[_FloatDType])#

Generic holder for a 3D R-Tree spatial index supporting different floating-point types.

Parameters:

spheroid (pyinterp.geometry.geographic.Spheroid | None) – Optional spheroid for geographic coordinate transformations.

bounds() → tuple[NDArray, NDArray] | None#

Get the bounding box of all inserted points.

clear() → None#

Clear the R-Tree by removing all stored points.

empty() → bool#

Check if the R-Tree is empty.

insert(coordinates: NDArray[TwoDims], values: NDArray[OneDim]) → None#

Insert points and associated values into the R-Tree.

inverse_distance_weighting(coordinates: NDArray[TwoDims], config: rtree.InverseDistanceWeighting | None = None) → tuple[NDArray[OneDim], NDArray[UInt32]]#

Perform Inverse Distance Weighting interpolation on the R-Tree.

kriging(coordinates: NDArray[TwoDims], config: rtree.Kriging | None = None) → tuple[NDArray[OneDim], NDArray[UInt32]]#

Perform Kriging interpolation on the R-Tree.

packing(coordinates: NDArray[TwoDims], values: NDArray[OneDim]) → None#

Pack points and values into the R-Tree for optimized queries.

query(coordinates: NDArray[TwoDims], config: rtree.Query | None = None) → tuple[NDArray[TwoDims], NDArray[TwoDims]]#

Query the R-Tree for nearest neighbors.

radial_basis_function(coordinates: NDArray[TwoDims], config: rtree.RadialBasisFunction | None = None) → tuple[NDArray[OneDim], NDArray[UInt32]]#

Perform Radial Basis Function interpolation on the R-Tree.

size() → int#

Get the number of points stored in the R-Tree.

window_function(coordinates: NDArray[TwoDims], config: rtree.InterpolationWindow | None = None) → tuple[NDArray[OneDim], NDArray[UInt32]]#

Perform window function interpolation on the R-Tree.

spheroid: pyinterp.geometry.geographic.Spheroid | None#

The spheroid associated with this R-Tree instance.

Geographic R-Tree Implementation#

Specialized R-Tree implementation for geographic (spherical/ellipsoidal) coordinates: pyinterp.geometry.geographic.RTree, documented with the geometric primitives.

Choosing between the two indexes#

Both accept longitude/latitude points. They differ by the distance they measure and by their speed:

  • RTree3D(spheroid), created with a spheroid (without one, the coordinates are taken as Cartesian), converts the points to ECEF and searches them with straight-line (chord) distances. It is the fastest index, 10 to 20 times faster to query than the geographic one (the gap grows with the size of the tree), and also supports altitudes, any spheroid and single precision.

  • RTree3D(spheroid, distance="geodesic") keeps the ECEF search but ranks the neighbors by geodesic distance on the spheroid, and returns geodesic distances: the same results as the geographic index, 5 to 10 times faster. The points must have no altitude. Radial basis functions and kriging keep straight-line distances between the neighbors in their kernels.

  • geographic.RTree uses geodesic distances on the WGS84 ellipsoid, and evaluates them to search its nodes, which makes it the slowest.

The chord is shorter than the geodesic by about 0.001% at 100 km, 0.1% at 1,000 km and 2.6% at 5,000 km: at short range, the default RTree3D finds the same neighbors as the geodesic searches, except for near-ties. Use distance="geodesic" when the distances, or the weights derived from them, must be geodesic over long ranges.