"""
.. _interpolate_sample_example:

Compare interpolation/sampling methods
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

There are two main methods of interpolating or sampling data from a target mesh
in PyVista. :func:`pyvista.DataSetFilters.interpolate` uses a distance weighting
kernel to interpolate point data from nearby points of the target mesh onto
the desired points.
:func:`pyvista.DataObjectFilters.sample` interpolates data using the
interpolation scheme of the enclosing cell from the target mesh.

If the target mesh is a point cloud, i.e. there is no connectivity in the cell
structure, then :func:`pyvista.DataSetFilters.interpolate` is typically
preferred.  If interpolation is desired within the cells of the target mesh, then
:func:`pyvista.DataObjectFilters.sample` is typically desired.

Here the two methods are compared and contrasted using a simple example of
sampling data from a mesh in a rectangular domain. This example demonstrates the
main differences above. For more complex uses, see :ref:`interpolate_example`
and :ref:`resampling_example`.

"""

# sphinx_gallery_thumbnail_number = 7
import numpy as np
import pyvista as pv

# %%
# Interpolating from point cloud
# ++++++++++++++++++++++++++++++
# A point cloud is a collection of points that have no connectivity in
# the mesh, i.e. the mesh contains no cells or the cells are 0D
# (vertex or polyvertex). The filter :func:`pyvista.DataSetFilters.interpolate`
# uses a distance-based weighting methodology to interpolate between the
# unconnected points.
#
# First, generate a point cloud mesh in a rectangular domain from
# ``(0, 0)`` to ``(3, 1)``. The data to be sampled is the square of the y position.

rng = np.random.default_rng(seed=0)
points = rng.uniform(low=[0, 0], high=[3, 1], size=(250, 2))
# Make points be z=0
points = np.hstack((points, np.zeros((250, 1))))
point_mesh = pv.PolyData(points)
point_mesh['ysquared'] = points[:, 1] ** 2

# %%
# The point cloud data looks like this.

pl = pv.Plotter()
pl.add_mesh(point_mesh, render_points_as_spheres=True, point_size=10)
pl.view_xy()
pl.show()

# %%
# Now estimate data on a regular grid from the point data.  Note
# that the distance parameter ``radius`` determines how far away to
# look for point cloud data.

grid = pv.ImageData(dimensions=(11, 11, 1), spacing=[3 / 10, 1 / 10, 1])
output = grid.interpolate(point_mesh, radius=0.1, null_value=-1)
output

# %%
# When using ``radius=0.1``, the expected extents of the data are
# captured reasonably well over the domain, but there are holes in the
# data (represented by the darkest blue colors) caused by no points within
# the ``radius`` to interpolate from.

pl = pv.Plotter()
pl.add_mesh(output, clim=[0, 1])
pl.add_mesh(points, render_points_as_spheres=True, point_size=10, color='red')
pl.view_xy()
pl.show()


# %%
# Now repeat with ``radius=0.25``.
# There are no holes but the extents of the data is much narrower
# than ``[0, 1]``. This is caused by more interior points involved
# in the weighting near the lower and upper edges of the domain.
# Other parameters such as ``sharpness`` could be tuned to try to
# lessen the issue.

grid = pv.ImageData(dimensions=(11, 11, 1), spacing=[3 / 10, 1 / 10, 1])
output = grid.interpolate(point_mesh, radius=0.25, null_value=-1)

pl = pv.Plotter()
pl.add_mesh(output, clim=[0, 1])
pl.add_mesh(points, render_points_as_spheres=True, point_size=10, color='red')
pl.view_xy()
pl.show()

# %%
# While this filter is very useful for point clouds, it is possible to use
# it to interpolate from the points on other mesh types. With
# unstuitable choice of ``radius`` the interpolation doesn't look very good.
# It is recommended consider using :func:`pyvista.DataObjectFilters.sample` in a
# case like this (see next section below). However, there may be cases with
# non-point cloud meshes where :func:`pyvista.DataSetFilters.interpolate` is
# still preferred.

sphere = pv.SolidSphere(center=(0.5, 0.5, 0), outer_radius=1.0)
sphere['ysquared'] = sphere.points[:, 1] ** 2
output = grid.interpolate(sphere, radius=0.1)

pl = pv.Plotter()
pl.add_mesh(output, clim=[0, 1])
pl.add_mesh(sphere, style='wireframe', color='white')
pl.view_xy()
pl.show()

# %%
# Sampling from a mesh with connectivity
# ++++++++++++++++++++++++++++++++++++++
# This example is in many ways the opposite of the prior one.
# A mesh with cell connectivity that spans 2 dimensions is
# sampled at discrete points using :func:`pyvista.DataObjectFilters.sample`.
# Importantly, the cell connectivity enables direct interpolation
# inside the domain without needing distance or weighting parametization.
#
# First, show that sample does not work with point clouds with data.
# Either :func:`pyvista.DataSetFilters.interpolate` or the
# ``snap_to_closest_point`` parameter must be used.

grid = pv.ImageData(dimensions=(11, 11, 1), spacing=[3 / 10, 1 / 10, 1])
output = grid.sample(point_mesh)
# value of (0, 0) shows that no data was sampled
print(f'(min, max): {output["ysquared"].min()}, {output["ysquared"].min()}')

# %%
#  Create the non-point cloud mesh that will be sampled from and plot it.

grid = pv.ImageData(dimensions=(11, 11, 1), spacing=[3 / 10, 1 / 10, 1])
grid['ysquared'] = grid.points[:, 1] ** 2

pl = pv.Plotter()
pl.add_mesh(grid, clim=[0, 1])
pl.view_xy()
pl.show()

# %%
# Now sample it at the discrete points used in the first example.
point_mesh = pv.PolyData(points)
output = point_mesh.sample(grid)
output

# %%
# This looks identical to the first plot of the first example as the
# data is not noisy, and there is little interpolation error.

pl = pv.Plotter()
pl.add_mesh(output, render_points_as_spheres=True, point_size=10)
pl.view_xy()
pl.show()

# %%
# Instead of sampling onto a point cloud, :func:`pyvista.DataObjectFilters.sample`
# can sample using other mesh types.  For example, sampling onto a rotated subset
# of the grid.
#
# Make subset (0.7, 0.7, 0) units in dimension and then rotate by 45 degrees around
# its center.
subset = pv.ImageData(dimensions=(8, 8, 1), spacing=[0.1, 0.1, 0], origin=(0.15, 0.15, 0))
rotated_subset = subset.rotate_vector(vector=(0, 0, 1), angle=45, point=(0.5, 0.5, 0))
output = rotated_subset.sample(grid)
output

# %%
# The data in the sampled region looks identical to the original grid
# due to the well-behaved nature of the data and
# low interpolation error.

pl = pv.Plotter()
pl.add_mesh(grid, style='wireframe', clim=[0, 1])
pl.add_mesh(output, clim=[0, 1])
pl.view_xy()
pl.show()

# %%
# Repeat the sphere interpolation example, but using
# :func:`pyvista.DataObjectFilters.sample`. This method
# is directly able to sample from the mesh in this case without
# fiddling with distance weighting parameters.

sphere = pv.SolidSphere(center=(0.5, 0.5, 0), outer_radius=1.0)
sphere['ysquared'] = sphere.points[:, 1] ** 2
output = grid.sample(sphere)

pl = pv.Plotter()
pl.add_mesh(output, clim=[0, 1])
pl.add_mesh(sphere, style='wireframe', color='white')
pl.view_xy()
pl.show()


# %%
# .. tags:: filter
