"""
Visualizing geometries
======================

Now that you can build a geometry (:doc:`/tutorials/01_first_bspline`), this tutorial
shows how to *see* it. PaNTr's :mod:`pantr.viz` module turns B-spline, Bézier, and
THB-spline geometries into `PyVista <https://docs.pyvista.org>`_ meshes backed by
native VTK Bézier cells that store the *exact* polynomial geometry. The interactive
viewer below subdivides those cells for display, and a ``.vtu`` opened in ParaView
(>= 5.10) renders them as exact Bézier cells, tessellated at ParaView's chosen
*Nonlinear Subdivision Level*. The toolkit is reused throughout the rest of the
tutorials:

- :func:`~pantr.viz.plot` -- one-call interactive viewing,
- :class:`~pantr.viz.Scene` -- compose several geometries with per-geometry options,
- **control polygons** and **knot lines** overlaid on the geometry,
- **scalar fields** drawn as a colour map or an elevation surface,
- :func:`~pantr.viz.save` -- export to a ``.vtu`` file for ParaView.

Requires the ``viz`` extra: ``pip install "pantr[viz]"``. The :doc:`/guide/visualization`
guide covers every rendering option in depth.
"""

import tempfile
from pathlib import Path

import numpy as np

from pantr import viz
from pantr.bspline import Bspline, BsplineSpace, BsplineSpace1D, get_greville_abscissae
from pantr.cad import create_circle, create_disk

# %%
# A curve with its control polygon and knot lines
# ------------------------------------------------
# :func:`~pantr.cad.create_circle` builds an *exact* circle as a rational quadratic
# (NURBS) curve. ``show_control_polygon`` draws the control net; ``show_knot_lines``
# marks the images of the interior knots.
arc = create_circle(radius=1.0, angle=(0.0, 1.5 * np.pi))
viz.plot(arc, show_control_polygon=True, show_knot_lines=True)

# %%
# A surface, knot lines on the geometry
# -------------------------------------
# For a surface the knot lines become iso-parametric curves lying on the surface.
disk = create_disk(radius_outer=1.0)
viz.plot(disk, color="lightsteelblue", show_knot_lines=True)

# %%
# Scalar fields: colour map vs. elevation
# ---------------------------------------
# A rank-1 geometry is a *scalar field* ``f(u, v)``. By default it is drawn as a flat
# colour map; ``elevation=True`` lifts the value into the third coordinate. Here we
# build a biquadratic field whose coefficients sample ``sin(pi u) sin(pi v)``.
space = BsplineSpace([BsplineSpace1D([0, 0, 0, 0.5, 1, 1, 1], 2) for _ in range(2)])
greville = get_greville_abscissae(space.spaces[0])
gu, gv = np.meshgrid(greville, greville, indexing="ij")
coeffs = (np.sin(np.pi * gu) * np.sin(np.pi * gv))[..., np.newaxis]
field = Bspline(space, coeffs)
viz.plot(field, elevation=True, show_knot_lines=True)

# %%
# Composing a scene
# -----------------
# :class:`~pantr.viz.Scene` overlays several geometries, each with its own options.
scene = viz.Scene()
scene.add(disk, color="wheat", opacity=0.5)
scene.add(arc, color="crimson", show_control_polygon=True)
scene.show()

# %%
# Exporting to VTK
# ----------------
# :func:`~pantr.viz.save` writes a ``.vtu`` file that ParaView (>= 5.10) renders with
# exact Bézier geometry -- handy for publication figures. In ParaView, switch the
# representation to *Surface With Edges* to see the knot lines: it draws the cells'
# curved edges, dynamically tessellated at the chosen *Nonlinear Subdivision Level*.
out_file = Path(tempfile.gettempdir()) / "pantr_disk.vtu"
viz.save(disk, out_file)
print(f"wrote {out_file}")