PaNTr

PaNTr (Polynomial And NURBS Toolkit) is a pure-Python library for geometric modeling and numerical analysis with B-splines, NURBS, Bézier patches, and truncated hierarchical B-splines. It is built on NumPy, SciPy, and Numba — typed across its public API and JIT-compiled for multi-core throughput — and targets isogeometric analysis, CAD-style modeling, and scientific computing.

import numpy as np
from pantr.bspline import Bspline, BsplineSpace, BsplineSpace1D

space = BsplineSpace([BsplineSpace1D([0, 0, 0, 1, 2, 3, 3, 3], 2)])  # quadratic curve space
curve = Bspline(space, np.array([[0, 0], [1, 2], [2, -1], [3, 1], [4, 0]], dtype=float))
points = curve.evaluate(np.linspace(0, 3, 50))  # (50, 2)
Getting started

Install PaNTr (and the optional extras) and run your first example.

Getting started
Tutorials

A guided, runnable path from your first spline to adaptive refinement.

Tutorials
User guide

The data model and topic-by-topic explanations behind the API.

Core concepts
API reference

Every module, class, and function, with full signatures.

API reference

What’s inside

  • B-spline & NURBS spaces — univariate and tensor-product BsplineSpace, exact rational geometry, evaluation and derivatives, knot insertion/removal, degree elevation, splitting.

  • Bézier toolkit — Bernstein/Bézier curves and patches, composition, products, degree reduction, and Bernstein-polynomial root finding (pantr.bezier).

  • Truncated hierarchical B-splines — THBSplineSpace for adaptive local refinement, mirroring the tensor-product API.

  • Constructive geometry — lines, arcs, disks, cylinders, extrusion, revolution, sweep, ruled and Coons surfaces/volumes (pantr.cad).

  • Grids & quadrature — tensor-product and hierarchical grids, BVH spatial queries, cell/facet tags, and quadrature rules (pantr.grid, pantr.quad).

  • Dependency-gated MPI & visualization — pantr.mpi distributes spaces across ranks (with mpi4py) and pantr.viz renders exact higher-order geometry through PyVista / VTK (with PyVista). Both ship with PaNTr; see Getting started for how the optional backends are enabled.