THB-DIFF: a GPU-accelerated differentiable programming framework for THB-spline.

Finished the important parts but lacks comments and documentation. This repository is still a work in progress.

The paper can be accessed here.

Installation

• Install conda (Follow the instructions on this webpage). Although, for MacOS it would be easier to install conda using Homebrew.

• Create a conda environment

  conda create -n THB python=3.10
  

• Activate the conda environment.

  conda activate THB
  

• Install the following dependencies using either pip or conda

  • numpy
  • matplotlib
  • jax
  • jaxlib
  • tqdm
  • numba
  • pyvista

  pip install jax jaxlib numba matplotlib tqdm numba pyvista
  

  Replace jax and jaxlib with pytorch if a pytorch version is preferred.

• To access CUDA-accelerated kernels or c++ functions for THB-spline evaluation using PyTorch, run the following command from the THB_extensions directory.

  python setup.py build
  python setup.py install
  

• Install source code THB-Diff

  pip install .
  

  for editable installtion

  pip install -e .
  

Example Usage

Create B-spline objects which constitute the initial tensor-product

For 2D THB-splines

from THB.THB_structures import BSpline, TensorProduct, Space

bs1 = BSpline(knotvector=np.array([0, 0, 0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1, 1, 1]), degree=2)
bs2 = BSpline(knotvector=np.array([0, 0, 0, 0, 0.2, 0.4, 0.5, 0.6, 0.8, 0.9, 1, 1, 1, 1], degree=3)

tp_2D = TensorProduct([bs1, bs2])

For 3D THB-splines

import THB
from THB.datastructures import BSpline, TensorProduct

bs1 = BSpline(knotvector=np.array([0, 0, 0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1, 1, 1]), degree=2)
bs2 = BSpline(knotvector=np.array([0, 0, 0, 0, 0.2, 0.4, 0.5, 0.6, 0.8, 0.9, 1, 1, 1, 1], degree=3)
bs3 = BSpline(knotvector=np.array([0, 0, 0, 0.2, 0.4, 0.6, 0.8, 1, 1, 1]), degree=2)

tp_3D = TensorProduct([bs1, bs2, bs3])

THB-Diff supports non-uniformly spaced knots as input knotvectors for constituent BSplines. The TensorProduct can have BSplines objects of varied degrees and knotvectors as input for tensor-product construction.

Create a Space object which handles queries and operations on THB-spline domain and function space

h_space = Space(tensor_product=tp, num_levels=3)

First we need to compute the status of basis functions on all levels, without any refinement only the basis functions in the most coarse level are active and the rest are passive. Before computing the refinement coefficients, the status of basis functions from all levels has to be computed.

h_space.build_hierarchy_from_domain_sequence()

THB-spline domain can be refined by refining the cells of h_space, Space.build_hierarchy_from_domain_sequence() should be called the completion of domain refinement.

h_space._refine_cell(cellIdx=(2, 2, 2), level=0)
h_space._refine_cell(cellIdx=(3, 1, 0), level=0)

h_space.build_hierarchy_from_domain_sequence()

Generate

params = THB.bspline_funcs.generate_parametric_coordinates((50, 50, 50))

ac_cells = compute_active_cells_active_supp(h_space.cells, h_space.fns, h_space.degrees)
fn_coeffs = compute_refinement_operators(h_space.fns, h_space.Coeff, h_space.degrees)
ac_cell_supp, num_supp = compute_active_span(params, h_space.knotvectors, h_space.cells, h_space.degrees, ac_cells)

PHI = THB_basis_fns(jnp.array(params), ac_cell_supp, num_supp, fn_coeffs, h_space.sh_fns, h_space.knotvectors, h_space.degrees)

documentation work in progress...

Citation

@Article{thbdiff,
author={Moola, Ajith and Balu, Aditya and Krishnamurthy, Adarsh and Pawar, Aishwarya},
title={THB-Diff: a GPU-accelerated differentiable programming framework for THB-splines},
journal={Engineering with Computers},
year={2023},}