Welcome to isoext — a Python library designed for efficient isosurface extraction, leveraging the power of GPU computing and comes with pytorch support. Our library attempts to implement a collection of classic isosurface extraction algorithms. Currently, only the following algorithms are supported, but more will come in the future:

• Marching cubes
  • lorensen: the original marching cubes algorithm from the paper Marching cubes: A high resolution 3D surface construction algorithm.
  • nagae: the marching cubes algorithm from the paper Surface construction and contour generation from volume data. It uses only rotation to transform the Marching Cubes cases, unlike lorensen which uses rotation and reflection. lorensen contains ambiguities which results in holes and cracks. This modification removes the ambiguities and produces a closed surface.

isoext also comes with a Marching Cubes table generator, which you can use to integrate Marching Cubes into your own project or extend isoext with more algorithms. All the lookup tables we used are generated by the generator.

To install isoext, make sure CUDA Toolkit is installed and run:

pip install isoext

Here's a simple example to get you started:

import isoext
from isoext.sdf import *

aabb = [-1, -1, -1, 1, 1, 1]
res = 128
grid = isoext.make_grid(aabb, res)

torus_a = TorusSDF(R=0.75, r=0.15)
torus_b = RotationOp(sdf=torus_a, axis=[1, 0, 0], angle=90)
torus_c = RotationOp(sdf=torus_a, axis=[0, 1, 0], angle=90)

sphere_a = SphereSDF(radius=0.75)

sdf = IntersectionOp([
    sphere_a, 
    NegationOp(UnionOp([
        torus_a, torus_b, torus_c
    ]))
])
sdf_v = sdf(grid) # must be a cuda pytorchtensor

isolevel = 0

v, f = isoext.marching_cubes(sdf_v, aabb=aabb, level=isolevel, method="nagae")

isoext.write_obj('test.obj', v, f)

isoext.marching_cubes accepts the following arguments:

• grid: A CUDA PyTorch tensor representing the scalar field. It should be a 3D tensor. If cells is provided, grid must be of shape (2N, 2, 2), where N is the number of cells.
• aabb: (Optional) A list or tuple of 6 floats representing the axis-aligned bounding box [xmin, ymin, zmin, xmax, ymax, zmax]. If provided, cells must not be given.
• cells: (Optional) A CUDA PyTorch tensor of shape (2N, 2, 2, 3) representing the cell positions. If provided, aabb must not be given.
• level: (Optional) The isovalue at which to extract the isosurface. Default is 0.0.
• method: (Optional) The marching cubes algorithm to use. Currently, lorensen and nagae are supported. Default is nagae.

The function returns a tuple (vertices, faces):

• vertices: A CUDA PyTorch tensor of shape (V, 3) representing the vertex positions.
• faces: A CUDA PyTorch tensor of shape (F, 3) representing the triangular faces.
• If no faces are found, both vertices and faces will be None.

You can find the generator in luts/gen_mc_lut.py. Available methods are in luts/mc_methods. For example, to generate the table for lorensen, run:

cd luts
python gen_mc_lut.py mc_methods/lorensen.json output

This will generate the luts and as well as the meshes of all the cases inside the output/lorensen folder.

For the cube annotation, refer to the script documentation in luts/gen_mc_lut.py. The cases are indexed in binary format, where the ith bit indicates the ith vertex is below the isosurface if it is 1 and vice versa.

• Fix docstring.
• Add more Marching Cubes variants.
• Add Dual Contouring.
• Add Dual Marching Cubes.

isoext is released under the MIT License. Feel free to use it in your projects.

• We use Thrust for GPU computing and nanobind for Python binding.