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pytorch3d/pytorch3d/ops/marching_cubes_data.py
Nikhila Ravi ebac66daeb Classic Marching Cubes algorithm implementation 
Summary:
Defines a function to run marching cubes algorithm on a single or batch of 3D scalar fields. Returns a mesh's faces and vertices.

UPDATES (12/18)
- Input data is now specified as a (B, D, H, W) tensor as opposed to a (B, W, H, D) tensor. This will now be compatible with the Volumes datastructure.
- Add an option to return output vertices in local coordinates instead of world coordinates.
Also added a small fix to remove the dype for device in Transforms3D - if passing in a torch.device instead of str it causes a pyre error.

Reviewed By: jcjohnson

Differential Revision: D24599019

fbshipit-source-id: 90554a200319fed8736a12371cc349e7108aacd0
2020-12-18 07:25:50 -08:00

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# Copyright (c) Facebook, Inc. and its affiliates. All rights reserved.
# A length 256 list which maps a cubeindex to a number
# with the intersected edges' bits set to 1.
# Each cubeindex corresponds to a given cube configuration, where
# it is composed of a bitstring where the 0th bit is flipped if vertex 0
# is below the isosurface (i.e. 0x01), for each of the 8 vertices.
EDGE_TABLE = [
0x0,
0x109,
0x203,
0x30A,
0x406,
0x50F,
0x605,
0x70C,
0x80C,
0x905,
0xA0F,
0xB06,
0xC0A,
0xD03,
0xE09,
0xF00,
0x190,
0x99,
0x393,
0x29A,
0x596,
0x49F,
0x795,
0x69C,
0x99C,
0x895,
0xB9F,
0xA96,
0xD9A,
0xC93,
0xF99,
0xE90,
0x230,
0x339,
0x33,
0x13A,
0x636,
0x73F,
0x435,
0x53C,
0xA3C,
0xB35,
0x83F,
0x936,
0xE3A,
0xF33,
0xC39,
0xD30,
0x3A0,
0x2A9,
0x1A3,
0xAA,
0x7A6,
0x6AF,
0x5A5,
0x4AC,
0xBAC,
0xAA5,
0x9AF,
0x8A6,
0xFAA,
0xEA3,
0xDA9,
0xCA0,
0x460,
0x569,
0x663,
0x76A,
0x66,
0x16F,
0x265,
0x36C,
0xC6C,
0xD65,
0xE6F,
0xF66,
0x86A,
0x963,
0xA69,
0xB60,
0x5F0,
0x4F9,
0x7F3,
0x6FA,
0x1F6,
0xFF,
0x3F5,
0x2FC,
0xDFC,
0xCF5,
0xFFF,
0xEF6,
0x9FA,
0x8F3,
0xBF9,
0xAF0,
0x650,
0x759,
0x453,
0x55A,
0x256,
0x35F,
0x55,
0x15C,
0xE5C,
0xF55,
0xC5F,
0xD56,
0xA5A,
0xB53,
0x859,
0x950,
0x7C0,
0x6C9,
0x5C3,
0x4CA,
0x3C6,
0x2CF,
0x1C5,
0xCC,
0xFCC,
0xEC5,
0xDCF,
0xCC6,
0xBCA,
0xAC3,
0x9C9,
0x8C0,
0x8C0,
0x9C9,
0xAC3,
0xBCA,
0xCC6,
0xDCF,
0xEC5,
0xFCC,
0xCC,
0x1C5,
0x2CF,
0x3C6,
0x4CA,
0x5C3,
0x6C9,
0x7C0,
0x950,
0x859,
0xB53,
0xA5A,
0xD56,
0xC5F,
0xF55,
0xE5C,
0x15C,
0x55,
0x35F,
0x256,
0x55A,
0x453,
0x759,
0x650,
0xAF0,
0xBF9,
0x8F3,
0x9FA,
0xEF6,
0xFFF,
0xCF5,
0xDFC,
0x2FC,
0x3F5,
0xFF,
0x1F6,
0x6FA,
0x7F3,
0x4F9,
0x5F0,
0xB60,
0xA69,
0x963,
0x86A,
0xF66,
0xE6F,
0xD65,
0xC6C,
0x36C,
0x265,
0x16F,
0x66,
0x76A,
0x663,
0x569,
0x460,
0xCA0,
0xDA9,
0xEA3,
0xFAA,
0x8A6,
0x9AF,
0xAA5,
0xBAC,
0x4AC,
0x5A5,
0x6AF,
0x7A6,
0xAA,
0x1A3,
0x2A9,
0x3A0,
0xD30,
0xC39,
0xF33,
0xE3A,
0x936,
0x83F,
0xB35,
0xA3C,
0x53C,
0x435,
0x73F,
0x636,
0x13A,
0x33,
0x339,
0x230,
0xE90,
0xF99,
0xC93,
0xD9A,
0xA96,
0xB9F,
0x895,
0x99C,
0x69C,
0x795,
0x49F,
0x596,
0x29A,
0x393,
0x99,
0x190,
0xF00,
0xE09,
0xD03,
0xC0A,
0xB06,
0xA0F,
0x905,
0x80C,
0x70C,
0x605,
0x50F,
0x406,
0x30A,
0x203,
0x109,
0x0,
]
# Maps each edge (by index) to the corresponding cube vertices
EDGE_TO_VERTICES = [
[0, 1],
[1, 2],
[3, 2],
[0, 3],
[4, 5],
[5, 6],
[7, 6],
[4, 7],
[0, 4],
[1, 5],
[2, 6],
[3, 7],
]
# A list of lists mapping a cube_index (a given configuration)
# to a list of faces corresponding to that configuration. Each face is represented
# by 3 consecutive numbers. A configuration will at most have 5 faces.
#
# Table taken from http://paulbourke.net/geometry/polygonise/
FACE_TABLE = [
[],
[0, 8, 3],
[0, 1, 9],
[1, 8, 3, 9, 8, 1],
[1, 2, 10],
[0, 8, 3, 1, 2, 10],
[9, 2, 10, 0, 2, 9],
[2, 8, 3, 2, 10, 8, 10, 9, 8],
[3, 11, 2],
[0, 11, 2, 8, 11, 0],
[1, 9, 0, 2, 3, 11],
[1, 11, 2, 1, 9, 11, 9, 8, 11],
[3, 10, 1, 11, 10, 3],
[0, 10, 1, 0, 8, 10, 8, 11, 10],
[3, 9, 0, 3, 11, 9, 11, 10, 9],
[9, 8, 10, 10, 8, 11],
[4, 7, 8],
[4, 3, 0, 7, 3, 4],
[0, 1, 9, 8, 4, 7],
[4, 1, 9, 4, 7, 1, 7, 3, 1],
[1, 2, 10, 8, 4, 7],
[3, 4, 7, 3, 0, 4, 1, 2, 10],
[9, 2, 10, 9, 0, 2, 8, 4, 7],
[2, 10, 9, 2, 9, 7, 2, 7, 3, 7, 9, 4],
[8, 4, 7, 3, 11, 2],
[11, 4, 7, 11, 2, 4, 2, 0, 4],
[9, 0, 1, 8, 4, 7, 2, 3, 11],
[4, 7, 11, 9, 4, 11, 9, 11, 2, 9, 2, 1],
[3, 10, 1, 3, 11, 10, 7, 8, 4],
[1, 11, 10, 1, 4, 11, 1, 0, 4, 7, 11, 4],
[4, 7, 8, 9, 0, 11, 9, 11, 10, 11, 0, 3],
[4, 7, 11, 4, 11, 9, 9, 11, 10],
[9, 5, 4],
[9, 5, 4, 0, 8, 3],
[0, 5, 4, 1, 5, 0],
[8, 5, 4, 8, 3, 5, 3, 1, 5],
[1, 2, 10, 9, 5, 4],
[3, 0, 8, 1, 2, 10, 4, 9, 5],
[5, 2, 10, 5, 4, 2, 4, 0, 2],
[2, 10, 5, 3, 2, 5, 3, 5, 4, 3, 4, 8],
[9, 5, 4, 2, 3, 11],
[0, 11, 2, 0, 8, 11, 4, 9, 5],
[0, 5, 4, 0, 1, 5, 2, 3, 11],
[2, 1, 5, 2, 5, 8, 2, 8, 11, 4, 8, 5],
[10, 3, 11, 10, 1, 3, 9, 5, 4],
[4, 9, 5, 0, 8, 1, 8, 10, 1, 8, 11, 10],
[5, 4, 0, 5, 0, 11, 5, 11, 10, 11, 0, 3],
[5, 4, 8, 5, 8, 10, 10, 8, 11],
[9, 7, 8, 5, 7, 9],
[9, 3, 0, 9, 5, 3, 5, 7, 3],
[0, 7, 8, 0, 1, 7, 1, 5, 7],
[1, 5, 3, 3, 5, 7],
[9, 7, 8, 9, 5, 7, 10, 1, 2],
[10, 1, 2, 9, 5, 0, 5, 3, 0, 5, 7, 3],
[8, 0, 2, 8, 2, 5, 8, 5, 7, 10, 5, 2],
[2, 10, 5, 2, 5, 3, 3, 5, 7],
[7, 9, 5, 7, 8, 9, 3, 11, 2],
[9, 5, 7, 9, 7, 2, 9, 2, 0, 2, 7, 11],
[2, 3, 11, 0, 1, 8, 1, 7, 8, 1, 5, 7],
[11, 2, 1, 11, 1, 7, 7, 1, 5],
[9, 5, 8, 8, 5, 7, 10, 1, 3, 10, 3, 11],
[5, 7, 0, 5, 0, 9, 7, 11, 0, 1, 0, 10, 11, 10, 0],
[11, 10, 0, 11, 0, 3, 10, 5, 0, 8, 0, 7, 5, 7, 0],
[11, 10, 5, 7, 11, 5],
[10, 6, 5],
[0, 8, 3, 5, 10, 6],
[9, 0, 1, 5, 10, 6],
[1, 8, 3, 1, 9, 8, 5, 10, 6],
[1, 6, 5, 2, 6, 1],
[1, 6, 5, 1, 2, 6, 3, 0, 8],
[9, 6, 5, 9, 0, 6, 0, 2, 6],
[5, 9, 8, 5, 8, 2, 5, 2, 6, 3, 2, 8],
[2, 3, 11, 10, 6, 5],
[11, 0, 8, 11, 2, 0, 10, 6, 5],
[0, 1, 9, 2, 3, 11, 5, 10, 6],
[5, 10, 6, 1, 9, 2, 9, 11, 2, 9, 8, 11],
[6, 3, 11, 6, 5, 3, 5, 1, 3],
[0, 8, 11, 0, 11, 5, 0, 5, 1, 5, 11, 6],
[3, 11, 6, 0, 3, 6, 0, 6, 5, 0, 5, 9],
[6, 5, 9, 6, 9, 11, 11, 9, 8],
[5, 10, 6, 4, 7, 8],
[4, 3, 0, 4, 7, 3, 6, 5, 10],
[1, 9, 0, 5, 10, 6, 8, 4, 7],
[10, 6, 5, 1, 9, 7, 1, 7, 3, 7, 9, 4],
[6, 1, 2, 6, 5, 1, 4, 7, 8],
[1, 2, 5, 5, 2, 6, 3, 0, 4, 3, 4, 7],
[8, 4, 7, 9, 0, 5, 0, 6, 5, 0, 2, 6],
[7, 3, 9, 7, 9, 4, 3, 2, 9, 5, 9, 6, 2, 6, 9],
[3, 11, 2, 7, 8, 4, 10, 6, 5],
[5, 10, 6, 4, 7, 2, 4, 2, 0, 2, 7, 11],
[0, 1, 9, 4, 7, 8, 2, 3, 11, 5, 10, 6],
[9, 2, 1, 9, 11, 2, 9, 4, 11, 7, 11, 4, 5, 10, 6],
[8, 4, 7, 3, 11, 5, 3, 5, 1, 5, 11, 6],
[5, 1, 11, 5, 11, 6, 1, 0, 11, 7, 11, 4, 0, 4, 11],
[0, 5, 9, 0, 6, 5, 0, 3, 6, 11, 6, 3, 8, 4, 7],
[6, 5, 9, 6, 9, 11, 4, 7, 9, 7, 11, 9],
[10, 4, 9, 6, 4, 10],
[4, 10, 6, 4, 9, 10, 0, 8, 3],
[10, 0, 1, 10, 6, 0, 6, 4, 0],
[8, 3, 1, 8, 1, 6, 8, 6, 4, 6, 1, 10],
[1, 4, 9, 1, 2, 4, 2, 6, 4],
[3, 0, 8, 1, 2, 9, 2, 4, 9, 2, 6, 4],
[0, 2, 4, 4, 2, 6],
[8, 3, 2, 8, 2, 4, 4, 2, 6],
[10, 4, 9, 10, 6, 4, 11, 2, 3],
[0, 8, 2, 2, 8, 11, 4, 9, 10, 4, 10, 6],
[3, 11, 2, 0, 1, 6, 0, 6, 4, 6, 1, 10],
[6, 4, 1, 6, 1, 10, 4, 8, 1, 2, 1, 11, 8, 11, 1],
[9, 6, 4, 9, 3, 6, 9, 1, 3, 11, 6, 3],
[8, 11, 1, 8, 1, 0, 11, 6, 1, 9, 1, 4, 6, 4, 1],
[3, 11, 6, 3, 6, 0, 0, 6, 4],
[6, 4, 8, 11, 6, 8],
[7, 10, 6, 7, 8, 10, 8, 9, 10],
[0, 7, 3, 0, 10, 7, 0, 9, 10, 6, 7, 10],
[10, 6, 7, 1, 10, 7, 1, 7, 8, 1, 8, 0],
[10, 6, 7, 10, 7, 1, 1, 7, 3],
[1, 2, 6, 1, 6, 8, 1, 8, 9, 8, 6, 7],
[2, 6, 9, 2, 9, 1, 6, 7, 9, 0, 9, 3, 7, 3, 9],
[7, 8, 0, 7, 0, 6, 6, 0, 2],
[7, 3, 2, 6, 7, 2],
[2, 3, 11, 10, 6, 8, 10, 8, 9, 8, 6, 7],
[2, 0, 7, 2, 7, 11, 0, 9, 7, 6, 7, 10, 9, 10, 7],
[1, 8, 0, 1, 7, 8, 1, 10, 7, 6, 7, 10, 2, 3, 11],
[11, 2, 1, 11, 1, 7, 10, 6, 1, 6, 7, 1],
[8, 9, 6, 8, 6, 7, 9, 1, 6, 11, 6, 3, 1, 3, 6],
[0, 9, 1, 11, 6, 7],
[7, 8, 0, 7, 0, 6, 3, 11, 0, 11, 6, 0],
[7, 11, 6],
[7, 6, 11],
[3, 0, 8, 11, 7, 6],
[0, 1, 9, 11, 7, 6],
[8, 1, 9, 8, 3, 1, 11, 7, 6],
[10, 1, 2, 6, 11, 7],
[1, 2, 10, 3, 0, 8, 6, 11, 7],
[2, 9, 0, 2, 10, 9, 6, 11, 7],
[6, 11, 7, 2, 10, 3, 10, 8, 3, 10, 9, 8],
[7, 2, 3, 6, 2, 7],
[7, 0, 8, 7, 6, 0, 6, 2, 0],
[2, 7, 6, 2, 3, 7, 0, 1, 9],
[1, 6, 2, 1, 8, 6, 1, 9, 8, 8, 7, 6],
[10, 7, 6, 10, 1, 7, 1, 3, 7],
[10, 7, 6, 1, 7, 10, 1, 8, 7, 1, 0, 8],
[0, 3, 7, 0, 7, 10, 0, 10, 9, 6, 10, 7],
[7, 6, 10, 7, 10, 8, 8, 10, 9],
[6, 8, 4, 11, 8, 6],
[3, 6, 11, 3, 0, 6, 0, 4, 6],
[8, 6, 11, 8, 4, 6, 9, 0, 1],
[9, 4, 6, 9, 6, 3, 9, 3, 1, 11, 3, 6],
[6, 8, 4, 6, 11, 8, 2, 10, 1],
[1, 2, 10, 3, 0, 11, 0, 6, 11, 0, 4, 6],
[4, 11, 8, 4, 6, 11, 0, 2, 9, 2, 10, 9],
[10, 9, 3, 10, 3, 2, 9, 4, 3, 11, 3, 6, 4, 6, 3],
[8, 2, 3, 8, 4, 2, 4, 6, 2],
[0, 4, 2, 4, 6, 2],
[1, 9, 0, 2, 3, 4, 2, 4, 6, 4, 3, 8],
[1, 9, 4, 1, 4, 2, 2, 4, 6],
[8, 1, 3, 8, 6, 1, 8, 4, 6, 6, 10, 1],
[10, 1, 0, 10, 0, 6, 6, 0, 4],
[4, 6, 3, 4, 3, 8, 6, 10, 3, 0, 3, 9, 10, 9, 3],
[10, 9, 4, 6, 10, 4],
[4, 9, 5, 7, 6, 11],
[0, 8, 3, 4, 9, 5, 11, 7, 6],
[5, 0, 1, 5, 4, 0, 7, 6, 11],
[11, 7, 6, 8, 3, 4, 3, 5, 4, 3, 1, 5],
[9, 5, 4, 10, 1, 2, 7, 6, 11],
[6, 11, 7, 1, 2, 10, 0, 8, 3, 4, 9, 5],
[7, 6, 11, 5, 4, 10, 4, 2, 10, 4, 0, 2],
[3, 4, 8, 3, 5, 4, 3, 2, 5, 10, 5, 2, 11, 7, 6],
[7, 2, 3, 7, 6, 2, 5, 4, 9],
[9, 5, 4, 0, 8, 6, 0, 6, 2, 6, 8, 7],
[3, 6, 2, 3, 7, 6, 1, 5, 0, 5, 4, 0],
[6, 2, 8, 6, 8, 7, 2, 1, 8, 4, 8, 5, 1, 5, 8],
[9, 5, 4, 10, 1, 6, 1, 7, 6, 1, 3, 7],
[1, 6, 10, 1, 7, 6, 1, 0, 7, 8, 7, 0, 9, 5, 4],
[4, 0, 10, 4, 10, 5, 0, 3, 10, 6, 10, 7, 3, 7, 10],
[7, 6, 10, 7, 10, 8, 5, 4, 10, 4, 8, 10],
[6, 9, 5, 6, 11, 9, 11, 8, 9],
[3, 6, 11, 0, 6, 3, 0, 5, 6, 0, 9, 5],
[0, 11, 8, 0, 5, 11, 0, 1, 5, 5, 6, 11],
[6, 11, 3, 6, 3, 5, 5, 3, 1],
[1, 2, 10, 9, 5, 11, 9, 11, 8, 11, 5, 6],
[0, 11, 3, 0, 6, 11, 0, 9, 6, 5, 6, 9, 1, 2, 10],
[11, 8, 5, 11, 5, 6, 8, 0, 5, 10, 5, 2, 0, 2, 5],
[6, 11, 3, 6, 3, 5, 2, 10, 3, 10, 5, 3],
[5, 8, 9, 5, 2, 8, 5, 6, 2, 3, 8, 2],
[9, 5, 6, 9, 6, 0, 0, 6, 2],
[1, 5, 8, 1, 8, 0, 5, 6, 8, 3, 8, 2, 6, 2, 8],
[1, 5, 6, 2, 1, 6],
[1, 3, 6, 1, 6, 10, 3, 8, 6, 5, 6, 9, 8, 9, 6],
[10, 1, 0, 10, 0, 6, 9, 5, 0, 5, 6, 0],
[0, 3, 8, 5, 6, 10],
[10, 5, 6],
[11, 5, 10, 7, 5, 11],
[11, 5, 10, 11, 7, 5, 8, 3, 0],
[5, 11, 7, 5, 10, 11, 1, 9, 0],
[10, 7, 5, 10, 11, 7, 9, 8, 1, 8, 3, 1],
[11, 1, 2, 11, 7, 1, 7, 5, 1],
[0, 8, 3, 1, 2, 7, 1, 7, 5, 7, 2, 11],
[9, 7, 5, 9, 2, 7, 9, 0, 2, 2, 11, 7],
[7, 5, 2, 7, 2, 11, 5, 9, 2, 3, 2, 8, 9, 8, 2],
[2, 5, 10, 2, 3, 5, 3, 7, 5],
[8, 2, 0, 8, 5, 2, 8, 7, 5, 10, 2, 5],
[9, 0, 1, 5, 10, 3, 5, 3, 7, 3, 10, 2],
[9, 8, 2, 9, 2, 1, 8, 7, 2, 10, 2, 5, 7, 5, 2],
[1, 3, 5, 3, 7, 5],
[0, 8, 7, 0, 7, 1, 1, 7, 5],
[9, 0, 3, 9, 3, 5, 5, 3, 7],
[9, 8, 7, 5, 9, 7],
[5, 8, 4, 5, 10, 8, 10, 11, 8],
[5, 0, 4, 5, 11, 0, 5, 10, 11, 11, 3, 0],
[0, 1, 9, 8, 4, 10, 8, 10, 11, 10, 4, 5],
[10, 11, 4, 10, 4, 5, 11, 3, 4, 9, 4, 1, 3, 1, 4],
[2, 5, 1, 2, 8, 5, 2, 11, 8, 4, 5, 8],
[0, 4, 11, 0, 11, 3, 4, 5, 11, 2, 11, 1, 5, 1, 11],
[0, 2, 5, 0, 5, 9, 2, 11, 5, 4, 5, 8, 11, 8, 5],
[9, 4, 5, 2, 11, 3],
[2, 5, 10, 3, 5, 2, 3, 4, 5, 3, 8, 4],
[5, 10, 2, 5, 2, 4, 4, 2, 0],
[3, 10, 2, 3, 5, 10, 3, 8, 5, 4, 5, 8, 0, 1, 9],
[5, 10, 2, 5, 2, 4, 1, 9, 2, 9, 4, 2],
[8, 4, 5, 8, 5, 3, 3, 5, 1],
[0, 4, 5, 1, 0, 5],
[8, 4, 5, 8, 5, 3, 9, 0, 5, 0, 3, 5],
[9, 4, 5],
[4, 11, 7, 4, 9, 11, 9, 10, 11],
[0, 8, 3, 4, 9, 7, 9, 11, 7, 9, 10, 11],
[1, 10, 11, 1, 11, 4, 1, 4, 0, 7, 4, 11],
[3, 1, 4, 3, 4, 8, 1, 10, 4, 7, 4, 11, 10, 11, 4],
[4, 11, 7, 9, 11, 4, 9, 2, 11, 9, 1, 2],
[9, 7, 4, 9, 11, 7, 9, 1, 11, 2, 11, 1, 0, 8, 3],
[11, 7, 4, 11, 4, 2, 2, 4, 0],
[11, 7, 4, 11, 4, 2, 8, 3, 4, 3, 2, 4],
[2, 9, 10, 2, 7, 9, 2, 3, 7, 7, 4, 9],
[9, 10, 7, 9, 7, 4, 10, 2, 7, 8, 7, 0, 2, 0, 7],
[3, 7, 10, 3, 10, 2, 7, 4, 10, 1, 10, 0, 4, 0, 10],
[1, 10, 2, 8, 7, 4],
[4, 9, 1, 4, 1, 7, 7, 1, 3],
[4, 9, 1, 4, 1, 7, 0, 8, 1, 8, 7, 1],
[4, 0, 3, 7, 4, 3],
[4, 8, 7],
[9, 10, 8, 10, 11, 8],
[3, 0, 9, 3, 9, 11, 11, 9, 10],
[0, 1, 10, 0, 10, 8, 8, 10, 11],
[3, 1, 10, 11, 3, 10],
[1, 2, 11, 1, 11, 9, 9, 11, 8],
[3, 0, 9, 3, 9, 11, 1, 2, 9, 2, 11, 9],
[0, 2, 11, 8, 0, 11],
[3, 2, 11],
[2, 3, 8, 2, 8, 10, 10, 8, 9],
[9, 10, 2, 0, 9, 2],
[2, 3, 8, 2, 8, 10, 0, 1, 8, 1, 10, 8],
[1, 10, 2],
[1, 3, 8, 9, 1, 8],
[0, 9, 1],
[0, 3, 8],
[],
]
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