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geometry.md

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Geometry

We implement the geometry class and operations in torch. Some CUDA Kernel is optional for acceleration.

projection

Function for cam projection from 3d points into image pixels

  • xyz_world -> xyz_cam -> pixel -> xyz_cam -> xyz_world
  • xyz_world -> xyz_cam: w2c
  • xyz_cam -> pixel: intrinsic
  • pixel -> xyz_cam: intrinsic
  • xyz_cam -> xyz_world: c2w
  • Distortion is allowed in world->pixel

transformation

Provide functions for geometrical transformation, including cam pose, vec, points

  • normalize: norm vec
  • rotation: rotate a matrix by R
  • axis/rot representation interchange

poses

Functions for create/modify cam poses

  • invert pose: c2w <-> w2c transfer
  • look_at/view_matrix: generate c2w
  • average/center poses: get avg pose and recenter all poses
  • get cam on sphere by different mode

cam_spiral camera_circle

sphere

Many function about sphere is provided, including:

  • uv-xyz transform
  • get sphere line/surface
  • get spiral line
  • get swing line

It provides help for camera path creation.

Any point on a unit sphere with (0,0,0) origin can be represented by (u, v), where u in (0, 2pi), v in (0, pi)

  • x = cos(u) * sin(v)
  • y = cos(v)
  • z = sin(u) * sin(v)

sphere_line sphere_ray

ray

Functions for ray point. ray is (rays_o, rays_d), rays_d is always assumed to be normalized.

  • get_ray_point_by_zvals: get the real point on ray using rays_o/rays_d/zvals.
  • closest_point_on_ray: find the closest point on ray to an existing point. zvals can not be negative.
  • closest_point_to_two_rays: two rays and their closest pts pair with distance. All case applied(parallel, zvals<0)
  • closest_distance_of_two_rays: distance of two ray. But need to assume rays are pointing inward.
  • closest_point_to_rays: a point close to all rays. Good for cam view centralization.
  • sphere_ray_intersection: find the ray-sphere intersection.
  • surface_ray_intersection: find the ray-surface intersection. Support sphere_tracing/root_finding.
  • aabb_ray_intersection: find the ray-volume intersection.

rays

triangle

Functions for triangle calculation.

  • get_tri_normal
  • get_tri_circumcircle

tri tri_norm

mesh

Function for mesh extraction, color extraction, etc.

  • extract_mesh: simple marching cubes on cpu
  • save_meshes: save mesh to .ply files
  • get_verts_by_faces: rearrange verts from (V, 3) to (F, 3, 3) by faces.
  • get_normals: get the vert/face normals
  • get_face_centers: get the triangle centers
  • simplify_mesh: simplify mesh
  • render_mesh: it will call open3d/pytorch3d backend to render the mesh by cam positions.

mesh

volume

Definition and function of a volume. For all the point you can get it in grid or fatten(by default)

  • n_grid: num of volume/line seg on each side
  • You can set the size of the volume by side or xyz_len
  • corner: 8 corner pts
  • grid_pts: all the grid points, in total (n_grid+1)^3
  • voxel_size: each voxel size, useful for marching cubes.
  • volume_pts: all the volume center points, in total (n_grid)^3
    • This can be sent to the network and get the volume density
  • voxel_pts: the partial volume pts of each voxel that selected
  • bound_lines: outside bounding lines, 12 lines with (2, 3) start-end pts.
  • dense_lines: inner+outside bounding lines, 3*(n+1)^3 lines with (2, 3) start-end pts.
  • bound_faces: outside bounding faces, 6 faces, tensor in (6, 4, 3) shape
  • dense_faces: inner+outside bounding faces, tensor in ((n_grid+1)n_grid^2*3, 4, 3) shape
  • convert_flatten_index_to_xyz_index/convert_xyz_index_to_flatten_index: index conversion

occupancy

You can manually set up an occupancy record for visual. This can help to save computation like ray sphere intersection.

  • set_up_voxel_bitfield: it creates a bool tensor of (n_grid, n_grid, n_grid) for recording this voxel's occupancy.
    • You can reset or update the occupied voxels as well. And take the occupied voxel's line/face for visualization.
    • get_occupied_voxel_idx/get_occupied_voxel_pts/get_occupied_grid_pts/get_occupied_lines/get_occupied_faces: You can get the occupied voxel for visualization or other computation.
    • get_occupied_bounding_corner/range: Get the smallest volume that bound all the occ voxels.
  • set_up_voxel_opafield: the opacity field is the float opacity value of each voxel in (n_grid, n_grid, n_grid).
    • You can update it, and use it to update the occupancy.

ray/pts in volume

For ray in pts in volume, we provide a lot of function like

  • check_pts_in_grid_boundary: check pts in voxel
  • get_voxel_idx_from_xyz: get voxel idx from pts position
  • get_grid_pts_idx_by_voxel_idx/get_grid_pts_by_voxel_idx: get grid pts index and position by voxel idx
  • cal_weights_to_grid_pts / interpolate: interpolate pts by grid_pts using trilinear interpolation
  • ray_volume_intersection: call the aabb intersection test and find the ray-volume intersection
    • ray_volume_intersect_in_occ_voxel: You can call to find the intersection in occupied voxels only
  • get_ray_pass_through: get the voxel_ids that the ray pass through

ray_pass volume_bound_sample

point cloud

Function of point cloud with pts and color.

  • save_point_cloud: export pc file as .ply file

pc