PolySignedDistance.jl

A package for ray tracing/point-in-polygon queries and SDF/Approximate-SDF computation in Julia using N-dimensional triangulated surfaces.

To build a surface for ray tracing, one may use:

using PolySignedDistance: RayTracing

surf = RayTracing.Surface(
    points, # matrix (ndims, npts)
    simplices; # matrix (ndims, nsimps)
    leaf_size = 10,
    ray_reference = nothing,
    reference_isin = false,
    digits = 12
)

• points indicates surface points;
• simplices indicates simplices in the triangulated surface;
• leaf_size indicates a max. leaf size for the bounding box tree;
• ray_reference indicates a standard reference (origin) point for the ray tracing. Defaults to a point far away from the surface if nothing;
• reference_isin: whether said ray reference is within the surface;
• digits: number of digits for point merging precision. We advise the user not to change this.

For a point-in-polygon query, you can use RayTracing.isin:

flag = isin(
    surf, point
) # true if within solid

To optimize the queries, one may use a custom ray tracing origin closer to the query point as:

flag = isin(
    surf, point;
    origin = [-1, 2, 0], # example
    origin_isin = true # for reference
)

To find a list of intersected simplex indices and the corresponding intersection points, you may also use:

face_inds, int_points = crossed_faces(surf, p1, p2)

@show size(int_points)
# (ndims, npoints)

For a signed distance function calculation, one may use:

using PolySignedDistance

tree = SDFTree(
    points,
    simplices;
    leaf_size = 10, # for search trees
    is_open = false, # if true, an open domain (distance is positive in the outside. Defs. to false)
)

x = rand(size(points, 1)) # random point

dist, proj = tree(x)

# dist: distance to surface (signed)
# proj: projection upon surface

# or, for open manifolds without spending time with the point in polygon query

dist, proj = projection_and_distance(tree, x)

The SDF estimation algorithms hereby implemented do not yield correct results if zero-area simplices or repeated points are provided. Checking and fixing their existence in the input geometry is up to the user.