Forgive me if my expectations for accuracy are unreasonable for the HEAT method. I have the following minimal example

import numpy as np
from potpourri3d import MeshHeatMethodDistanceSolver

solver = MeshHeatMethodDistanceSolver(np.array([[0, 0, 0], [1, 0, 0], [0, 1, 0]]), np.array([[0, 1, 2]]))
solver.compute_distance(0) # -> array([0.        , 0.70710654, 0.70710654])
solver.compute_distance(1) # -> array([0.91430181, 0.        , 1.31933315])
solver.compute_distance(2) # -> array([0.91430181, 1.31933315, 0.        ])

The fact that the first example is returning distances of sqrt(2)/2 makes it seem like this is a bug rather than a limitation of the method somehow.

Its worth noting that setting t_coef=0.001 makes the results of the second two cases more accurate, but the first case returns [0. , 0.70710654, 0.70710654] no matter the value of t_coef

I load a mesh with triangle faces. Then I try to execute these code lines: ` path_solver = pp3d.EdgeFlipGeodesicSolver(V, F) # shares precomputation for repeated solves

path_pts = path_solver.find_geodesic_path(v_start=0, v_end=100)`

But launch "RuntimeError: vertices lie on disconnected components of the surface".

How to solve this problem??

Thank you so much for making the python binding! I use mainly use python for geometry stuff, so this is extremely helpful.

I'm working on some anthropometry, and trying to extract the rise curve, from the navel down the crotch and up to the lower back. I'm trying to use the edge flip solver for this, but the shorter path it found is around the side of the torso. According to the paper, it seems it should be possible to optimize a path through a different direction. Would that be possible to do with the python binding?

Hello!

I've been trying to figure out how to generate a 2D circle mesh for use with potpourri3d, but I keep getting this error: self-edge in face list [x] -- [x]. While investigating, I came across your test functions, generate_verts() and generate_faces(). When I tried to load a mesh using those two, I also got self-edge in face list. However, puzzlingly, I could use the bunny mesh without any errors.

Other errors I got while trying to make my circle mesh work include vertex [x] appears in more than one boundary loop and duplicate edge in list [i] -- [j].

I'm confused because polyscope renders the meshes correctly, but potpourri3d has a hard time with the same meshes.

Thank you!

import numpy as np
import polyscope as ps
import potpourri3d as pp3d

# Initialize polyscope
ps.init()

def generate_verts(n_pts=999):
    np.random.seed(777)        
    return np.random.rand(n_pts, 3)

def generate_faces(n_pts=999):
    # n_pts should be a multiple of 3 for indexing to work out
    np.random.seed(777)        
    rand_faces = np.random.randint(0, n_pts, size=(2*n_pts,3))
    coverage_faces = np.arange(n_pts).reshape(-1, 3)
    faces = np.vstack((rand_faces, coverage_faces))
    return faces

verts = generate_verts()
faces = generate_faces()
solver = pp3d.MeshVectorHeatSolver(verts, faces)
ps.register_surface_mesh("random mesh", verts, faces, smooth_shade=True)

verts, faces = pp3d.read_mesh("bunny_small.ply")
solver = pp3d.MeshVectorHeatSolver(verts, faces)
ps.register_surface_mesh("bunny mesh", verts, faces, smooth_shade=True)

radians = np.linspace(0, 2*np.pi-(2*np.pi/40), 40)
unit_circle = np.stack((np.cos(radians), np.sin(radians), radians*0), axis=1)
verts = unit_circle
faces = []
for i in range(0, verts.shape[0]):
    if i == verts.shape[0]-1:
        faces.append([i, 0, 0])
    else:
        faces.append([i, i+1, 0])
faces = np.array(faces)
solver = pp3d.MeshVectorHeatSolver(verts, faces)
ps.register_surface_mesh("unit circle mesh", verts, faces, smooth_shade=True)

ps.show()

Hey Nicholas,

Thank you for making an excellent github repository, it has been awesome to use for my research. I have found that the lack of typings to be tough when passing values in and out. In this PR I have begun the process of gradually adding types to the python code so that way users can get typed inputs and outputs to their functions and nice hover support.

I have added some doc comments but I wanted you to see the general tone of these first couple before I wrote the rest to ensure that they align with what you'd have ideally done. Let me know if you'd like to see any changes.

Currently we are building a feature that requires us to find which face IDs the edges that connects geodesic point pairs lie on. Currently, we have to solve this in R3 since we have to perform barycentric check on all of the faces, and it gets extremely slow on large meshes. Similar performance is observed when we use trimesh. It would be very useful to have EdgeFlipGeodesicSolver to return geodesic points, geodesic edges, and the face id on which the geodesic edges lie on (instead of just geodesic points) in the case that the mesh is triangular. I hope it would be useful for other users too, especially if they have to propagate linear equations from the derived geodesic path.

I am attempting to compute a geodesic loop through a specific point, but when I use either find_geodesic_loop or find_geodesic_path_poly, the returned path does not contain any of the input points. What I would like is to find a loop through a given point, and use the seed path (loop) to determine the isotopy group of the path.

This image shows what I get currently. The red points are what I input to either find_geodesic_loop or find_geodesic_path_poly. The red line is the result of both of those methods, while the blue line is what I'm hoping for; a loop that starts and ends at the point pointed to in green.

Is there a way to achieve this?

Hello,

Thank you for the amazing library! I was wondering if there is planned support for using any point on the mesh's surface (not exclusively vertices) as inputs for MeshHeatMethodDistanceSolver and EdgeFlipGeodesicSolver. From what I gather it's already a feature within geometry-central as SurfacePoint().

Thanks!

Hi,

I would like to get the geodesic pairwise distance of a mesh. I saw that there are some methods to get the distance for a specific each. However, I did not see how to get efficiently the pairwise distance.

Thanks,

Thank you for this super useful tool ! At present, we cannot have access to the connection Laplacian operator used for Heat Diffusion on tangent vector fields (defined on vertices). It would be useful to be able to access it from the solver (with point cloud and with mesh if possible), for instance L = solver.connection_laplacian() The idea would be to use this laplacian to write gradients (defined at points) in spectral basis. In this spirit, it could be useful to access gradient operators from within the solver too (since they have to be written in the local complex basis at each point which has to be the same as the one for the laplacian I suppose) for instance G = solver.complex_gradient(). Alternatively, one could use for instance gradients defined in DiffusionNet but they would have to agree with the local basis of the connection Laplacian of the solver.

I hope this is enough information, thanks again for your huge help !