Geometrical queries

estimate_local_Lipschitz_constant(model, queries, device, stdv=0.01, n_samples=100, batch_size=5000)

Estimates the lipschitz constant near a point. This function samples points around the query points and returns the max of the gradient norm over the samples.

Parameters:

Name	Type	Description	Default
model	Module	the neural model to evaluate.	required
queries	ndarray	points at which the lipschitz constant needs to be evaluated	required
device	str	device onto which computations are performed.	required
stdv	float	standard deviation of the gaussian noise applied for sampling around query points. Standard deviation can be given as an array of size (queries.shape[0]) to specify different values for each query points. Defaults to 1e-2.	0.01
n_samples	int	number of drawn samples for each query point. Defaults to 100.	100
batch_size	int	batch size for parallel computation. Defaults to 5000.	5000

Returns:

Type	Description
	np.ndarray : a numpy array containing the value of the local Lipschitz constant at each query point.

gradient_descent(query_pts, model, device='cpu', step_size=1.0, batch_size=1000, use_dist=False, normalize_grad=False, max_steps=100)

Performs steps of gradient descent of the given neural implicit function.

Given a point \(x\) and a neural implicit \(f\), this function will iterate: $\(x \leftarrow x - \nabla f(x)\)$

until max_steps is reached.

Parameters:

Name	Type	Description	Default
query_pts	ndarray	starting points.	required
model	Module	the neural implicit function.	required
device	str	device onto which the computation is performed. Defaults to "cpu".	'cpu'
step_size	float	multiplicative parameter of the gradient at each step ("learning rate"). Defaults to 1..	1.0
batch_size	int	batch size for forward/backward computation on the neural implicit. Defaults to 1000.	1000
use_dist	bool	whether to multiply the step by the value of the function at each point. Defaults to False.	False
normalize_grad	bool	whether to normalize the neural implicit gradient at each steps. Defaults to False.	False
max_steps	int	maximum number of steps. Defaults to 100.	100

Returns:

Type	Description
ndarray	np.ndarray: output points

project_onto_iso(query_pts, model, iso=0.0, device='cpu', batch_size=1000, normalize_grad=False, max_steps=100, precision=1e-06)

Project the input points onto the nearest point of a given isosurface.

Parameters:

Name	Type	Description	Default
query_pts	ndarray	input point	required
model	Module	the neural implicit function.	required
iso	float	which isovalue the points should be projected to. Defaults to 0..	0.0
device	str	device onto which the computation is performed. Defaults to "cpu".	'cpu'
batch_size	int	batch size for forward/backward computation on the neural implicit. Defaults to 1000.	1000
normalize_grad	bool	whether to normalize the neural implicit gradient at each steps. Defaults to False.	False
max_steps	int	maximum number of steps. Defaults to 100.	100
precision	float	. Defaults to 1e-6.	1e-06

Returns:

Type	Description
ndarray	np.ndarray: the projected points

sample_iso_projection(init_pts, model, iso=0.0, device='cpu', n_nearest=10, stdv=0.2, step_size=0.1, batch_size=1000, normalize_grad=False, max_steps=10)

Sample a neural implicit isosurface by projecting points onto it and make them repel themselves.

Parameters:

Name	Type	Description	Default
init_pts	ndarray	initial points to be projected onto the isosurface.	required
model	Module	the neural implicit function.	required
iso	float	which isovalue the points should be projected to. Defaults to 0..	0.0
device	str	device onto which the computation is performed. Defaults to "cpu".	'cpu'
n_nearest	int	number of nearest neighbors to consider for the repelling phase. Defaults to 10.	10
stdv	float	standard deviation of the weights of near samples. Defaults to 0.2.	0.2
step_size	float	multiplicative parameter of the gradient at each step ("learning rate"). Defaults to 1..	0.1
batch_size	int	batch size for forward/backward computation on the neural implicit. Defaults to 1000.	1000
normalize_grad	bool	whether to normalize the neural implicit gradient at each steps. Defaults to False.	False
max_steps	int	maximum number of steps. Defaults to 100.	10

Returns:

Type	Description
ndarray	np.ndarray: points sampled on the given isosurface.

References

Iso-Points: Optimizing Neural Implicit Surfaces with Hybrid Representations, Yifan et al. (2021)

sample_iso_raytraced(model, n_rays, iso=0.0, device='cpu', threshold=0.0001, max_iter=1000)

Sample an isosurface of a neural implicit function by tracing rays intersecting the object and returning all ray-shape intersection points.

Parameters:

Name	Type	Description	Default
model	Module	the neural implicit function.	required
n_rays	int	number of rays to sample. The number of sampled points is related to the number of rays	required
iso	float	description. Defaults to 0..	0.0
device	str	description. Defaults to "cpu".	'cpu'
threshold	float	description. Defaults to 1e-4.	0.0001
max_iter	int	description. Defaults to 1000.	1000

Returns:

Type	Description
ndarray	np.ndarray: sampled points

References

• Uniform Sampling of Surfaces by Casting Rays, Ling et al., 2025
• https://github.com/iszihan/implicit-uniform-sampler/blob/main/ImplicitUniformSampler/sampler.py

sample_skeleton(model, res, device='cpu', batch_size=1000, margin=-0.01, grad_norm_threshold=0.5, descent_steps=0)

Samples the skeleton of a neural signed distance field. The skeleton of a shape is defined as the inside discontinuities of its distance field's gradient. This function works by sampling and rejecting points depending on the norm of the gradient at each point. If the neural implicit is well behaved (for instance, a 1-Lip SDF), then the discontinuities have low gradient.

Parameters:

Name	Type	Description	Default
model	Module	the neural implicit function.	required
res	int	resolution of the sampling.	required
device	str	device onto which the computation is performed. Defaults to "cpu".	'cpu'
batch_size	int	batch size for forward/backward computation on the neural implicit. Defaults to 1000.	1000
margin	float	the maximal value of the implicit function for a point to be considered inside the shape. Defaults to -1e-2.	-0.01
grad_norm_threshold	float	the threshold for rejecting non-skeleton points. Defaults to 0.5.	0.5
descent_steps	int	number of gradient descent step to perform on the sampled points to project them to the skeleton. Defaults to 0.	0

Returns:

Type	Description
ndarray	np.ndarray: sampled points on the skeleton of the shape