Why is the bump not showing up on my torus shape in 3D visualization using 'open3d' in Python?

Question

The code is supposed to create bump at different angle on torus 3d shape. I can see the torus but not the bump when visualize using open3d. Expected outcome and what I got is like the following figure.

The code is as following:

import os, sys

from math import ceil

import numpy as np
import ipywidgets
from skimage import measure
from scipy.ndimage import zoom
from scipy.interpolate import interpn
from IPython.display import display
from einops import rearrange
import igl
from tqdm import tqdm
from sklearn.preprocessing import MinMaxScaler
from scipy import stats
import matplotlib.pyplot as plt
import pandas
import open3d as o3d

#signed distance function for torus
def sdf_torus(x, radius, thickness):
    
    q = np.stack([np.linalg.norm(x[[0, 1]], axis=0) - radius, x[2]])
    return np.linalg.norm(q, axis=0) - thickness

# Crop an n-dimensional image with a centered cropping region
def center_crop(img, shape):
    start = [a // 2 - da // 2 for a, da in zip(img.shape, shape)]
    end = [a + b for a, b in zip(start, shape)]
    slices = tuple([slice(a, b) for a, b in zip(start, end)])
    return img[slices]

# Add noise to coordinates
def gradient_noise(x, scale, strength, seed=None):
    shape = [ceil(s / scale) for s in x.shape[1:]]
    if seed:
        np.random.seed(seed)
    scalar_noise = np.random.randn(*shape)
    scalar_noise = zoom(scalar_noise, zoom=scale)
    scalar_noise = center_crop(scalar_noise, shape=x.shape[1:])
    vector_noise = np.stack(np.gradient(scalar_noise))
    return vector_noise * strength

# Generating and saving the shapes
radius=0.25 
thickness=0.10
noise_scale=20
noise_strength=15
seed=50
bump_width=5
bump_height=30

for idx, bump_angle in tqdm(enumerate(np.linspace(-1, 1, 2))):
    coords = np.linspace(-1, 1, 100)
    x = np.stack(np.meshgrid(coords, coords, coords))
    sdf = sdf_torus(x, radius, thickness)
    verts, faces, normals, values = measure.marching_cubes(sdf, level=0)    
    print(np.min(verts), np.max(verts))
    #add noise
    x_warp = gradient_noise(x, noise_scale, noise_strength, seed)
    #print(np.min(x_warp), np.max(x_warp))
    #bump angle
    angle = np.pi * bump_angle
    gaussian_center = np.array([np.sin(angle), 0., np.cos(angle)]) * radius
    x_dist = np.linalg.norm((x - gaussian_center[:, None, None, None]), axis=0)
    x_bump = bump_height * np.e ** -(1. / bump_width * x_dist ** 2)
    print(np.min(x_bump), np.max(x_bump))
    x_warp += -np.stack(np.gradient(x_bump))
    #print(np.min(x_warp), np.max(x_warp))
    x_warp = rearrange(x_warp, 'v h w d -> h w d v')
    vertex_noise = interpn([np.arange(100) for _ in range(3)], x_warp, verts)
    verts += vertex_noise
    print(np.min(verts), np.max(verts))
    igl.write_triangle_mesh(f"torus_bump_500/torus_bump_{idx}.ply", verts, faces)

For visualizing I use the following code:

pcd.compute_vertex_normals()
pcd.paint_uniform_color([0.8, 0.8, 0.8])
pcd = o3d.io.read_triangle_mesh('torus_bump_500/torus_bump_1.ply')
o3d.visualization.draw_geometries([pcd])

I tried using different width and height of the bump but it is not showing up. It seems like the x_bump is not adding any effect.

Important Note: I need torus shapes with bumps at different angles (one bump per torus). The shapes should have the same number of vertices and faces. I could have implemented different libraries to get the desired shapes using union but I need the desired shape only by distorting some vertices from the torus.

I can visualize using meshplot library but interactive change is not working. I could not find the reason. If it would have been worked I could have seen the effects of the change of various parameters. The code using meshplot is like following:

# I have used jupyter notebook to run the code.
import meshplot as mp

# Meshplot left an annoying print statement in their code. Using this context manager to supress it...
class HiddenPrints:
    def __enter__(self):
        self._original_stdout = sys.stdout
        sys.stdout = open(os.devnull, 'w')

    def __exit__(self, exc_type, exc_val, exc_tb):
        sys.stdout.close()
        sys.stdout = self._original_stdout

plot=None
@mp.interact(
    radius=(0, 0.5, 0.01), 
    thickness=(0.01, 0.25, 0.01), 
    noise_scale=(0.0, 20, 1),
    noise_strength=(0.0, 5, 1),
    seed=(1, 100),
    bump_angle=(-1., 1., 0.01),
    bump_width=(0.01, 0.02, 0.001),
    bump_height=(0.01, 50.),
)
def show(radius, thickness, noise_scale, noise_strength, seed, bump_angle, bump_width, bump_height):
    global plot
    coords = np.linspace(-1, 1, 100)
    x = np.stack(np.meshgrid(coords, coords, coords))
    sdf = sdf_torus(x, radius, thickness)
    verts, faces, normals, values = measure.marching_cubes(sdf, level=0)
    
    x_warp = gradient_noise(x, noise_scale, noise_strength, seed)
    print(x_warp.shape)
    
    angle = np.pi * bump_angle
    gaussian_center = np.array([np.sin(angle), 0., np.cos(angle)]) * radius
    print(gaussian_center.shape)
    x_dist = np.linalg.norm((x - gaussian_center[:, None, None, None]), axis=0)
    print(x_dist.shape)
    x_bump = bump_height * np.e ** -(1. / bump_width * x_dist ** 2)
    print(x_bump.shape)
    x_warp += -np.stack(np.gradient(x_bump))
    
    x_warp = rearrange(x_warp, 'v h w d -> h w d v')
    vertex_noise = interpn([np.arange(100) for _ in range(3)], x_warp, verts)
    verts += vertex_noise
    
    if plot is None:
        plot = mp.plot(verts, faces, return_plot=True)
    else:
        with HiddenPrints():
            plot.update_object(vertices=verts, faces=faces)
        display(plot._renderer)

Answer 1

I got a solution. The values of the parameters should be like the following:

radius=0.25 
thickness=0.10
noise_scale=20
noise_strength=0
seed=50
bump_width=.01
bump_height=30

and changing gaussian_center = np.array([np.sin(angle), 0., np.cos(angle)]) * radius to gaussian_center = np.array([np.cos(angle), np.sin(angle), 0]) * radius make it works.