### Install TorchSDF

Source: https://github.com/wrc042/torchsdf/blob/main/README.md

Installation script for TorchSDF. This script requires PyTorch to be pre-installed on the system.

```bash
#!/bin/bash
# This script installs TorchSDF
# Requires PyTorch to be installed first

# Example installation command (replace with actual command if available)
echo "Installing TorchSDF..."
# pip install . # or other installation method
echo "TorchSDF installation complete."
```

--------------------------------

### Install TorchSDF via Shell

Source: https://context7.com/wrc042/torchsdf/llms.txt

Instructions for cloning the repository and executing the installation script to set up the environment.

```bash
git clone <repository-url>
cd torchsdf
bash install.sh
```

--------------------------------

### Load OBJ Mesh and Compute SDF

Source: https://context7.com/wrc042/torchsdf/llms.txt

A complete workflow example for TorchSDF. It includes loading an OBJ mesh, converting it to face-vertex format, sampling points, computing SDF values, and optionally generating an SDF grid. Requires trimesh for mesh loading.

```python
import torch
import trimesh
from torchsdf import index_vertices_by_faces, compute_sdf

def load_mesh_to_face_vertices(obj_path, device='cuda'):
    """Load OBJ file and convert to face vertices format."""
    mesh = trimesh.load(obj_path, force='mesh', process=False)
    vertices = torch.tensor(mesh.vertices, device=device, dtype=torch.float32)
    faces = torch.tensor(mesh.faces, device=device, dtype=torch.long)
    face_vertices = index_vertices_by_faces(vertices, faces)
    return face_vertices, vertices, faces

def compute_sdf_grid(face_vertices, resolution=64, bounds=(-1, 1)):
    """Compute SDF on a regular 3D grid."""
    # Create 3D grid
    lin = torch.linspace(bounds[0], bounds[1], resolution, device='cuda')
    grid_x, grid_y, grid_z = torch.meshgrid(lin, lin, lin, indexing='ij')
    points = torch.stack([grid_x, grid_y, grid_z], dim=-1).reshape(-1, 3)

    # Compute SDF
    squared_dist, signs, normals, closest = compute_sdf(points, face_vertices)
    signed_dist = signs.float() * torch.sqrt(squared_dist)

    # Reshape to grid
    sdf_grid = signed_dist.reshape(resolution, resolution, resolution)
    return sdf_grid

# Example usage
device = 'cuda'

# Load mesh (ensure mesh is manifold with correct normals)
face_vertices, verts, faces = load_mesh_to_face_vertices('mesh.obj', device)
print(f"Loaded mesh: {verts.shape[0]} vertices, {faces.shape[0]} faces")

# Sample random points in bounding box
num_samples = 1000000
points = torch.rand((num_samples, 3), device=device) * 2 - 1
points.requires_grad_(True)

# Compute SDF values
squared_dist, signs, normals, closest_points = compute_sdf(points, face_vertices)

# Get signed distances
signed_distance = signs.float() * torch.sqrt(squared_dist)

# Statistics
inside_count = (signs == -1).sum().item()
outside_count = (signs == 1).sum().item()
print(f"Inside: {inside_count}, Outside: {outside_count}")
print(f"Distance range: [{signed_distance.min():.4f}, {signed_distance.max():.4f}]")

# Optional: Compute SDF on regular grid for visualization
sdf_grid = compute_sdf_grid(face_vertices, resolution=64)
print(f"SDF grid shape: {sdf_grid.shape}")
```

--------------------------------

### Perform Gradient Computation with Autograd

Source: https://context7.com/wrc042/torchsdf/llms.txt

Demonstrates how to use PyTorch autograd to compute gradients of SDF values with respect to query points, enabling optimization-based 3D applications.

```python
import torch
from torchsdf import index_vertices_by_faces, compute_sdf

# ... (setup face_vertices) ...
points = torch.rand((1000, 3), device='cuda', requires_grad=True)
squared_dist, signs, normals, closest_points = compute_sdf(points, face_vertices)

loss = squared_dist.sum()
gradients = torch.autograd.grad(loss, points, create_graph=True, retain_graph=True)[0]
print(f"Gradient shape: {gradients.shape}")
```

--------------------------------

### Optimize Mesh using SDF in PyTorch Loop

Source: https://context7.com/wrc042/torchsdf/llms.txt

Demonstrates using torch.optim.Adam to optimize point positions based on SDF computation within a PyTorch training loop. It calculates the mean squared distance to the surface and uses backpropagation to update the points.

```python
optimizer = torch.optim.Adam([points], lr=0.01)
for step in range(100):
    optimizer.zero_grad()
    squared_dist, _, _, _ = compute_sdf(points, face_vertices)
    loss = squared_dist.mean()  # Minimize distance to surface
    loss.backward()
    optimizer.step()
    if step % 20 == 0:
        print(f"Step {step}: mean squared dist = {loss.item():.6f}")
```

--------------------------------

### Index Vertices by Faces in TorchSDF

Source: https://github.com/wrc042/torchsdf/blob/main/README.md

Prepares face vertices required by the `compute_sdf` function. It takes a list of vertices and their corresponding faces to construct the face vertex data structure.

```python
import torch

def index_vertices_by_faces(vertices_features: torch.Tensor, faces: torch.Tensor):
    """
    Returns face_verts required by compute_sdf(pointclouds, face_vertices).

    Args:
        vertices_features (torch.Tensor): Tensor containing vertex coordinates or features.
        faces (torch.Tensor): Tensor containing face definitions (indices of vertices).

    Returns:
        torch.Tensor: Tensor containing the coordinates of vertices for each face.
    """
    # This function uses PyTorch's advanced indexing to gather vertex data for each face.
    # It assumes vertices_features is indexed by the values in faces.
    # Example: if faces[i] = [v1_idx, v2_idx, v3_idx], then face_vertices[i] will contain
    # the coordinates/features of vertices v1_idx, v2_idx, and v3_idx.
    
    # Ensure faces are on the same device as vertices_features
    faces = faces.to(vertices_features.device)
    
    # Use torch.gather or advanced indexing to create face_vertices
    # The exact implementation depends on the structure of vertices_features and faces.
    # Assuming vertices_features is (N, 3) for coordinates and faces is (M, 3) for indices:
    face_vertices = vertices_features[faces]
    
    print("index_vertices_by_faces called with vertices_features shape:", vertices_features.shape)
    print("index_vertices_by_faces called with faces shape:", faces.shape)
    print("Generated face_vertices shape:", face_vertices.shape)
    
    return face_vertices
```

--------------------------------

### index_vertices_by_faces

Source: https://github.com/wrc042/torchsdf/blob/main/README.md

Prepares mesh data by indexing vertices based on face definitions to be used by the compute_sdf function.

```APIDOC
## index_vertices_by_faces(vertices_features, faces)

### Description
Returns the face vertices required by the compute_sdf function by mapping vertex features to face indices.

### Parameters
- **vertices_features** (Tensor) - Required - The feature set or coordinates of the mesh vertices.
- **faces** (Tensor) - Required - The face connectivity indices.

### Returns
- **face_verts** (Tensor) - The formatted face vertices array compatible with compute_sdf.
```

--------------------------------

### Index Vertices by Faces

Source: https://context7.com/wrc042/torchsdf/llms.txt

Utility function to convert vertex and face tensors into a face-vertex format required for SDF computation. It maps mesh connectivity into a (num_faces, 3, 3) tensor structure.

```python
import torch
from torchsdf import index_vertices_by_faces

vertices = torch.tensor([
    [0.0, 0.0, 0.0],
    [1.0, 0.0, 0.0],
    [0.5, 1.0, 0.0],
    [0.5, 0.5, 1.0],
], device='cuda')

faces = torch.tensor([
    [0, 1, 2],
    [0, 1, 3],
    [1, 2, 3],
    [0, 2, 3],
], device='cuda', dtype=torch.long)

face_vertices = index_vertices_by_faces(vertices, faces)
print(f"Face vertices shape: {face_vertices.shape}")
```

--------------------------------

### Compute Signed Distance Field

Source: https://context7.com/wrc042/torchsdf/llms.txt

Computes the SDF for query points relative to a mesh, returning squared distances, inside/outside signs, surface normals, and closest points. This is the primary function for spatial analysis of 3D meshes.

```python
import torch
from torchsdf import index_vertices_by_faces, compute_sdf

# ... (vertices and faces defined as in previous snippet) ...
face_vertices = index_vertices_by_faces(vertices, faces)

query_points = torch.rand((10000, 3), device='cuda') * 2 - 1
query_points.requires_grad_(True)

squared_dist, signs, normals, closest_points = compute_sdf(query_points, face_vertices)

signed_distance = signs.float() * torch.sqrt(squared_dist)
interior_mask = signs == -1
print(f"Points inside mesh: {interior_mask.sum().item()}")
```

--------------------------------

### Compute SDF with TorchSDF

Source: https://github.com/wrc042/torchsdf/blob/main/README.md

Computes the Signed Distance Field (SDF) for a given set of point clouds and mesh face vertices. It returns the squared distance, gradient-defined normals, distance signs (inside -1, outside 1), and the closest points on the mesh surface. This function is designed for CUDA execution.

```python
import torch

def compute_sdf(pointclouds: torch.Tensor, face_vertices: torch.Tensor):
    """
    Computes SDF for point clouds against mesh faces.

    Args:
        pointclouds (torch.Tensor): Unbatched points with shape (num_point, 3).
        face_vertices (torch.Tensor): Unbatched face vertices with shape (num_face, 3, 3).

    Returns:
        tuple: A tuple containing:
            - squared_distance (torch.Tensor): Squared distances from points to the mesh.
            - normals (torch.Tensor): Normals defined by the gradient (p - closest_point).normalized().
            - distance_signs (torch.Tensor): Signs of the distance (-1 for inside, 1 for outside).
            - closest_points (torch.Tensor): Closest points on the mesh surface.
    """
    # This is a placeholder for the actual CUDA kernel implementation
    # The actual implementation would involve complex geometric calculations on the GPU
    print("compute_sdf called with pointclouds shape:", pointclouds.shape)
    print("compute_sdf called with face_vertices shape:", face_vertices.shape)
    
    # Dummy return values for demonstration
    num_points = pointclouds.shape[0]
    squared_distance = torch.rand(num_points, device=pointclouds.device)
    normals = torch.rand(num_points, 3, device=pointclouds.device)
    distance_signs = torch.randint(-1, 2, (num_points,), device=pointclouds.device)
    closest_points = torch.rand(num_points, 3, device=pointclouds.device)
    
    return squared_distance, normals, distance_signs, closest_points
```

--------------------------------

### compute_sdf

Source: https://github.com/wrc042/torchsdf/blob/main/README.md

Computes the signed distance field for a set of points relative to a mesh defined by face vertices.

```APIDOC
## compute_sdf(pointclouds, face_vertices)

### Description
Computes the squared distance, normals, distance signs, and closest points for a given point cloud relative to a mesh.

### Parameters
- **pointclouds** (Tensor) - Required - Unbatched points with shape (num_point, 3).
- **face_vertices** (Tensor) - Required - Unbatched face vertices with shape (num_face, 3, 3).

### Returns
- **squared_distance** (Tensor) - The squared distance from points to the mesh.
- **normals** (Tensor) - Normals defined by the gradient.
- **signs** (Tensor) - Distance signs (inside: -1, outside: 1).
- **closest_points** (Tensor) - The coordinates of the closest points on the mesh surface.
```

=== COMPLETE CONTENT === This response contains all available snippets from this library. No additional content exists. Do not make further requests.