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signed_distance

signed_distance(Q, V, F=None, use_cpp=True)

Signed distances from a set of points in space.

General-purpose function which computes the squared distance from a set of points to a mesh (in 3D) or polyline (in 2D). In 3D, this uses an AABB tree for efficient computation.

Parameters:

Name Type Description Default
Q (p,dim) numpy double array

Matrix of query point positions

 required
V (v,dim) numpy double array

Matrix of mesh/polyline/pointcloud coordinates

 required
F (f,s) numpy int array (optional, default None)

Matrix of mesh/polyline/pointcloud indices into V. If None, input is assumed to be an ordered closed polyline in 2D.

 None
use_cpp bool, optional (default False)

If True, uses a C++ implementation to compute the squared distances. This is much faster but requires compilation of the C++ code.

 True

Returns:

Name Type Description
signed_distances (p,) numpy double array

Vector of minimum signed distances
indices (p,) numpy int array

Indices into F (or V, if F is None) of closest elements to each query point
lmbs (p,s) numpy double array

Barycentric coordinates into the closest element of each closest mesh point to each query point

See Also

squared_distance, winding_number

Examples:

v,f = gpytoolbox.read_mesh("bunny.obj") # Read a mesh
v = gpytoolbox.normalize_points(v) # Normalize mesh
# Generate query points
P = 2*np.random.rand(num_samples,3)-4
# Compute distances
signed_distance,ind,b = gpytoolbox.squared_distance(P,v,F=f,use_aabb=True)
Source code in src/gpytoolbox/signed_distance.py 
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def signed_distance(Q,V,F=None,use_cpp=True):
    """Signed distances from a set of points in space.

    General-purpose function which computes the squared distance from a set of points to a mesh (in 3D) or polyline (in 2D). In 3D, this uses an AABB tree for efficient computation.

    Parameters
    ----------
    Q : (p,dim) numpy double array
        Matrix of query point positions
    V : (v,dim) numpy double array
        Matrix of mesh/polyline/pointcloud coordinates
    F : (f,s) numpy int array (optional, default None)
        Matrix of mesh/polyline/pointcloud indices into V. If None, input is assumed to be an ordered *closed* polyline in 2D.
    use_cpp : bool, optional (default False)
        If True, uses a C++ implementation to compute the squared distances. This is much faster but requires compilation of the C++ code.

    Returns
    -------
    signed_distances : (p,) numpy double array
        Vector of minimum signed distances
    indices : (p,) numpy int array
        Indices into F (or V, if F is None) of closest elements to each query point
    lmbs : (p,s) numpy double array
        Barycentric coordinates into the closest element of each closest mesh point to each query point

    See Also
    --------
    squared_distance, winding_number

    Examples
    --------
    ```python
    v,f = gpytoolbox.read_mesh("bunny.obj") # Read a mesh
    v = gpytoolbox.normalize_points(v) # Normalize mesh
    # Generate query points
    P = 2*np.random.rand(num_samples,3)-4
    # Compute distances
    signed_distance,ind,b = gpytoolbox.squared_distance(P,v,F=f,use_aabb=True)
    ```
    """
    # Step 1: Get squared distances
    dim = V.shape[1]
    if F is None:
        # Assume polyline
        assert dim==2
        F = edge_indices(V.shape[0],closed=True)
    sqrD, I, lmbd = squared_distance(Q,V,F,use_cpp=use_cpp,use_aabb=True)

    # Step 2: Get the signs
    W = winding_number(Q,V,F)
    W = np.sign(-2*W+1)

    # Step 3: Compute signed distance
    dist = np.sqrt(sqrD)
    signed_distance = W*dist

    return signed_distance, I, lmbd