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minimum_distance

minimum_distance(v1, f1, v2, f2)

Compute the minimum distance between two triangle meshes in 3D.

Parameters:

Name Type Description Default
v1 (n1,3) array

Vertices of first mesh.

 required
f1 (m1,3) array

Faces of first mesh.

 required
v2 (n2,3) array

Vertices of second mesh.

 required
f2 (m2,3) array

Faces of second mesh.

 required

Returns:

Name Type Description
d float

Minimum distance value.

Notes

This function could be extended with polyline and pointcloud functionality without much trouble.

Examples:

# meshes in v,f and u,g
# Minimum distance value
d = gpytoolbox.minimum_distance(v,f,u,g)
Source code in src/gpytoolbox/minimum_distance.py 
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def minimum_distance(v1,f1,v2,f2):
    """
    Compute the minimum distance between two triangle meshes in 3D.

    Parameters
    ----------
    v1 : (n1,3) array
        Vertices of first mesh.
    f1 : (m1,3) array
        Faces of first mesh.
    v2 : (n2,3) array
        Vertices of second mesh.
    f2 : (m2,3) array
        Faces of second mesh.

    Returns
    -------
    d : float
        Minimum distance value.

    Notes
    -----
    This function could be extended with polyline and pointcloud functionality without much trouble.

    Examples
    --------
    ```python
    # meshes in v,f and u,g
    # Minimum distance value
    d = gpytoolbox.minimum_distance(v,f,u,g)
    ```
    """

    dim = v1.shape[1]
    # Initialize AABB tree for mesh 1
    C1,W1,CH1,PAR1,D1,tri_ind1,_ = initialize_aabbtree(v1,f1)
    # Initialize AABB tree for mesh 2
    C2,W2,CH2,PAR2,D2,tri_ind2,_ = initialize_aabbtree(v2,f2)

    first_queue_pair = [0,0]
    queue = [first_queue_pair]
    current_best_guess = np.Inf
    while len(queue)>0:
        q1, q2 = queue.pop()
        # print("-----------")
        # print("Queue length : {}".format(len(queue)))
        # print("q1: ",q1)
        # print("q2: ",q2)
        # print("CH1[q1,]: ",CH1[q1,:])
        # print("CH2[q2,]: ",CH2[q2,:])
        # print("current_best_guess: ",current_best_guess)
        is_leaf1 = (CH1[q1,1]==-1)
        is_leaf2 = (CH2[q2,1]==-1)
        if (is_leaf1 and is_leaf2):
            # Compute distance between triangles
            t1 = tri_ind1[q1].item()
            t2 = tri_ind2[q2].item()
            # print("t1: ",t1)
            # print("t2: ",t2)
            d = triangle_triangle_distance(v1[f1[t1,0],:],v1[f1[t1,1],:],v1[f1[t1,2],:],v2[f2[t2,0],:],v2[f2[t2,1],:],v2[f2[t2,2],:])
            # print("d: ",d)
            if d<current_best_guess:
                current_best_guess = d
        else:
            # Find distance between boxes
            d = np.max(np.abs(C1[q1,:] - C2[q2,:]) - (W1[q1,:] + W2[q2,:])/2)
            # print("d: ",d)
            if d<current_best_guess:
                # Add children to queue

                if (not is_leaf1) and (is_leaf2):
                    queue.append([CH1[q1,0],q2])
                    queue.append([CH1[q1,1],q2])
                    # queue.append([CH1[q1,2],q2])
                    # queue.append([CH1[q1,3],q2])
                    # if dim==3:
                    #     queue.append([CH1[q1,4],q2])
                    #     queue.append([CH1[q1,5],q2])
                    #     queue.append([CH1[q1,6],q2])
                    #     queue.append([CH1[q1,7],q2])
                if (not is_leaf2) and (is_leaf1):
                    queue.append([q1,CH2[q2,0]])
                    queue.append([q1,CH2[q2,1]])
                    # queue.append([q1,CH2[q2,2]])
                    # queue.append([q1,CH2[q2,3]])
                    # if dim==3:
                    #     queue.append([q1,CH2[q2,4]])
                    #     queue.append([q1,CH2[q2,5]])
                    #     queue.append([q1,CH2[q2,6]])
                    #     queue.append([q1,CH2[q2,7]])
                if (not is_leaf1) and (not is_leaf2):
                    queue.append([CH1[q1,0],CH2[q2,0]])
                    queue.append([CH1[q1,1],CH2[q2,0]])
                    queue.append([CH1[q1,0],CH2[q2,1]])
                    queue.append([CH1[q1,1],CH2[q2,1]])

    return current_best_guess