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barycentric_coordinates

barycentric_coordinates(p, v1, v2, v3)

Per-vertex weights of point inside triangle

Computes the barycentric coordinates of a point inside a triangle in two or three dimensions. If 3D, computes the coordinates of the point's projection to the triangle's plane.

Parameters:

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

Query point coordinates

 required
v1 (dim,) numpy double array

First triangle vertex coordinate

 required
v2 (dim,) numpy double array

Second triangle vertex coordinate

 required
v3 (dim,) numpy double array

Third triangle vertex coordinate

 required

Returns:

Name Type Description
b (3,) numpy double array

Vector of barycentric coordinates

Examples:

from gpytoolbox import barycentric_coordinates
# Generate random triangle points
v1 = np.random.rand(3)
v2 = np.random.rand(3)
v3 = np.random.rand(3)
# Generate random query point using barycentric coordinates
q = 0.2*v1 + 0.3*v2 + 0.5*v3
# Find barycentric coordinates
b = gpytoolbox.barycentric_coordinates(q,v1,v2,v3)
Source code in src/gpytoolbox/barycentric_coordinates.py 
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def barycentric_coordinates(p,v1,v2,v3):
    """Per-vertex weights of point inside triangle

    Computes the barycentric coordinates of a point inside a triangle in two or three dimensions. If 3D, computes the coordinates of the point's *projection* to the triangle's plane.

    Parameters
    ---------
    p : (dim,) numpy double array
        Query point coordinates
    v1 : (dim,) numpy double array
        First triangle vertex coordinate
    v2 : (dim,) numpy double array
        Second triangle vertex coordinate
    v3 : (dim,) numpy double array
        Third triangle vertex coordinate

    Returns
    -------
    b : (3,) numpy double array
        Vector of barycentric coordinates

    Examples
    --------
    ```python
    from gpytoolbox import barycentric_coordinates
    # Generate random triangle points
    v1 = np.random.rand(3)
    v2 = np.random.rand(3)
    v3 = np.random.rand(3)
    # Generate random query point using barycentric coordinates
    q = 0.2*v1 + 0.3*v2 + 0.5*v3
    # Find barycentric coordinates
    b = gpytoolbox.barycentric_coordinates(q,v1,v2,v3)
    ```
    """
    p = np.ravel(p)
    v1 = np.ravel(v1)
    v2 = np.ravel(v2)
    v3 = np.ravel(v3)
    dim = p.shape[0]
    if dim==2:
        tri1_verts = np.vstack((
            p[None,:],
            v2[None,:],
            v3[None,:]
        ))
        tri2_verts = np.vstack((
            v1[None,:],
            p[None,:],
            v3[None,:]
        ))
        tri3_verts = np.vstack((
            v1[None,:],
            v2[None,:],
            p[None,:]
        ))
        tri_verts = np.vstack((
            v1[None,:],
            v2[None,:],
            v3[None,:]
        ))
        a1 = np.squeeze(doublearea(tri1_verts,np.array([[0,1,2]]),signed=True))
        a2 = np.squeeze(doublearea(tri2_verts,np.array([[0,1,2]]),signed=True))
        a3 = np.squeeze(doublearea(tri3_verts,np.array([[0,1,2]]),signed=True))
        a = np.squeeze(doublearea(tri_verts,np.array([[0,1,2]]),signed=True))
        b = np.array([a1/a, a2/a, a3/a])
    elif dim==3:
        u = v2-v1
        v = v3-v1
        n = np.cross(u,v)
        w = p-v1
        n2 = np.sum(n**2.0)
        gamma = np.dot(np.cross(u,w),n)/n2
        beta = np.dot(np.cross(w,v),n)/n2
        alpha = 1 - beta - gamma
        b = np.array([alpha,beta,gamma])
    return b