linear_blend_skinning

linear_blend_skinning(V, Ws, Rs, Ts)

Deform a mesh using linear blend skinning, given a list of weights, rotations and translations.

Parameters:

Name	Type	Description	Default
V	(n,3) numpy array	vertex list of a triangle mesh	required
Ws	(n,m) numpy array	weights for each vertex and each handle	required
Rs	(m,3,3) numpy array	rotations for each handle	required
Ts	(m,3) numpy array	translations for each handle	required
Returns			required
U	(n,3) numpy array	deformed vertex list of a triangle mesh	required

Examples:

import numpy as np
import gpytoolbox as gpt
# Create a mesh
V = np.array([[0,0,0],[1,0,0],[0,1,0],[1,1,0]])
F = np.array([[0,1,2],[1,2,3]])
# Create a set of handles
Rs = np.array([np.eye(3),np.eye(3)])
Ts = np.array([[0,0,0],[1,0,0]])
# Create a set of weights
Ws = np.array([[1,0],[0,1],[0,1],[1,0]])
# Deform the mesh
U = gpt.linear_blend_skinning(V,Ws,Rs,Ts)
# Check the result
assert np.allclose(U,np.array([[0,0,0],[2,0,0],[1,1,0],[1,1,0]]))

Source code in src/gpytoolbox/linear_blend_skinning.py

def linear_blend_skinning(V,Ws,Rs,Ts):
    """
    Deform a mesh using linear blend skinning, given a list of weights, rotations and translations.

    Parameters
    ----------
    V : (n,3) numpy array
        vertex list of a triangle mesh
    Ws : (n,m) numpy array
        weights for each vertex and each handle
    Rs : (m,3,3) numpy array
        rotations for each handle
    Ts : (m,3) numpy array
        translations for each handle

    Returns
    -------
    U : (n,3) numpy array
        deformed vertex list of a triangle mesh

    Examples
    --------
    ```python
    import numpy as np
    import gpytoolbox as gpt
    # Create a mesh
    V = np.array([[0,0,0],[1,0,0],[0,1,0],[1,1,0]])
    F = np.array([[0,1,2],[1,2,3]])
    # Create a set of handles
    Rs = np.array([np.eye(3),np.eye(3)])
    Ts = np.array([[0,0,0],[1,0,0]])
    # Create a set of weights
    Ws = np.array([[1,0],[0,1],[0,1],[1,0]])
    # Deform the mesh
    U = gpt.linear_blend_skinning(V,Ws,Rs,Ts)
    # Check the result
    assert np.allclose(U,np.array([[0,0,0],[2,0,0],[1,1,0],[1,1,0]]))
    ```
    """

    U = np.zeros_like(V,dtype=float)
    # print(Ws.shape[1])
    for i in range(Ws.shape[1]):
        rotations = np.dot(V,Rs[i].T)
        rep_weights = np.repeat(Ws[:,i,None],V.shape[1],axis=1)
        rep_translations = np.repeat(Ts[i][None,:],V.shape[0],axis=0)
        U += rep_weights*(rotations + rep_translations)
        # print(U)
    return U