PyFFD 0.0.6

Tools to create FFD operator from point cloud.

PyFFD

PyFFD is an open-source Free Form Deformation (FFD) library.

Mathematics

We define the FFD opperator as $R_s = \left[ B_i \left( x_j \right) \right]_{(i,j)}$ using B-Spline functions such as:

B(x) = 
    \begin{bmatrix}
        B_1(x) \\
        B_2(x)\\
        \vdots\\
        B_i(x)
    \end{bmatrix}

We can easily project a vector like :

$$ b_s = R_s^T ~ b $$

Code

Quick start

(1) Define a FEM mesh :

n = np.array([[x0, y0], [x1, y1], ...])

(2) Define the elements size and degree for the B-Spline box in each direction :

# Element size per directions
size = [size_x, size_y]
# global setting
size = 0.1 # example

# Element degree per directions
deg = [deg_x, deg_y]
# global setting
deg = 3 # example

(3) Create the B-Spline box python object :

sbox = pf.FFD(n, size, deg)

(4) Compute the FFD opperator $R_s$ :

Rs = sbox.OperatorFFD()