# cylinders#

cylinders(shape: List[int], r: int, ncylinders: Optional[int] = None, porosity: Optional[float] = None, phi_max: float = 0, theta_max: float = 90, length: Optional[float] = None, maxiter: int = 3, seed=None)[source]#

Generates a binary image of overlapping cylinders given porosity OR number of cylinders.

This is a good approximation of a fibrous mat.

Parameters:
• shape (list) – The size of the image to generate in [Nx, Ny, Nz] where N is the number of voxels. 2D images are not permitted.

• r (scalar) – The radius of the cylinders in voxels

• ncylinders (int) – The number of cylinders to add to the domain. Adjust this value to control the final porosity, which is not easily specified since cylinders overlap and intersect different fractions of the domain.

• porosity (float) – The targeted value for the porosity of the generated mat. The function uses an algorithm for predicted the number of required number of cylinder, and refines this over a certain number of fractional insertions (according to the ‘iterations’ input).

• phi_max (int) – A value between 0 and 90 that controls the amount that the cylinders lie out of the XY plane, with 0 meaning all cylinders lie in the XY plane, and 90 meaning that cylinders are randomly oriented out of the plane by as much as +/- 90 degrees.

• theta_max (int) – A value between 0 and 90 that controls the amount of rotation in the XY plane, with 0 meaning all cylinders point in the X-direction, and 90 meaning they are randomly rotated about the Z axis by as much as +/- 90 degrees.

• length (int) – The length of the cylinders to add. If `None` (default) then the cylinders will extend beyond the domain in both directions so no ends will exist. If a scalar value is given it will be interpreted as the Euclidean distance between the two ends of the cylinder. Note that one or both of the ends may still lie outside the domain, depending on the randomly chosen center point of the cylinder.

• maxiter (int) – The number of fractional fiber insertions used to target the requested porosity. By default a value of 3 is used (and this is typically effective in getting very close to the targeted porosity), but a greater number can be input to improve the achieved porosity.

• seed (int, optional, default = None) – Initializes numpy’s random number generator to the specified state. If not provided, the current global value is used. This means calls to `np.random.state(seed)` prior to calling this function will be respected.

Returns:

image – A boolean array with `True` values denoting the pore space

Return type:

ndarray

Notes

The cylinders_porosity function works by estimating the number of cylinders needed to be inserted into the domain by estimating cylinder length, and exploiting the fact that, when inserting any potentially overlapping objects randomly into a volume v_total (which has units of pixels and is equal to dimx x dimy x dimz, for example), such that the total volume of objects added to the volume is v_added (and includes any volume that was inserted but overlapped with already occupied space), the resulting porosity will be equal to exp(-v_added/v_total).

After intially estimating the cylinder number and inserting a small fraction of the estimated number, the true cylinder volume is calculated, the estimate refined, and a larger fraction of cylinders inserted. This is repeated a number of times according to the `maxiter` argument, yielding an image with a porosity close to the goal.

Examples