carputils.mesh.Ellipsoid

class carputils.mesh.Ellipsoid(r_a, r_b, r_c, aout=None, bout=None, cout=None, v0=1.0471975511965976, v1=3.141592653589793, div_trans=2, div_vert=25, div_circ=50, flat_top=True, cumulative_offset=True, *args, **kwargs)

Generate a mesh of an ellipsoidal shell.

An ellipsoidal shell is generated with hexahedral and prism elements, divided into tetrahedra if desired. The shell is defined in terms of its internal axes a, b and c, with the outer axes currently being a scalar multiple of those (thickness).

v0 determines the azimuthal angle of the top (base) of the geometry, and v1 determines the azimuthal angle of the bottom (apex). By default, v1 is at the maximum of pi, and is therefore closed at that point. The mesh may be adjusted to have a flat (constant z coordiate) base place by use of the flat_top argument (on by default). Disabling this will case a constant-v base place.

Mesh discretisation is controlled by the div_trans, div_vert and div_circ arguments. div_trans controls the number of hexahedra/prisms generated transmurally, div_vert controls the number of layers of elements are generated between the apex and base, and div_circ controls the number of hexahedra/prisms are in the layer at the equator (v=pi/2) layer of the ellipsoid. This is used to calculate a target circumferential element size, which is in turn used to determine the number of elements to be generated at other layers such that they are of a consistent size.

Args:

r_a : float

Internal radius (x direction) of the ellipsoid shell

r_b : float

Internal radius (y direction) of the ellipsoid shell

r_c : float

Internal radius (z direction) of the ellipsoid shell

aout : float

External radius (x direction) of the ellipsoid shell, defaults to 1.25a

bout : float

External radius (y direction) of the ellipsoid shell, defaults to 1.25b

cout : float

External radius (z direction) of the ellipsoid shell, defaults to 1.15c

v0 : float, optional

Azimuthal angle of the top of the mesh, defaults to pi/3

v1 : float, optional

Aximuthal angle of the bottom of the mesh, defaults to pi (closed apex)

div_trans : int, optional

Number of elements across the radial thickness, defaults to 2

div_vert : int, optional

Number of layers of elements vertically, defaults to 25

div_circ : int, optional

Number of elements around the equator (v=pi/2), defaults to 50

flat_top : bool, optional

True to make a flat (constant z) top to the mesh, defaults to true

cumulative_offset : bool, optional

True to add a cumulative offset to the points, defaults to true

tetrahedrise : bool, optional

True to subdivide the mesh into tetrahedra

fibre_rule : callable, optional

Function describing the transmural variation of fibre angle, takes a single normalised transmural distance on [0,1] and returns a helix angle in radians, defaults to circumferentially oriented fibres

cavity_volume()

Calculate the volume of the cavity analytically.

The actual volume may be less due to discretisation effects.

Returns:

float

The cavity volume

generate_carp_apex_vtx(basename)

Generate vtx file with apex node.

Args:

basename : str

Mesh base name (without extension)

classmethod with_resolution(radius, resolution, lengthratio=1.5, wallthickness=None, apexthickness=None, v0=1.0471975511965976, v1=3.141592653589793, **kwargs)

Simplified interface to generate ellipsoid with target resolution.

Args:

radius : float

Inner radius of ellipsoid cavity

resolution : float

Target mesh edge length

lengthratio : float, optional

Ratio of ellipsoid apical-basal radius to short axis-radius (default: 1.5)

wallthickness : float, optional

Thickness of ellipsoid wall (default: radius/5)

apexthickness : float, optional

Thickness of wall at apex (default: wallthickness)