gustaf 0.0.9

Process and visualize numerical-analysis-geometries.

gustaf is a python library to process and visualize numerical-analysis-geometries; especially for Finite Element Methods (FEM) and Isogemetric Analysis (IGA). gustaf currently supports linear elements:

• triangle,
• quadrilateral,
• tetrahedron, and
• hexahedron,

as well as both single and multi-patch splines (with splinepy extension):

• Bezier,
• Rational Bezier,
• BSpline, and
• NURBS.

Installation

gustaf only has numpy for its strict dependency. The minimal version can be installed using pip.

pip install gustaf

To install all the optional dependencies at the same time, you can use:

pip install gustaf[all]

For the latest develop version of gustaf:

pip install git+https://github.com/tataratat/gustaf.git@main

Quick Start

This example shows how to visualize and extract properties of tetrahedrons and NURBS using gustaf. For visualization, gustaf uses vedo as main backend.

import gustaf as gus
import numpy as np


# create tet mesh using Volumes
# it requires vertices and connectivity info, volumes
tet = gus.Volumes(
    vertices=[
        [0.0, 0.0, 0.0],
        [1.0, 0.0, 0.0],
        [0.0, 1.0, 0.0],
        [1.0, 1.0, 0.0],
        [0.0, 0.0, 1.0],
        [1.0, 0.0, 1.0],
        [0.0, 1.0, 1.0],
        [1.0, 1.0, 1.0],
    ],
    volumes=[
        [0, 2, 7, 3],
        [0, 2, 6, 7],
        [0, 6, 4, 7],
        [5, 0, 4, 7],
        [5, 0, 7, 1],
        [7, 0, 3, 1],
    ],
)
tet.show()

# elements can transform to their subelement types
# set unique=True, if you don't want duplicating internal subelements
as_faces = tet.to_faces(unique=False)
as_edges = tet.to_edges(unique=False)

# as geometry classes inherit from its subelement class, we can
# extract subelement connectivity directly.
# Volumes' subelements are faces and subsubelements are edges
face_connectivity = tet.faces()
edge_connectivity = tet.edges()

# this holds
assert np.allclose(face_connectivity, as_faces.faces)
assert np.allclose(edge_connectivity, as_edges.edges)

# the uniqueness of subelement connectivity is useful for finding
# boundary elements, especially ones that appear only once.
# first, general information about connectivity uniqueness
unique_face_infos = tet.unique_faces()  # returns namedtuple
print(unique_face_infos.values)
print(unique_face_infos.ids)
print(unique_face_infos.inverse)
print(unique_face_infos.counts)

# there's a shortcut - single_volumes(), single_faces(), single_edges()
assert np.allclose(
    tet.single_faces(),
    unique_face_infos.ids[unique_face_infos.counts == 1]
)

# let's visualize some scalar data and vector data defined on vertices
tet.vertex_data["arange"] = np.arange(len(tet.vertices))  # scalar
tet.show_options["data_name"] = "arange"
tet.vertex_data["random"] = np.random.random((len(tet.vertices), 3))  # vector
tet.show_options["arrow_data"] = "random"
tet.show()


# create a 2D NURBS disc and visualize
# all the spline types inherits from splinepy's splines and equipped with
# additional functionalities
nurbs = gus.NURBS(
    degrees=[1, 2],
    knot_vectors=[
        [0, 0, 1, 1],
        [0, 0, 0, 1, 1, 2, 2, 2],
    ],
    control_points=[
        [ 1.        ,  0.        ],
        [ 0.5       ,  0.        ],
        [ 1.        ,  0.59493748],
        [ 0.5       ,  0.29746874],
        [ 0.47715876,  0.87881711],
        [ 0.23857938,  0.43940856],
        [-0.04568248,  1.16269674],
        [-0.02284124,  0.58134837],
        [-0.54463904,  0.83867057],
        [-0.27231952,  0.41933528],
    ],
    weights=[
        [1.        ],
        [1.        ],
        [0.85940641],
        [0.85940641],
        [1.        ],
        [1.        ],
        [0.85940641],
        [0.85940641],
        [1.        ],
        [1.        ]
    ]
)
nurbs.show()

# extract / sample using Extractor helper class
# they are all "show()"-able
nurbs_as_faces = nurbs.extract.faces(resolutions=[100, 50])
bezier_patches = nurbs.extract.beziers()  # returns list
boundaries = nurbs.extract.boundaries()  # list of boundary splines
subspline = nurbs.extract.spline(
    {0: [.4, .8], 1: .7}  # define range dimension-wise
)

# create derived spline using Creator helper class
extruded = nurbs.create.extruded(extrusion_vector=[0, 0, 1])
revolved = nurbs.create.revolved(axis=[1, 0, 0], angle=70)
parametric_view = nurbs.create.parametric_view()

# just like vertex_data, you can define spline_data
# for more options, checkout `gus.spline.SplineDataAdaptor`
# following will plot the norm of nurbs' physical coordinates
nurbs.spline_data["coords"] = nurbs
nurbs.show_options["data_name"] = "coords"

# show them all together. each arg is plotted on a separate subplot
# translate tet a bit to avoid overlapping
tet.vertices += [2, 0, 0]
gus.show(
    ["NURBS and translated tet together", nurbs, tet],
    ["Extruded NURBS", extruded],
    ["Revolved NURBS", revolved],
    ["NURBS parametric view", parametric_view],
)

Check out documentations and examples for more!

Dependencies

• numpy
• splinepy
• vedo
• scipy
• meshio
• pytest