Geoms#

The EasyFEA.Geoms module in EasyFEA provides essential tools for creating and managing _Geom objects. These geometric objects are used to construct Mesh using the Mesher.

With this module, you can construct:

`Point`([x, y, z, isOpen, r])	Point class.
`Points`(points[, meshSize, isHollow, isOpen])	Points class.
`Domain`(pt1, pt2[, meshSize, isHollow])	Domain (2d or 3d domain) class.
`Line`(pt1, pt2[, meshSize, isOpen])	Line class.
`Circle`(center, diam[, meshSize, isHollow, ...])	Circle class.
`CircleArc`(pt1, pt2[, center, R, P, ...])	CircleArc class.
`Contour`(geoms[, isHollow, isOpen])	Contour class.

Once the geometric objects are created, you can manipulate them using copy(), Translate(), Rotate(), or Symmetry() (see the example for details).

Creating a `Line`#

from EasyFEA.Geoms import Line

line = Line((0,0), (1,1))
line.Plot()

<Axes: >

Creating a `Domain`#

2D Domain#

from EasyFEA.Geoms import Domain

domain = Domain((0, 0), (1, 1))
domain.Plot()

<Axes: >

3D Domain#

from EasyFEA.Geoms import Domain

domain = Domain((0, 0, 0), (1, 1, 1))
domain.Plot()

<Axes3D: >

Creating a `Circle`#

from EasyFEA.Geoms import Circle

circle = Circle((0, 0), 1.0)
circle.Plot()

<Axes: >

Using an axis normal to the circle#

from EasyFEA.Geoms import Circle

circle = Circle((0, 0), 1.0, n=(0.5, 0.5, 0.5))
circle.Plot()

<Axes3D: >

Creating a `CircleArc`#

From 2 `Point` and a Center#

from EasyFEA.Geoms import CircleArc

circleArc = CircleArc((1, 0), (0, 1), center=(0, 0))
circleArc.Plot()

<Axes: >

From 2 `Point` and a Radius#

from EasyFEA.Geoms import CircleArc

circleArc = CircleArc((1, 0), (0, 1), R=0.5)
circleArc.Plot()

<Axes: >

From 2 `Point` and a Point#

from EasyFEA.Geoms import CircleArc

circleArc = CircleArc((1, 0), (0, 1), P=(0.8, 0.8))
circleArc.Plot()

<Axes: >

Creating a `Contour` from `Points`#

from EasyFEA.Geoms import Points

contour = Points([(0, 0), (1,0), (1,1), (0,1)]).Get_Contour()
contour.Plot()

<Axes: >

Add a fillet#

from EasyFEA.Geoms import Point, Points

contour = Points([Point(0, 0, r=0.5), (1,0), (1,1), (0,1)]).Get_Contour()
contour.Plot()

<Axes: >

from EasyFEA.Geoms import Point, Points

contour = Points([Point(0, 0, r=-0.5), (1,0), (1,1), (0,1)]).Get_Contour()
contour.Plot()

<Axes: >

Creating a `Contour` with `Line`, `CircleArc` and `Points`#

from EasyFEA.Geoms import Line, CircleArc, Points, Contour

line = Line((0, 0), (1, 0))
points = Points([(1,0), (1.5, 0.5), (1, 1)])
circleArc = CircleArc((1,1), (0,0), center=(1,0))
contour = Contour([line, points, circleArc])
contour.Plot()

<Axes: >

Manipulate a `_Geom` object using the `copy()`, `Translate()`, `Rotate()`, and `Symmetry()` functions#

from EasyFEA.Geoms import Points

contour1 = Points([(0,0), (1,0), (1,1), (0,1)]).Get_Contour()
contour2 = contour1.copy(); contour2.Translate(dx=4)
contour3 = contour2.copy(); contour3.Rotate(90, (0,0), (0,0,1))
contour4 = contour3.copy(); contour4.Symmetry((0,0), (0,1))

ax = contour1.Plot_Geoms([contour1, contour2, contour3, contour4], plotPoints=False)
ax.legend(["contour1", "contour2", "contour3", "contour4"])

<matplotlib.legend.Legend at 0x78692856050>

Geoms API#

Module containing the geometric functions used to build meshes.

class EasyFEA.Geoms.Circle(center, diam, meshSize=0.0, isHollow=True, isOpen=False, n=(0, 0, 1))[source]#

Bases: _Geom

Circle class.

Get_Contour()[source]#: Creates the contour object associated with the circle

Get_coord_for_plot()[source]#

Returns lines and points coordinates for plotting.

Returns:: Lines and points coordinates as NumPy arrays.
Return type:: tuple of ndarray

property diam: float[source]#: circle’s diameter

property length: float[source]#: circle perimeter

property n: ndarray[tuple[Any, ...], dtype[Any]] | Collection[int | float][source]#: axis normal to the circle

class EasyFEA.Geoms.CircleArc( pt1, pt2, center=None, R=None, P=None, meshSize=0.0, n=(0, 0, 1), isOpen=False, coef=1, )[source]#

Bases: _Geom

CircleArc class.

Get_coord_for_plot()[source]#

Returns lines and points coordinates for plotting.

Returns:: Lines and points coordinates as NumPy arrays.
Return type:: tuple of ndarray

property angle[source]#: circular arc angle [rad]

center#: Point at the center of the arc.

property length: float[source]#: circular arc length

property n: ndarray[tuple[Any, ...], dtype[Any]] | Collection[int | float][source]#: axis normal to the circle arc

pt1#: Starting point of the arc.

pt2#: Ending point of the arc.

pt3#: Midpoint of the circular arc.

property r[source]#: circular arc radius

class EasyFEA.Geoms.Contour(geoms, isHollow=True, isOpen=False)[source]#

Bases: _Geom

Contour class.

Get_coord_for_plot()[source]#

Returns lines and points coordinates for plotting.

Returns:: Lines and points coordinates as NumPy arrays.
Return type:: tuple of ndarray

property length: float[source]#

class EasyFEA.Geoms.Domain(pt1, pt2, meshSize=0.0, isHollow=True)[source]#

Bases: _Geom

Domain (2d or 3d domain) class.

Get_coord_for_plot()[source]#

Returns lines and points coordinates for plotting.

Returns:: Lines and points coordinates as NumPy arrays.
Return type:: tuple of ndarray

class EasyFEA.Geoms.Line(pt1, pt2, meshSize=0.0, isOpen=False)[source]#

Bases: _Geom

Line class.

static distance(pt1, pt2)[source]#

Computes the distance between two points.

Return type:: float

static get_unitVector(pt1, pt2)[source]#

Creates the unit vector between two points.

Return type:: ndarray[tuple[Any, ...], dtype[floating]]

Get_coord_for_plot()[source]#

Returns lines and points coordinates for plotting.

Returns:: Lines and points coordinates as NumPy arrays.
Return type:: tuple of ndarray

property length: float[source]#: distance between the two points of the line

property unitVector: ndarray[tuple[Any, ...], dtype[floating]][source]#: The unit vector for the two points on the line (p2-p1)

class EasyFEA.Geoms.Point(x=0.0, y=0.0, z=0.0, isOpen=False, r=0.0)[source]#

Bases: object

Point class.

Check(coord)[source]#

Checks if coordinates are identical

Return type:: bool

Rotate(theta, center=(0, 0, 0), direction=(0, 0, 1))[source]#

Rotates the point with around an axis.

Parameters:

theta (float) – rotation angle [deg]
center (_types.Coords, optional) – rotation center, by default (0,0,0)
direction (_types.Coords, optional) – rotation direction, by default (0,0,1)

Return type:

None

Symmetry(point=(0, 0, 0), n=(1, 0, 0))[source]#

Symmetrizes the point coordinates with a plane.

Parameters:

point (_types.Coords, optional) – a point belonging to the plane, by default (0,0,0)
n (_types.Coords, optional) – normal to the plane, by default (1,0,0)

Return type:

None

Translate(dx=0.0, dy=0.0, dz=0.0)[source]#

Translates the point.

Return type:: None

copy()[source]#

property coord: ndarray[tuple[Any, ...], dtype[floating]][source]#: [x,y,z] coordinates

isOpen: bool#: point is open

r: float#: radius used for fillet

property x: float[source]#: x coordinate

property y: float[source]#: y coordinate

property z: float[source]#: z coordinate

class EasyFEA.Geoms.Points(points, meshSize=0.0, isHollow=True, isOpen=False)[source]#

Bases: _Geom

Points class.

Get_Contour()[source]#

Creates a contour from the points.

Creates a fillet if a point has a radius which is not 0.

Get_coord_for_plot()[source]#

Returns lines and points coordinates for plotting.

Returns:: Lines and points coordinates as NumPy arrays.
Return type:: tuple of ndarray

property length: float[source]#

pt1#: First point

pt2#: Last point

class EasyFEA.Geoms._Geom(points, meshSize, name, isHollow, isOpen)[source]#

Bases: ABC

Geometric class.

static Plot_Geoms(geoms, ax=None, color='', name='', plotPoints=True, plotLegend=True)[source]#

Plots a list of geometric objects on the same axis.

Parameters:

geoms (list of _Geom) – Geometries to plot.
ax (matplotlib axis, optional) – Axis to use. If None, a new one is created.
color (str, optional) – Line color.
name (str, optional) – Label for the geometries.
plotPoints (bool, optional) – Whether to plot defining points.
plotLegend (bool, optional) – Whether to display the legend.

Returns:

The axis with the plotted geometries.

Return type:

Axes

abstractmethod Get_coord_for_plot()[source]#

Returns lines and points coordinates for plotting.

Returns:: Lines and points coordinates as NumPy arrays.
Return type:: tuple of ndarray

Mesh_2D( inclusions=[], elemType=ElemType.TRI3, cracks=[], refineGeoms=[], isOrganised=False, additionalSurfaces=[], additionalLines=[], additionalPoints=[], folder='', )[source]#

Creates a 2D mesh from a contour and inclusions that must form a closed plane surface.

Parameters:

inclusions (list[Domain, Circle, Points, Contour], optional) – list of hollow and filled geom objects inside the domain
elemType (ElemType, optional) – element type, by default “TRI3” [“TRI3”, “TRI6”, “TRI10”, “TRI15”, “QUAD4”, “QUAD8”, “QUAD9”]
cracks (list[Line | Points | Contour | CircleArc]) – list of geom object used to create open or closed cracks
refineGeoms (list[Domain|Circle|str], optional) – list of geom object for mesh refinement, by default []
isOrganised (bool, optional) – mesh is organized, by default False
additionalSurfaces (list[Domain, Circle, Points, Contour]) – additional surfaces that will be added to or removed from the surfaces created by the contour and the inclusions. (e.g Domain, Circle, Contour, Points). Tip: if the mesh is not well generated, you can also give the inclusions.
additionalLines (list[Union[Line,CircleArc]]) – additional lines that will be added to the surfaces created by the contour and the inclusions. (e.g Domain, Circle, Contour, Points). WARNING: lines must be within the domain.
additionalPoints (list[Point]) – additional points that will be added to the surfaces created by the contour and the inclusions. WARNING: points must be within the domain.
folder (str, optional) – default mesh.msh folder, by default “” does not save the mesh

Returns:

Created mesh

Return type:

Mesh

Mesh_Extrude( inclusions=[], extrude=(0, 0, 1), layers=[], elemType=ElemType.TETRA4, cracks=[], refineGeoms=[], isOrganised=False, additionalSurfaces=[], additionalLines=[], additionalPoints=[], folder='', )[source]#

Creates a 3D mesh by extruding a surface constructed from a contour and inclusions.

Parameters:

inclusions (list[Domain, Circle, Points, Contour], optional) – list of hollow and filled geom objects inside the domain
extrude (Coords, optional) – extrusion vector, by default [0,0,1]
layers (list[int], optional) – layers in the extrusion, by default []
elemType (ElemType, optional) – element type, by default “TETRA4” [“TETRA4”, “TETRA10”, “HEXA8”, “HEXA20”, “HEXA27”, “PRISM6”, “PRISM15”, “PRISM18”]
cracks (list[Line | Points | Contour | CircleArc]) – list of geom object used to create open or closed cracks
refineGeoms (list[Domain|Circle|str], optional) – list of geom object for mesh refinement, by default []
isOrganised (bool, optional) – mesh is organized, by default False
additionalSurfaces (list[Domain, Circle, Points, Contour]) – additional surfaces that will be added to or removed from the surfaces created by the contour and the inclusions. (e.g Domain, Circle, Contour, Points). Tip: if the mesh is not well generated, you can also give the inclusions.
additionalLines (list[Union[Line,CircleArc]]) – additional lines that will be added to the surfaces created by the contour and the inclusions. (e.g Domain, Circle, Contour, Points). WARNING: lines must be within the domain.
additionalPoints (list[Point]) – additional points that will be added to the surfaces created by the contour and the inclusions. WARNING: points must be within the domain.
folder (str, optional) – default mesh.msh folder, by default “” does not save the mesh

Returns:

Created mesh

Return type:

Mesh

Mesh_Revolve( inclusions=[], axis=None, angle=360, layers=[30], elemType=ElemType.TETRA4, cracks=[], refineGeoms=[], isOrganised=False, additionalSurfaces=[], additionalLines=[], additionalPoints=[], folder='', )[source]#

Creates a 3D mesh by rotating a surface along an axis.

Parameters:

inclusions (list[Domain, Circle, Points, Contour], optional) – list of hollow and filled geom objects inside the domain
axis (Line, optional) – revolution axis, by default Line((0, 0), (0, 1))
angle (float|int, optional) – revolution angle in [deg], by default 360
layers (list[int], optional) – layers in extrusion, by default [30]
elemType (ElemType, optional) – element type, by default “TETRA4” [“TETRA4”, “TETRA10”, “HEXA8”, “HEXA20”, “HEXA27”, “PRISM6”, “PRISM15”, “PRISM18”]
cracks (list[Line | Points | Contour | CircleArc]) – list of geom object used to create open or closed cracks
refineGeoms (list[Domain|Circle|str], optional) – list of geom object for mesh refinement, by default []
isOrganised (bool, optional) – mesh is organized, by default False
additionalSurfaces (list[Domain, Circle, Points, Contour]) – additional surfaces that will be added to or removed from the surfaces created by the contour and the inclusions. (e.g Domain, Circle, Contour, Points). Tip: if the mesh is not well generated, you can also give the inclusions.
additionalLines (list[Union[Line,CircleArc]]) – additional lines that will be added to the surfaces created by the contour and the inclusions. (e.g Domain, Circle, Contour, Points). WARNING: lines must be within the domain.
additionalPoints (list[Point]) – additional points that will be added to the surfaces created by the contour and the inclusions. WARNING: points must be within the domain.
folder (str, optional) – default mesh.msh folder, by default “” does not save the mesh

Returns:

Created mesh

Return type:

Mesh

Plot(ax=None, color='', name='', lw=None, ls=None, plotPoints=True)[source]#

Plots the geometry using Matplotlib.

Parameters:

ax (matplotlib axis, optional) – Axis to plot on. If None, a new one is created.
color (str, optional) – Line color.
name (str, optional) – Label for the object.
lw (float, optional) – Line width.
ls (str, optional) – Line style.
plotPoints (bool, optional) – If True, display the object’s defining points.

Returns:

The axis with the plotted geometry.

Return type:

Axes

Rotate(theta, center=(0, 0, 0), direction=(0, 0, 1))[source]#

Rotates the object coordinates around an axis.

Parameters:

theta (float) – rotation angle in [deg]
center (tuple, optional) – rotation center, by default (0,0,0)
direction (tuple, optional) – rotation direction, by default (0,0,1)

Return type:

None

Symmetry(point=(0, 0, 0), n=(1, 0, 0))[source]#

Reflects the geometry with respect to a plane.

Parameters:

point (Coords, optional) – A point on the reflection plane, by default (0, 0, 0).
n (Coords, optional) – Normal vector of the plane, by default (1, 0, 0).

Return type:

None

Translate(dx=0.0, dy=0.0, dz=0.0)[source]#

Translates the geometry in 3D space.

Parameters:

dx (float, optional) – Translation along the x-axis, by default 0.0.
dy (float, optional) – Translation along the y-axis, by default 0.0.
dz (float, optional) – Translation along the z-axis, by default 0.0.

Return type:

None

copy()[source]#

property coord: ndarray[tuple[Any, ...], dtype[floating]][source]#: Returns the coordinates of all points as a NumPy array.

isHollow: bool#: Indicates whether the formed geometry is hollow.

isOpen: bool#: Indicates whether the geometry is open, typically to model cracks.

meshSize: float#: Element size used for meshing.

name: str#: Name of the geometric object.

property points: list[Point][source]#: The list of points used to build the geometric object.

EasyFEA.Geoms.Angle_Between(a, b)[source]#

Computes the angle between vectors a and b (rad). https://math.stackexchange.com/questions/878785/how-to-find-an-angle-in-range0-360-between-2-vectors

Return type:: float

EasyFEA.Geoms.AsCoords(value)[source]#

Returns value as a 3D vector

Return type:: ndarray[tuple[Any, ...], dtype[floating]]

EasyFEA.Geoms.AsPoint(coords)[source]#

Returns coords as a point.

Return type:: Point

EasyFEA.Geoms.Circle_Coords(coord, R, n)[source]#

Returns center from coordinates a radius and and a vector normal to the circle.

return center

Return type:: ndarray[tuple[Any, ...], dtype[floating]]

EasyFEA.Geoms.Circle_Triangle(p1, p2, p3)[source]#

Returns triangle’s center for the circumcicular arc formed by 3 points.

returns center

Return type:: ndarray[tuple[Any, ...], dtype[floating]]

EasyFEA.Geoms.Fillet(P0, P1, P2, r)[source]#

Computes fillet in a corner P0.

returns A, B, C

Parameters:

P0 (_types.AnyArray) – coordinates of point with radius
P1 (_types.AnyArray) – coordinates before P0 coordinates
P2 (_types.AnyArray) – coordinates after P0 coordinates
r (float) – radius (or fillet) at point P0

Returns:

coordinates calculated to construct the radius

Return type:

tuple[_types.FloatArray, _types.FloatArray, _types.FloatArray]

EasyFEA.Geoms.Jacobian_Matrix(i, k)[source]#

Computes the Jacobian matrix to transform local coordinates (i,j,k) to global (x,y,z) coordinates.

p(x,y,z) = J • p(i,j,k) and p(i,j,k) = inv(J) • p(x,y,z)

ix jx kx

iy jy ky

iz jz kz

Parameters:

i (_types.Coords) – i vector
k (_types.Coords) – k vector

Return type:

ndarray[tuple[Any, ...], dtype[floating]]

EasyFEA.Geoms.Normalize(array)[source]#

Must be a vector or matrix.

Return type:: ndarray[tuple[Any, ...], dtype[floating]]

EasyFEA.Geoms.Points_Intersect_Circles(circle1, circle2)[source]#

Computes the coordinates at the intersection of the two circles (i,3).

This only works if they’re on the same plane.

Parameters:

circle1 (Circle) – circle 1
circle2 (Circle) – circle 2

Return type:

ndarray[tuple[Any, ...], dtype[Any]]

EasyFEA.Geoms.Rotate(coord, theta, center=(0, 0, 0), direction=(0, 0, 1))[source]#

Rotates the coordinates arround a specified center and axis.

Parameters:

coord (_types.AnyArray) – coordinates to rotate (n,3)
theta (float) – rotation angle [deg]
center (_types.Iterable, optional) – rotation center, by default (0,0,0)
direction (_types.Iterable, optional) – rotation direction, by default (0,0,1)

Returns:

rotated coordinates

Return type:

_types.FloatArray

EasyFEA.Geoms.Symmetry(coord, point=(0, 0, 0), n=(1, 0, 0))[source]#

Symmetrizes coordinates with a plane.

Parameters:

coord (_types.AnyArray) – coordinates that we want to symmetrise
point (tuple, optional) – a point belonging to the plane, by default (0,0,0)
n (tuple, optional) – normal to the plane, by default (1,0,0)

Returns:

the new coordinates

Return type:

_types.FloatArray

EasyFEA.Geoms.Translate(coord, dx=0.0, dy=0.0, dz=0.0)[source]#

Translates the coordinates.

Return type:: ndarray[tuple[Any, ...], dtype[floating]]

Geoms#

Creating a Line#

Creating a Domain#

2D Domain#

3D Domain#

Creating a Circle#

Using an axis normal to the circle#

Creating a CircleArc#

From 2 Point and a Center#

From 2 Point and a Radius#

From 2 Point and a Point#

Creating a Contour from Points#

Add a fillet#

Creating a Contour with Line, CircleArc and Points#

Manipulate a _Geom object using the copy(), Translate(), Rotate(), and Symmetry() functions#

Geoms API#

This Page

Creating a `Line`#

Creating a `Domain`#

Creating a `Circle`#

Creating a `CircleArc`#

From 2 `Point` and a Center#

From 2 `Point` and a Radius#

From 2 `Point` and a Point#

Creating a `Contour` from `Points`#

Creating a `Contour` with `Line`, `CircleArc` and `Points`#

Manipulate a `_Geom` object using the `copy()`, `Translate()`, `Rotate()`, and `Symmetry()` functions#