Geometry#
- class sectionproperties.pre.geometry.Geometry(geom: Polygon, material: Material = Material(name='default', elastic_modulus=1, poissons_ratio=0, yield_strength=1, density=1, color='w'), control_points: Point | tuple[float, float] | None = None, tol: int = 12)[source]#
Bases:
object
Class for defining the geometry of a contiguous section of a single material.
Provides an interface for the user to specify the geometry defining a section. A method is provided for generating a triangular mesh, transforming the section (e.g. translation, rotation, perimeter offset, mirroring), aligning the geometry to another geometry, and designating stress recovery points.
Methods
Aligns the geometry to a center point.
Aligns the geometry to another Geometry object.
Assigns a control point to the geometry.
Calculates the area of the geometry.
Calculates the centroid of the geometry.
Calculate geometry extents.
Calculates the exterior perimeter of the geometry.
Alias for
create_facets_and_control_points()
.Creates geometry data from shapely data.
Creates a quadratic triangular mesh from the Geometry object.
Creates a Geometry object from a Rhino
.3dm
file.An interface for the creation of Geometry objects from CAD .dxf files.
Creates Geometry from points, facets, a control point and holes.
Load an encoded single surface planer brep.
Mirrors the geometry about a point on either the x or y-axis.
Dilates or erodes the section perimeter by a discrete amount.
Plots the geometry defined by the input section.
Rotate the Geometry object.
Shifts the points in the geometry.
Returns a new Geometry object translated by (
x_offset
,y_offset
).Splits geometry about a line.
Attributes
Returns the recovery points.
- __init__(geom: Polygon, material: Material = Material(name='default', elastic_modulus=1, poissons_ratio=0, yield_strength=1, density=1, color='w'), control_points: Point | tuple[float, float] | None = None, tol: int = 12) None [source]#
Inits the Geometry class.
- Parameters:
geom (Polygon) – A Shapely Polygon object that defines the geometry
material (Material) – A material to associate with this geometry
control_points (Point | tuple[float, float] | None) – An
(x, y)
coordinate within the geometry that represents a pre-assigned control point (aka, a region identification point) to be used instead of the automatically assigned control point generated withshapely.Polygon.representative_point()
.tol (int) – Number of decimal places to round the geometry vertices to. A lower value may reduce accuracy of geometry but increases precision when aligning geometries to each other.
- Raises:
ValueError – If
geom
is not valid, i.e. not a shapely object, or a MultiPolygon object
- assign_control_point(control_point: tuple[float, float]) Geometry [source]#
Assigns a control point to the geometry.
Returns a new Geometry object with
control_point
assigned as the control point for the new Geometry. The assignment of a control point is intended to replace the control point automatically generated byshapely.Polygon.representative_point()
.An assigned control point is carried through and transformed with the Geometry whenever it is shifted, aligned, mirrored, unioned, and/or rotated. If a perimeter_offset operation is applied, a check is performed to see if the assigned control point is still valid (within the new region) and, if so, it is kept. If not, a new control point is auto-generated.
The same check is performed when the geometry undergoes a difference operation (with the
-
operator) or a shift_points operation. If the assigned control point is valid, it is kept. If not, a new one is auto-generated.For all other operations (e.g. symmetric difference, intersection, split), the assigned control point is discarded and a new one auto-generated.
- static from_points(points: list[tuple[float, float]], facets: list[tuple[int, int]], control_points: list[tuple[float, float]], holes: list[tuple[float, float]] | None = None, material: Material = Material(name='default', elastic_modulus=1, poissons_ratio=0, yield_strength=1, density=1, color='w')) Geometry [source]#
Creates Geometry from points, facets, a control point and holes.
- Parameters:
points (list[tuple[float, float]]) – List of points (
x
,y
) defining the vertices of the section geometry. If the geometry simply contains a continuous list of exterior points, consider creating ashapely.Polygon
object (only requiring points), and create aGeometry
object using the constructor.facets (list[tuple[int, int]]) – A list of (
start
,end
) indices of vertices defining the edges of the section geoemtry. Can be used to define both external and internal perimeters of holes. Facets are assumed to be described in the order of exterior perimeter, interior perimeter 1, interior perimeter 2, etc.control_points (list[tuple[float, float]]) – An (
x
,y
) coordinate that describes the distinct, contiguous, region of a single material within the geometry. Must be entered as a list of coordinates, e.g. [(0.5, 3.2)]. Exactly one point is required for each geometry with a distinct material. If there are multiple distinct regions, then usesectionproperties.pre.geometry.CompoundGeometry.from_points()
holes (list[tuple[float, float]] | None) – A list of points (
x
,y
) that define interior regions as being holes or voids. The point can be located anywhere within the hole region. Only one point is required per hole region.material (Material) – A
Material
object that is to be assigned.
- Raises:
ValueError – If there is not exactly one control point specified
- Returns:
Geometry object
- Return type:
Example
from sectionproperties.pre import Geometry points = [(0, 0), (10, 5), (15, 15), (5, 10), (6, 6), (9, 7), (7, 9)] facets = [(0, 1), (1, 2), (2, 3), (3, 0), (4, 5), (5, 6), (6, 4)] control_points = [(4, 4)] holes = [(7, 7)] Geometry.from_points( points=points, facets=facets, control_points=control_points, holes=holes, ).plot_geometry()
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- static from_dxf(dxf_filepath: str | Path, spline_delta: float = 0.1, degrees_per_segment: float = 1) Geometry | CompoundGeometry [source]#
An interface for the creation of Geometry objects from CAD .dxf files.
- Parameters:
- Returns:
Geometry or CompoundGeometry object
- Return type:
- classmethod from_3dm(filepath: str | Path, **kwargs: Any) Geometry [source]#
Creates a Geometry object from a Rhino
.3dm
file.- Parameters:
- Keyword Arguments:
refine_num (Optional[int]) – Bézier curve interpolation number. In Rhino a surface’s edges are nurb based curves. Shapely does not support nurbs, so the individual Bézier curves are interpolated using straight lines. This parameter sets the number of straight lines used in the interpolation. Default is 1.
vec1 (Optional[numpy.ndarray]) – A 3d vector in the Shapely plane. Rhino is a 3D geometry environment. Shapely is a 2D geometric library. Thus a 2D plane needs to be defined in Rhino that represents the Shapely coordinate system.
vec1
represents the 1st vector of this plane. It will be used as Shapely’s x direction. Default is [1,0,0].vec2 (Optional[numpy.ndarray]) – Continuing from
vec1
,vec2
is another vector to define the Shapely plane. It must not be [0,0,0] and it’s only requirement is that it is any vector in the Shapely plane (but not equal tovec1
). Default is [0,1,0].plane_distance (Optional[float]) – The distance to the Shapely plane. Default is 0.
project (Optional[bool]) – Controls if the breps are projected onto the plane in the direction of the Shapley plane’s normal. Default is True.
parallel (Optional[bool]) – Controls if only the rhino surfaces that have the same normal as the Shapely plane are yielded. If true, all non parallel surfaces are filtered out. Default is False.
- Raises:
RuntimeError – A RuntimeError is raised if two or more polygons are found. This is dependent on the keyword arguments. Try adjusting the keyword arguments if this error is raised.
ImportError – If
rhino3dm
is not installed. To enable rhino features usepip install sectionproperties[rhino]
.
- Returns:
A Geometry object.
- Return type:
- classmethod from_rhino_encoding(r3dm_brep: str, **kwargs: Any) Geometry [source]#
Load an encoded single surface planer brep.
- Parameters:
- Keyword Arguments:
refine_num (Optional[int]) – Bézier curve interpolation number. In Rhino a surface’s edges are nurb based curves. Shapely does not support nurbs, so the individual Bézier curves are interpolated using straight lines. This parameter sets the number of straight lines used in the interpolation. Default is 1.
vec1 (Optional[numpy.ndarray]) – A 3d vector in the Shapely plane. Rhino is a 3D geometry environment. Shapely is a 2D geometric library. Thus a 2D plane needs to be defined in Rhino that represents the Shapely coordinate system.
vec1
represents the 1st vector of this plane. It will be used as Shapely’s x direction. Default is [1,0,0].vec2 (Optional[numpy.ndarray]) – Continuing from
vec1
,vec2
is another vector to define the Shapely plane. It must not be [0,0,0] and it’s only requirement is that it is any vector in the Shapely plane (but not equal tovec1
). Default is [0,1,0].plane_distance (Optional[float]) – The distance to the Shapely plane. Default is 0.
project (Optional[bool]) – Controls if the breps are projected onto the plane in the direction of the Shapley plane’s normal. Default is True.
parallel (Optional[bool]) – Controls if only the rhino surfaces that have the same normal as the Shapely plane are yielded. If true, all non parallel surfaces are filtered out. Default is False.
- Raises:
ImportError – If
rhino3dm
is not installed. To enable rhino features usepip install sectionproperties[rhino]
.- Returns:
A Geometry object found in the encoded string.
- Return type:
- create_facets_and_control_points() None [source]#
Creates geometry data from shapely data.
Generates points, facets, control points, holes and perimeter from the shapely geometry.
- compile_geometry() None [source]#
Alias for
create_facets_and_control_points()
.Alters attributes .points, .facets, .holes, .control_points to represent the data in the shapely geometry.
- create_mesh(mesh_sizes: float | list[float], min_angle: float = 30.0, coarse: bool = False) Geometry [source]#
Creates a quadratic triangular mesh from the Geometry object.
- Parameters:
mesh_sizes (float | list[float]) – A float describing the maximum mesh element area to be used within the Geometry-object finite-element mesh (may also be a list of length 1).
min_angle (float) – The meshing algorithm adds vertices to the mesh to ensure that no angle smaller than the minimum angle (in degrees, rounded to 1 decimal place). Note that small angles between input segments cannot be eliminated. If the minimum angle is 20.7 deg or smaller, the triangulation algorithm is theoretically guaranteed to terminate (given sufficient precision). The algorithm often doesn’t terminate for angles greater than 33 deg. Some meshes may require angles well below 20 deg to avoid problems associated with insufficient floating-point precision.
coarse (bool) – If set to True, will create a coarse mesh (no area or quality constraints)
- Raises:
ValueError –
mesh_sizes
is not valid- Returns:
Geometry
object with mesh data stored in.mesh
attribute. ReturnedGeometry
object is self, not a new instance.- Return type:
Example
The following example creates a circular cross-section with a diameter of 50 mm with 64 points, and generates a mesh with a maximum triangular area of 2.5 mm2.
from sectionproperties.pre.library import circular_section from sectionproperties.analysis import Section geom = circular_section(d=50, n=64) geom = geom.create_mesh(mesh_sizes=2.5) Section(geom).plot_mesh(materials=False)
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- align_to(other: Geometry | CompoundGeometry | tuple[float, float], on: str, inner: bool = False) Geometry [source]#
Aligns the geometry to another Geometry object.
Returns a new Geometry object, representing
self
translated so that is alignedon
one of the outer bounding box edges ofother
.If
other
is a tuple representing an (x
,y
) coordinate, then the new Geometry object will represent ‘self’ translated so that it is alignedon
that side of the point.- Parameters:
other (Geometry | CompoundGeometry | tuple[float, float]) – Either another Geometry or a tuple representing an (
x
,y
) coordinate point thatself
should align to.on (str) – A str of either “left”, “right”, “bottom”, or “top” indicating which side of
other
thatself
should be aligned to.inner (bool) – If True, align
self
toother
in such a way thatself
is aligned to the “inside” ofother
. In other words, alignself
toother
on the specified edge so they overlap.
- Returns:
Geometry object translated to alignment location
- Return type:
Example
from sectionproperties.pre.library import rectangular_section from sectionproperties.pre.library import triangular_section rect = rectangular_section(b=100, d=50) tri = triangular_section(b=50, h=50) tri = tri.align_to(other=rect, on="top") (rect + tri).plot_geometry()
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- align_center(align_to: Geometry | tuple[float, float] | None = None) Geometry [source]#
Aligns the geometry to a center point.
Returns a new Geometry object, translated in both
x
andy
, so that the the new object’s centroid will be aligned with the centroid of the object inalign_to
. Ifalign_to
is an (x
,y
) coordinate, then the centroid will be aligned to the coordinate. Ifalign_to
isNone
then the new object will be aligned with its centroid at the origin.- Parameters:
align_to (Geometry | tuple[float, float] | None) – Another Geometry to align to, an (
x
,y
) coordinate orNone
- Raises:
ValueError –
align_to
is not valid- Returns:
Geometry object translated to new alignment
- Return type:
Example
from sectionproperties.pre.library import rectangular_section from sectionproperties.pre.library import triangular_section rect = rectangular_section(b=200, d=200) tri = triangular_section(b=50, h=50) tri = tri.align_center(align_to=rect) geom = rect + tri geom.holes = [(100, 100)] geom.control_points = [(25, 25)] geom.plot_geometry()
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- shift_section(x_offset: float = 0.0, y_offset: float = 0.0) Geometry [source]#
Returns a new Geometry object translated by (
x_offset
,y_offset
).- Parameters:
- Returns:
New Geometry object shifted by
x_offset
andy_offset
- Return type:
Example
from sectionproperties.pre.library import rectangular_section rect1 = rectangular_section(b=200, d=100) rect2 = rect1.shift_section(x_offset=100, y_offset=100) (rect1 + rect2).plot_geometry()
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- rotate_section(angle: float, rot_point: tuple[float, float] | str = 'center', use_radians: bool = False) Geometry [source]#
Rotate the Geometry object.
Rotates the geometry and specified angle about a point. If the rotation point is not provided, rotates the section about the center of the geometry’s bounding box.
- Parameters:
angle (float) – Angle (degrees by default) by which to rotate the section. A positive angle leads to a counter-clockwise rotation.
rot_point (tuple[float, float] | str) – Point (
x
,y
) about which to rotate the section. If not provided, will rotate about the “center” of the geometry’s bounding box.use_radians (bool) – Boolean to indicate whether
angle
is in degrees or radians. If True,angle
is interpreted as radians.
- Returns:
New Geometry object rotated by
angle
aboutrot_point
- Return type:
Example
from sectionproperties.pre.library import i_section geom = i_section(d=203, b=133, t_f=7.8, t_w=5.8, r=8.9, n_r=8) geom.rotate_section(angle=-30).plot_geometry()
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- mirror_section(axis: str = 'x', mirror_point: tuple[float, float] | str = 'center') Geometry [source]#
Mirrors the geometry about a point on either the x or y-axis.
- Parameters:
- Returns:
New Geometry object mirrored on
axis
aboutmirror_point
- Return type:
Example
The following example mirrors a 200PFC section about the y-axis:
from sectionproperties.pre.library import channel_section geom = channel_section(d=200, b=75, t_f=12, t_w=6, r=12, n_r=8) geom.mirror_section(axis="y", mirror_point=(0, 0)).plot_geometry()
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- split_section(point_i: tuple[float, float], point_j: tuple[float, float] | None = None, vector: tuple[float, float] | None | ndarray[Any, dtype[float64]] = None) tuple[list[Geometry], list[Geometry]] [source]#
Splits geometry about a line.
Splits, or bisects, the geometry about a line, as defined by two points on the line or by one point on the line and a vector. Either
point_j
orvector
must be given. Ifpoint_j
is given,vector
is ignored.Returns a tuple of two lists each containing new Geometry instances representing the
"top"
and"bottom"
portions, respectively, of the bisected geometry.If the line is a vertical line then the
"right"
and"left"
portions, respectively, are returned.- Parameters:
point_i (tuple[float, float]) – A tuple of (
x
,y
) coordinates to define a first point on the linepoint_j (tuple[float, float] | None) – A tuple of (
x
,y
) coordinates to define a second point on the linevector (tuple[float, float] | None | ndarray[Any, dtype[float64]]) – A tuple or numpy array of (
x
,y
) components to define the line direction
- Raises:
ValueError – Line definition is invalid
- Returns:
A tuple of lists containing Geometry objects that are bisected about the line defined by the two given points. The first item in the tuple represents the geometries on the
"top"
of the line (or to the"right"
of the line, if vertical) and the second item represents the geometries to the"bottom"
of the line (or to the"left"
of the line, if vertical).- Return type:
Example
The following example splits a 200PFC section about the x-axis at
y=100
:from sectionproperties.pre.library import channel_section geom = channel_section(d=200, b=75, t_f=12, t_w=6, r=12, n_r=8) top_geoms, bot_geoms = geom.split_section( point_i=(0, 100), point_j=(1, 100), ) (top_geoms[0] + bot_geoms[0]).plot_geometry()
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- offset_perimeter(amount: float = 0.0, where: str = 'exterior', resolution: int = 12) Geometry | CompoundGeometry [source]#
Dilates or erodes the section perimeter by a discrete amount.
- Parameters:
amount (float) – Distance to offset the section by. A negative value “erodes” the section. A positive value “dilates” the section.
where (str) – One of either
"exterior"
,"interior"
, or"all"
to specify which edges of the geometry to offset. If geometry has no interiors, then this parameter has no effect.resolution (int) – Number of segments used to approximate a quarter circle around a point
- Raises:
ValueError –
where
is invalidValueError – Attempted to offset internally where there are no holes
- Returns:
Geometry object translated to new alignment
- Return type:
Example
The following example erodes a 200PFC section by 2 mm:
from sectionproperties.pre.library import channel_section geom = channel_section(d=200, b=75, t_f=12, t_w=6, r=12, n_r=8) geom.offset_perimeter(amount=-2.0).plot_geometry()
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- shift_points(point_idxs: int | list[int], dx: float = 0.0, dy: float = 0.0, abs_x: float | None = None, abs_y: float | None = None) Geometry [source]#
Shifts the points in the geometry.
Translates one (or many points) in the geometry by either a relative amount or to a new absolute location. Returns a new Geometry representing the original with the selected point(s) shifted to the new location.
Points are identified by their index, their relative location within the points list found in
self.points
. You can callself.plot_geometry(labels="points")
to see a plot with the points labeled to find the appropriate point indexes.- Parameters:
point_idxs (int | list[int]) – An integer representing an index location or a list of integer index locations.
dx (float) – The number of units in the x-direction to shift the point(s) by
dy (float) – The number of units in the y-direction to shift the point(s) by
abs_x (float | None) – Absolute x-coordinate in coordinate system to shift the point(s) to. If
abs_x
is provided,dx
is ignored. If providing a list topoint_idxs
, all points will be moved to this absolute location.abs_y (float | None) – Absolute y-coordinate in coordinate system to shift the point(s) to. If
abs_y
is provided,dy
is ignored. If providing a list topoint_idxs
, all points will be moved to this absolute location.
- Returns:
Geometry object with selected points translated to the new location
- Return type:
Example
The following example expands the sides of a rectangle, one point at a time, to make it a square:
from sectionproperties.pre.library import rectangular_section geom = rectangular_section(d=200, b=150) # using relative shifting geom_step_1 = geom.shift_points(point_idxs=1, dx=50) # using absolute relocation geom_step_1.shift_points(point_idxs=2, abs_x=200).plot_geometry()
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- plot_geometry(labels: tuple[str] = ('control_points',), title: str = 'Cross-Section Geometry', cp: bool = True, legend: bool = True, **kwargs: Any) matplotlib.axes.Axes [source]#
Plots the geometry defined by the input section.
- Parameters:
labels (tuple[str]) – A tuple of str which indicate which labels to plot. Can be one or a combination of
"points"
,"facets"
,"control_points"
, or an empty tuple to indicate no labels.title (str) – Plot title
cp (bool) – If set to True, plots the control points
legend (bool) – If set to True, plots the legend
kwargs (Any) – Passed to
plotting_context()
- Returns:
Matplotlib axes object
- Return type:
- calculate_extents() tuple[float, float, float, float] [source]#
Calculate geometry extents.
Calculates the minimum and maximum x and y-values amongst the list of points; the points that describe the bounding box of the Geometry instance.
- calculate_perimeter() float [source]#
Calculates the exterior perimeter of the geometry.
- Returns:
Geometry perimeter
- Return type:
- calculate_area() float [source]#
Calculates the area of the geometry.
- Returns:
Geometry area
- Return type:
- property recovery_points: list[tuple[float, float]] | list[Point]#
Returns the recovery points.
- Returns:
Recovery points
- __or__(other: Geometry | CompoundGeometry) Geometry | CompoundGeometry [source]#
Performs a union on Geometry objects with the
|
operator.- Parameters:
other (Geometry | CompoundGeometry) – Geometry object to perform the union with
- Raises:
ValueError – Unable to perform union
- Returns:
New Geometry object
- Return type:
Example
The following example combines two rectangles using the
|
operator:from sectionproperties.pre.library import rectangular_section rect1 = rectangular_section(d=100, b=200) rect2 = rectangular_section(d=100, b=200).shift_section( x_offset=150, y_offset=70, ) (rect1 | rect2).plot_geometry()
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- __xor__(other: Geometry | CompoundGeometry) Geometry | CompoundGeometry [source]#
Performs a symmetric difference on Geometry objects with the
^
operator.Returns the regions of geometry that are not overlapping.
- Parameters:
other (Geometry | CompoundGeometry) – Geometry object to perform the symmetric difference with
- Raises:
ValueError – Unable to perform symmetric difference
- Returns:
New Geometry object
- Return type:
Example
The following example performs a symmetric difference on two circles with the
^
operator:from sectionproperties.pre.library import circular_section from sectionproperties.analysis import Section circ1 = circular_section(d=100, n=64) circ2 = circular_section(d=100, n=64).shift_section(x_offset=35) (circ1 ^ circ2).plot_geometry()
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- __sub__(other: Geometry | CompoundGeometry) Geometry | CompoundGeometry [source]#
Performs a difference operation on Geometry objects with the
-
operator.Subtracts the second geometry from the first geometry.
- Parameters:
other (Geometry | CompoundGeometry) – Geometry object to perform the difference operation with
- Raises:
ValueError – Unable to perform difference
- Returns:
New Geometry object
- Return type:
Example
The following example creates a hollow box using the
-
operator:from sectionproperties.pre.library import rectangular_section rect1 = rectangular_section(d=400, b=200) rect2 = rectangular_section(d=300, b=100).align_center(align_to=rect1) (rect1 - rect2).plot_geometry()
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- __add__(other: Geometry | CompoundGeometry) CompoundGeometry [source]#
Combine Geometry objects into a CompoundGeometry using the
+
operator.- Parameters:
other (Geometry | CompoundGeometry) – Geometry object to perform the combination with
- Raises:
ValueError – Unable to perform combination operation
- Returns:
New Geometry object
- Return type:
Example
The following example creates a tee section the
+
operator:from sectionproperties.pre.library import rectangular_section flange = rectangular_section(d=16, b=200) web = ( rectangular_section(d=284, b=16) .align_center(align_to=flange) .align_to(other=flange, on="bottom") ) (flange + web).plot_geometry()
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- __and__(other: Geometry | CompoundGeometry) Geometry | CompoundGeometry [source]#
Performs an intersection on Geometry objects with the
&
operator.Returns the regions of geometry common to both geometries.
- Parameters:
other (Geometry | CompoundGeometry) – Geometry object to perform the intersection with
- Raises:
ValueError – Unable to perform intersection
- Returns:
New Geometry object
- Return type:
Example
The following example performs an intersection of a square and circle using the
&
operator:from sectionproperties.pre.library import rectangular_section from sectionproperties.pre.library import circular_section rect = rectangular_section(d=200, b=200).align_center(align_to=(0, 0)) circle = circular_section(d=250, n=64) (rect & circle).plot_geometry()
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