Faces#

Surfaces & faces.

class volmdlr.faces.BSplineFace3D(surface3d: BSplineSurface3D, surface2d: Surface2D, name: str = '')#

Bases: Face3D

A 3D face with a B-spline surface.

This class represents a 3D face with a B-spline surface, which is a smooth surface defined by a set of control points and knots. It is a subclass of the Face3D class and inherits all of its attributes and methods.

Parameters:

surface3d (BSplineSurface3D) – The 3D B-spline surface of the face.
surface2d (Surface2D) – The 2D projection of the face onto the parametric domain (u, v).
name (str) – The name of the face.

adjacent_direction(other_bspline_face3d)#: Find directions (u or v) between two faces, in the nearest edges between them.

adjacent_direction_uu(other_bspline_face3d, corresponding_directions)#: Return the side of the faces that are adjacent.

adjacent_direction_uv(other_bspline_face3d, corresponding_directions)#: Return the sides that are adjacents to other BSpline face.

adjacent_direction_vu(other_bspline_face3d, corresponding_directions)#: Return the sides that are adjacents to other BSpline face.

adjacent_direction_vv(other_bspline_face3d, corresponding_directions)#: Return the side of the faces that are adjacent.

adjacent_direction_xy(other_face3d)#

Find out in which direction the faces are adjacent.

Returns:: adjacent_direction

static approximate_with_arc(edge)#

Return an arc that approximates the given edge.

Parameters:: edge – curve to be approximated by an arc.
Returns:: An arc if possible, otherwise None.

divide_face(list_cutting_contours: list[Contour2D], abs_tol: float = 1e-05)#

Divides a Face 3D with a list of cutting contours.

DEVELOPER NOTE: method repeated on purspose. It was a way to say that bsplineface needs a specific abs_tol, diferents from other faces.

Parameters:

list_cutting_contours – list of contours cutting the face.
abs_tol – tolerance.

extremities(other_bspline_face3d)#: Find points extremities for nearest edges of two faces.

face_tolerance = 0.001#

classmethod from_surface_rectangular_cut(bspline_surface3d, u1: float = 0.0, u2: float = 1.0, v1: float = 0.0, v2: float = 1.0, name: str = '')#: Cut a rectangular piece of the BSplineSurface3D object and return a BSplineFace3D object.

get_approximating_arc_parameters(curve_list)#

Approximates the given curves with arcs and returns the arcs, radii, and centers.

Parameters:: curve_list (list) – A list of curves to approximate.
Returns:: A tuple containing the radius and centers of the approximating arcs.
Return type:: tuple

get_bounding_box()#: Create a bounding box from the face mesh.

grid_size()#: Specify an adapted size of the discretization grid used in face triangulation.

linesegment_intersections(linesegment: LineSegment3D, abs_tol: float = 1e-05) → list[Point3D]#

Get intersections between a BSpline face 3d and a Line Segment 3D.

DEVELOPER NOTE: method repeated on purspose. It was a way to say that bsplineface needs a specific abs_tol, diferents from other faces.

Parameters:

linesegment – other linesegment.
abs_tol – tolerance used.

Returns:

a list of intersections.

merge_with(other_bspline_face3d)#

Merge two adjacent faces.

Type:: other_bspline_face3d : volmdlr.faces.BSplineFace3D
Return type:: merged_face : volmdlr.faces.BSplineFace3D

neutral_fiber()#: Return the faces’ neutral fiber.

neutral_fiber_points(resid_threshold=1e-05, radius_var_threshold=0.25)#

Calculate the neutral fiber points of the face.

Parameters:

resid_threshold – Maximum allowable residual for the arc approximation.
radius_var_threshold – Maximum allowable variation in the radius.

Returns:

The neutral fiber points if they exist, otherwise None.

Return type:

Union[list, None]

pair_with(other_bspline_face3d)#

Find out how the uv parametric frames are located.

It does it by comparing to each other and also how grid 3d can be defined respected to these directions.

Parameters:: other_bspline_face3d (volmdlr.faces.BSplineFace3D) – BSplineFace3D
Returns:: corresponding_direction, grid2d_direction
Return type:: Tuple[?, ?]

to_planeface3d(plane3d: Plane3D | None = None)#

Convert a Bspline face 3d to a Plane face 3d (using or without a reference Plane3D).

Parameters:: plane3d (Plane3D, optional) – A reference Plane3D, defaults to None
Returns:: A Plane face 3d.
Return type:: PlaneFace3D

triangulation_lines(resolution=25)#: Specify the number of subdivision when using triangulation by lines. (Old triangulation).

class volmdlr.faces.ConicalFace3D(surface3d: ConicalSurface3D, surface2d: Surface2D, name: str = '')#

Bases: PeriodicalFaceMixin, Face3D

Defines a ConicalFace3D class.

Parameters:

surface3d (ConicalSurface3D.) – a conical surface 3d.
surface2d (Surface2D.) – a 2d surface to define the conical face.

circle_inside(circle: Circle3D)#

Verify if a circle 3D lies completely on the Conical face.

Parameters:: circle – Circle to be verified.
Returns:: True if circle inside face. False otherwise.

classmethod from_base_and_vertex(conical_surface3d, contour: Contour3D, vertex: Point3D, name: str = '')#

Return the conical face defined by the contour of the base and the cone vertex.

Parameters:

conical_surface3d – surface 3d.
contour (volmdlr.wires.Contour3D) – Cone, contour base.
name – the name to inject in the new face

Returns:

Conical face.

Return type:

ConicalFace3D

classmethod from_surface_rectangular_cut(conical_surface3d, theta1: float, theta2: float, z1: float, z2: float, name: str = '')#: Cut a rectangular piece of the ConicalSurface3D object and return a ConicalFace3D object.

neutral_fiber()#: Return the faces’ neutral fiber.

triangulation_lines(angle_resolution=5)#: Specify the number of subdivision when using triangulation by lines. (Old triangulation).

class volmdlr.faces.CylindricalFace3D(surface3d: CylindricalSurface3D, surface2d: Surface2D, name: str = '')#

Bases: PeriodicalFaceMixin, Face3D

Defines a CylindricalFace3D class.

Parameters:

surface3d (CylindricalSurface3D.) – a cylindrical surface 3d.
surface2d (Surface2D.) – a 2d surface to define the cylindrical face.

Example:

contours 2d is rectangular and will create a classic cylinder with x= 2*pi*radius, y=h

adjacent_direction(other_face3d)#

Find out in which direction the faces are adjacent.

Parameters:: other_face3d (volmdlr.faces.CylindricalFace3D) – The face to evaluation.

arc_inside(arc: Arc3D)#

Verify if Arc3D is inside a CylindricalFace3D.

Parameters:: arc – Arc3D to be verified.
Returns:: True if it is inside, False otherwise.

arcellipse_inside(arcellipse: ArcEllipse3D)#

Verify if ArcEllipse3D is inside a CylindricalFace3D.

Parameters:: arcellipse – ArcEllipse3D to be verified.
Returns:: True if it is inside, False otherwise.

copy(deep=True, memo=None)#: Return a copy of the CylindricalFace3D.

face_inside(face2, abs_tol: float = 1e-06)#

Verify if a face is inside another one.

It returns True if face2 is inside or False if the opposite.

face_tolerance = 0.0001#

classmethod from_ocp(ocp_face: TopoDS_Shape)#: Translate an occt face into a volmdlr face.

classmethod from_surface_rectangular_cut(cylindrical_surface, theta1: float, theta2: float, param_z1: float, param_z2: float, name: str = '')#: Cut a rectangular piece of the CylindricalSurface3D object and return a CylindricalFace3D object.

fullarc_inside(fullarc: FullArc3D)#

Verify if FullArc3D is inside a CylindricalFace3D.

Parameters:: fullarc – FullArc3D to be verified.
Returns:: True if it is inside, False otherwise.

get_geo_lines(tag: int, line_loop_tag: list[int])#: Get the lines that define a CylindricalFace3D in a .geo file.

min_x_density = 5#

min_y_density = 1#

neutral_fiber()#: Return the faces’ neutral fiber.

parametrized_grid_size(angle_resolution, z_resolution)#

Get size for parametrized grid.

Parameters:

angle_resolution – angle resolution.
z_resolution – z resolution.

Returns:

number of points in x and y.

planeface_intersections(planeface: PlaneFace3D)#

Find intersections with the given plane face.

Parameters:: planeface – Plane face to evaluate the intersections.

triangulation_lines(angle_resolution=5)#: Specify the number of subdivision when using triangulation by lines. (Old triangulation).

class volmdlr.faces.ExtrusionFace3D(surface3d: ExtrusionSurface3D, surface2d: Surface2D, name: str = '')#

Bases: Face3D

A 3D face with a ruled surface.

This class represents a 3D face with a ruled surface, which is a surface formed by straight lines connecting two input curves. It is a subclass of the Face3D class and inherits all of its attributes and methods.

Parameters:

surface3d (RuledSurface3D) – The 3D ruled surface of the face.
surface2d (Surface2D) – The 2D projection of the face onto the parametric domain (u, v).
name (str) – The name of the face.

classmethod from_surface_rectangular_cut(extrusion_surface3d: ExtrusionSurface3D, x1: float = 0.0, x2: float = 0.0, y1: float = 0.0, y2: float = 1.0, name: str = '')#: Cut a rectangular piece of the ExtrusionSurface3D object and return a ExtrusionFace3D object.

min_x_density = 50#

min_y_density = 1#

class volmdlr.faces.Face3D(surface3d, surface2d: Surface2D, reference_path: str = '#', name: str = '')#

Bases: Primitive3D

Abstract method to define 3D faces.

area()#: Compute the area of the surface 2d.

property bounding_box#: Return the surface bounding box.

copy(deep=True, memo=None)#: Return a copy of the Face3D.

divide_face(list_cutting_contours: list[Contour2D], abs_tol: float = 1e-06)#

Divides a Face 3D with a list of cutting contours.

Parameters:

list_cutting_contours – list of contours cutting the face.
abs_tol – tolerance.

divide_face_with_closed_cutting_contours(list_closed_cutting_contours, list_faces)#

Divides a Face3D with a list of Open cutting contours.

Contours going from one side to another of the Face, or from the outer contour to one inner contour.

Parameters:

list_closed_cutting_contours – list containing the closed cutting contours
list_faces – list of already divided faces

Returns:

list divided faces

divide_face_with_open_cutting_contours(list_open_cutting_contours, abs_tol: float = 1e-06)#

Divides a face 3D with a list of closed cutting contour, that is, it will cut holes on the face.

Parameters:

list_open_cutting_contours – list containing the open cutting contours.
abs_tol – tolerance.

Returns:

list divided faces.

edge3d_inside(edge3d, abs_tol: float = 1e-06)#: Return True if edge 3d is coplanar to the face.

edge_intersections(edge)#: Get the intersections of an edge and a 3D face.

face_border_intersections(face2)#: Return the intersections of the face outer and inner contour with other given face.

face_decomposition()#: Decompose the face discretization triangle faces inside eight boxes from a bounding box octree structure.

face_inside(face2, abs_tol: float = 1e-06)#

Verify if a face is inside another one.

It returns True if face2 is inside or False if the opposite.

face_intersections(face2, tol=1e-06) → list[Wire3D]#: Calculate the intersections between two Face3D.

face_intersections_outer_contour(face2)#: Return the intersections of the face outer contour with other given face.

face_minimum_distance(other_face, return_points: bool = False)#

Get the minimum distance between two faces.

Parameters:

other_face – second face to search for minimum distance.
return_points – return corresponding point or not.

Returns:

face_tolerance = 1e-06#

frame_mapping(frame: Frame3D, side: str)#

Change frame_mapping and return a new Face3D.

side = ‘old’ or ‘new’

classmethod from_contours3d(surface, contours3d: list[Contour3D], name: str = '', tol: float = 5e-05)#

Return the face generated by a list of contours. Finds out which are outer or inner contours.

Parameters:

surface – Surface3D where the face is defined.
contours3d – List of 3D contours representing the face’s BREP.
name – the name to inject in the new face.
tol – tolerance.

static from_contours3d_with_inner_contours(surface, contours3d, abs_tol: float = 1e-06)#: Helper function to class.

classmethod from_ocp(ocp_face: TopoDS_Shape)#: Translate an occt face into a volmdlr face.

classmethod from_step(arguments, object_dict, **kwargs)#

Convert a step primitive to a Face3D.

Parameters:

arguments (list) – The arguments of the step primitive.
object_dict (dict) – The dictionary containing all the step primitives that have already been instantiated.

Returns:

The corresponding Face3D object.

Return type:

volmdlr.faces.Face3D

fullarc_intersections(fullarc: FullArc3D) → list[Point3D]#

Get intersections between a face 3d and a Full Arc 3D.

Parameters:: fullarc – other fullarc.
Returns:: a list of intersections.

geo_lines()#: Get the lines that define a Face3D in a .geo file.

get_bounding_box()#: General method to get the bounding box of a face 3D.

get_closed_contour_divided_faces_inner_contours(list_faces, new_contour)#

If there is any inner contour, verifies which ones belong to the new divided faces.

Parameters:

list_faces – list of new faces.
new_contour – current new face outer contour.

Returns:

a list of new faces with its inner contours.

get_coincident_face_intersections(face)#

Get intersections for two faces which have coincident faces.

Parameters:: face – other face.
Returns:: two lists of intersections. one list containing wires intersecting face1, the other those for face2.

static get_edge_discretization_size(edge3d)#: Helper function to polygonize the face boundaries.

get_face_cutting_contours(dict_intersecting_combinations)#

Get all contours cutting the face, resulting from multiple faces intersections.

Parameters:: dict_intersecting_combinations – dictionary containing as keys the combination of intersecting faces

and as the values the resulting primitive from the intersection of these two faces return a list all contours cutting one particular face.

get_face_intersections(face2)#

Get the intersections between two faces.

Parameters:: face2 – second face.
Returns:: intersections.

get_face_polygons()#: Get face polygons.

get_geo_lines(tag: int, line_loop_tag: list[int])#: Get the lines that define a PlaneFace3D in a .geo file.

get_open_contour_divided_faces_inner_contours(new_faces_contours, abs_tol: float = 1e-06)#

If there is any inner contour, verifies which ones belong to the new divided faces.

Parameters:

new_faces_contours – new faces outer contour.
abs_tol – tolerance.

Returns:

valid_new_faces_contours, valid_new_faces_contours.

grid_points(grid_size, polygon_data=None)#: Parametric tessellation points.

grid_size()#: Specify an adapted size of the discretization grid used in face triangulation.

static helper_repair_inner_contours_periodicity(surface, outer_contour2d, inner_contours2d, primitives_mapping)#: Translate inner contours if it’s not inside the outer contour of the face.

helper_to_mesh(polygon_data=None) → Mesh2D#

Triangulates the Surface2D using the Triangle library.

Parameters:: polygon_data (Union[Tuple((wires.ClosedPolygon2D), list[wires.ClosedPolygon2D], None]) – Face’s outer polygon.
Returns:: The triangulated surface as a display mesh.
Return type:: volmdlr.display.Mesh2D

static helper_triangulation_without_holes(vertices, segments, points_grid, tri_opt)#

Triangulates a surface without holes.

Parameters:

vertices – vertices of the surface.
segments – segments defined as tuples of vertices.
points_grid – to do.
tri_opt – triangulation option: “p”

Returns:

property inner_contours3d: list[Contour3D]#: Gives the 3d version of the inner contours of the face.

is_adjacent(face2: Face3D)#

Verify if two faces are adjacent or not.

Parameters:: face2 – other face.
Returns:: True or False.

is_intersecting(face2, list_coincident_faces=None, tol: float = 1e-06)#

Verify if two face are intersecting.

Parameters:

face2 – face 2
list_coincident_faces – list of coincident faces, if existent
tol – tolerance for calculations

Returns:

True if faces intersect, False otherwise

is_linesegment_crossing(linesegment)#: Verify if a face 3d is being crossed by a line segment 3d.

line_intersections(line: Line3D) → list[Point3D]#

Get intersections between a face 3d and a Line 3D.

Parameters:: line – other line.
Returns:: a list of intersections.

linesegment_intersections(linesegment: LineSegment3D, abs_tol: float = 1e-06) → list[Point3D]#

Get intersections between a face 3d and a Line Segment 3D.

Parameters:

linesegment – other linesegment.
abs_tol – tolerance used.

Returns:

a list of intersections.

min_x_density = 1#

min_y_density = 1#

normal_at_point(point)#

Get Normal vector at a given point on the face.

Parameters:: point – point on the face.
Returns:

property outer_contour3d: Contour3D#: Gives the 3d version of the outer contour of the face.

plane_intersections(plane3d: Plane3D)#

Get intersections with a 3D plane surface.

Parameters:: plane3d (Plane3D) – The Plane3D instance to find intersections with.
Returns:: List of Wire3D instances representing the intersections with the plane.
Return type:: list[wires.Wire3D]

plot(ax=None, color='k', alpha=1, edge_details=False)#: Plot the face.

plot2d(ax=None, color='k', alpha=1)#: Plot 2D of the face using matplotlib.

point_belongs(point3d: Point3D, tol: float = 1e-06)#: Tells you if a point is on the 3D face and inside its contour.

point_distance(point, return_other_point: bool = False)#

Calculate the distance from a face 3d and a point.

Parameters:

point – point to verify.
return_other_point – bool to decide if corresponding point on face should be returned.

Returns:

distance to face3D.

property primitives_mapping#: Gives the 3d version of the inner contours of the face.

random_point_inside()#: Get a random point on the face.

rotation(center: Point3D, axis: Vector3D, angle: float)#

Face3D rotation.

Parameters:

center – rotation center
axis – rotation axis
angle – angle rotation

Returns:

a new rotated Face3D

select_face_intersecting_primitives(dict_intersecting_combinations)#

Select face intersecting primitives from a dictionary containing all intersection combinations.

Parameters:: dict_intersecting_combinations – dictionary containing all intersection combinations
Returns:: list of intersecting primitives for current face

set_operations_new_faces(intersecting_combinations)#

Get boolean operations new faces after splitting.

Parameters:: intersecting_combinations – faces intersecting combinations dictionary.
Returns:: new split faces.

split_by_plane(plane3d: Plane3D)#: Split face with a plane.

split_inner_contour_intersecting_cutting_contours(list_cutting_contours)#

Given a list contours cutting the face, it calculates inner contours intersections with these contours.

Then, these inner contours were split at the found intersecting points. :param list_cutting_contours: list of contours cutting face. :return:

to_dict(*args, **kwargs)#: Avoids storing points in memo that makes serialization slow.

to_geo(file_name: str)#: Get the .geo file for the Face3D.

to_ocp()#: Return an OCP shape equivalent to the volmdlr object.

to_ocp_from_2d()#: Return an OCP shape equivalent to the volmdlr object using Surface2D data.

to_ocp_from_3d()#: Return an OCP shape equivalent to the volmdlr object using 3D data.

to_step(current_id)#: Transform a Face 3D into a Step object.

translation(offset: Vector3D)#

Face3D translation.

Parameters:: offset (volmdlr.Vector3D) – Translation vector.
Returns:: A new translated Face3D

triangulation()#: Triangulates the face.

triangulation_lines()#: Specify the number of subdivision when using triangulation by lines. (Old triangulation).

property wrapped#: Get the corresponding ocp face and stores it in a cache variable.

class volmdlr.faces.PeriodicalFaceMixin#

Bases: object

Abstract class for mutualizing methods for faces constructed on periodic surfaces.

face_inside(face2, abs_tol: float = 1e-06)#

Verify if a face is inside another one.

It returns True if face2 is inside or False if the opposite.

point_belongs(point3d: Point3D, tol: float = 1e-06) → bool#

Check if a 3D point lies on the face.

Parameters:

point3d (volmdlr.Point3D) – The 3D point to be checked.
tol (float, optional) – Tolerance for the check.

Returns:

True if the point is on the ConicalFace3D, False otherwise.

Return type:

bool

class volmdlr.faces.PlaneFace3D(surface3d: Plane3D, surface2d: Surface2D, reference_path: str = '#', name: str = '')#

Bases: Face3D

Defines a PlaneFace3D class.

Parameters:

surface3d (Plane3D.) – a plane 3d.
surface2d (Surface2D.) – a 2d surface to define the plane face.

add_fillets(vertices: list[Point3D], radius: float)#

Add fillets to given vertices of the face.

Parameters:

vertices – faces vertices where to add a fillet.
radius – fillet radius.

check_inner_contours(face)#: Check face inner contours.

circle_inside(circle: Circle3D)#

Verify if a circle 3D is completely inside the plane face.

Parameters:: circle – the circle to verify.
Returns:: True if circle is inside False otherwise.

conicalface_intersections(conical_face: ConicalFace3D)#

Calculate the intersections between a plane face 3D and Conical Face3D.

Parameters:: conical_face – the Conical Face 3D to verify intersections with Plane Face 3D.
Returns:: list of intersecting wires.

copy(deep=True, memo=None)#: Return a copy of the PlaneFace3D.

cut_by_coincident_face(face)#

Cuts face1 with another coincident face2.

Parameters:: face (Face3D.) – a face 3d.
Returns:: a list of faces 3d.
Return type:: list[Face3D].

cylindricalface_intersections(cylindricalface: CylindricalFace3D)#

Calculate the intersections between a plane face 3D and Cylindrical Face3D.

Parameters:: cylindricalface – the Cylindrical Face 3D to verify intersections with Plane Face 3D.
Returns:: list of intersecting wires.

distance_to_point(point, return_other_point=False)#

Evaluate the distance to a given point.

distance_to_point is deprecated, please use point_distance.

classmethod from_ocp(ocp_face: TopoDS_Shape)#: Translate an occt face into a volmdlr face.

classmethod from_surface_rectangular_cut(plane3d, x1: float, x2: float, y1: float, y2: float, name: str = '')#: Cut a rectangular piece of the Plane3D object and return a PlaneFace3D object.

get_geo_lines(tag: int, line_loop_tag: list[int])#: Get the lines that define a PlaneFace3D in a .geo file.

is_adjacent(face2: Face3D)#

Verify if two plane faces are adjacent to each other.

Parameters:: face2 – other face.
Returns:: True if adjacent, False otherwise.

linesegment_inside(linesegment: LineSegment3D)#

Verify if a line segment 3D is completely inside the plane face.

Parameters:: linesegment – the line segment to verify.
Returns:: True if circle is inside False otherwise.

static merge_faces(list_coincident_faces: list[Face3D])#: Merge faces from a list of faces in the same plane, if any are adjacent to one another.

minimum_distance_points_plane(other_plane_face, return_points=False)#

Given two plane faces, calculates the points which corresponds to the minimal distance between these two faces.

Parameters:

other_plane_face – Second plane face.
return_points – Boolean to return corresponding points or not.

Returns:

minimal distance.

planeface_intersections(planeface)#

Calculate the intersections between two plane faces.

Parameters:: planeface – the other Plane Face 3D to verify intersections with Plane Face 3D.
Returns:: list of intersecting wires.

planeface_minimum_distance(planeface: PlaneFace3D, return_points: bool = False)#

Get the minimal distance from another PlaneFace3D.

Parameters:

planeface (PlaneFace3D) – Another PlaneFace3D instance to calculate the minimum distance.
return_points (bool, optional) – If True, returns a tuple containing the two points that give the minimum distance.

Returns:

If return_points is False, returns the minimum distance between the two plane faces. If return_points is True, returns a tuple containing the two points that give the minimum distance.

Return type:

float or tuple(float, Tuple3D, Tuple3D)

point_distance(point, return_other_point=False)#

Calculate the distance from a plane face and a point.

Parameters:

point – point to verify.
return_other_point – bool to decide if corresponding point on face should be returned.

Returns:

distance to planeface3D.

project_faces(faces)#

Divide self based on the faces outer, and inner contours.

Parameters:: faces (TYPE) – DESCRIPTION
Returns:: DESCRIPTION
Return type:: TYPE

toroidalface_intersections(toroidal_face)#

Calculate the intersections between a plane face 3D and Conical Face3D.

Parameters:: toroidal_face – the Toroidal Face 3D to verify intersections with Plane Face 3D.
Returns:: list of intersecting wires.

triangle_intersections(triangleface)#

Get the intersections between a Plane Face3D and a Triangle3D.

Parameters:: triangleface – the other triangle face.
Returns:

static update_faces_with_divided_faces(divided_faces, face2_2, used, list_faces)#: Update divided faces from project_faces.

class volmdlr.faces.RevolutionFace3D(surface3d: RevolutionSurface3D, surface2d: Surface2D, name: str = '')#

Bases: Face3D

A 3D face with a ruled surface.

This class represents a 3D face with a ruled surface, which is a surface formed by straight lines connecting two input curves. It is a subclass of the Face3D class and inherits all of its attributes and methods.

Parameters:

surface3d (RuledSurface3D) – The 3D ruled surface of the face.
surface2d (Surface2D) – The 2D projection of the face onto the parametric domain (u, v).
name (str) – The name of the face.

classmethod from_surface_rectangular_cut(revolution_surface3d, x1: float, x2: float, y1: float, y2: float, name: str = '')#: Cut a rectangular piece of the RevolutionSurface3D object and return a RevolutionFace3D object.

get_face_polygons()#: Get face polygons.

grid_points(grid_size, polygon_data=None)#: Parametric tessellation points.

grid_size()#: Specify an adapted size of the discretization grid used in face triangulation.

min_x_density = 50#

min_y_density = 1#

triangulation()#: Triangulates the face.

class volmdlr.faces.RuledFace3D(surface3d: RuledSurface3D, surface2d: Surface2D, name: str = '')#

Bases: Face3D

A 3D face with a ruled surface.

This class represents a 3D face with a ruled surface, which is a surface formed by straight lines connecting two input curves. It is a subclass of the Face3D class and inherits all of its attributes and methods.

Parameters:

surface3d (RuledSurface3D) – The 3D ruled surface of the face.
surface2d (Surface2D) – The 2D projection of the face onto the parametric domain (u, v).
name (str) – The name of the face.
color (tuple) – The color of the face.

classmethod from_surface_rectangular_cut(ruled_surface3d, x1: float = 0.0, x2: float = 1.0, y1: float = 0.0, y2: float = 1.0, name: str = '')#: Cut a rectangular piece of the RuledSurface3D object and return a RuledFace3D object.

get_bounding_box()#

General method to get the bounding box.

To be enhanced by restricting wires to cut

grid_size()#: Specify an adapted size of the discretization grid used in face triangulation.

min_x_density = 50#

min_y_density = 1#

triangulation_lines(angle_resolution=10)#: SpecifY the number of subdivision when using triangulation by lines. (Old triangulation).

class volmdlr.faces.SphericalFace3D(surface3d: SphericalSurface3D, surface2d: Surface2D, name: str = '')#

Bases: PeriodicalFaceMixin, Face3D

Defines a SpehericalFace3D class.

Parameters:

surface3d (SphericalSurface3D.) – a spherical surface 3d.
surface2d (Surface2D.) – a 2d surface to define the spherical face.

classmethod from_contours3d_and_rectangular_cut(surface3d, contours: list[Contour3D], point: Point3D, name: str = '')#

Face defined by contours and a point indicating the portion of the parametric domain that should be considered.

Parameters:

surface3d – surface 3d.
contours (list[volmdlr.wires.Contour3D]) – Cone, contour base.
name – the name to inject in the new face

Returns:

Spherical face.

Return type:

SphericalFace3D

classmethod from_ocp(ocp_face: TopoDS_Shape)#: Translate an occt face into a volmdlr face.

classmethod from_surface_rectangular_cut(spherical_surface, theta1: float = 0.0, theta2: float = 6.283185307179586, phi1: float = -1.5707963267948966, phi2: float = 1.5707963267948966, name='')#: Cut a rectangular piece of the SphericalSurface3D object and return a SphericalFace3D object.

get_bounding_box()#

Calculate the bounding box of a spherical face.

Returns:: Bounding Box.

grid_points(grid_size, polygon_data=None)#: Parametric tessellation points.

grid_size()#

Specify an adapted size of the discretization grid used to calculate the grid_points.

For the sphere the grid size is given in angle resolution in both theta and phi direction.

min_x_density = 5#

min_y_density = 5#

triangulation_lines(angle_resolution=7)#: Specify the number of subdivision when using triangulation by lines. (Old triangulation).

class volmdlr.faces.ToroidalFace3D(surface3d: ToroidalSurface3D, surface2d: Surface2D, name: str = '')#

Bases: PeriodicalFaceMixin, Face3D

Defines a ToroidalFace3D class.

Parameters:

surface3d (ToroidalSurface3D.) – a toroidal surface 3d.
surface2d (Surface2D.) – a 2d surface to define the toroidal face.

Example:

contours 2d is rectangular and will create a classic tore with x:2*pi, y:2*pi x is for exterior, and y for the circle to revolute points = [pi, 2*pi] for a half tore

copy(deep=True, memo=None)#: Return a copy of the ToroidalFace3D.

face_inside(face2, abs_tol: float = 1e-06)#

Verify if a face is inside another one.

It returns True if face2 is inside or False if the opposite.

face_tolerance = 0.001#

classmethod from_ocp(ocp_face: TopoDS_Shape)#: Translate an occt face into a volmdlr face.

classmethod from_surface_rectangular_cut(toroidal_surface3d, theta1: float = 0.0, theta2: float = 6.283185307179586, phi1: float = 0.0, phi2: float = 6.283185307179586, name: str = '')#

Cut a rectangular piece of the ToroidalSurface3D object and return a ToroidalFace3D object.

Parameters:

toroidal_surface3d – surface 3d,
theta1 – Start angle of the cut in theta direction.
theta2 – End angle of the cut in theta direction.
phi1 – Start angle of the cut in phi direction.
phi2 – End angle of the cut in phi direction.
name – (optional) Name of the returned ToroidalFace3D object. Defaults to “”.

Returns:

A ToroidalFace3D object created by cutting the ToroidalSurface3D object.

Return type:

ToroidalFace3D

grid_size()#: Specify an adapted size of the discretization grid used in face triangulation.

min_x_density = 5#

min_y_density = 1#

neutral_fiber()#: Return the faces’ neutral fiber.

planeface_intersections(planeface: PlaneFace3D)#

Get intersections between a Toroidal Face 3D and a Plane Face 3D.

Parameters:: planeface – other plane face.
Returns:: intersections.

static points_resolution(line, pos, resolution)#: Legacy?.

triangulation_lines(angle_resolution=5)#: Specify the number of subdivision when using triangulation by lines. (Old triangulation).

class volmdlr.faces.Triangle3D(point1: Point3D, point2: Point3D, point3: Point3D, alpha=1, color=None, name: str = '')#

Bases: PlaneFace3D

Defines a Triangle3D class.

Parameters:

point1 (volmdlr.Point3D.) – The first point.
point2 (volmdlr.Point3D.) – The second point.
point3 (volmdlr.Point3D.) – The third point.

area() → float#

Calculate the area for the Triangle3D.

Returns:: area triangle.
Return type:: float.

Formula explained here: https://www.triangle-calculator.com/?what=vc

copy(deep=True, memo=None)#: Return a copy of the Triangle3D.

classmethod dict_to_object(dict_, *args, **kwargs)#

Create a Triangle3D object from a dictionary representation.

This class method takes a dictionary containing the necessary data for creating a Triangle3D object and returns an instance of the Triangle3D class. It expects the dictionary to have the following keys:

Parameters:

cls – The Triangle3D class itself (automatically passed).
dict – A dictionary containing the required data for object creation.
args – Additional positional arguments (if any).
kwargs – Additional keyword arguments (if any).

Returns:

Triangle3D: An instance of the Triangle3D class created from the provided dictionary.

frame_mapping(frame: Frame3D, side: str)#

Change frame_mapping and return a new Triangle3D.

Parameters:

frame – frame used.
side – ‘old’ or ‘new’.

get_bounding_box()#: General method to get the bounding box.

static get_subdescription_points(new_points, resolution, max_length)#: Get sub-description points.

height()#: Get Triangle height.

middle()#: Get the middle point of the face: center of gravity.

normal()#: Get the normal vector to the face.

Return#

normal to the face

rotation(center: Point3D, axis: Vector3D, angle: float)#

Triangle3D rotation.

Parameters:

center – rotation center.
axis – rotation axis.
angle – angle rotation.

Returns:

a new rotated Triangle3D.

subdescription(resolution=0.01)#: Return a list of Point3D with resolution as max between Point3D.

subdescription_to_triangles(resolution=0.01)#: Return a list of Triangle3D with resolution as max length of sub triangles side.

property surface2d#: Boundary representation of the face.

property surface3d#: Get the plane on which the triangle is contained.

to_dict(*args, **kwargs)#: Create a Dictionary with the object’s instance attributes.

translation(offset: Vector3D)#

Plane3D translation.

Parameters:: offset – translation vector.
Returns:: A new translated Plane3D.

triangle_minimum_distance(triangle_face, return_points=False)#: Get the minimum distance between two triangle.

triangulation()#: Compute the triangulation of the Triangle3D, basically returns itself.

volmdlr.faces.octree_decomposition(bbox, faces)#: Decomposes a list of faces into eight Bounding boxes subdivided boxes.

volmdlr.faces.octree_face_decomposition(face)#

Decomposes the face discretization triangle faces inside eight boxes from a bounding box octree structure.

Parameters:: face – given face.
Returns:: returns a dictionary containing bounding boxes as keys and as values, a list of faces

inside that bounding box.

volmdlr.faces.parametric_face_inside(face1, face2, abs_tol: float = 1e-06)#

Verify if a face2 is inside face1.

It returns True if face2 is inside or False if the opposite.

Faces#

Return#