Faces

Surfaces & faces.

class design3d.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)

Returns the side of the faces that are adjacent.

adjacent_direction_uv(other_bspline_face3d, corresponding_directions)

Returns the sides that are adjacents to other BSpline face.

adjacent_direction_vu(other_bspline_face3d, corresponding_directions)

Returns the sides that are adjacents to other BSpline face.

adjacent_direction_vv(other_bspline_face3d, corresponding_directions)

Returns 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)

Returns an arc that approximates the given edge.

Parameters:

edge – curve to be approximated by an arc.

Returns:

An arc if possible, otherwise None.

extremities(other_bspline_face3d)

Find points extremities for nearest edges of two faces.

face_tolerance = 1e-05

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()

Creates a bounding box from the face mesh.

grid_size()

Specifies an adapted size of the discretization grid used in face triangulation.

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

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

Parameters:

• linesegment – other linesegment.

• abs_tol – tolerance.

Returns:

a list of intersections.

merge_with(other_bspline_face3d)

Merge two adjacent faces.

Type:

other_bspline_face3d : design3d.faces.BSplineFace3D

Return type:

merged_face : design3d.faces.BSplineFace3D

neutral_fiber()

Returns the faces’ neutral fiber.

neutral_fiber_points()

Calculates the neutral fiber points of the face.

Returns:

The neutral fiber points if they exist, otherwise None.

Return type:

Union[list, None]

pair_with(other_bspline_face3d)

Finds 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 (design3d.faces.BSplineFace3D) – BSplineFace3D

Returns:

corresponding_direction, grid2d_direction

Return type:

Tuple[?, ?]

to_planeface3d(plane3d: Plane3D = None)

Converts 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)

Specifies the number of subdivision when using triangulation by lines. (Old triangulation).

class design3d.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)

Verifies 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 = '')

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

Parameters:

• conical_surface3d – surface 3d.

• contour (design3d.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()

Returns the faces’ neutral fiber.

triangulation_lines(angle_resolution=5)

Specifies the number of subdivision when using triangulation by lines. (Old triangulation).

class design3d.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 (design3d.faces.CylindricalFace3D) – The face to evaluation.

arc_inside(arc: Arc3D)

Verifies if Arc3D is inside a CylindricalFace3D.

Parameters:

arc – Arc3D to be verified.

Returns:

True if it is inside, False otherwise.

arcellipse_inside(arcellipse: ArcEllipse3D)

Verifies 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)

Returns a copy of the CylindricalFace3D.

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.

get_geo_lines(tag: int, line_loop_tag: List[int])

Gets the lines that define a CylindricalFace3D in a .geo file.

min_x_density = 5

min_y_density = 1

neutral_fiber()

Returns the faces’ neutral fiber.

parametrized_grid_size(angle_resolution, z_resolution)

Gets 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)

Finds intersections with the given plane face.

Parameters:

planeface – Plane face to evaluate the intersections.

triangulation_lines(angle_resolution=5)

Specifies the number of subdivision when using triangulation by lines. (Old triangulation).

class design3d.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 design3d.faces.Face3D(surface3d, surface2d: Surface2D, reference_path: str = '#', name: str = '')

Bases: Primitive3D

Abstract method to define 3D faces.

area()

Computes the area of the surface 2d.

property bounding_box

Returns the surface bounding box.

copy(deep=True, memo=None)

Returns 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)

Returns True if edge 3d is coplanar to the face.

edge_intersections(edge)

Gets the intersections of an edge and a 3D face.

face_border_intersections(face2)

Returns the intersections of the face outer and inner contour with other given face.

face_decomposition()

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

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

Verifies 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]

Calculates the intersections between two Face3D.

face_intersections_outer_contour(face2)

Returns the intersections of the face outer contour with other given face.

face_minimum_distance(other_face, return_points: bool = False)

Gets 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)

Changes frame_mapping and return a new Face3D.

side = ‘old’ or ‘new’

classmethod from_contours3d(surface, contours3d: List[Contour3D], name: str = '')

Returns 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

static from_contours3d_with_inner_contours(surface, contours3d)

Helper function to class.

classmethod from_step(arguments, object_dict, **kwargs)

Converts 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:

design3d.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()

Gets 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)

Gets 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)

Gets 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])

Gets 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 tesselation points.

grid_size()

Specifies 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:

design3d.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)

Verifies 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)

Verifies 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.

linesegment_intersections_approximation(linesegment: LineSegment3D, abs_tol: float = 1e-06) → List[Point3D]

Approximation of intersections face 3D and a line segment 3D.

min_x_density = 1

min_y_density = 1

normal_at_point(point)

Gets 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)

Gets 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)

Plots 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)

Calculates 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()

Gets 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)

Gets 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_geo(file_name: str)

Gets the .geo file for the Face3D.

to_step(current_id)

Transforms a Face 3D into a Step object.

translation(offset: Vector3D)

Face3D translation.

Parameters:

offset (design3d.Vector3D) – Translation vector.

Returns:

A new translated Face3D

triangulation()

Triangulates the face.

triangulation_lines()

Specifies the number of subdivision when using triangulation by lines. (Old triangulation).

class design3d.faces.PeriodicalFaceMixin

Bases: object

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

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

Verifies 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

Checks if a 3D point lies on the face.

Parameters:

• point3d (design3d.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 design3d.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.

check_inner_contours(face)

Checks face inner contours.

circle_inside(circle: Circle3D)

Verifies 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)

Calculates 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)

Returns 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)

Calculates 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)

Evaluates the distance to a given point.

distance_to_point is deprecated, please use point_distance.

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])

Gets the lines that define a PlaneFace3D in a .geo file.

is_adjacent(face2: Face3D)

Verifies if two plane faces are adjacent to eachother.

Parameters:

face2 – other face.

Returns:

True if adjacent, False otherwise.

linesegment_inside(linesegment: LineSegment3D)

Verifies 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])

Merges 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)

Calculates 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)

Gets 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)

Calculates 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)

Calculates 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)

Gets 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 design3d.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 tesselation points.

grid_size()

Specifies an adapted size of the discretization grid used in face triangulation.

min_x_density = 50

min_y_density = 1

triangulation()

Triangulates the face.

class design3d.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()

Specifies an adapted size of the discretization grid used in face triangulation.

min_x_density = 50

min_y_density = 1

triangulation_lines(angle_resolution=10)

Specifies the number of subdivision when using triangulation by lines. (Old triangulation).

class design3d.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[design3d.wires.Contour3D]) – Cone, contour base.

• name – the name to inject in the new face

Returns:

Spherical face.

Return type:

SphericalFace3D

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.

grid_points(grid_size, polygon_data=None)

Parametric tesselation points.

grid_size()

Specifies 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)

Specifies the number of subdivision when using triangulation by lines. (Old triangulation).

class design3d.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)

Returns a copy of the ToroidalFace3D.

face_tolerance = 0.001

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()

Specifies an adapted size of the discretization grid used in face triangulation.

min_x_density = 5

min_y_density = 1

neutral_fiber()

Returns the faces’ neutral fiber.

planeface_intersections(planeface: PlaneFace3D)

Gets 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)

Specifies the number of subdivision when using triangulation by lines. (Old triangulation).

class design3d.faces.Triangle3D(point1: Point3D, point2: Point3D, point3: Point3D, alpha=1, color=None, name: str = '')

Bases: PlaneFace3D

Defines a Triangle3D class.

Parameters:

• point1 (design3d.Point3D.) – The first point.

• point2 (design3d.Point3D.) – The second point.

• point3 (design3d.Point3D.) – The third point.

area() → float

Calculates 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)

Returns 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)

Changes 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)

Gets sub-description points.

height()

Gets Triangle height.

middle()

Gets the middle point of the face: center of gravity.

normal()

Get the normal vector to the face.

Returns

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)

Returns a list of Point3D with resolution as max between Point3D.

subdescription_to_triangles(resolution=0.01)

Returns a list of Triangle3D with resolution as max length of sub triangles side.

property surface2d

Boundary representation of the face.

property surface3d

Gets the plane on which the triangle is contained.

to_dict(*args, **kwargs)

Creates 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)

Gets the minimum distance between two triangle.

triangulation()

Computes the triangulation of the Triangle3D, basically returns itself.

design3d.faces.octree_decomposition(bbox, faces)

Decomposes a list of faces into eight Bounding boxes subdivided boxes.

design3d.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.

design3d.faces.parametric_face_inside(face1, face2, abs_tol: float = 1e-06)

Verifies if a face2 is inside face1.

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