Experimental

Experimental parts, proofs of concept. See Deformable shapes for the guide.

class DeformableShape(shape: Face | Shape, h: float, min_distance: float | None = None, clean: bool = False, topology_changed_callback: Callable[[DeformableShape], Any] | None = None)

A face as dense closed polylines whose vertices follow displacement arrays or NGSolve GridFunctions.

Every edge is sampled at most h apart; outer loops run counterclockwise, holes clockwise. Boundary parts that move closer than min_distance to each other are cut out.

Parameters:

• shape – the Face or Shape whose faces are sampled.

• h – the largest segment length.

• min_distance – the smallest distance between boundary parts; None takes h.

• clean – True cleans the given shape of parts closer than min_distance right away.

• topology_changed_callback – called with the DeformableShape whenever SetDeformation, Clean or Defeature changes its loops.

Examples

px.DeformableShape(face, 0.01)
px.DeformableShape(shape, 0.01, min_distance=0.005, topology_changed_callback=print)

Clean() → bool

Cuts the loops against each other and keeps the boundary of the material without parts too close.

The material is where the winding number is 1 or more; parts closer than min_distance to each other are removed. If anything changed, the current vertices become the reference.

Returns:

True if anything changed.

Examples

deformableShape.Clean()

Commit() → DeformableShape

Makes the current vertices the reference.

Returns:

this DeformableShape.

Examples

shape.Commit()

Copy() → DeformableShape

An independent copy; copy.copy and copy.deepcopy give the same.

Examples

b = a.Copy()

Defeature() → bool

Removes boundary vertices closer than min_distance to another part of the boundary and joins the loose ends.

The loose ends are joined by straight segments, nearest first.

Returns:

True if anything changed.

Examples

deformableShape.Defeature()

IsValid() → bool

True if the polylines do not intersect themselves or each other.

Examples

shape.IsValid()

Plot(plane: Plane | None = None, /, ax: Any = None, line_col: Color = 'black', arc_col: Color = '#ff7f0e', spline_col: Color = '#2ca02c', face_col: Color | None = '#dde6f0', mark_edges_smaller: float | None = None, mark_free_edges: bool = False, highlight: Ids | Any = None, legend: bool = True, show_constraints: bool | None = None, show_ends: bool = False, show_direction: bool = False, show_parent: bool | None = None, backend: str | None = None) → Any

Draws a planex object in its plane with matplotlib or plotly.

A sketch is drawn as sk.Plot draws it (show_constraints, show_ends, show_direction, show_parent); the other options are for the other objects, e.g. px.Plot(sk.Shape(), face_col=”C0”). An OCC shape is cut at the plane (px.Intersect3d(plane, shape)), or without one drawn flat in its own plane as px.FromOCC gives it. Fields: px.PlotField; meshes: px.PlotMesh.

Parameters:

• obj – a Face, Shape, Wire, Compound, sketch, selection, DeformableShape or OCC shape, or an id that names one (“Sketch.1”, “Shape.2.Line.3”).

• plane – the plane that cuts an OCC shape; None draws it flat in its own plane.

• ax – a matplotlib Axes or a plotly Figure to draw into, which also selects the backend.

• line_col – the colour of every edge; “type” draws lines in black, arcs in arc_col and splines in spline_col, with a legend entry each; “property” takes each edge’s own col where it has one.

• arc_col – the colour of arcs with line_col=”type”.

• spline_col – the colour of splines with line_col=”type”.

• face_col – fills the closed loops (faces and shapes; a wire on its own stays an outline unless face_col is given); a fill other than the default gets a legend entry labelled with the object’s id (‘Face.3’), the default fill none; None draws the outlines only.

• mark_edges_smaller – marks the edges shorter than this at their midpoints.

• mark_free_edges – True marks the edges with an end no other edge shares.

• highlight – marks the edges given: ids (“Line.3”, “Shape.1.Line.3”), selected edges or faces (a face: its edges), a selection, or indices or a boolean mask over obj.edges (for a Compound those of its parts in turn).

• legend – True shows the legend.

• show_constraints – for a sketch, as sk.Plot.

• show_ends – for a sketch, as sk.Plot.

• show_direction – for a sketch, as sk.Plot.

• show_parent – for a sketch, as sk.Plot.

• backend – “matplotlib” or “plotly” without ax; None is matplotlib.

Returns:

the matplotlib Axes or the plotly Figure.

Raises:

ValueError – a sketch with an option for other objects, an option for sketches with another object, a plane with a planex object, obj is a plane, or backend is unknown.

Examples

px.Plot(face, line_col="type")
px.Plot(solid, px.XY)

ReferenceVertices() → np.ndarray

The vertices the displacements refer to, an (n, 2) array.

Examples

shape.ReferenceVertices()

Refine() → DeformableShape

Halves the segments longer than h and drops interior vertices closer than h/4.

Returns:

this DeformableShape.

Examples

shape.Refine()

RingSizes() → list[int]

The number of vertices of every loop, in the order of Vertices().

Examples

shape.RingSizes()

SetDeformation(d: ndarray | Any, commit: bool = True) → bool

Moves the vertices to the reference vertices plus displacements, then refines and cleans the loops.

With commit the result becomes the new reference; without, the reference stays and the next call replaces the deformation (like mesh.SetDeformation) until the topology changes, which always commits.

Parameters:

• d – the displacements, shape (n, 2), or a vector GridFunction on a mesh of the reference shape, evaluated on the mesh boundary at the reference vertices.

• commit – True makes the result the new reference.

Returns:

True if the topology changed.

Raises:

ValueError – d is an array not of shape (n, 2).

Examples

deformableShape.SetDeformation([(0, 0)] * len(deformableShape))
deformableShape.SetDeformation(gfu, commit=False)

Shape() → Shape

The current outline as a Shape, one edge per original edge: a line where its points are collinear, else the spline through them.

Examples

shape.Shape()

ToSVG(size: float = 300, **options: Any) → str | None

The object as the text of an SVG picture in its plane coordinates, its faces filled.

A sketch is drawn in its own look: every element in the colour of its state (green fully constrained, black free, pink over-constrained) with its id when hovered, construction dashed, in a frame with numbered ticks on a grid.

Parameters:

• obj – a Face, Shape, Wire, Compound, sketch or DeformableShape.

• size – the larger side of the picture in pixels.

• options – for a sketch: show_constraints=True adds a sign per constraint, show_ends=True a blue start and an orange end piece on every line and arc, show_direction=True an arrow from start to end; other objects ignore them.

Returns:

the SVG text; None if the object has no extent.

Examples

face.ToSVG()
sk.ToSVG(size=500, show_constraints=True)

VertexNames() → list[str]

The name of the original edge every vertex lies on, in the order of Vertices().

Examples

shape.VertexNames()

Vertices() → np.ndarray

The current vertices, an (n, 2) array.

Examples

shape.Vertices()

Wires() → list[Wire]

The current polylines as wires of lines with the original edges’ properties.

Examples

shape.Wires()

property bounding_box

tuple[tuple[float, float], tuple[float, float]]

Its bounding box in the plane, ((hmin, vmin), (hmax, vmax)).

Type:

bounding_box

property h

float

The largest segment length.

Type:

h

property mass

float

The area.

Type:

mass

property min_distance

float

The smallest distance between boundary parts.

Type:

min_distance