Measurements

The analysis functions of planex.measurements. The measurements of every object, such as mass, center and Measure(), are listed with their classes. See Measuring for the guide.

measurements to call or store: obj.Measure(f), obj.Measure(f, id=”gap”) and obj.measures.

A measurement is a callable f(obj, **params) returning its value. One that can be drawn also takes plot=True (and samples=n) and then returns {“points”: [(h, v), …], “values”: […], “label”: …, “value”: …, “marks”: […]} for px.PlotField(f, obj); with “discs”: [(h, v, r, value), …] a point inside takes the largest value of the discs covering it instead of the interpolation.

Clearance(a: str | Callable | Any, b: str | Callable | Any) → Callable

A measurement: the smallest distance between the elements a and b of the object.

Parameters:

  • a – the first elements: an id, a name of edges or faces, a callable of the object returning them, or elements.

  • b – the second elements, as a.

Returns:

the measurement f(obj), for obj.Measure(f).

Examples

shape.Measure(px.measurements.Clearance("pad", "trace"))
sk.Measure(px.measurements.Clearance("Circle.1", "Line.4"), id="gap")
Hausdorff(a: str | Callable | Any, b: str | Callable | Any, /, samples: int = 64) → Callable

A measurement: the Hausdorff distance between the elements a and b of the object.

The Hausdorff distance is the largest distance from a point of a to b or of b to a: how far apart two curves are at their worst.

Parameters:

  • a – the first elements: an id, a name of edges or faces, a callable of the object returning them, or elements.

  • b – the second elements, as a.

  • samples – the samples per edge before the search for the largest distance refines.

Returns:

the measurement f(obj), for obj.Measure(f).

Examples

shape.Measure(px.measurements.Hausdorff("Line.1", "Arc.2"))
sk.Measure(px.measurements.Hausdorff("inner", "outer", samples=128), id="gap")
HydraulicDiameter(*args: Any) → Callable

A measurement: the hydraulic diameter 4 A / P, four times the area over the perimeter (every edge wetted).

Returns:

the measurement f(obj), for obj.Measure(f).

Raises:

TypeError – given an object: the measurement is HydraulicDiameter(), with brackets.

Examples

face.Measure(px.measurements.HydraulicDiameter())
px.measurements.HydraulicDiameter()(face)
MaxThickness(method: str = 'ball', samples: int = 400, ignore_corners: float | None = None) → Callable

A measurement: the thickest wall of the faces, as MinThickness; px.PlotField draws it.

Parameters:

  • method – “ball” (the largest disc inside) or “ray” (along the inward normal), as MinThickness.

  • samples – the number of samples along the boundary.

  • ignore_corners – leaves out where a convex corner sharper than this many degrees pinches the disc or ray.

Returns:

the measurement f(obj, plot=False, samples=samples), for obj.Measure(f) and px.PlotField(f, obj).

Raises:

ValueError – method is neither “ball” nor “ray”.

Examples

face.Measure(px.measurements.MaxThickness())
shape.Measure(px.measurements.MaxThickness(samples=1000), id="thickest")
MinThickness(method: str = 'ball', samples: int = 400, ignore_corners: float | None = None) → Callable

A measurement: the thinnest wall of the faces; px.PlotField draws it.

A sharp corner is infinitely thin: without ignore_corners a warning says when the minimum is such a corner’s tip and which value leaves it out.

Parameters:

  • method – “ball”: at each sample the diameter of the largest disc inside that touches the boundary there; “ray”: the distance along the inward normal to the other side, which never finds less than the disc and can miss thin spots at tapers.

  • samples – the number of samples along the boundary.

  • ignore_corners – leaves out where a convex corner sharper than this many degrees pinches the disc or ray.

Returns:

the measurement f(obj, plot=False, samples=samples), for obj.Measure(f) and px.PlotField(f, obj); it raises ValueError when no sample finds a wall.

Raises:

ValueError – method is neither “ball” nor “ray”.

Examples

face.Measure(px.measurements.MinThickness())
px.PlotField(px.measurements.MinThickness(method="ray", ignore_corners=60), shape)
TorsionConstant(order: int = 3, maxh: float | None = None) → Callable

A measurement: the St. Venant torsion constant J of the faces, a cross-section in the xy plane.

J is computed by NGSolve from the warping function w: J = integral of x^2 + y^2 + x dw/dy - y dw/dx about the centroid, with laplace(w) = 0 and dw/dn = y n_x - x n_y on every boundary (holes included). The measurement raises ImportError without NGSolve.

Parameters:

  • order – the polynomial order of the finite elements and of the curved mesh.

  • maxh – the mesh size; None takes a twentieth of the larger side of the bounding box.

Returns:

the measurement f(obj), for obj.Measure(f).

Examples

face.Measure(px.measurements.TorsionConstant())
face.Measure(px.measurements.TorsionConstant(order=4, maxh=0.001))