--- jupyter: description: 'Measuring in planex2d: areas, centroids and second moments, boxes, distances, inside tests, sketch dimensions by id, and measurements as functions, such as thickness maps, clearances, Hausdorff distances and torsion.' --- # Measuring

The wall thickness of a flange mapped over its face, thinnest between the bolt holes and the bore

A flange's wall thickness, mapped over the part

The distance to the nearest cooling channel over a plate, after SciPy moved the channels

Channels placed by SciPy, so that no point is far from one

A cam and the polygon of its 164 segments, with the largest distance between them

How far a polygon strays from its cam

The coast of Great Britain walked with dividers of 80 and 20 km

Example A coast measured with dividers

Every object provides its area, length, center and bounding box directly, and `Measure()` returns them all as a dict together with the second moments and principal axes. Distances, closest points and inside tests take a point or an array of points. In a sketch, `Measure(id)` measures elements by their ids, so a drawing can be checked against its intent. A measurement can also be a function of your own, stored on a sketch and evaluated again after every change, such as the thinnest wall, the largest end mill that fits, or the point farthest from a cooling channel. `planex.measurements` provides thickness maps, clearances, Hausdorff distances and torsion constants. See [Field solvers as measurements](../../integrations/netgen/field-solvers.md) for measurements that need a field solver.

In this section

## Measurements - [Areas, centroids and second moments](sections.md) - [Boxes, crossings and open ends](queries.md) - [Distances and clearances](distances.md) - [Inside or outside](inside.md) - [Dimensions in a sketch](sketch-dimensions.md)

Areas, centroids and second momentsMeasure() as a dict, and the centroids and principal axes of two sections.

Boxes, crossings and open endsBounding boxes, edges by name, crossings, and the outline and holes.

Distances and clearancesShortest distances and connections, in the plane and in 3D.

Inside or outsidePoints tested against a face, one at a time or by the thousand.

Dimensions in a sketchLengths, angles and distances of sketch elements, by their ids.

## Analysis - [Part analysis](analysis.md)

Part analysisMeasurements as functions, from thickness maps to checks that follow the sketch and optimization.

## Everything at a glance | | | |---|---| | **Size** | `mass` (the area of faces, the length of wires), `bounding_box`, `outer`, `inner` | | **Mass properties** | `center` (3D), `inertia` (3D, about the center), `Measure()`: `Ih`, `Iv`, `Ihv`, `I1`, `I2`, `principal_angle` | | **Distances** | `Distance(target, project=False, components=None, signed=False)`, `ClosestPoint(point)` | | **Inside** | `Contains(point, boundary=True)` | | **Edges** | `Distance(..., on_carrier=True)`, `Measure(to=...)` | | **Sketches** | `sketch.Measure(id, to=...)`: lengths, radii, angles and distances between elements, by id | | **Analysis** | [Selectors](analysis.md) by id, name, kind and position; `vertex.angle`, `vertex.radius`; `planex.measurements` with thickness maps, clearance, Hausdorff distance and torsion; `Measure(f, id=...)`, `measures` | See [Field solvers as measurements](../../integrations/netgen/field-solvers.md) for measurements that need a field solver, NGSolve or FEniCSx, such as a peak temperature or a stress concentration.