geometry box

Describes the entry box at version 0.1.0, registered by mime.scene._solids.Box.

At a glance

• geometry box, version 0.1.0, namespace mime

• Derivative: piecewise_jump

• Validity: none declared

What it models, and when not to use it

box

A solid rectangular box, given by the three lengths of its edges (size), along the part frame’s axes and centred on its centroid: a block, a slab, the body of a rectangular magnet. As a body’s part it gives the body its volume and inertia (both closed forms), its extent (half its diagonal about any axis), its reach along a direction and its surface samples by patch, for a solver that integrates over the surface. At run time a node evaluates it through its regions, three slabs between the pairs of opposite faces (span_x, span_y, span_z), the body being their intersection; its patches are the three pairs of faces.

When not to use it.

• For a body that is not a box: its extent and anything read from its samples would be a box’s.

• Where a consumer needs the body’s deepest point in a direction (support): the kind answers a reach, not a support, and a consumer that needs one is refused when it plans, naming both.

• Where the stage must show it as a USD primitive: it has no native form, so the stage writer draws it (the capabilities table says so).

Its derivative is its slabs’, as their switch declares: at a slab’s mid-plane the distance has a kink. Its volume and inertia are exact.

Its sampling. At a spacing, for a solver whose unknowns sit at the samples (the MRS rung), it samples its surface quasi-uniformly, chosen from its quadrature (mime.scene.quasi_uniform); the quadrature is Gauss-Legendre along both edges of each face, so that its divergence integrals are exact. The choice of samples is discrete, so it is not continuous in size: rebuilt at a slightly moved edge, the sampling can choose again and the MRS resistance step with it (the numbers are MIME-ANO-127’s).

Regions, surfaces, directions and frames. What a kind names and how a law or a stage reads it: the scene note.

Versions. 0.1.0 is its first.

Settings

Setting	Type	Default	Dimension	Role	Default’s kind
size	Annotated[Quantity, Length]	{"required": true}	length (m)	physical	none

Each role and default’s kind is the entry’s setting_roles (mime.registry.SettingRole); a setting that declares none is required.

Capabilities

Generated from which of the optional methods of mime.registry.Geometry the kind implements; a consumer that needs one it lacks is refused when it plans, naming both.

Capability	What it gives	Used by	This kind
samples	surface samples by named patch, at a resolution the consumer chooses	the MRS; immersed-boundary markers	yes
area	the area of each patch	the samples’ weights	yes
mass_properties	volume and inertia at a density	the part resolver	yes
radial_reach	the hull’s radial reach about its axis	a body’s extent; contact on the hull	no
family_parameters	the parameters of the family it is	a surrogate trained on one family	no
tangent	a tangent it declares at a surface point	a law anisotropic along it	no
native	its native form, one of USD’s own primitives	the stage writer	no
drawing	a drawing, tessellated at the writer’s resolution	the stage writer, for a kind with no native form	yes
region_primitive	its regions as OpenMaterica’s primitives: exactly, or (a region with no end along an axis) clipped at the kind’s own length, or refused	OpenMaterica’s manifest and stage	no
reach	reach	not stated	yes
sampling	sampling	not stated	yes
support	support	not stated	no

native: none, so the stage writes it in MIME’s schema with its drawing.

placement: none: its own frame is the frame its settings are written in.

Run-time capabilities (signed distance, outward normal, nearest point) are its regions’ and surfaces’ shapes, listed below.

Nodes it builds

Builds no node of its own.

Gradient status

The derivative through this entry is piecewise_jump: not the exact derivative of what it computes everywhere.

Validity

none declared

References

[@WeissteinCuboid], [@WeissteinMomentOfInertia]

Other declarations

Class variable	Type	Value
directions	ClassVar[tuple[str, ...]]	[]
moving	ClassVar[bool]	false
patches	ClassVar[Mapping[str, str]]	{"faces_x": "span_x", "faces_y": "span_y", "faces_z": "span_z"}
reach_envelope	ClassVar[float]	0.0
region_shapes	ClassVar[Mapping[str, str]]	{"span_x": "slab", "span_y": "slab", "span_z": "slab"}
regions	ClassVar[tuple[str, ...]]	["span_x", "span_y", "span_z"]
support_basis	ClassVar[str]	``
support_error	ClassVar[float]	0.0
surfaces	ClassVar[Mapping[str, str]]	{}