geometry capsule

Describes the entry capsule at version 0.2.0, registered by mime.scene._solids.Capsule.

Kept registered beside it: capsule at version 0.1.0, by mime.scene._previous.CapsuleGrid, which a document naming that version loads; its differences are in the hand-written part’s versions.

At a glance

• geometry capsule, version 0.2.0, namespace mime

• Derivative: piecewise_jump

• Validity: none declared

What it models, and when not to use it

capsule

A solid capsule: a cylinder of a radius and a height (between the centres of its caps, as USD’s Capsule counts it) along an axis, capped by two hemispheres, centred on its centroid. An elongated body pulled by a field gradient, or a rod. As a body’s part it gives the body its volume and inertia, its extent (its radius, about its own axis) and its surface samples by patch, lateral and caps; at run time a node evaluates it by the shape capsule.

When not to use it. For a body whose extent across its axis is not its radius all along: a tapered or a threaded body. A capsule tilted in a tube reaches further than its radius from the tube’s axis, which the extent does not hold.

Its derivative is the shape’s: the distance from its segment less the radius, so on the segment the distance is a cone and the normal has no limit; across the planes through the segment’s ends only the curvature changes.

Its sampling. At a spacing, for a solver whose unknowns sit at the samples (the MRS rung), it samples its surface quasi-uniformly: as many samples as its quadrature has at that spacing, chosen from its quadrature at a finer spacing by farthest points and Lloyd’s relaxation (mime.scene.quasi_uniform), each a quadrature sample with its cell’s area as its weight, so that no two crowd. Its hull query, its reach in a direction, is the sphere’s about the end of its segment that lies that way.

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

Versions. 0.2.0 samples its surface quasi-uniformly; 0.1.0, the first, sampled it by its quadrature, whose polar grids crowd the caps’ poles (MIME-ANO-123). 0.1.0 stays registered so that a folder saved with it loads and reproduces; a script that writes Capsule(...) gets 0.2.0. The quadrature, the shape and every closed form are unchanged.

Settings

Setting	Type	Default	Dimension	Role	Default’s kind
axis	Annotated[DirectionLike, Direction]	{"required": true}	marked Direction	physical	none
height	Annotated[Quantity, Length]	{"required": true}	length (m)	physical	none
radius	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	yes
family_parameters	the parameters of the family it is	a surrogate trained on one family	yes
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	yes
drawing	a drawing, tessellated at the writer’s resolution	the stage writer, for a kind with no native form	no
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	yes
reach	reach	not stated	yes
sampling	sampling	not stated	yes
support	support	not stated	yes

native: written as USD’s Capsule, its attributes the kind’s settings (height holds height, radius holds radius, axis is Z).

placement: axis is its prim’s z axis; on a stage, the prim’s transform, never an attribute.

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

[@WeissteinCylinder], [@WeissteinEllipsoid]

Other declarations

Class variable	Type	Value
directions	ClassVar[tuple[str, ...]]	[]
moving	ClassVar[bool]	false
patches	ClassVar[Mapping[str, str]]	{"caps": "solid", "lateral": "solid"}
reach_envelope	ClassVar[float]	0.0
region_shapes	ClassVar[Mapping[str, str]]	{"solid": "capsule"}
regions	ClassVar[tuple[str, ...]]	["solid"]
support_basis	ClassVar[str]	closed form
support_error	ClassVar[float]	0.0
surfaces	ClassVar[Mapping[str, str]]	{}