geometry cylinder#

Describes the entry cylinder at version 0.1.0, registered by mime.scene._solids.Cylinder.

At a glance#

  • geometry cylinder, version 0.1.0, namespace mime

  • Derivative: piecewise_jump

  • Validity: none declared

What it models, and when not to use it#

cylinder#

A solid circular cylinder, given by its radius, its length and its axis, centred on its centroid: a rod, a disc, the body of a cylindrical magnet. As a body’s part it gives the body its volume and inertia (closed forms), its extent, its reach along a direction and its surface samples by patch. At run time a node evaluates it through its regions, the unbounded cylinder side and the span between its end planes, the body being their intersection; its patches are the lateral side and the two flat caps. On a stage it is written as USD’s own Cylinder, its height holding length, and its axis is the prim’s z axis.

When not to use it.

  • For a body that is not round about an axis: a cylinder’s extent and samples are a cylinder’s.

  • Where a consumer needs the hull’s radial reach about its axis (radial_reach): the kind implements a reach in a direction and a support in a direction, not that; a consumer that needs it is refused when it plans, naming both.

  • For a hollow tube or a wall: that is the tube, which is a structure, not a solid body.

Its derivative is its regions’ shapes’, as their switches declare: on the axis the distance is a cone and the normal has no limit, and at the mid-plane the distance has a kink. Its support in a direction is a closed form, and along the axis the farthest set is the whole cap, so the farthest point jumps from the cap’s centre to its rim as the direction leaves the axis (the switch cylinder.support, with no route). 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 trapezoid rule round the axis with Gauss-Legendre nodes along it, and each cap in rings about a sample at its centre, the layout the screw’s caps use, which no ring crowds. The quadrature is built to integrate the area and the divergence integrals exactly. The choice of samples is discrete, so it is not continuous in the settings: rebuilt at a slightly moved radius or length, 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

axis

Annotated[DirectionLike, Direction]

{"required": true}

marked Direction

physical

none

length

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

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

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

no

reach

reach

not stated

yes

sampling

sampling

not stated

yes

support

support

not stated

yes

native: written as USD’s Cylinder, its attributes the kind’s settings (height holds length, 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.

Switches the law evaluates, each declared once by its owner:

Switch

Indicator

Orders, per output group

Route to exact

cylinder.support

the length of the direction’s part across the cylinder’s axis, in the direction’s units; along the axis within AXIS_ULPS units in the last place of the direction’s length (a band)

support -1 (a jump)

none: along the axis the farthest set is the whole cap, so the farthest point jumps from the cap’s centre to its rim as the direction leaves the axis, as the body’s own does

Validity#

none declared

References#

[@WeissteinCylinder]

Other declarations#

Class variable

Type

Value

directions

ClassVar[tuple[str, ...]]

[]

moving

ClassVar[bool]

false

patches

ClassVar[Mapping[str, str]]

{"caps": "span", "lateral": "side"}

reach_envelope

ClassVar[float]

0.0

region_shapes

ClassVar[Mapping[str, str]]

{"side": "cylinder", "span": "slab"}

regions

ClassVar[tuple[str, ...]]

["side", "span"]

support_basis

ClassVar[str]

closed form

support_error

ClassVar[float]

0.0

surfaces

ClassVar[Mapping[str, str]]

{}