revolution

The solid swept out by turning the region under y = f(x) about an axis. About x its cross-sections are discs, or washers with inner:; about y it is the solid the shell method cuts up. Space only.

revolutionNode
The region under y = √x on [0, 4] turned about the x axis into a solid like a bell lying on its side.The region under y = √x on [0, 4] turned about the x axis into a solid like a bell lying on its side.

#Attributes

expressionRequiredImplicitAnimatable
The profile, y = f(x).
parametised-expression
Also written: f, outerCan be written as shorthand: revolution:value
innerAnimatable
An inner profile, which makes the cross-sections washers.
parametised-expression
Also written: g
aboutAnimatable
The axis it turns about.
xy
enum
Defaultx
xRequiredAnimatable
The interval of x the profile runs over.
parametised-interval
Also written: domain
colourAnimatable
Its colour — purple when not given. Faces are shaded in steps of the hue by how squarely they face a light fixed to the camera.
bluelight-bluedark-blueredlight-reddark-redorangelight-orangedark-orangeyellowlight-yellowdark-yellowteallight-tealdark-tealgreenlight-greendark-greenpinklight-pinkdark-pinkpurplelight-purpledark-purplegreylight-greydark-greyneutralhex(…)rgb(…)
Also written: color
Defaultpurple
opacityAnimatable
How solid it is, 0 to 1.
number
Default0.4
label
Words drawn beside it, over everything.
rich-text
hiddenAnimatable
Declared but not drawn — animatable, so hidden: true !cue.to{false}(at: 2) is its reveal.
boolean
Defaultfalse
lock
A reader may not edit it.
boolean
Also written: locked
Defaultfalse
layerAnimatable
Accepted for parity with the flat marks; in space the paint order is depth.
parametised-number

#Examples

The region between y = √x and y = x/2 turned about the x axis, a solid with a hollow core, with a washer cut at x = 2.The region between y = √x and y = x/2 turned about the x axis, a solid with a hollow core, with a washer cut at x = 2.
graph:xyz{
    revolution#vase(expression: sqrt(x); inner: x / 2; x: [0, 4]; opacity: 0.5)
    section(of: #vase; x: 2; width: 0.15)
}(
    x domain: [0, 4]
    y domain: [-2, 2]
    z domain: [-2, 2]
    aspect: equal
)
The region under y = 2x² − x³ on [0, 2] turned about the y axis — the solid the shell method cuts up.The region under y = 2x² − x³ on [0, 2] turned about the y axis — the solid the shell method cuts up.
graph:xyz{
    revolution(expression: 2x^2 - x^3; about: y; x: [0, 2]; colour: blue)
}(
    x domain: [-2, 2]
    y domain: [0, 2]
    z domain: [-2, 2]
    aspect: equal
)

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