plane

A plane in space, drawn as its exact intersection with the box. plane(z: 4x + 2y - 3) is a height over the floor; plane(equation: x + 2y + 3z = 6) is any plane, a vertical slicing plane x = c among them. Either must be linear in x, y and z — a product or a power of them is refused — though a parameter may be a coefficient. A plane cuts every surface it passes through exactly, so a tangent plane meets its surface cleanly. Space only (graph:xyz).

planeNode
The saddle z = x² − y² with its tangent plane at (1, 0.5, 0.75) touching it, and the vertical plane y = 0.5 slicing through both.The saddle z = x² − y² with its tangent plane at (1, 0.5, 0.75) touching it, and the vertical plane y = 0.5 slicing through both.

#Attributes

zImplicitAnimatable
The height over the floor, linear in x and y: 4x + 2y - 3.
plane-height
Can be written as shorthand: plane:value
equationAnimatable
Any plane as an equation in x, y and z: x + 2y + 3z = 6, x = c.
plane-equation
Also written: eq
meshAnimatable
Rule the plane into a hairline grid.
boolean
Defaulttrue
colourAnimatable
Its colour — green 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
Defaultgreen
opacityAnimatable
How solid it is, 0 to 1.
number
Default0.45
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 bowl z = 2x² + y² with its tangent plane z = 4x + 2y − 3 touching it at P = (1, 1, 3).The bowl z = 2x² + y² with its tangent plane z = 4x + 2y − 3 touching it at P = (1, 1, 3).
graph:xyz{
    surface(expression: 2 * x^2 + y^2)
    plane(z: 4x + 2y - 3)
    point(x: 1; y: 1; z: 3; label: $P$)
}(
    x domain: [-2, 2]
    y domain: [-2, 2]
    z domain: [0, 12]
    view: (35, 25)
)
The plane x + 2y + 3z = 6 cut to the box, and the vertical plane x = 1 crossing it.The plane x + 2y + 3z = 6 cut to the box, and the vertical plane x = 1 crossing it.
graph:xyz{
    plane(equation: x + 2y + 3z = 6)
    plane(equation: x = 1; colour: orange)
}(
    x domain: [-3, 3]
    y domain: [-3, 3]
    z domain: [-3, 3]
)

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