Object Reference

Complete object reference

On this page

• ArcPolygon
• AnimatedBoundary
• Union
• Difference
• Intersection
• Exclusion
• ImageMobject
• ImageSequence
• Matrix
• DecimalMatrix
• IntegerMatrix
• BarChart
• SampleSpace
• Graph
• DiGraph
• PictureInPicture
• Point
• Line
• Arrow
• DoubleArrow
• DashedLine
• ArcBetweenPoints
• CurvedArrow
• CurvedDoubleArrow
• Angle
• RightAngle
• Triangle
• SurroundingRectangle
• BackgroundRectangle
• Brace
• Elbow
• Annulus
• AnnularSector
• RegularPolygram
• ConvexHull
• Polyhedron
• ConvexHull3D
• Icosahedron
• Dodecahedron
• RoundedRectangle
• ImplicitFunction
• ArrowVectorField
• StreamLines
• TracedPath
• Polyline
• Polygon
• RegularPolygon
• Star
• Rectangle
• Square
• Circle
• Ellipse
• Arc
• Sector
• Bezier
• FunctionGraph
• PolarGraph
• ParametricCurve
• PointOnCurve
• Tangent
• Group
• Text
• MathTex
• DecimalNumber
• Sphere
• Cube
• Cuboid
• Cone
• Cylinder
• Torus
• Surface

All 71 supported object types are listed below. Fields marked required must be supplied in addition to id and type. Optional fields may be omitted; the engine applies its per-type defaults. Constraints shown here come from the structural schema; compilation also checks dimensions, geometry and references.

Each example is a single object to append to a space’s objects array. Most examples use plane2d; spatial solids explicitly use space3d. These choices demonstrate valid usage rather than an exhaustive compatibility matrix.

For examples with references, start with this document and append one example at a time. Use space3d instead of plane2d and omit the helper objects for the solid examples. Image examples need actual files at their source URLs when rendered in a browser.

{
  "version": 1,
  "duration": 5,
  "spaces": [
    {
      "name": "s",
      "type": "plane2d",
      "objects": [
        {
          "id": "l",
          "type": "Line",
          "from": [
            0,
            0
          ],
          "to": [
            2,
            1
          ]
        },
        {
          "id": "first",
          "type": "Square",
          "size": 2
        },
        {
          "id": "second",
          "type": "Square",
          "size": 2,
          "position": [
            1,
            0
          ]
        },
        {
          "id": "source",
          "type": "Point",
          "at": [
            "t",
            "sin(t)"
          ]
        }
      ]
    }
  ]
}

ArcPolygon

Join successive vertices with signed circular arcs. Supply one angle per edge; zero produces a straight edge.

Example space: plane2d.

Field	Required	Type and structural constraints
points	Yes	array of (array of (number or string; length ≥ 1; length ≤ 2000); 1–3 items); 3–128 items
angles	No	array of (number or string; length ≥ 1; length ≤ 2000); 3–128 items

{
  "id": "object",
  "type": "ArcPolygon",
  "points": [
    [
      0,
      0
    ],
    [
      1,
      0
    ],
    [
      0,
      1
    ]
  ],
  "angles": [
    0,
    0.5,
    0
  ]
}

AnimatedBoundary

Draw a repeating stroke window over a referenced continuous path. Colors cycle over time; set document duration for playback.

Example space: plane2d.

Field	Required	Type and structural constraints
target	Yes	string; qualified object reference
period	No	number; > 0
colors	No	array of (string; six-digit hex color); 1–32 items
timeWidth	No	number; ≤ 1; > 0

{
  "id": "object",
  "type": "AnimatedBoundary",
  "target": "s.l"
}

Union

Combine closed planar operands, preserving disconnected components and holes.

Example space: plane2d.

Field	Required	Type and structural constraints
operands	Yes	array of (string; qualified object reference); 2–32 items

{
  "id": "object",
  "type": "Union",
  "operands": [
    "s.first",
    "s.second"
  ]
}

Difference

Subtract subsequent operands from the first closed planar operand.

Example space: plane2d.

Field	Required	Type and structural constraints
operands	Yes	array of (string; qualified object reference); 2–32 items

{
  "id": "object",
  "type": "Difference",
  "operands": [
    "s.first",
    "s.second"
  ]
}

Intersection

Keep the area common to the closed planar operands. An empty result is valid.

Example space: plane2d.

Field	Required	Type and structural constraints
operands	Yes	array of (string; qualified object reference); 2–32 items

{
  "id": "object",
  "type": "Intersection",
  "operands": [
    "s.first",
    "s.second"
  ]
}

Exclusion

Keep regions covered by an odd number of closed planar operands (symmetric difference).

Example space: plane2d.

Field	Required	Type and structural constraints
operands	Yes	array of (string; qualified object reference); 2–32 items

{
  "id": "object",
  "type": "Exclusion",
  "operands": [
    "s.first",
    "s.second"
  ]
}

ImageMobject

Place a raster image in plane2d. source is a browser-resolved URL; supply a real image asset when rendering.

Example space: plane2d.

Field	Required	Type and structural constraints
source	Yes	string; length ≥ 1; length ≤ 2000000; supported raster URL
width	No	number or string; length ≥ 1; length ≤ 2000
height	No	number or string; length ≥ 1; length ≤ 2000

{
  "id": "object",
  "type": "ImageMobject",
  "source": "./test.png"
}

ImageSequence

Select raster frames from document time using fps, start and loop. Browser playback requires all referenced image assets.

Example space: plane2d.

Field	Required	Type and structural constraints
sources	Yes	array of (string; length ≥ 1; length ≤ 2000000; supported raster URL); 1–128 items
fps	No	number; > 0
start	No	number; ≥ 0
loop	No	boolean
width	No	number or string; length ≥ 1; length ≤ 2000
height	No	number or string; length ≥ 1; length ≤ 2000

{
  "id": "object",
  "type": "ImageSequence",
  "sources": [
    "./a.png",
    "./b.png"
  ]
}

Matrix

Lay out entries as KaTeX labels between brackets in plane2d. Entries are a rectangular matrix.

Example space: plane2d.

Field	Required	Type and structural constraints
entries	Yes	array of (array of (number or string; length ≥ 1; length ≤ 2000); 1–32 items); 1–32 items
cellWidth	No	number; > 0
cellHeight	No	number; > 0
decimals	No	integer; ≥ 0; ≤ 12

{
  "id": "object",
  "type": "Matrix",
  "entries": [
    [
      "x",
      "y"
    ]
  ]
}

DecimalMatrix

Lay out numeric/expression entries with a configurable decimal count in plane2d.

Example space: plane2d.

Field	Required	Type and structural constraints
entries	Yes	array of (array of (number or string; length ≥ 1; length ≤ 2000); 1–32 items); 1–32 items
cellWidth	No	number; > 0
cellHeight	No	number; > 0
decimals	No	integer; ≥ 0; ≤ 12

{
  "id": "object",
  "type": "DecimalMatrix",
  "entries": [
    [
      1,
      2
    ]
  ]
}

IntegerMatrix

Lay out numeric/expression entries rounded for display with zero decimal places.

Example space: plane2d.

Field	Required	Type and structural constraints
entries	Yes	array of (array of (number or string; length ≥ 1; length ≤ 2000); 1–32 items); 1–32 items
cellWidth	No	number; > 0
cellHeight	No	number; > 0
decimals	No	integer; ≥ 0; ≤ 12

{
  "id": "object",
  "type": "IntegerMatrix",
  "entries": [
    [
      1,
      2
    ]
  ]
}

BarChart

Create signed bars with optional labels in plane2d. Axes are authored separately.

Example space: plane2d.

Field	Required	Type and structural constraints
values	Yes	array of (number or string; length ≥ 1; length ≤ 2000); 1–256 items
labels	No	array of (string); 1–256 items
barWidth	No	number; > 0
gap	No	number; ≥ 0

{
  "id": "object",
  "type": "BarChart",
  "values": [
    1,
    2
  ]
}

SampleSpace

Divide a rectangle horizontally into probability regions. Positive probabilities must sum to one; labels are optional.

Example space: plane2d.

Field	Required	Type and structural constraints
probabilities	Yes	array of (number; > 0); 1–128 items
labels	No	array of (string); 1–128 items
width	No	number; > 0
height	No	number; > 0

{
  "id": "object",
  "type": "SampleSpace",
  "probabilities": [
    0.5,
    0.5
  ]
}

Graph

Create an undirected graph using circle, line or explicit vertex positions in plane2d.

Example space: plane2d.

Field	Required	Type and structural constraints
vertices	Yes	array of (string ; identifier); 1–128 items
edges	Yes	array of (array of (string ; identifier); exactly 2 items); 0–2048 items
layout	No	"circle" or "line"
radius	No	number; > 0
positions	No	map to (array of (number); exactly 2 items)
labels	No	boolean

{
  "id": "object",
  "type": "Graph",
  "vertices": [
    "a",
    "b"
  ],
  "edges": [
    [
      "a",
      "b"
    ]
  ]
}

DiGraph

Create a directed graph with arrowed edges using circle, line or explicit positions in plane2d.

Example space: plane2d.

Field	Required	Type and structural constraints
vertices	Yes	array of (string ; identifier); 1–128 items
edges	Yes	array of (array of (string ; identifier); exactly 2 items); 0–2048 items
layout	No	"circle" or "line"
radius	No	number; > 0
positions	No	map to (array of (number); exactly 2 items)
labels	No	boolean

{
  "id": "object",
  "type": "DiGraph",
  "vertices": [
    "a",
    "b"
  ],
  "edges": [
    [
      "a",
      "b"
    ]
  ]
}

PictureInPicture

Display another space in a CSS-pixel rectangle relative to the player’s top-left. A self-space inset does not recursively create more insets.

Example space: plane2d.

Field	Required	Type and structural constraints
space	Yes	string ; identifier
x	Yes	number
y	Yes	number
width	Yes	number; > 0
height	Yes	number; > 0

{
  "id": "object",
  "type": "PictureInPicture",
  "space": "s",
  "x": 0,
  "y": 0,
  "width": 200,
  "height": 100
}

Point

Place a point at native coordinates; optionally bind a coordinate to a draggable parameter.

Example space: plane2d.

Field	Required	Type and structural constraints
at	Yes	array of (number or string; length ≥ 1; length ≤ 2000); 1–3 items
drag	No	object: parameter: string ; identifier; coordinate?: integer; ≥ 0; ≤ 2; min?: number; max?: number

{
  "id": "object",
  "type": "Point",
  "at": [
    0,
    0
  ]
}

Line

Draw a straight segment between native endpoints.

Example space: plane2d.

Field	Required	Type and structural constraints
from	Yes	array of (number or string; length ≥ 1; length ≤ 2000); 1–3 items
to	Yes	array of (number or string; length ≥ 1; length ≤ 2000); 1–3 items

{
  "id": "object",
  "type": "Line",
  "from": [
    0,
    0
  ],
  "to": [
    1,
    1
  ]
}

Arrow

Draw a segment with an arrowhead at its end.

Example space: plane2d.

Field	Required	Type and structural constraints
from	Yes	array of (number or string; length ≥ 1; length ≤ 2000); 1–3 items
to	Yes	array of (number or string; length ≥ 1; length ≤ 2000); 1–3 items

{
  "id": "object",
  "type": "Arrow",
  "from": [
    0,
    0
  ],
  "to": [
    1,
    1
  ]
}

DoubleArrow

Draw a segment with arrowheads at both endpoints.

Example space: plane2d.

Field	Required	Type and structural constraints
from	Yes	array of (number or string; length ≥ 1; length ≤ 2000); 1–3 items
to	Yes	array of (number or string; length ≥ 1; length ≤ 2000); 1–3 items

{
  "id": "object",
  "type": "DoubleArrow",
  "from": [
    0,
    0
  ],
  "to": [
    1,
    1
  ]
}

DashedLine

Draw a segment using world-space dash lengths. dashRatio sets the drawn fraction of each dash period.

Example space: plane2d.

Field	Required	Type and structural constraints
from	Yes	array of (number or string; length ≥ 1; length ≤ 2000); 1–3 items
to	Yes	array of (number or string; length ≥ 1; length ≤ 2000); 1–3 items
dashLength	No	number or string; length ≥ 1; length ≤ 2000
dashRatio	No	number; > 0

{
  "id": "object",
  "type": "DashedLine",
  "from": [
    0,
    0
  ],
  "to": [
    1,
    1
  ]
}

ArcBetweenPoints

Connect endpoints with a circular arc using a signed sweep angle.

Example space: plane2d.

Field	Required	Type and structural constraints
from	Yes	array of (number or string; length ≥ 1; length ≤ 2000); 1–3 items
to	Yes	array of (number or string; length ≥ 1; length ≤ 2000); 1–3 items
angle	No	number or string; length ≥ 1; length ≤ 2000

{
  "id": "object",
  "type": "ArcBetweenPoints",
  "from": [
    0,
    0
  ],
  "to": [
    1,
    1
  ]
}

CurvedArrow

Draw an endpoint-defined circular arc with an end arrowhead.

Example space: plane2d.

Field	Required	Type and structural constraints
from	Yes	array of (number or string; length ≥ 1; length ≤ 2000); 1–3 items
to	Yes	array of (number or string; length ≥ 1; length ≤ 2000); 1–3 items
angle	No	number or string; length ≥ 1; length ≤ 2000

{
  "id": "object",
  "type": "CurvedArrow",
  "from": [
    0,
    0
  ],
  "to": [
    1,
    1
  ]
}

CurvedDoubleArrow

Draw an endpoint-defined circular arc with arrowheads at both ends.

Example space: plane2d.

Field	Required	Type and structural constraints
from	Yes	array of (number or string; length ≥ 1; length ≤ 2000); 1–3 items
to	Yes	array of (number or string; length ≥ 1; length ≤ 2000); 1–3 items
angle	No	number or string; length ≥ 1; length ≤ 2000

{
  "id": "object",
  "type": "CurvedDoubleArrow",
  "from": [
    0,
    0
  ],
  "to": [
    1,
    1
  ]
}

Angle

Mark the angle between rays from vertex toward from and to. otherAngle selects the alternative angle.

Example space: plane2d.

Field	Required	Type and structural constraints
from	Yes	array of (number or string; length ≥ 1; length ≤ 2000); 1–3 items
vertex	Yes	array of (number or string; length ≥ 1; length ≤ 2000); 1–3 items
to	Yes	array of (number or string; length ≥ 1; length ≤ 2000); 1–3 items
radius	No	number or string; length ≥ 1; length ≤ 2000
otherAngle	No	boolean

{
  "id": "object",
  "type": "Angle",
  "from": [
    1,
    0
  ],
  "vertex": [
    0,
    0
  ],
  "to": [
    0,
    1
  ]
}

RightAngle

Mark perpendicular rays with a square corner. Nonperpendicular or degenerate rays are rejected.

Example space: plane2d.

Field	Required	Type and structural constraints
from	Yes	array of (number or string; length ≥ 1; length ≤ 2000); 1–3 items
vertex	Yes	array of (number or string; length ≥ 1; length ≤ 2000); 1–3 items
to	Yes	array of (number or string; length ≥ 1; length ≤ 2000); 1–3 items
size	No	number or string; length ≥ 1; length ≤ 2000

{
  "id": "object",
  "type": "RightAngle",
  "from": [
    1,
    0
  ],
  "vertex": [
    0,
    0
  ],
  "to": [
    0,
    1
  ]
}

Triangle

Create an equilateral triangle using its circumradius.

Example space: plane2d.

Field	Required	Type and structural constraints
radius	No	number or string; length ≥ 1; length ≤ 2000

{
  "id": "object",
  "type": "Triangle"
}

SurroundingRectangle

Follow a referenced 2D point/path’s bounds with padding. Measured text and group bounds are unsupported.

Example space: plane2d.

Field	Required	Type and structural constraints
target	Yes	string; qualified object reference
padding	No	number or string; length ≥ 1; length ≤ 2000

{
  "id": "object",
  "type": "SurroundingRectangle",
  "target": "s.l"
}

BackgroundRectangle

Follow a referenced 2D point/path’s bounds with a filled rectangle. Declare it before the foreground object.

Example space: plane2d.

Field	Required	Type and structural constraints
target	Yes	string; qualified object reference
padding	No	number or string; length ≥ 1; length ≤ 2000

{
  "id": "object",
  "type": "BackgroundRectangle",
  "target": "s.l"
}

Brace

Place a brace on a side of referenced 2D point/path bounds. depth controls its extension.

Example space: plane2d.

Field	Required	Type and structural constraints
target	Yes	string; qualified object reference
side	No	"left" or "right" or "top" or "bottom"
padding	No	number or string; length ≥ 1; length ≤ 2000
depth	No	number or string; length ≥ 1; length ≤ 2000

{
  "id": "object",
  "type": "Brace",
  "target": "s.l"
}

Elbow

Draw an L-shaped corner with a width and angle.

Example space: plane2d.

Field	Required	Type and structural constraints
width	No	number or string; length ≥ 1; length ≤ 2000
angle	No	number or string; length ≥ 1; length ≤ 2000

{
  "id": "object",
  "type": "Elbow"
}

Annulus

Create a ring with a preserved hole. Radii must satisfy 0 < innerRadius < radius.

Example space: plane2d.

Field	Required	Type and structural constraints
innerRadius	No	number or string; length ≥ 1; length ≤ 2000
radius	No	number or string; length ≥ 1; length ≤ 2000

{
  "id": "object",
  "type": "Annulus"
}

AnnularSector

Create part of a ring. Radii must satisfy 0 < innerRadius < radius; use a nonzero sweep of at most one turn.

Example space: plane2d.

Field	Required	Type and structural constraints
innerRadius	No	number or string; length ≥ 1; length ≤ 2000
radius	No	number or string; length ≥ 1; length ≤ 2000
startAngle	No	number or string; length ≥ 1; length ≤ 2000
angle	No	number or string; length ≥ 1; length ≤ 2000

{
  "id": "object",
  "type": "AnnularSector"
}

RegularPolygram

Connect regularly spaced vertices using step. This is stroke-only geometry; disconnected cycles cannot be morphed as one continuous path.

Example space: plane2d.

Field	Required	Type and structural constraints
sides	Yes	integer; ≥ 3; ≤ 512
step	Yes	integer; ≥ 1; ≤ 511
radius	No	number or string; length ≥ 1; length ≤ 2000

{
  "id": "object",
  "type": "RegularPolygram",
  "sides": 5,
  "step": 2
}

ConvexHull

Compute a planar convex hull, discarding interior and duplicate points.

Example space: plane2d.

Field	Required	Type and structural constraints
points	Yes	array of (array of (number or string; length ≥ 1; length ≤ 2000); 1–3 items); 3–2048 items

{
  "id": "object",
  "type": "ConvexHull",
  "points": [
    [
      0,
      0
    ],
    [
      2,
      0
    ],
    [
      0,
      2
    ],
    [
      0.2,
      0.2
    ]
  ]
}

Polyhedron

Build a closed spatial shell from vertices and indexed planar convex faces. Invalid, open or degenerate shells are rejected.

Example space: space3d.

Field	Required	Type and structural constraints
points	Yes	array of (array of (number or string; length ≥ 1; length ≤ 2000); 1–3 items); 4–2048 items
faces	Yes	array of (array of (integer; ≥ 0); 3–128 items); 4–4096 items

{
  "id": "object",
  "type": "Polyhedron",
  "points": [
    [
      0,
      0,
      0
    ],
    [
      1,
      0,
      0
    ],
    [
      0,
      1,
      0
    ],
    [
      0,
      0,
      1
    ]
  ],
  "faces": [
    [
      0,
      1,
      2
    ],
    [
      0,
      1,
      3
    ],
    [
      0,
      2,
      3
    ],
    [
      1,
      2,
      3
    ]
  ]
}

ConvexHull3D

Compute a spatial convex hull from noncoplanar points; coplanar faces are merged.

Example space: space3d.

Field	Required	Type and structural constraints
points	Yes	array of (array of (number or string; length ≥ 1; length ≤ 2000); 1–3 items); 4–64 items

{
  "id": "object",
  "type": "ConvexHull3D",
  "points": [
    [
      0,
      0,
      0
    ],
    [
      1,
      0,
      0
    ],
    [
      0,
      1,
      0
    ],
    [
      0,
      0,
      1
    ]
  ]
}

Icosahedron

Create the regular 20-face solid using its circumradius.

Example space: space3d.

Field	Required	Type and structural constraints
radius	No	number or string; length ≥ 1; length ≤ 2000

{
  "id": "object",
  "type": "Icosahedron"
}

Dodecahedron

Create the regular 12-face solid using its circumradius.

Example space: space3d.

Field	Required	Type and structural constraints
radius	No	number or string; length ≥ 1; length ≤ 2000

{
  "id": "object",
  "type": "Dodecahedron"
}

RoundedRectangle

Create a rectangle with rounded corners; corner size must fit its dimensions.

Example space: plane2d.

Field	Required	Type and structural constraints
width	No	number or string; length ≥ 1; length ≤ 2000
height	No	number or string; length ≥ 1; length ≤ 2000
cornerRadius	No	number or string; length ≥ 1; length ≤ 2000

{
  "id": "object",
  "type": "RoundedRectangle"
}

ImplicitFunction

Sample the zero contour of expression over explicit x/y ranges using marching squares. Disconnected contours remain separate.

Example space: plane2d.

Field	Required	Type and structural constraints
expression	Yes	string
xRange	Yes	array of (number); exactly 2 items
yRange	Yes	array of (number); exactly 2 items
resolution	No	integer; ≥ 4; ≤ 256

{
  "id": "object",
  "type": "ImplicitFunction",
  "expression": "x^2+y^2-1",
  "xRange": [
    -2,
    2
  ],
  "yRange": [
    -2,
    2
  ]
}

ArrowVectorField

Sampling uses Cartesian coordinates, including in polar spaces. Defaults: spacing 1, lengthScale 0.6, maxLength 0.8 × spacing. Without zRange, 3D sampling lies on z=0. At most 4096 arrows are generated; zero/non-finite vectors are skipped.

Sample a Cartesian vector field on a bounded grid. In space3d use three expressions and zRange for a volume; lengthScale and maxLength control arrows.

Example space: plane2d.

Field	Required	Type and structural constraints
expressions	Yes	array of (number or string; length ≥ 1; length ≤ 2000); 1–3 items
xRange	Yes	array of (number); exactly 2 items
yRange	Yes	array of (number); exactly 2 items
zRange	No	array of (number); exactly 2 items
spacing	No	number; > 0
lengthScale	No	number or string; length ≥ 1; length ≤ 2000
maxLength	No	number; > 0

{
  "id": "object",
  "type": "ArrowVectorField",
  "expressions": [
    "-y",
    "x"
  ],
  "xRange": [
    -1,
    1
  ],
  "yRange": [
    -1,
    1
  ]
}

StreamLines

The field is frozen at the current scene time and integrated with fourth-order Runge–Kutta. Defaults are step 0.04 and 256 steps, with at most 100000 total integration steps. Integration stops at stationary or non-finite results.

Integrate a Cartesian vector field from each seed using bounded numerical steps. Separate streams remain separate strokes.

Example space: plane2d.

Field	Required	Type and structural constraints
expressions	Yes	array of (number or string; length ≥ 1; length ≤ 2000); 1–3 items
seeds	Yes	array of (array of (number or string; length ≥ 1; length ≤ 2000); 1–3 items); 1–256 items
step	No	number; > 0
steps	No	integer; ≥ 1; ≤ 2048

{
  "id": "object",
  "type": "StreamLines",
  "expressions": [
    "-y",
    "x"
  ],
  "seeds": [
    [
      1,
      0
    ]
  ]
}

TracedPath

Current parameter overrides apply to every historical sample; this does not record mouse-gesture history. Destination object/group/space transforms apply after trace generation.

Sample a referenced point’s historical positions deterministically. start establishes its initial time; duration optionally limits the trailing history window.

Example space: plane2d.

Field	Required	Type and structural constraints
point	Yes	string; qualified object reference
start	No	number; ≥ 0
duration	No	number; > 0
samples	No	integer; ≥ 8; ≤ 2048

{
  "id": "object",
  "type": "TracedPath",
  "point": "s.source"
}

Polyline

Join vertices with open line segments.

Example space: plane2d.

Field	Required	Type and structural constraints
points	Yes	array of (array of (number or string; length ≥ 1; length ≤ 2000); 1–3 items); 2–10000 items

{
  "id": "object",
  "type": "Polyline",
  "points": [
    [
      0,
      0
    ],
    [
      1,
      1
    ]
  ]
}

Polygon

Join vertices into a closed polygon.

Example space: plane2d.

Field	Required	Type and structural constraints
points	Yes	array of (array of (number or string; length ≥ 1; length ≤ 2000); 1–3 items); 3–10000 items

{
  "id": "object",
  "type": "Polygon",
  "points": [
    [
      0,
      0
    ],
    [
      1,
      0
    ],
    [
      0,
      1
    ]
  ]
}

RegularPolygon

Create a regular polygon from side count and circumradius.

Example space: plane2d.

Field	Required	Type and structural constraints
sides	Yes	integer; ≥ 3; ≤ 512
radius	No	number or string; length ≥ 1; length ≤ 2000

{
  "id": "object",
  "type": "RegularPolygon",
  "sides": 5
}

Star

Alternate outer and inner radii around the specified number of tips.

Example space: plane2d.

Field	Required	Type and structural constraints
tips	Yes	integer; ≥ 2; ≤ 256
radius	No	number or string; length ≥ 1; length ≤ 2000
innerRadius	No	number or string; length ≥ 1; length ≤ 2000

{
  "id": "object",
  "type": "Star",
  "tips": 5
}

Rectangle

Create a centered rectangle with width and height.

Example space: plane2d.

Field	Required	Type and structural constraints
width	No	number or string; length ≥ 1; length ≤ 2000
height	No	number or string; length ≥ 1; length ≤ 2000

{
  "id": "object",
  "type": "Rectangle"
}

Square

Create a centered square with side length size.

Example space: plane2d.

Field	Required	Type and structural constraints
size	No	number or string; length ≥ 1; length ≤ 2000

{
  "id": "object",
  "type": "Square"
}

Circle

Create a sampled circle with radius.

Example space: plane2d.

Field	Required	Type and structural constraints
radius	No	number or string; length ≥ 1; length ≤ 2000

{
  "id": "object",
  "type": "Circle"
}

Ellipse

Create a sampled ellipse with independent x/y radii.

Example space: plane2d.

Field	Required	Type and structural constraints
radiusX	No	number or string; length ≥ 1; length ≤ 2000
radiusY	No	number or string; length ≥ 1; length ≤ 2000

{
  "id": "object",
  "type": "Ellipse"
}

Arc

Create an open circular arc using startAngle and signed angle.

Example space: plane2d.

Field	Required	Type and structural constraints
radius	No	number or string; length ≥ 1; length ≤ 2000
startAngle	No	number or string; length ≥ 1; length ≤ 2000
angle	No	number or string; length ≥ 1; length ≤ 2000

{
  "id": "object",
  "type": "Arc"
}

Sector

Create a filled-capable circular sector bounded by an arc and radial edges.

Example space: plane2d.

Field	Required	Type and structural constraints
radius	No	number or string; length ≥ 1; length ≤ 2000
startAngle	No	number or string; length ≥ 1; length ≤ 2000
angle	No	number or string; length ≥ 1; length ≤ 2000

{
  "id": "object",
  "type": "Sector"
}

Bezier

Create chained cubic Bezier segments. Use 3n+1 control points for n segments.

Example space: plane2d.

Field	Required	Type and structural constraints
points	Yes	array of (array of (number or string; length ≥ 1; length ≤ 2000); 1–3 items); 4–10000 items

{
  "id": "object",
  "type": "Bezier",
  "points": [
    [
      0,
      0
    ],
    [
      0,
      1
    ],
    [
      1,
      1
    ],
    [
      1,
      0
    ]
  ]
}

FunctionGraph

Plot Cartesian y = expression(x). Optional domain limits the graph; Canvas can adapt sampling to the current viewport.

Example space: plane2d.

Field	Required	Type and structural constraints
expression	Yes	string
domain	No	array of (number); exactly 2 items
samples	No	integer; ≥ 8; ≤ 2048

{
  "id": "object",
  "type": "FunctionGraph",
  "expression": "sin(x)",
  "domain": [
    -1,
    1
  ]
}

PolarGraph

Plot radius = expression(theta). Domain is an angular interval in radians.

Example space: plane2d.

Field	Required	Type and structural constraints
expression	Yes	string
domain	No	array of (number); exactly 2 items
samples	No	integer; ≥ 8; ≤ 2048

{
  "id": "object",
  "type": "PolarGraph",
  "expression": "cos(theta)",
  "domain": [
    0,
    6
  ]
}

ParametricCurve

Evaluate coordinate expressions in u over a domain. Expression count follows the containing space’s native dimension.

Example space: plane2d.

Field	Required	Type and structural constraints
expressions	Yes	array of (number or string; length ≥ 1; length ≤ 2000); 1–3 items
domain	No	array of (number); exactly 2 items
samples	No	integer; ≥ 8; ≤ 2048

{
  "id": "object",
  "type": "ParametricCurve",
  "expressions": [
    "u",
    "u^2"
  ],
  "domain": [
    0,
    1
  ]
}

PointOnCurve

Place a point at normalized sampled arc length on a continuous curve. Optionally bind that parameter for dragging.

Example space: plane2d.

Field	Required	Type and structural constraints
curve	Yes	string; qualified object reference
parameter	Yes	number or string; length ≥ 1; length ≤ 2000
drag	No	object: parameter: string ; identifier; coordinate?: integer; ≥ 0; ≤ 2; min?: number; max?: number

{
  "id": "object",
  "type": "PointOnCurve",
  "curve": "s.l",
  "parameter": 0.5
}

Tangent

Estimate a tangent to a continuous curve at normalized sampled arc length.

Example space: plane2d.

Field	Required	Type and structural constraints
curve	Yes	string; qualified object reference
parameter	Yes	number or string; length ≥ 1; length ≤ 2000
length	No	number or string; length ≥ 1; length ≤ 2000

{
  "id": "object",
  "type": "Tangent",
  "curve": "s.l",
  "parameter": 0.5
}

Group

Group qualified child IDs for inherited transforms/style behavior. Each child has at most one parent; cycles are invalid.

Example space: plane2d.

Field	Required	Type and structural constraints
children	Yes	array of (string; qualified object reference); 1–10000 items

{
  "id": "object",
  "type": "Group",
  "children": [
    "s.l"
  ]
}

Text

Render plain text at position. Text is not interpreted as HTML.

Example space: plane2d.

Field	Required	Type and structural constraints
text	Yes	string; length ≤ 10000

{
  "id": "object",
  "type": "Text",
  "text": "hello"
}

MathTex

Render a KaTeX expression at position. Escape backslashes in JSON, for example "\frac{1}{2}".

Example space: plane2d.

Field	Required	Type and structural constraints
text	Yes	string; length ≤ 10000

{
  "id": "object",
  "type": "MathTex",
  "text": "x^2"
}

DecimalNumber

Render a scalar expression as a decimal label with configurable precision.

Example space: plane2d.

Field	Required	Type and structural constraints
value	Yes	number or string; length ≥ 1; length ≤ 2000
decimals	No	integer; ≥ 0; ≤ 12

{
  "id": "object",
  "type": "DecimalNumber",
  "value": 1
}

Sphere

Create a sphere with radius.

Example space: space3d.

Field	Required	Type and structural constraints
radius	No	number or string; length ≥ 1; length ≤ 2000

{
  "id": "object",
  "type": "Sphere"
}

Cube

Create a cube with side length size.

Example space: space3d.

Field	Required	Type and structural constraints
size	No	number or string; length ≥ 1; length ≤ 2000

{
  "id": "object",
  "type": "Cube"
}

Cuboid

Create a box with width, height and depth.

Example space: space3d.

Field	Required	Type and structural constraints
width	No	number or string; length ≥ 1; length ≤ 2000
height	No	number or string; length ≥ 1; length ≤ 2000
depth	No	number or string; length ≥ 1; length ≤ 2000

{
  "id": "object",
  "type": "Cuboid"
}

Cone

Create a cone centered on the z axis using radius and height.

Example space: space3d.

Field	Required	Type and structural constraints
radius	No	number or string; length ≥ 1; length ≤ 2000
height	No	number or string; length ≥ 1; length ≤ 2000

{
  "id": "object",
  "type": "Cone"
}

Cylinder

Create a cylinder centered on the z axis using radius and height.

Example space: space3d.

Field	Required	Type and structural constraints
radius	No	number or string; length ≥ 1; length ≤ 2000
height	No	number or string; length ≥ 1; length ≤ 2000

{
  "id": "object",
  "type": "Cylinder"
}

Torus

Create a torus around the z axis using major radius and tubeRadius.

Example space: space3d.

Field	Required	Type and structural constraints
radius	No	number or string; length ≥ 1; length ≤ 2000
tubeRadius	No	number or string; length ≥ 1; length ≤ 2000

{
  "id": "object",
  "type": "Torus"
}

Surface

Sample three coordinate expressions in u and v to create a triangulated surface. resolution specifies the two grid dimensions.

Example space: space3d.

Field	Required	Type and structural constraints
expressions	Yes	array of (number or string; length ≥ 1; length ≤ 2000); exactly 3 items
uRange	Yes	array of (number); exactly 2 items
vRange	Yes	array of (number); exactly 2 items
resolution	No	array of (integer; ≥ 2; ≤ 128); exactly 2 items

{
  "id": "object",
  "type": "Surface",
  "expressions": [
    "u",
    "v",
    "u*v"
  ],
  "uRange": [
    -1,
    1
  ],
  "vRange": [
    -1,
    1
  ]
}

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