.3MF File Format – Volumetric and implicit

General rules

• Consumers must parse every element; the only one they must actually support is the level set shape.
• A file that uses level sets must list the volumetric extension as required. One that only adds colour, composition or properties may list it as required or recommended.
• When the extension is required, objects, functions, 3D images, volume data and level sets may appear in <resources> in any order (relaxing the core’s rule that objects come last), but each must still be defined before it is used.
• Every sampled element has a transform from object coordinates into the function’s coordinates: a point (x, y, z) is sampled at T × (x, y, z).
• An undefined function result (for example a division by zero) makes the element use its fallbackvalue.

Functions

A function resource has an id (ST_ResourceID, required) and an optional displayname. It takes inputs and gives named outputs of four data types: scalar, vector (three numbers), matrix (4×4) and resource ID. There are three kinds.

v:functionfromimage3d

Input: pos (vector), the UVW coordinate, with (0,0,0) at the left-front-bottom corner of the voxel grid and (1,1,1) at the right-back-top. Outputs, each 0 to 1 before scaling: color (vector of red, green, blue), red, green, blue and alpha (scalars).

i:implicitfunction

A graph of nodes; see Implicit extension below.

Private extension function

A function element from a vendor namespace (with id, displayname and its namespace), taking a scalar or vector and returning a scalar or vector. Support is optional.

3D images

All sheets share size, pixel layout and bit depth. Each count is at most 1024³ and the total voxels at most 1024⁵. Values are normalised by dividing by 2^N−1 for an N-bit channel. Grey images are read as Y, Y, Y; missing alpha is 1. Sheets are recommended at /3D/volumetric/image/sheet.png; 16-bit channels are recommended where precision matters, and single-channel images for level-set data (such as a signed distance field).

v:levelset

A shape, used in an object in place of a mesh: the surface is where the function equals zero, evaluated only inside a closed mesh that bounds it.

v:volumedata

A resource (id required) describing properties inside a shape. A mesh refers to it with v:volumeid, a level set with volumeid. It holds at most one color, at most one composite and up to 2³¹−1 property elements. The data is clipped to the shape. Where a surface property (from the core or the Materials extension) disagrees, the surface wins in a layer as thin as possible. Where objects overlap, only the last object’s volume data applies. Volume data must not be used on a mesh that another mesh refers to as its original (mirrored) mesh.

Material mapping order follows the base material order. Each material’s share at a point is its value divided by the sum of all values there; producers must not let the sum fall below 10⁻⁵.

Implicit extension

An i:implicitfunction (attributes id and displayname) declares its inputs in i:in with i:scalar, i:vector, i:matrix or i:resourceid elements (each with an identifier and optional displayname), then lists nodes, then its outputs in i:out as references. Every node has an identifier (letters, digits and underscores; never inputs or outputs) and an optional displayname, its own i:in of references and i:out of typed outputs.

Each reference has an identifier (the input’s name), an optional displayname and ref in the form node.output; the function’s own inputs are inputs.name. The graph must be directed and acyclic, with no function calling itself directly or through others, and each reference must match the type of what it points to; otherwise the file is rejected.

<i:implicitfunction id="5" displayname="sphere">
  <i:in>
    <i:vector identifier="pos"/>
    <i:scalar identifier="radius"/>
  </i:in>
  <i:length identifier="Length_3">
    <i:in><i:vectorref identifier="A" ref="inputs.pos"/></i:in>
    <i:out><i:scalar identifier="result"/></i:out>
  </i:length>
  <i:subtraction identifier="Subtraction_4">
    <i:in>
      <i:scalarref identifier="A" ref="Length_3.result"/>
      <i:scalarref identifier="B" ref="inputs.radius"/>
    </i:in>
    <i:out><i:scalar identifier="result"/></i:out>
  </i:subtraction>
  <i:out>
    <i:scalarref identifier="shape" ref="Subtraction_4.result"/>
  </i:out>
</i:implicitfunction>

Native nodes

“Componentwise” nodes accept scalars, vectors or (where marked) matrices, with both inputs of the same type, and work on each component.