2D ↔ 3D#

Four operations that change dimensionality. Two give a profile thickness; two take a cross-section of a solid.

Each unions its children before acting on them, and each insists on the dimensionality it takes: "extrude" takes 2D geometry, got 3D.

extrude#

Sweeps a 2D profile along Z, optionally twisting and tapering as it goes.

extrude { height = 20  circle { radius = 10 } }

extrude {
  height    = 40
  twist     = 90
  scale_top = [0.5, 0.5]
  divisions = 24
  rect { size = [20, 20]  center = true }
}

Attributes#

Caveats#

• divisions matters whenever twist or scale_top is set. With the default 0 the sides are straight lines between the two end faces, so a twist becomes a single sheared step rather than a helix. Set it to the number of intermediate layers you want.
• A height of 0 or less yields empty geometry rather than an error, so a parameter sweeping to zero does not break the model.
• scale_top = [0, 0] gives a point, which is one way to build a pyramid from any profile.
• The profile is swept as drawn - extrude does not centre it. A rect that is not centred produces a box in the positive quadrant.

revolve#

Spins a 2D profile about the Y axis into a solid of revolution.

revolve { segments = 96  polygon { points = profile } }
revolve { angle = 180  segments = 64  polygon { points = profile } }

Attributes#

Caveats#

• The profile is written in the XY plane, and its Y becomes the result's Z. X is the radius. A profile drawn from [0, 0] upwards produces a solid standing on the XY plane.
• Every X must be ≥ 0. A profile that crosses the axis revolves through itself and the result is not what you drew.
• The profile does not have to touch the axis. One that does not produces a tube - which is how torus is built internally.
• An angle of 0 or less yields empty geometry rather than an error.

project#

The shadow a solid casts on the XY plane - its full outline, from any Z.

project { bracket { } }

Attributes#

None.

Caveats#

• Takes 3D geometry and produces 2D: "project" takes 3D geometry, got 2D.
• The result is the union of everything, seen from above. Internal voids that are covered from above do not appear.

slice#

The cross-section of a solid at one height.

slice { z = 12  bracket { } }

Attributes#

Caveats#

• Takes 3D geometry and produces 2D.
• A plane that misses the solid gives an empty cross-section, not an error.
• A plane exactly on a flat face is ambiguous - offset it slightly.

Usage#

Profiles are where the modelling happens#

Most shapes are easier to describe in 2D and then given thickness. A rounded box, for instance, has no primitive - it is a rounded rectangle with a height:

extrude {
  height = 12
  rounded_rect { size = [40, 30]  radius = 4  center = true }
}

Turning a bottle, a vase, a knob#

revolve on a hand-written profile is how anything with rotational symmetry is built. Read the points as (radius, height):

local profile = [
  [0, 0], [26, 0], [24, 6], [16, 26],
  [14, 48], [18, 66], [22, 74], [0, 74],
]

// The same silhouette walked inwards by one wall, so the difference leaves a shell.
local cavity = [
  [0, 3], [21, 3], [20, 8], [13, 26],
  [11, 48], [15, 66], [19, 72], [0, 72],
]

model "vase" {
  part "vase" {
    difference {
      revolve { segments = 96  polygon { points = profile } }
      translate {
        offset = [0, 0, 3]
        revolve { segments = 96  polygon { points = cavity } }
      }
    }
  }
}

The hollowing is the same trick as anywhere else: the solid minus a slightly smaller copy of itself.

Twisted extrusions#

A twist needs divisions, or there is nothing to twist between:

extrude {
  height    = 60
  twist     = 180
  divisions = 40        // without this the sides are two straight lines
  regular_polygon { sides = 6  radius = 12 }
}

Tapers and pyramids#

extrude { height = 30  scale_top = 0.4   rect { size = [40, 40]  center = true } }  // frustum
extrude { height = 30  scale_top = 0     rect { size = [40, 40]  center = true } }  // pyramid

Deriving a base plate from a part#

project turns a finished solid back into an outline, which is useful for a footprint, a gasket or a support pad:

model "m" {
  part "body" { bracket { } }

  part "pad" {
    color = "#c8842f"
    translate {
      offset = [0, 0, -3]
      extrude {
        height = 3
        offset { amount = 2  project { bracket { } } }   // footprint, grown 2 mm
      }
    }
  }
}

Inspecting a cross-section#

slice is a debugging tool as much as a modelling one - extrude the slice thinly to see where the walls actually fell:

part "section" {
  color = "#ff6b7f"
  extrude { height = 0.5  slice { z = 40  bottle { } } }
}

Troubleshooting#

"extrude" takes 2D geometry, got 3D#

The child is already a solid. Extrusion is for profiles:

extrude { height = 10  box { size = [1, 1, 1] } }        // ✗
extrude { height = 10  rect { size = [1, 1] } }          // ✓

"extrude" cannot mix 2D and 3D shapes#

Two children of different dimensionality. Extrude each profile separately, or union the profiles before extruding.

part "body" is 2D - extrude or revolve it before rendering#

A profile reached the renderer. Somewhere the extrude or revolve is missing, or is wrapped around the wrong block.

My twist looks like a single shear#

divisions defaults to 0, which means the extrusion has no intermediate layers. Set it to 20–60 for a smooth twist.

My revolved solid is inside out, or has a spike through the middle#

Part of the profile has a negative X, so it crossed the axis of revolution. Every point must have X ≥ 0.

My revolved solid is lying down#

revolve maps the profile's Y to the result's Z. A profile written as (x, z) with the height in the first component produces a solid on its side - swap the components.

revolve produced nothing#

Either the angle reached 0, or the profile has zero area. Both yield empty geometry silently, by design, so that a parameter at the end of its range does not break a model.