# OpenSCAD User Manual/2D to 3D Extrusion

Extrusion is the process of creating an object with a fixed cross-sectional profile. OpenSCAD provides two commands to create 3D solids from a 2D shape: linear_extrude and rotate_extrude. Linear extrusion is similar to pushing Playdoh through a press with a die of a specific shape.
Rotational extrusion is similar to the process of turning or "throwing" a bowl on the Potter's wheel.
Both extrusion methods work on a (possibly disjointed) 2D shape which exists on the X-Y plane. While transformations that operates on both 2D shapes and 3D solids can move a shape off the X-Y plane, when the extrusion is performed the end result is not very intuitive. What actually happens is that any information in the third coordinate (the Z coordinate) is ignored for any 2D shape, this process amounts to an implicit projection performed on any 2D shape before the extrusion is executed. It is recommended to perform extrusion on shapes that remains strictly on the X-Y plane.

### linear_extrude

Linear Extrusion is an operation that takes a 2D object as input and generates a 3D object as a result.
Extrusion follows the V vector which defaults to the Z axis, for specifying a custom value a version > 2021.01 is needed.
In OpenSCAD Extrusion is always performed on the projection (shadow) of the 2d object xy plane; so if you rotate or apply other transformations to the 2d object before extrusion, its shadow shape is what is extruded.
Although the extrusion is linear along the V vector, a twist parameter is available that causes the object to be rotated around the V vector as it is extruding upward. This can be used to rotate the object at its center, as if it is a spiral pillar, or produce a helical extrusion around the V vector, like a pig's tail.
A scale parameter is also included so that the object can be expanded or contracted over the extent of the extrusion, allowing extrusions to be flared inward or outward.

#### Usage

You must use parameter names due to a backward compatibility issue.
height must be positive.
v is a 3D vector that must point into positive Z direction [Note: Requires version Development snapshot]
$fn is optional and specifies the resolution of the linear_extrude (higher number brings more "smoothness", but more computation time is needed).
If the extrusion fails for a non-trivial 2D shape, try setting the convexity parameter (the default is not 10, but 10 is a "good" value to try). See explanation further down.

#### Twist

Twist is the number of degrees of through which the shape is extruded. Setting the parameter twist = 360 extrudes through one revolution. The twist direction follows the left hand rule.
0° of Twist
-100° of Twist
100° of Twist
-500° of Twist

#### Center

It is similar to the parameter center of cylinders. If center is false the linear extrusion Z range is from 0 to height; if it is true, the range is from -height/2 to height/2.
center = true
center = false

#### Mesh Refinement

The slices parameter defines the number of intermediate points along the Z axis of the extrusion. Its default increases with the value of twist. Explicitly setting slices may improve the output refinement. Additional the segments parameter adds vertices (points) to the extruded polygon resulting in smoother twisted geometries. Segments need to be a multiple of the polygon's fragments to have an effect (6 or 9.. for a circle($fn=3), 8,12.. for a square ).
The special variables $fn, $fs and $fa can also be used to improve the output. If slices is not defined, its value is taken from the defined $fn value.

#### Scale

Scales the 2D shape by this value over the height of the extrusion. Scale can be a scalar or a vector:
Note that if scale is a vector, the resulting side walls may be nonplanar. Use twist=0 and the slices parameter to avoid asymmetry.

### Using with imported SVG

A common usage of this function is to import a 2D svg

### rotate_extrude

Rotational extrusion spins a 2D shape around the Z-axis to form a solid which has rotational symmetry. One way to think of this operation is to imagine a Potter's wheel placed on the X-Y plane with its axis of rotation pointing up towards +Z. Then place the to-be-made object on this virtual Potter's wheel (possibly extending down below the X-Y plane towards -Z). The to-be-made object is the cross-section of the object on the X-Y plane (keeping only the right half, X >= 0). That is the 2D shape that will be fed to rotate_extrude as the child in order to generate this solid. Note that the object started on the X-Y plane but is tilted up (rotated +90 degrees about the X-axis) to extrude.
Since a 2D shape is rendered by OpenSCAD on the X-Y plane, an alternative way to think of this operation is as follows: spins a 2D shape around the Y-axis to form a solid. The resultant solid is placed so that its axis of rotation lies along the Z-axis.
Just like the linear_extrude, the extrusion is always performed on the projection of the 2D polygon to the XY plane. Transformations like rotate, translate, etc. applied to the 2D polygon before extrusion modify the projection of the 2D polygon to the XY plane and therefore also modify the appearance of the final 3D object.
* A translation in Z of the 2D polygon has no effect on the result (as also the projection is not affected).
* A translation in X increases the diameter of the final object.
* A translation in Y results in a shift of the final object in Z direction.
* A rotation about the X or Y axis distorts the cross section of the final object, as also the projection to the XY plane is distorted.
Don't get confused, as OpenSCAD displays 2D polygons with a certain height in the Z direction, so the 2D object (with its height) appears to have a bigger projection to the XY plane. But for the projection to the XY plane and also for the later extrusion only the base polygon without height is used.
It can not be used to produce a helix or screw threads. Those are surprisingly difficult to do right; it's best to find a library that does them for you.
The 2D shape must lie completely on either the right (recommended) or the left side of the Y-axis. More precisely speaking, every vertex of the shape must have either x >= 0 or x <= 0. If the shape spans the X axis a warning appears in the console windows and the rotate_extrude is ignored. If the 2D shape touches the Y axis, i.e. at x=0, it must be a line that touches, not a point, as a point results in a zero thickness 3D object, which is invalid and results in a CGAL error. For OpenSCAD versions prior to 2016.xxxx, if the shape is in the negative axis the resulting faces are oriented inside-out, which may cause undesired effects.

#### Usage

In 2021.01 and previous, you must use parameter names due to a backward compatibility issue.
    convexity : If the extrusion fails for a non-trival 2D shape, try setting the convexity parameter (the default is not 10, but 10 is a "good" value to try). See explanation further down.
    angle [Note: Requires version 2019.05] : Defaults to 360. Specifies the number of degrees to sweep, starting at the positive X axis. The direction of the sweep follows the Right Hand Rule, hence a negative angle sweeps clockwise.
    start [Note: Requires version Development snapshot] : Defaults to 0 if angle is specified, and 180 if not. Specifies the starting angle of the extrusion, counter-clockwise from the positive X axis.
    $fa : minimum angle (in degrees) of each fragment.
    $fs : minimum circumferential length of each fragment.
    $fn : fixed number of fragments in 360 degrees. Values of 3 or more override $fa and $fs
       $fa, $fs and $fn must be named parameters. click here for more details,.

#### Examples

A simple torus can be constructed using a rotational extrude.

#### Mesh Refinement

Increasing the number of fragments composing the 2D shape improves the quality of the mesh, but takes longer to render.
The number of fragments used by the extrusion can also be increased.
Using the parameter angle (with OpenSCAD versions 2016.xx), a hook can be modeled .

#### Extruding a Polygon

Extrusion can also be performed on polygons with points chosen by the user.
Here is a simple polygon and its 200 step rotational extrusion. (Note it has been rotated 90 degrees to show how the rotation appears; the rotate_extrude needs it flat).
For more information on polygons, please see: 2D Primitives: Polygon.

#### Orientation

If you're making a round 360 degree extrusion, it doesn't matter where it starts. If, on the other hand, you're using $fn to make an extrusion with some specific number of sides, it can matter. With an odd number of sides, there will be a vertex on either the left or the right, and a side opposite it.
With angle not specified, the extrusion starts along the negative X axis, to the left of the origin. With an odd number of sides, there is a vertex on the left and a side on the right. (Note that this is inconsistent with the behavior for angle less than 360, and with the behavior for circle and other round primitives.)
With angle specified, and not equal to 360, the extrusion starts along the positive X axis, to the right of the origin.
For 2021.01 and earlier, if angle is equal to 360, the extrusion starts along the negative X axis, as for angle not being specified.
For the development snapshot, if angle is 360, the extrusion starts along the positive X axis, as for other cases where angle is specified. Explicitly specifying angle=360 thus yields results consistent with other round primitives.
A future release may change this behavior so that when angle is not specified the extrusion starts along the positive X axis, making all of these cases consistent.
start directly controls the start point. [Note: Requires version Development snapshot]

### Description of extrude parameters
#### Extrude parameters for all extrusion modes

| convexity | Integer. The convexity parameter specifies the maximum number of front sides (or back sides) a ray intersecting the object might penetrate. This parameter is only needed for correctly displaying the object in OpenCSG preview mode when using the standard Goldfeather algorithm and has no effect on the polyhedron rendering (the mesh generation). The convexity of a primitive is the maximum number of front (or back) faces of the primitive at a single position. For example, the convexity of a sphere is one and the convexity of a torus is two. |
This image shows a 2D shape with a convexity of 2, as the ray indicated in red crosses the 2D shape a maximum of 4 times (2 front sides and 2 back sides). The convexity of a 3D shape would be determined in a similar way. Setting it to 10 should work fine for most cases. Just setting high numbers in general may result in slower preview rendering.

#### Extrude parameters for linear extrusion only

| height | The extrusion height |
| center | If true, the solid is centered after extrusion |
| twist | The extrusion twist in degrees |
| scale | Scales the 2D shape by this value over the height of the extrusion. |
| slices | Similar to special variable $fn without being passed down to the child 2D shape. |
| segments | Similar to slices but adding points on the polygon's segments without changing the polygon's shape. |