---
title: "patternTransform"
excerpt: "Repeat a 3-dimensional solid by successively applying a transformation (such"
layout: manual
---

Repeat a 3-dimensional solid by successively applying a transformation (such

as rotation, scale, translation, visibility) on each repetition.

```js
patternTransform(num_repetitions: u32, transform_function: FunctionParam, extrude_group_set: ExtrudeGroupSet) -> [ExtrudeGroup]
```

### Examples

```js
// Parameters
const r = 50 // base radius
const h = 10 // layer height
const t = 0.005 // taper factor [0-1)
// Defines how to modify each layer of the vase.
// Each replica is shifted up the Z axis, and has a smoothly-varying radius
fn transform = (replicaId) => {
  let scale = r * abs(1 - (t * replicaId)) * (5 + cos(replicaId / 8))
  return {
  translate: [0, 0, replicaId * 10],
  scale: [scale, scale, 0]
}
}
// Each layer is just a pretty thin cylinder.
fn layer = () => {
  return startSketchOn("XY")
  // or some other plane idk
  |> circle([0, 0], 1, %, $tag1)
  |> extrude(h, %)
}
// The vase is 100 layers tall.
// The 100 layers are replica of each other, with a slight transformation applied to each.
let vase = layer()
  |> patternTransform(100, transform, %)
```

![Rendered example of patternTransform 0](data:image/png;base64,[encoded data, 313816 characters])

### Arguments

* `num_repetitions`: `u32` (REQUIRED)
* `transform_function`: `FunctionParam` (REQUIRED)
* `extrude_group_set`: `ExtrudeGroupSet` - A extrude group or a group of extrude groups. (REQUIRED)
```js
{
	// Chamfers or fillets on this extrude group.
	edgeCuts: [{
	// The engine id of the edge to fillet.
	edgeId: uuid,
	// The id of the engine command that called this fillet.
	id: uuid,
	radius: number,
	tag: {
	digest: [number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number],
	end: number,
	start: number,
	value: string,
},
	type: "fillet",
} |
{
	// The engine id of the edge to chamfer.
	edgeId: uuid,
	// The id of the engine command that called this chamfer.
	id: uuid,
	length: number,
	tag: {
	digest: [number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number],
	end: number,
	start: number,
	value: string,
},
	type: "chamfer",
}],
	// The id of the extrusion end cap
	endCapId: uuid,
	// The height of the extrude group.
	height: number,
	// The id of the extrude group.
	id: uuid,
	// The sketch group.
	sketchGroup: {
	// The id of the sketch group (this will change when the engine's reference to it changes.
	id: uuid,
	// What the sketch is on (can be a plane or a face).
	on: {
	// The id of the plane.
	id: uuid,
	// Origin of the plane.
	origin: {
	x: number,
	y: number,
	z: number,
},
	type: "plane",
	// Type for a plane.
	value: "XY" | "XZ" | "YZ" | "Custom",
	// What should the plane’s X axis be?
	xAxis: {
	x: number,
	y: number,
	z: number,
},
	// What should the plane’s Y axis be?
	yAxis: {
	x: number,
	y: number,
	z: number,
},
	// The z-axis (normal).
	zAxis: {
	x: number,
	y: number,
	z: number,
},
} |
{
	// The extrude group the face is on.
	extrudeGroup: {
	// Chamfers or fillets on this extrude group.
	edgeCuts: [{
	// The engine id of the edge to fillet.
	edgeId: uuid,
	// The id of the engine command that called this fillet.
	id: uuid,
	radius: number,
	tag: {
	digest: [number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number],
	end: number,
	start: number,
	value: string,
},
	type: "fillet",
} |
{
	// The engine id of the edge to chamfer.
	edgeId: uuid,
	// The id of the engine command that called this chamfer.
	id: uuid,
	length: number,
	tag: {
	digest: [number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number],
	end: number,
	start: number,
	value: string,
},
	type: "chamfer",
}],
	// The id of the extrusion end cap
	endCapId: uuid,
	// The height of the extrude group.
	height: number,
	// The id of the extrude group.
	id: uuid,
	// The sketch group.
	sketchGroup: SketchGroup,
	// The id of the extrusion start cap
	startCapId: uuid,
	// The extrude surfaces.
	value: [{
	// The face id for the extrude plane.
	faceId: uuid,
	// The id of the geometry.
	id: uuid,
	// The source range.
	sourceRange: [number, number],
	// The tag.
	tag: {
	digest: [number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number],
	end: number,
	start: number,
	value: string,
},
	type: "extrudePlane",
} |
{
	// The face id for the extrude plane.
	faceId: uuid,
	// The id of the geometry.
	id: uuid,
	// The source range.
	sourceRange: [number, number],
	// The tag.
	tag: {
	digest: [number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number],
	end: number,
	start: number,
	value: string,
},
	type: "extrudeArc",
} |
{
	// The id for the chamfer surface.
	faceId: uuid,
	// The id of the geometry.
	id: uuid,
	// The source range.
	sourceRange: [number, number],
	// The tag.
	tag: {
	digest: [number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number],
	end: number,
	start: number,
	value: string,
},
	type: "chamfer",
} |
{
	// The id for the fillet surface.
	faceId: uuid,
	// The id of the geometry.
	id: uuid,
	// The source range.
	sourceRange: [number, number],
	// The tag.
	tag: {
	digest: [number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number],
	end: number,
	start: number,
	value: string,
},
	type: "fillet",
}],
},
	// The id of the face.
	id: uuid,
	type: "face",
	// The tag of the face.
	value: string,
	// What should the face’s X axis be?
	xAxis: {
	x: number,
	y: number,
	z: number,
},
	// What should the face’s Y axis be?
	yAxis: {
	x: number,
	y: number,
	z: number,
},
	// The z-axis (normal).
	zAxis: {
	x: number,
	y: number,
	z: number,
},
},
	// The starting path.
	start: {
	// The from point.
	from: [number, number],
	// The tag of the path.
	tag: {
	digest: [number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number],
	end: number,
	start: number,
	value: string,
},
	// The to point.
	to: [number, number],
},
	// Tag identifiers that have been declared in this sketch group.
	tags: {
},
	// The paths in the sketch group.
	value: [{
	// The from point.
	from: [number, number],
	// The tag of the path.
	tag: {
	digest: [number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number],
	end: number,
	start: number,
	value: string,
},
	// The to point.
	to: [number, number],
	type: "ToPoint",
} |
{
	// arc's direction
	ccw: bool,
	// the arc's center
	center: [number, number],
	// The from point.
	from: [number, number],
	// The tag of the path.
	tag: {
	digest: [number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number],
	end: number,
	start: number,
	value: string,
},
	// The to point.
	to: [number, number],
	type: "TangentialArcTo",
} |
{
	// arc's direction
	ccw: bool,
	// the arc's center
	center: [number, number],
	// The from point.
	from: [number, number],
	// The tag of the path.
	tag: {
	digest: [number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number],
	end: number,
	start: number,
	value: string,
},
	// The to point.
	to: [number, number],
	type: "TangentialArc",
} |
{
	// The from point.
	from: [number, number],
	// The tag of the path.
	tag: {
	digest: [number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number],
	end: number,
	start: number,
	value: string,
},
	// The to point.
	to: [number, number],
	type: "Horizontal",
	// The x coordinate.
	x: number,
} |
{
	// The from point.
	from: [number, number],
	// The tag of the path.
	tag: {
	digest: [number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number],
	end: number,
	start: number,
	value: string,
},
	// The to point.
	to: [number, number],
	type: "AngledLineTo",
	// The x coordinate.
	x: number,
	// The y coordinate.
	y: number,
} |
{
	// The from point.
	from: [number, number],
	// The tag of the path.
	tag: {
	digest: [number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number],
	end: number,
	start: number,
	value: string,
},
	// The to point.
	to: [number, number],
	type: "Base",
}],
},
	// The id of the extrusion start cap
	startCapId: uuid,
	type: "extrudeGroup",
	// The extrude surfaces.
	value: [{
	// The face id for the extrude plane.
	faceId: uuid,
	// The id of the geometry.
	id: uuid,
	// The source range.
	sourceRange: [number, number],
	// The tag.
	tag: {
	digest: [number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number],
	end: number,
	start: number,
	value: string,
},
	type: "extrudePlane",
} |
{
	// The face id for the extrude plane.
	faceId: uuid,
	// The id of the geometry.
	id: uuid,
	// The source range.
	sourceRange: [number, number],
	// The tag.
	tag: {
	digest: [number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number],
	end: number,
	start: number,
	value: string,
},
	type: "extrudeArc",
} |
{
	// The id for the chamfer surface.
	faceId: uuid,
	// The id of the geometry.
	id: uuid,
	// The source range.
	sourceRange: [number, number],
	// The tag.
	tag: {
	digest: [number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number],
	end: number,
	start: number,
	value: string,
},
	type: "chamfer",
} |
{
	// The id for the fillet surface.
	faceId: uuid,
	// The id of the geometry.
	id: uuid,
	// The source range.
	sourceRange: [number, number],
	// The tag.
	tag: {
	digest: [number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number, number],
	end: number,
	start: number,
	value: string,
},
	type: "fillet",
}],
} |
{
	type: "extrudeGroups",
}
```

### Returns

`[ExtrudeGroup]`



