CATransform3D manipulation made easy.

What's New

Release v0.3.0

  • Bump Deployment Targets to iOS 13, macOS 11, tvOS 13. Fixes #2
  • Lower target devices should use v0.2.0


Tests Docs

Manipulating and using CATransform3D for animations and interactions is pretty challenging… Decomposed makes CATransform3D, matrix_double4x4, and matrix_float4x4 much easier to work with.

Note: The API for Decomposed is still heavily being changed / optimized, so please feel free to give feedback and expect breaking changes as time moves on.

Specifically, I really want to figure out what to do about the Vector types introduced in this repository. If there are any issues with them please let me know; I'm actively sourcing ways to make it better.


Typically on iOS if you wanted to transform a CALayer you'd do something like:

let layer: CAlayer = ...
layer.transform = CATransform3DMakeScale(0.5, 0.5, 1.0)

However, what if you were given a transform from somewhere else? How would you know what the scale of the layer is? What if you wanted to set the scale or translation of a transform? Without lots of complex linear algebra, it's not easy to do!

Decomposed aims to simplify this by allowing for CATransform3D, matrix_double4x4, and matrix_float4x4, to be decomposed, recomposed, and mutated without complex math.

Decomposition is the act of breaking something down into smaller components, in this case transformation matrices into things like translation, scale, etc. in a way that they can all be individually changed or reset. The following are supported:

  • Translation
  • Scale
  • Rotation (using Quaternions or Euler Angles)
  • Skew
  • Perspective

It's also powered by Accelerate, so it should introduce relatively low overhead for matrix manipulations.


API Documentation is here.

Transform Modifications


Create a transform with a translation of 44pts on the Y-axis, rotated by .pi / 4.0 on the X-axis

var transform: CATransform3D = CATransform3DIdentity
  .translatedBy(y: 44.0)
  .rotatedBy(angle: .pi / 4.0, x: 1.0)


Create a transform with a translation of 44pts on the Y-axis, rotated by .pi / 40 on the X-axis.

CATransform3DDecomposed *decomposed = [DEDecomposedCATransform3D decomposedTransformWithTransform:CATransform3DIdentity];
decomposed.translation = CGPoint(0.0, 44.0);
decomposed.rotation = simd_quaternion(M_PI / 4.0, simd_make_double3(1.0, 0.0, 0.0));
transform = [decomposed recompose];

CALayer Extensions

Typically when doing interactive gestures with UIView and CALayer you'll wind up dealing with implicit actions (animations) when changing transforms. Instead of wrapping your code in CATransactions's and disabling actions, Decomposed does this automatically for you.


// In some UIPanGestureRecognizer handling method
layer.translation = panGestureRecognizer.translation(in: self)
layer.scale = CGPoint(x: 0.75, y: 0.75)


Since namespace collision happens in Objective-C, you're able to do similar changes via the transformProxy property. Changes to this proxy object will be applied to the layer's transform with implicit animations disabled.

// In some UIPanGestureRecognizer handling method
layer.transformProxy.translation = [panGestureRecognizer translationInView:self];
layer.transformProxy.scale = CGPoint(x: 0.75, y: 0.75);


Anytime you change a property on a CATransform3D or matrix_double4x4, it needs to be decomposed, changed, and then recomposed. This can be expensive if done a lot, so it should be limited. If you're making multiple changes at once, it's better to change the DecomposedTransform and then call its recomposed() function to get a recomposed transform.


var decomposed = transform.decomposed()
decomposed.translation = Translation(44.0, 44.0, 0.0)
decomposed.scale = Scale(0.75, 0.75, 0.0)
decomposed.rotation = CGQuaternion(angle: .pi / 4.0, axis: CGVector3(1.0, 0.0, 0.0))

let changedTransform = decomposed.recomposed()


DEDecomposedCATransform3D *decomposed = [DEDecomposedCATransform3D decomposedTransformWithTransform:transform];
decomposed.translation = CGPointMake(44.0, 44.0);
decomposed.scale = CGPointMake(0.75, 0.75);
decomposed.rotation = simd_quaternion(M_PI / 4.0, simd_make_double3(1.0, 0.0, 0.0));

CATransform3D changedTransform = [decomposed recomposed];

CGVector3 / CGVector4 / CGQuaternion

Sadly, simd doesn't support storing CGFloat (even when they're Double). To make this library easier to use (i.e. without casting everything to doubles all the time Double(some CGFloat) you'll find CGVector3, CGVector4, and CGQuaternion, which wrap simd counterparts: simd_double3, simd_double4, and simd_quatd, respectively.

Translation, Scale, etc. are all type aliased (i.e. CGVector3 or CGVector4), and they all conform to ArrayLiteralRepresentable so you can use Array<CGFloat> to initialize them.

layer.translation = Translation(44.0, 44.0, 0.0)
layer.scale = Scale(0.5, 0.75, 0.0)

Note: This API is questionable in its current form as it collides with Swift's Vector types (which are just simd types and part of me thinks everything should be exposed as simd types), so I'm happy to take feedback!


It also provides functionality to linearly interpolate from any transform to any transform via the Interpolatable protocol. This lets you easily animate / transition between transforms in a controlled manner.

let transform: CATransform3D = CATransform3DIdentity
  .translatedBy(x: 44.0, y: 44.0)

let transform2 = CATransform3DIdentity
  .translatedBy(x: 120.0, y: 240.0)
  .scaled(by: [0.5, 0.75, 1.0])
  .rotatedBy(angle: .pi / 4.0, x: 1.0)

let interpolatedTransform = transform.lerp(to: transform2, fraction: 0.5)



  • iOS 13+, macOS 10.15+
  • Swift 5.0 or higher

Currently Decomposed supports Swift Package Manager, CocoaPods, Carthage, being used as an xcframework, and being used manually as an Xcode subproject. Pull requests for other dependency systems / build systems are welcome!

Swift Package Manager

Add the following to your Package.swift (or add it via Xcode's GUI):

.package(url: "", from: "0.0.1")


Add the following to your Podfile:

pod 'Decomposed'


A built xcframework is available for each tagged release.


For some reason, when using CocoaPods and the Objective-C parts of this library, you may see an error like:

Declaration of 'DEDecomposedCATransform3D' must be imported from module 'Decomposed.Swift' before it is required.

To fix this, you'll need to use Objective-C++ files (i.e. rename from .m to .mm) or change your imports to:

#import <Decomposed/Decomposed.h>
#import <Decomposed/Decomposed-Swift.h>

I don't have any other workarounds at the moment, but if I do, I'll make an update.


Add the following to your Cartfile:


Xcode Subproject

  • Add Decomposed.xcodeproj to your project
  • Add Decomposed.framework as an embedded framework (it's a static library, so it should not be embedded).

Objective-C Notes

  • Objective-C support is not available through Swift Package Manager. Please use the manual Xcode subproject instead.
  • You'll want to use #import <Decomposed/Decomposed.h> as this contains both the generated Swift interfaces for the Objective-C classes and CALayer categories.
  • Not all of the API is available due to limitations of how Swift / Objective-C interop. Sadly the API can't be as nice, but CATransform3DDecomposed will allow for decomposition and recomposition of CATransform3D (similar classes exist for matrix_double4x4 and matrix_float4x4 and are wrappers around their Swift counterparts) as well as convenience categories on CALayer.

Other Recommendations


This library pairs very nicely with Motion, an animation engine for gesturally-driven user interfaces, animations, and interactions on iOS, macOS, and tvOS.

Animating a layer on a spring by modifying its transform has never been easier! Usually you'd have to manually wrap things in a CATransaction with actions disabled, and usage of CATransform3DTranslate gets pretty cumbersome.

With Decomposed + Motion this is super easy.

let layer = ...
let springAnimation = SpringAnimation<CGPoint>(initialValue: .zero)
springAnimation.onValueChanged(disableActions: true) { [layer] translation in
  layer.translation = translation

// In your pan gesture recognizer callback

let translation = panGestureRecognizer.translation(in: self.view)
let velocity = panGestureRecognizer.velocity(in: self.view)

switch panGestureRecognizer.state {
  case .began:
    springAnimation.updateValue(to: .zero)
  case .changed:
    springAnimation.updateValue(to: translation)
    layer.translation = translation
  case .ended:
    springAnimation.velocity = velocity
    springAnimation.toValue = CGPoint(x: 200.0, y: 200.0) // wherever you want it to go

See the DraggingCard demo for a good example of this :)


Decomposed is licensed under the BSD 2-clause license.

Contact Info

Feel free to follow me on twitter: @b3ll!


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Last updated: Sun Jan 15 2023 13:30:01 GMT-0500 (GMT-05:00)