Matrix Value Types

Matrix4x4F and Matrix3x3D are the package’s own column-major matrix values (#2759). They replaced simd_float4x4 and simd_double3x3 in the public API so that the API is the same on every platform, including WebAssembly where Apple’s simd module does not exist. They are plain Swift over the standard library’s SIMD3 and SIMD4, Equatable and Sendable.

They carry a matrix the kernel produced and do the few things a caller does with one first. They are not linear algebra: there is no multiplication, inverse or transpose here, and a consumer that multiplies converts to its own matrix type.

Topics

• Matrix4x4F · Matrix3x3D · Migrating from simd

Matrix4x4F

Matrix4x4F.init(_:_:_:_:)

Builds a matrix from four columns.

public init(_ column0: SIMD4<Float>, _ column1: SIMD4<Float>, _ column2: SIMD4<Float>, _ column3: SIMD4<Float>)

• Example:

  let translate = Matrix4x4F(
      SIMD4(1, 0, 0, 0), SIMD4(0, 1, 0, 0), SIMD4(0, 0, 1, 0), SIMD4(5, 6, 7, 1))
  print(translate[3])          // SIMD4<Float>(5.0, 6.0, 7.0, 1.0)
  

Matrix4x4F.identity and Matrix4x4F.zero

public static let identity: Matrix4x4F
public static let zero: Matrix4x4F

zero is the all-zero matrix, as simd_float4x4() was. Use identity for the identity.

Matrix4x4F.columns, column0 to column3, subscript(_:)

public var columns: (SIMD4<Float>, SIMD4<Float>, SIMD4<Float>, SIMD4<Float>) { get set }
public subscript(_ index: Int) -> SIMD4<Float> { get set }

m[i] is column i and m[i][j] is the element in column i, row j, which is what simd_float4x4 indexing gave. An index outside 0 through 3 is a precondition failure.

Matrix4x4F.columnMajorElements

The sixteen elements, column 0 first: the layout Metal, OpenGL, WebGL and glTF take.

public var columnMajorElements: [Float] { get }

• Example:

  let flat = Matrix4x4F.identity.columnMajorElements
  print(flat.count)            // 16
  

Matrix4x4F.determinant

public var determinant: Float { get }

Laplace expansion along the first row. det(A) == det(Aᵀ), so the result does not depend on how the columns are read.

Matrix3x3D

Matrix3x3D.init(_:_:_:)

Builds a matrix from three columns.

public init(_ column0: SIMD3<Double>, _ column1: SIMD3<Double>, _ column2: SIMD3<Double>)

Matrix3x3D.identity and Matrix3x3D.zero

public static let identity: Matrix3x3D
public static let zero: Matrix3x3D

Matrix3x3D.columns, column0 to column2, subscript(_:)

public var columns: (SIMD3<Double>, SIMD3<Double>, SIMD3<Double>) { get set }
public subscript(_ index: Int) -> SIMD3<Double> { get set }

m[i][j] is column i, row j. An inertia tensor is symmetric, so its row and column readings agree; any other 3x3 matrix is not, and a symmetric test matrix cannot tell the two apart.

• Example:

  if let box = Shape.box(width: 2, height: 3, depth: 4), let p = box.properties() {
      let ixx = p.momentOfInertia[0][0]
      let izz = p.momentOfInertia[2][2]
      print(ixx > 0, izz > 0)
  }
  

Matrix3x3D.columnMajorElements

The nine elements, column 0 first.

public var columnMajorElements: [Double] { get }

Matrix3x3D.determinant

The scalar triple product of the columns.

public var determinant: Double { get }

Migrating from simd

Code that read the old properties through .columns or [column][row] compiles unchanged. Code that passed the value to an Apple API, or multiplied it, converts at the boundary. There is no conversion in this package, on purpose: it would need Apple’s module imported here, which is the dependency #2759 removed, and it would make the public surface differ by platform.

```swift no-typecheck: needs Apple’s simd module, which this package does not import import simd

extension simd_float4x4 { init(_ m: Matrix4x4F) { self.init(m.column0, m.column1, m.column2, m.column3) } } extension Matrix4x4F { init(_ m: simd_float4x4) { self.init(m.columns.0, m.columns.1, m.columns.2, m.columns.3) } } extension simd_double3x3 { init(_ m: Matrix3x3D) { self.init(m.column0, m.column1, m.column2) } }

let viewProjection = simd_float4x4(camera.projectionMatrix) * simd_float4x4(camera.viewMatrix) ```