diff --git a/Sources/SwiftSCAD/Values/Transforms/AffineTransform.swift b/Sources/SwiftSCAD/Values/Transforms/AffineTransform.swift
new file mode 100644
index 0000000..83dae17
--- /dev/null
+++ b/Sources/SwiftSCAD/Values/Transforms/AffineTransform.swift
@@ -0,0 +1,17 @@
+import Foundation
+
+protocol AffineTransform {
+    associatedtype Vector: SwiftSCAD.Vector
+
+    static var identity: Self { get }
+
+    init(_ values: [[Double]])
+    subscript(_ row: Int, _ column: Int) -> Double { get set }
+    func setting(row: Int, column: Int, to: Double) -> Self
+    func applying(_ function: (_ row: Int, _ column: Int, _ value: Double) -> Double) -> Self
+    static func linearInterpolation(_ from: Self, _ to: Self, factor: Double) -> Self
+
+    var inverse: Self { get }
+    func concatenated(with: Self) -> Self
+    func apply(to point: Vector) -> Vector
+}
diff --git a/Sources/SwiftSCAD/Values/Transforms/AffineTransform2D.swift b/Sources/SwiftSCAD/Values/Transforms/AffineTransform2D.swift
index 5f7ee1b..7a06c5e 100644
--- a/Sources/SwiftSCAD/Values/Transforms/AffineTransform2D.swift
+++ b/Sources/SwiftSCAD/Values/Transforms/AffineTransform2D.swift
@@ -4,7 +4,8 @@ import simd
 #endif
 
 /// An `AffineTransform2D` represents a 2D affine transformation using a 3x3 matrix.
-public struct AffineTransform2D: Equatable {
+public struct AffineTransform2D: AffineTransform, Equatable {
+    typealias Vector = Vector2D
     private var matrix: Matrix3x3
 
     internal init(_ matrix: Matrix3x3) {
diff --git a/Sources/SwiftSCAD/Values/Transforms/AffineTransform3D.swift b/Sources/SwiftSCAD/Values/Transforms/AffineTransform3D.swift
index 1d20ba8..f04e061 100644
--- a/Sources/SwiftSCAD/Values/Transforms/AffineTransform3D.swift
+++ b/Sources/SwiftSCAD/Values/Transforms/AffineTransform3D.swift
@@ -4,7 +4,7 @@ import simd
 #endif
 
 /// An `AffineTransform3D` represents a 3D affine transformation using a 4x4 matrix.
-public struct AffineTransform3D: Equatable {
+public struct AffineTransform3D: AffineTransform, Equatable {
     private var matrix: Matrix4x4
 
     private init(_ matrix: Matrix4x4) {
@@ -61,6 +61,19 @@ public struct AffineTransform3D: Equatable {
         AffineTransform3D(other.matrix * matrix)
     }
 
+    /// Creates a new `AffineTransform3D` by setting a value at the given row and column indices.
+    ///
+    /// - Parameters:
+    ///   - row: The row index (0 to 3).
+    ///   - column: The column index (0 to 3).
+    ///   - value: The value to set at the specified row and column.
+    /// - Returns: A new `AffineTransform3D` with the specified value set.
+    public func setting(row: Int, column: Int, to value: Double) -> Self {
+        var transform = self
+        transform[row, column] = value
+        return transform
+    }
+
     public var inverse: AffineTransform3D {
         .init(matrix.inverse)
     }
diff --git a/Sources/SwiftSCAD/Values/Transforms/BasicMatrix3x3.swift b/Sources/SwiftSCAD/Values/Transforms/Matrix/BasicMatrix3x3.swift
similarity index 100%
rename from Sources/SwiftSCAD/Values/Transforms/BasicMatrix3x3.swift
rename to Sources/SwiftSCAD/Values/Transforms/Matrix/BasicMatrix3x3.swift
diff --git a/Sources/SwiftSCAD/Values/Transforms/BasicMatrix4x4.swift b/Sources/SwiftSCAD/Values/Transforms/Matrix/BasicMatrix4x4.swift
similarity index 100%
rename from Sources/SwiftSCAD/Values/Transforms/BasicMatrix4x4.swift
rename to Sources/SwiftSCAD/Values/Transforms/Matrix/BasicMatrix4x4.swift
diff --git a/Sources/SwiftSCAD/Values/Transforms/Matrix.swift b/Sources/SwiftSCAD/Values/Transforms/Matrix/Matrix.swift
similarity index 100%
rename from Sources/SwiftSCAD/Values/Transforms/Matrix.swift
rename to Sources/SwiftSCAD/Values/Transforms/Matrix/Matrix.swift