diff --git a/Sources/PlaydateKit/Geometry/AffineTransform.swift b/Sources/PlaydateKit/Geometry/AffineTransform.swift
new file mode 100644
index 00000000..16ab6c77
--- /dev/null
+++ b/Sources/PlaydateKit/Geometry/AffineTransform.swift
@@ -0,0 +1,194 @@
+// MARK: - AffineTransformable
+
+public protocol AffineTransformable {
+    mutating func transform(by transform: AffineTransform)
+}
+
+public extension AffineTransformable {
+    func transformed(by transform: AffineTransform) -> Self {
+        var result = self
+        result.transform(by: transform)
+        return result
+    }
+
+    mutating func translateBy(dx: Float, dy: Float) {
+        transform(by: .init(translationX: dx, y: dy))
+    }
+
+    func translatedBy(dx: Float, dy: Float) -> Self {
+        transformed(by: .init(translationX: dx, y: dy))
+    }
+
+    mutating func rotateBy(angle: Float) {
+        transform(by: .init(rotationAngle: angle))
+    }
+
+    func rotatedBy(angle: Float) -> Self {
+        transformed(by: .init(rotationAngle: angle))
+    }
+
+    mutating func scaleBy(x: Float, y: Float) {
+        transform(by: .init(scaleX: x, y: y))
+    }
+
+    func scaledBy(x: Float, y: Float) -> Self {
+        transformed(by: .init(scaleX: x, y: y))
+    }
+}
+
+// MARK: - AffineTransform
+
+public struct AffineTransform: Equatable {
+    // MARK: Lifecycle
+
+    /// Returns an affine transformation matrix constructed from translation values you provide.
+    public init(translationX x: Float, y: Float) {
+        m11 = 1
+        m12 = 0
+        m21 = 0
+        m22 = 1
+        tx = x
+        ty = y
+    }
+
+    /// Returns an affine transformation matrix constructed from a rotation value you provide.
+    /// `rotationAngle` is specified in degrees.
+    public init(rotationAngle: Float) {
+        let rotationAngleRadians = rotationAngle * Float.pi / 180
+        m11 = cosf(rotationAngleRadians)
+        m12 = -sinf(rotationAngleRadians)
+        m21 = sinf(rotationAngleRadians)
+        m22 = cosf(rotationAngleRadians)
+        tx = 0
+        ty = 0
+    }
+
+    /// Returns an affine transformation matrix constructed from scaling values you provide.
+    public init(scaleX x: Float, y: Float) {
+        m11 = x
+        m12 = 0
+        m21 = 0
+        m22 = y
+        tx = 0
+        ty = 0
+    }
+
+    public init(m11: Float, m12: Float, m21: Float, m22: Float, tx: Float, ty: Float) {
+        self.m11 = m11
+        self.m12 = m12
+        self.m21 = m21
+        self.m22 = m22
+        self.tx = tx
+        self.ty = ty
+    }
+
+    // MARK: Public
+
+    /// The identity transform.
+    public nonisolated(unsafe) static let identity = AffineTransform(m11: 1, m12: 0, m21: 0, m22: 1, tx: 0, ty: 0)
+
+    /// The entry at position [1,1] in the matrix.
+    public var m11: Float
+    /// The entry at position [1,2] in the matrix.
+    public var m12: Float
+    /// The entry at position [2,1] in the matrix.
+    public var m21: Float
+    /// The entry at position [2,2] in the matrix.
+    public var m22: Float
+    /// The entry at position [3,1] in the matrix.
+    public var tx: Float
+    /// The entry at position [3,2] in the matrix.
+    public var ty: Float
+
+    /// Returns an affine transformation matrix constructed by combining two existing affine transforms.
+    public func concatenating(_ transform: AffineTransform) -> AffineTransform {
+        AffineTransform(
+            m11: m11 * transform.m11 + m12 * transform.m21,
+            m12: m11 * transform.m12 + m12 * transform.m22,
+            m21: m21 * transform.m11 + m22 * transform.m21,
+            m22: m21 * transform.m12 + m22 * transform.m22,
+            tx: tx + transform.tx,
+            ty: ty + transform.ty
+        )
+    }
+
+    /// Inverts the affine transform.
+    ///
+    /// If the affine transform cannot be inverted, the affine transform is unchanged.
+    public mutating func invert() {
+        let determinant = m11 * m22 - m12 * m21
+        if determinant != 0 {
+            let inverseDet = 1 / determinant
+            let tmp11 = m22 * inverseDet
+            let tmp12 = -m12 * inverseDet
+            let tmp21 = -m21 * inverseDet
+            let tmp22 = m11 * inverseDet
+            let tmpTx = (m21 * ty - m22 * tx) * inverseDet
+            let tmpTy = (m12 * tx - m11 * ty) * inverseDet
+            m11 = tmp11
+            m12 = tmp12
+            m21 = tmp21
+            m22 = tmp22
+            tx = tmpTx
+            ty = tmpTy
+        }
+    }
+
+    /// Returns an affine transformation matrix constructed by inverting the affine transform.
+    ///
+    /// If the affine transform cannot be inverted, the affine transform is returned unchanged.
+    public func inverted() -> AffineTransform {
+        var result = self
+        result.invert()
+        return result
+    }
+
+    /// Translates the affine transform.
+    public mutating func translateBy(dx: Float, dy: Float) {
+        tx += dx
+        ty += dy
+    }
+
+    /// Returns an affine transformation matrix constructed by translating the affine transform.
+    public func translatedBy(dx: Float, dy: Float) -> AffineTransform {
+        var result = self
+        result.translateBy(dx: dx, dy: dy)
+        return result
+    }
+
+    /// Rotates the affine transform.
+    public mutating func rotateBy(angle: Float) {
+        let cosAngle = cosf(angle)
+        let sinAngle = sinf(angle)
+        let new11 = m11 * cosAngle + m12 * sinAngle
+        let new12 = m12 * cosAngle - m11 * sinAngle
+        let new21 = m21 * cosAngle + m22 * sinAngle
+        let new22 = m22 * cosAngle - m21 * sinAngle
+        m11 = new11
+        m12 = new12
+        m21 = new21
+        m22 = new22
+    }
+
+    /// Returns an affine transformation matrix constructed by rotating the affine transform.
+    public func rotatedBy(angle: Float) -> AffineTransform {
+        var result = self
+        result.rotateBy(angle: angle)
+        return result
+    }
+
+    /// Scales the affine transform.
+    public mutating func scaleBy(x: Float, y: Float) {
+        m11 *= x
+        m12 *= y
+        m21 *= x
+        m22 *= y
+    }
+
+    /// Returns an affine transformation matrix constructed by scaling the affine transform.
+    public func scaledBy(x: Float, y: Float) -> AffineTransform {
+        var result = self
+        result.scaleBy(x: x, y: y)
+        return result
+    }
+}
diff --git a/Sources/PlaydateKit/Geometry/Line.swift b/Sources/PlaydateKit/Geometry/Line.swift
index 9b7aba47..c37848b7 100644
--- a/Sources/PlaydateKit/Geometry/Line.swift
+++ b/Sources/PlaydateKit/Geometry/Line.swift
@@ -14,17 +14,16 @@ public struct Line<T: Numeric>: Equatable {
     public var start, end: Point<T>
 }
 
-public extension Line {
-    /// The line whose start and end are both located at (0, 0).
-    static var zero: Line<T> { Line(start: .zero, end: .zero) }
+// MARK: AffineTransformable
+
+extension Line: AffineTransformable where T == Float {
+    public mutating func transform(by transform: AffineTransform) {
+        start.transform(by: transform)
+        end.transform(by: transform)
+    }
 }
 
 public extension Line {
-    /// Returns a line with a start and end that is offset from that of the source line.
-    func offsetBy(dx: T, dy: T) -> Line {
-        Line(
-            start: start.offsetBy(dx: dx, dy: dy),
-            end: end.offsetBy(dx: dx, dy: dy)
-        )
-    }
+    /// The line whose start and end are both located at (0, 0).
+    static var zero: Line<T> { Line(start: .zero, end: .zero) }
 }
diff --git a/Sources/PlaydateKit/Geometry/Point.swift b/Sources/PlaydateKit/Geometry/Point.swift
index 55720f0f..09398545 100644
--- a/Sources/PlaydateKit/Geometry/Point.swift
+++ b/Sources/PlaydateKit/Geometry/Point.swift
@@ -14,14 +14,17 @@ public struct Point<T: Numeric>: Equatable {
     public var x, y: T
 }
 
-public extension Point {
-    /// The point with location (0,0).
-    static var zero: Point<T> { Point(x: 0, y: 0) }
+// MARK: AffineTransformable
+
+extension Point: AffineTransformable where T == Float {
+    public mutating func transform(by transform: AffineTransform) {
+        let newX = transform.m11 * x + transform.m12 * y + transform.tx
+        let newY = transform.m21 * x + transform.m22 * y + transform.ty
+        self = Point(x: newX, y: newY)
+    }
 }
 
 public extension Point {
-    /// Returns a point that is offset from that of the source point.
-    func offsetBy(dx: T, dy: T) -> Point {
-        Point(x: x + dx, y: y + dy)
-    }
+    /// The point with location (0,0).
+    static var zero: Point<T> { Point(x: 0, y: 0) }
 }
diff --git a/Sources/PlaydateKit/Geometry/Polygon.swift b/Sources/PlaydateKit/Geometry/Polygon.swift
index 852ce812..f69ca655 100644
--- a/Sources/PlaydateKit/Geometry/Polygon.swift
+++ b/Sources/PlaydateKit/Geometry/Polygon.swift
@@ -1,3 +1,5 @@
+// MARK: - Polygon
+
 /// A structure that contains a two-dimensional open or closed polygon.
 public struct Polygon<T: Numeric>: Equatable {
     // MARK: Lifecycle
@@ -21,3 +23,21 @@ public struct Polygon<T: Numeric>: Equatable {
         vertices.append(first)
     }
 }
+
+// MARK: - Array + AffineTransformable
+
+extension [Point<Float>]: AffineTransformable {
+    public mutating func transform(by transform: AffineTransform) {
+        for i in indices {
+            self[i].transform(by: transform)
+        }
+    }
+}
+
+// MARK: - Polygon + AffineTransformable
+
+extension Polygon: AffineTransformable where T == Float {
+    public mutating func transform(by transform: AffineTransform) {
+        vertices.transform(by: transform)
+    }
+}
diff --git a/Sources/PlaydateKit/Geometry/Rect.swift b/Sources/PlaydateKit/Geometry/Rect.swift
index e7041246..5a3dc09a 100644
--- a/Sources/PlaydateKit/Geometry/Rect.swift
+++ b/Sources/PlaydateKit/Geometry/Rect.swift
@@ -23,16 +23,22 @@ public struct Rect<T: Numeric>: Equatable {
     public var x, y, width, height: T
 }
 
-public extension Rect {
-    /// The point with location (0,0).
-    static var zero: Rect<T> { Rect(x: 0, y: 0, width: 0, height: 0) }
+// MARK: AffineTransformable
+
+extension Rect: AffineTransformable where T == Float {
+    public mutating func transform(by transform: AffineTransform) {
+        let transformedOrigin = Point(x: x, y: y).transformed(by: transform)
+        let transformedTopRight = Point(x: x + width, y: y + height).transformed(by: transform)
+        x = transformedOrigin.x
+        y = transformedOrigin.y
+        width = transformedTopRight.x - transformedOrigin.x
+        height = transformedTopRight.y - transformedOrigin.y
+    }
 }
 
 public extension Rect {
-    /// Returns a rectangle with an origin that is offset from that of the source rectangle.
-    func offsetBy(dx: T, dy: T) -> Rect {
-        Rect(x: x + dx, y: y + dy, width: width, height: height)
-    }
+    /// The point with location (0,0).
+    static var zero: Rect<T> { Rect(x: 0, y: 0, width: 0, height: 0) }
 }
 
 extension Rect where T == CInt {