[Math] Sort out Vector3, make it conform to Vector protocol

Math/Math.xcodeproj/project.pbxproj

@@ -10,6 +10,7 @@
 		C005DFFE1BE1CBA700F1BD3C /* Math.h in Headers */ = {isa = PBXBuildFile; fileRef = C005DFFD1BE1CBA700F1BD3C /* Math.h */; settings = {ATTRIBUTES = (Public, ); }; };
 		C005E0051BE1CBA800F1BD3C /* Math.framework in Frameworks */ = {isa = PBXBuildFile; fileRef = C005DFFA1BE1CBA700F1BD3C /* Math.framework */; };
 		C005E00A1BE1CBA800F1BD3C /* MathTests.swift in Sources */ = {isa = PBXBuildFile; fileRef = C005E0091BE1CBA800F1BD3C /* MathTests.swift */; };
+		C005E0391BE1CC7A00F1BD3C /* Matrices.swift in Sources */ = {isa = PBXBuildFile; fileRef = C005E0381BE1CC7A00F1BD3C /* Matrices.swift */; };
 /* End PBXBuildFile section */
 
 /* Begin PBXContainerItemProxy section */
@@ -29,6 +30,7 @@
 		C005E0041BE1CBA800F1BD3C /* MathTests.xctest */ = {isa = PBXFileReference; explicitFileType = wrapper.cfbundle; includeInIndex = 0; path = MathTests.xctest; sourceTree = BUILT_PRODUCTS_DIR; };
 		C005E0091BE1CBA800F1BD3C /* MathTests.swift */ = {isa = PBXFileReference; lastKnownFileType = sourcecode.swift; path = MathTests.swift; sourceTree = "<group>"; };
 		C005E00B1BE1CBA800F1BD3C /* Info.plist */ = {isa = PBXFileReference; lastKnownFileType = text.plist.xml; path = Info.plist; sourceTree = "<group>"; };
+		C005E0381BE1CC7A00F1BD3C /* Matrices.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; path = Matrices.swift; sourceTree = "<group>"; };
 /* End PBXFileReference section */
 
 /* Begin PBXFrameworksBuildPhase section */
@@ -72,6 +74,7 @@
 			isa = PBXGroup;
 			children = (
 				C005DFFD1BE1CBA700F1BD3C /* Math.h */,
+				C005E0381BE1CC7A00F1BD3C /* Matrices.swift */,
 				C005DFFF1BE1CBA700F1BD3C /* Info.plist */,
 			);
 			path = Math;
@@ -194,6 +197,7 @@
 			isa = PBXSourcesBuildPhase;
 			buildActionMask = 2147483647;
 			files = (
+				C005E0391BE1CC7A00F1BD3C /* Matrices.swift in Sources */,
 			);
 			runOnlyForDeploymentPostprocessing = 0;
 		};
@@ -305,6 +309,7 @@
 		C005E00F1BE1CBA800F1BD3C /* Debug */ = {
 			isa = XCBuildConfiguration;
 			buildSettings = {
+				CLANG_ENABLE_MODULES = YES;
 				COMBINE_HIDPI_IMAGES = YES;
 				DEFINES_MODULE = YES;
 				DYLIB_COMPATIBILITY_VERSION = 1;
@@ -317,12 +322,14 @@
 				PRODUCT_BUNDLE_IDENTIFIER = me.erynwells.graphics.Math;
 				PRODUCT_NAME = "$(TARGET_NAME)";
 				SKIP_INSTALL = YES;
+				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
 			};
 			name = Debug;
 		};
 		C005E0101BE1CBA800F1BD3C /* Release */ = {
 			isa = XCBuildConfiguration;
 			buildSettings = {
+				CLANG_ENABLE_MODULES = YES;
 				COMBINE_HIDPI_IMAGES = YES;
 				DEFINES_MODULE = YES;
 				DYLIB_COMPATIBILITY_VERSION = 1;
@@ -379,6 +386,7 @@
 				C005E0101BE1CBA800F1BD3C /* Release */,
 			);
 			defaultConfigurationIsVisible = 0;
+			defaultConfigurationName = Release;
 		};
 		C005E0111BE1CBA800F1BD3C /* Build configuration list for PBXNativeTarget "MathTests" */ = {
 			isa = XCConfigurationList;
@@ -387,6 +395,7 @@
 				C005E0131BE1CBA800F1BD3C /* Release */,
 			);
 			defaultConfigurationIsVisible = 0;
+			defaultConfigurationName = Release;
 		};
 /* End XCConfigurationList section */
 	};

Math/Math/Matrices.swift

@@ -0,0 +1,169 @@
+//
+//  Matrices.swift
+//  Game
+//
+//  Created by Eryn Wells on 2015-10-24.
+//  Copyright © 2015 Eryn Wells. All rights reserved.
+//
+
+/** A square matrix. */
+protocol Matrix {
+    typealias ElementType
+
+    static func dimension() -> Int
+    static func size() -> Int
+
+    init()
+    init?(values: [ElementType])
+
+    subscript(idx: Int) -> ElementType { get set }
+    subscript(row: Int, col: Int) -> ElementType { get set }
+}
+
+/** A vector. */
+protocol Vector {
+    init()
+
+    /** Number of elements in the vector. */
+    var count: Int { get }
+    /** Element access by index. */
+    subscript(idx: Int) -> Float { get set }
+
+    /** Length of the vector. */
+    var length2: Float { get }
+    /** Length-squared of the vector. */
+    var length: Float { get }
+}
+
+// MARK: - Matrices
+
+public struct Matrix4<T: FloatingPointType>: Matrix {
+    static func dimension() -> Int {
+        return 4
+    }
+
+    static func size() -> Int {
+        return dimension() * dimension()
+    }
+
+    public private(set) var data: [T]
+
+    public init() {
+        data = [T](count: Matrix4.size(), repeatedValue: T(0))
+    }
+
+    public init?(values: [T]) {
+        guard values.count == Matrix4.size() else { return nil }
+        data = values
+    }
+
+    public subscript(idx: Int) -> T {
+        get {
+            return data[idx]
+        }
+        set(value) {
+            data[idx] = value
+        }
+    }
+
+    public subscript(row: Int, col: Int) -> T {
+        get {
+            return data[indexFromCoordinates(row, col)]
+        }
+        set(value) {
+            data[indexFromCoordinates(row, col)] = value
+        }
+    }
+
+    /** Convert a (row, col) pair into an index into the data array. */
+    private func indexFromCoordinates(row: Int, _ col: Int) -> Int {
+        return row * Matrix4.dimension() + col
+    }
+}
+
+
+struct Matrix3 {
+    static let Rows = 3
+    static let Cols = 3
+    static let Size = Matrix3.Rows * Matrix3.Cols
+}
+
+// MARK: Vectors
+
+public struct Vector4<T: FloatingPointType> {
+    static func size() -> Int {
+        return 4
+    }
+
+    public private(set) var data: [T]
+
+    init() {
+        self.init(x: T(0), y: T(0), z: T(0), w: T(0))
+    }
+
+    init(x: T, y: T, z: T, w: T = T(1)) {
+        data = [x, y, z, w]
+    }
+
+    subscript(idx: Int) -> T {
+        get {
+            return data[idx]
+        }
+        set(value) {
+            data[idx] = value
+        }
+    }
+}
+
+
+public struct Vector3: Vector {
+    private var data: [Float]
+
+    init() {
+        self.init(x: 0.0, y: 0.0, z: 0.0)
+    }
+
+    init(x: Float, y: Float, z: Float) {
+        data = [x, y, z]
+    }
+
+    var length: Float {
+        return sqrtf(length2)
+    }
+
+    var length2: Float {
+        return data.reduce(0.0) { $0 + $1 * $1 }
+    }
+
+    // MARK: Sequence-ish
+
+    var count: Int {
+        return 3
+    }
+
+    public subscript(idx: Int) -> Float {
+        get {
+            return data[idx]
+        }
+        set(value) {
+            data[idx] = value
+        }
+    }
+}
+
+// MARK: - Matrix-Scalar Multiplication
+
+
+//func *<T: FloatingPointType>(matrix: Matrix4<T>, scalar: T) -> Matrix4<T> {
+//    var out: Matrix4<T>
+//    for i in 0..<out.data.count {
+//        out[i] = matrix.data[i] * scalar
+//    }
+//    return out
+//}
+
+// MARK: - Matrix-Vector Multiplication
+
+//func *<T: FloatingPointType>(matrix: Matrix4<T>, vector: Vector4<T>) -> Vector4<T> {
+//    return Vector4<T>()
+//}