Add basic quaternion struct

vec3/src/vec3.zig

@@ -85,6 +85,32 @@ pub fn vec3MulMat3(comptime T: type, a: Vec3(T), b: Mat3(T)) Vec3(T) {
     };
 }
 
+// Uses the Quaternion definition of q = w + xi + yj + zk
+// and with i^2 = j^2 = k^2 = ijk = -1
+// I grabbed a lot of this math from https://imadrahmoune.com/rotations-with-quaternions/
+pub fn Quat(comptime T: type) type {
+    return struct {
+        w: T,
+        x: T,
+        y: T,
+        z: T,
+
+        pub fn mag(q: Quat(T)) T {
+            return std.math.sqrt(q.x * q.x + q.y * q.y + q.z * q.z + q.w * q.w);
+        }
+
+        pub fn normalized(q: Quat(T)) Quat(T) {
+            const magnitude = q.mag();
+            return .{
+                .x = q.x / magnitude,
+                .y = q.y / magnitude,
+                .z = q.z / magnitude,
+                .w = q.w / magnitude,
+            };
+        }
+    };
+}
+
 test "vec3Add adds properly" {
     const a: Vec3(i8) = .{ .x = 1, .y = 2, .z = 3 };
     const b: Vec3(i8) = .{ .x = 3, .y = 1, .z = 0 };
@@ -209,3 +235,25 @@ test "vec3 mul mat3 works" {
     try std.testing.expect(c.y == 3);
     try std.testing.expect(c.z == 5);
 }
+
+test "quat magnitude" {
+    const q: Quat(f32) = .{ .x = 1.0, .y = 2.0, .z = 3.0, .w = 4.0 };
+    try std.testing.expect(std.math.approxEqAbs(f32, q.mag(), std.math.sqrt(30.0), 1e-7));
+}
+
+test "quat normalized" {
+    const q: Quat(f32) = .{ .x = 1.0, .y = 2.0, .z = 3.0, .w = 4.0 };
+    const expected: Quat(f32) = .{
+        .x = 1.0 / std.math.sqrt(30.0),
+        .y = 2.0 / std.math.sqrt(30.0),
+        .z = 3.0 / std.math.sqrt(30.0),
+        .w = 4.0 / std.math.sqrt(30.0),
+    };
+
+    const normalized = q.normalized();
+
+    try std.testing.expect(std.math.approxEqAbs(f32, normalized.x, expected.x, 1e-7));
+    try std.testing.expect(std.math.approxEqAbs(f32, normalized.y, expected.y, 1e-7));
+    try std.testing.expect(std.math.approxEqAbs(f32, normalized.z, expected.z, 1e-7));
+    try std.testing.expect(std.math.approxEqAbs(f32, normalized.w, expected.w, 1e-7));
+}