Add approx equal functions

src/vec3.zig

@@ -43,10 +43,24 @@ pub fn vec3Cross(a: Vec3F64, b: Vec3F64) Vec3F64 {
     return .init(x_component, y_component, z_component);
 }
 
+pub fn vec3ApproxEq(a: Vec3F64, b: Vec3F64, tol: f64) bool {
+    return @abs(a.x() - b.x()) < tol and
+        @abs(a.y() - b.y()) < tol and
+        @abs(a.z() - b.z()) < tol;
+}
+
 pub const Mat3F64 = struct {
     row1: Vec3F64,
     row2: Vec3F64,
     row3: Vec3F64,
+
+    pub fn identity() Mat3F64 {
+        return .{
+            .row1 = .init(1, 0, 0),
+            .row2 = .init(0, 1, 0),
+            .row3 = .init(0, 0, 1),
+        };
+    }
 };
 
 pub fn mat3Add(a: Mat3F64, b: Mat3F64) Mat3F64 {
@@ -134,6 +148,12 @@ pub fn vec3MulMat3(a: Mat3F64, b: Vec3F64) Vec3F64 {
     );
 }
 
+pub fn mat3ApproxEq(a: Mat3F64, b: Mat3F64, tol: f64) bool {
+    return vec3ApproxEq(a.row1, b.row1, tol) and
+        vec3ApproxEq(a.row2, b.row2, tol) and
+        vec3ApproxEq(a.row3, b.row3, tol);
+}
+
 // 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/
@@ -243,6 +263,16 @@ test "vec3Cross crosses properly" {
     try std.testing.expect(c.z() == -5);
 }
 
+test "vec3approxEq works" {
+    const a = Vec3F64.init(1, 0, 0);
+    var b = Vec3F64.init(1, 0, 0);
+
+    try std.testing.expect(vec3ApproxEq(a, b, 1e-12));
+    b.data[0] += 1e-11;
+    try std.testing.expect(!vec3ApproxEq(a, b, 1e-12));
+    try std.testing.expect(vec3ApproxEq(a, b, 1e-10));
+}
+
 test "Mat3 add works" {
     const a: Mat3F64 = .{
         .row1 = Vec3F64.init(1, 2, 3),
@@ -346,6 +376,25 @@ test "mat inverse works" {
     try std.testing.expectApproxEqAbs(-1.0 / 7.0, ainv.row3.y(), 1e-12);
     try std.testing.expectApproxEqAbs(1.0 / 5.0, ainv.row3.z(), 1e-12);
 }
+
+test "mat3approxEq works" {
+    const a: Mat3F64 = .{
+        .row1 = Vec3F64.init(1, 2, 3),
+        .row2 = Vec3F64.init(4, 1, 5),
+        .row3 = Vec3F64.init(3, 1, 9),
+    };
+    var b: Mat3F64 = .{
+        .row1 = Vec3F64.init(1, 2, 3),
+        .row2 = Vec3F64.init(4, 1, 5),
+        .row3 = Vec3F64.init(3, 1, 9),
+    };
+
+    try std.testing.expect(mat3ApproxEq(a, b, 1e-12));
+    b.row2.data[1] += 1e-11;
+    try std.testing.expect(!mat3ApproxEq(a, b, 1e-12));
+    try std.testing.expect(mat3ApproxEq(a, b, 1e-12));
+}
+
 test "vec3 mul mat3 works" {
     const b: Mat3F64 = .{
         .row1 = Vec3F64.init(0, 1, 0),