tiny.linear.Mat3

1pub const Mat3 = extern struct {2    cols: [3]Vec3 = .{3        .{ .x = 1 },4        .{ .y = 1 },5        .{ .z = 1 },6    },78    pub const identity: Mat3 = .{};910    pub fn fromCols(c0: Vec3, c1: Vec3, c2: Vec3) Mat3 {11        return .{ .cols = .{ c0, c1, c2 } };12    }1314    pub fn fromScale(s: Vec3) Mat3 {15        return fromCols(.{ .x = s.x }, .{ .y = s.y }, .{ .z = s.z });16    }1718    /// The rotation matrix of the unit quaternion `q`.19    pub fn fromQuat(q: Quat) Mat3 {20        const xx = q.x * q.x;21        const yy = q.y * q.y;22        const zz = q.z * q.z;23        const xy = q.x * q.y;24        const xz = q.x * q.z;25        const yz = q.y * q.z;26        const wx = q.w * q.x;27        const wy = q.w * q.y;28        const wz = q.w * q.z;29        return fromCols(30            .{ .x = 1 - 2 * (yy + zz), .y = 2 * (xy + wz), .z = 2 * (xz - wy) },31            .{ .x = 2 * (xy - wz), .y = 1 - 2 * (xx + zz), .z = 2 * (yz + wx) },32            .{ .x = 2 * (xz + wy), .y = 2 * (yz - wx), .z = 1 - 2 * (xx + yy) },33        );34    }3536    pub fn row(m: Mat3, index: usize) Vec3 {37        assert(index < 3);38        const lanes = [3][3]f32{ m.cols[0].toArray(), m.cols[1].toArray(), m.cols[2].toArray() };39        return .{ .x = lanes[0][index], .y = lanes[1][index], .z = lanes[2][index] };40    }4142    pub fn transpose(m: Mat3) Mat3 {43        return fromCols(m.row(0), m.row(1), m.row(2));44    }4546    /// `m v`, summed as `c0 v.x + c1 v.y + c2 v.z`.47    pub fn mulVec(m: Mat3, v: Vec3) Vec3 {48        return m.cols[0].scale(v.x).add(m.cols[1].scale(v.y)).add(m.cols[2].scale(v.z));49    }5051    /// `a b`: applying `b`, then `a`.52    pub fn mul(a: Mat3, b: Mat3) Mat3 {53        return fromCols(a.mulVec(b.cols[0]), a.mulVec(b.cols[1]), a.mulVec(b.cols[2]));54    }5556    pub fn scale(m: Mat3, s: f32) Mat3 {57        return fromCols(m.cols[0].scale(s), m.cols[1].scale(s), m.cols[2].scale(s));58    }5960    pub fn determinant(m: Mat3) f32 {61        return m.cols[0].dot(m.cols[1].cross(m.cols[2]));62    }6364    /// The inverse, or null when the determinant is zero, NaN, or too small65    /// for its reciprocal to be a finite nonzero f32.66    pub fn inverse(m: Mat3) ?Mat3 {67        const inverse_transposed = m.inverseTranspose() orelse return null;68        return inverse_transposed.transpose();69    }7071    /// The transpose of the inverse, which carries surface normals through72    /// `m`. Null under the same condition as `inverse`.73    pub fn inverseTranspose(m: Mat3) ?Mat3 {74        const c0 = m.cols[1].cross(m.cols[2]);75        const c1 = m.cols[2].cross(m.cols[0]);76        const c2 = m.cols[0].cross(m.cols[1]);77        const inverse_determinant = reciprocal(m.cols[0].dot(c0)) orelse return null;78        return fromCols(c0, c1, c2).scale(inverse_determinant);79    }80};

1pub const Mat3 = matrix.Mat3;