tiny.linear.Mat4

1pub const Mat4 = extern struct {2    cols: [4]Vec4 = .{3        .{ .x = 1 },4        .{ .y = 1 },5        .{ .z = 1 },6        .{ .w = 1 },7    },89    pub const identity: Mat4 = .{};1011    pub fn fromCols(c0: Vec4, c1: Vec4, c2: Vec4, c3: Vec4) Mat4 {12        return .{ .cols = .{ c0, c1, c2, c3 } };13    }1415    /// The homogeneous matrix of a linear part and a translation.16    pub fn fromLinearTranslation(linear: Mat3, translation: Vec3) Mat4 {17        return fromCols(18            Vec4.fromVec3(linear.cols[0], 0),19            Vec4.fromVec3(linear.cols[1], 0),20            Vec4.fromVec3(linear.cols[2], 0),21            Vec4.fromVec3(translation, 1),22        );23    }2425    pub fn row(m: Mat4, index: usize) Vec4 {26        assert(index < 4);27        const lanes = [4][4]f32{28            m.cols[0].toArray(),29            m.cols[1].toArray(),30            m.cols[2].toArray(),31            m.cols[3].toArray(),32        };33        return .{ .x = lanes[0][index], .y = lanes[1][index], .z = lanes[2][index], .w = lanes[3][index] };34    }3536    pub fn transpose(m: Mat4) Mat4 {37        return fromCols(m.row(0), m.row(1), m.row(2), m.row(3));38    }3940    /// `m v`, summed as `c0 v.x + c1 v.y + c2 v.z + c3 v.w`.41    pub fn mulVec(m: Mat4, v: Vec4) Vec4 {42        return m.cols[0].scale(v.x)43            .add(m.cols[1].scale(v.y))44            .add(m.cols[2].scale(v.z))45            .add(m.cols[3].scale(v.w));46    }4748    /// `a b`: applying `b`, then `a`.49    pub fn mul(a: Mat4, b: Mat4) Mat4 {50        return fromCols(51            a.mulVec(b.cols[0]),52            a.mulVec(b.cols[1]),53            a.mulVec(b.cols[2]),54            a.mulVec(b.cols[3]),55        );56    }5758    pub fn scale(m: Mat4, s: f32) Mat4 {59        return fromCols(m.cols[0].scale(s), m.cols[1].scale(s), m.cols[2].scale(s), m.cols[3].scale(s));60    }6162    pub fn determinant(m: Mat4) f32 {63        const minors = Minors.of(m);64        return minors.determinant();65    }6667    /// The inverse, or null when the determinant is zero, NaN, or too small68    /// for its reciprocal to be a finite nonzero f32.69    pub fn inverse(m: Mat4) ?Mat4 {70        const minors = Minors.of(m);71        const inverse_determinant = reciprocal(minors.determinant()) orelse return null;72        const a = m.cols;73        const adjugate = fromCols(74            .{75                .x = a[1].y * minors.c5 - a[1].z * minors.c4 + a[1].w * minors.c3,76                .y = -a[0].y * minors.c5 + a[0].z * minors.c4 - a[0].w * minors.c3,77                .z = a[3].y * minors.s5 - a[3].z * minors.s4 + a[3].w * minors.s3,78                .w = -a[2].y * minors.s5 + a[2].z * minors.s4 - a[2].w * minors.s3,79            },80            .{81                .x = -a[1].x * minors.c5 + a[1].z * minors.c2 - a[1].w * minors.c1,82                .y = a[0].x * minors.c5 - a[0].z * minors.c2 + a[0].w * minors.c1,83                .z = -a[3].x * minors.s5 + a[3].z * minors.s2 - a[3].w * minors.s1,84                .w = a[2].x * minors.s5 - a[2].z * minors.s2 + a[2].w * minors.s1,85            },86            .{87                .x = a[1].x * minors.c4 - a[1].y * minors.c2 + a[1].w * minors.c0,88                .y = -a[0].x * minors.c4 + a[0].y * minors.c2 - a[0].w * minors.c0,89                .z = a[3].x * minors.s4 - a[3].y * minors.s2 + a[3].w * minors.s0,90                .w = -a[2].x * minors.s4 + a[2].y * minors.s2 - a[2].w * minors.s0,91            },92            .{93                .x = -a[1].x * minors.c3 + a[1].y * minors.c1 - a[1].z * minors.c0,94                .y = a[0].x * minors.c3 - a[0].y * minors.c1 + a[0].z * minors.c0,95                .z = -a[3].x * minors.s3 + a[3].y * minors.s1 - a[3].z * minors.s0,96                .w = a[2].x * minors.s3 - a[2].y * minors.s1 + a[2].z * minors.s0,97            },98        );99        return adjugate.scale(inverse_determinant);100    }101102    /// The view matrix of a camera at `eye` looking at `target`, or null when103    /// the two coincide or the view direction is parallel to `up`.104    pub fn lookAt(eye: Vec3, target: Vec3, up: Vec3) ?Mat4 {105        const forward = target.sub(eye).normalized(0) orelse return null;106        const side = forward.cross(up).normalized(0) orelse return null;107        const camera_up = side.cross(forward);108        return fromCols(109            .{ .x = side.x, .y = camera_up.x, .z = -forward.x },110            .{ .x = side.y, .y = camera_up.y, .z = -forward.y },111            .{ .x = side.z, .y = camera_up.z, .z = -forward.z },112            .{ .x = -side.dot(eye), .y = -camera_up.dot(eye), .z = forward.dot(eye), .w = 1 },113        );114    }115116    /// A perspective projection with vertical field of view `fov_y` radians117    /// and `aspect` width over height, mapping view depth `-near` to clip118    /// depth 0 and `-far` to 1.119    pub fn perspective(fov_y: f32, aspect: f32, near: f32, far: f32) Mat4 {120        assert(fov_y > 0);121        assert(fov_y < std.math.pi);122        assert(aspect > 0);123        assert(near > 0);124        assert(far > near);125        const focal = 1 / @tan(fov_y * 0.5);126        const depth = 1 / (near - far);127        return fromCols(128            .{ .x = focal / aspect },129            .{ .y = focal },130            .{ .z = far * depth, .w = -1 },131            .{ .z = near * far * depth },132        );133    }134135    /// An orthographic projection of the view-space box between the given136    /// planes, mapping view depth `-near` to clip depth 0 and `-far` to 1.137    pub fn orthographic(left: f32, right: f32, bottom: f32, top: f32, near: f32, far: f32) Mat4 {138        assert(right != left);139        assert(top != bottom);140        assert(far != near);141        const width = 1 / (right - left);142        const height = 1 / (top - bottom);143        const depth = 1 / (near - far);144        return fromCols(145            .{ .x = 2 * width },146            .{ .y = 2 * height },147            .{ .z = depth },148            .{ .x = -(right + left) * width, .y = -(top + bottom) * height, .z = near * depth, .w = 1 },149        );150    }151};

1pub const Mat4 = matrix.Mat4;