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Refactor math for no good reason; I just really like math

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This commit is contained in:
Szymon Nowakowski
2025-11-13 02:22:22 +01:00
parent 2e8cfd36fd
commit 4cbf151fd9
6 changed files with 529 additions and 201 deletions
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1
src/math.zig
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@@ -1,4 +1,5 @@
pub const Matrix4x4 = @import("math/Matrix4x4.zig").Matrix4x4;
pub const Quaternion = @import("math/Quaternion.zig").Quaternion;
pub const Vector2 = @import("math/Vector2.zig").Vector2;
pub const Vector3 = @import("math/Vector3.zig").Vector3;
pub const Vector4 = @import("math/Vector4.zig").Vector4;

254
src/math/Matrix4x4.zig
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@@ -17,6 +17,8 @@ pub const Matrix4x4 = extern struct {
// zig fmt: on
);
// --- INIT ---
pub inline fn init(
// zig fmt: off
ix: f32, iy: f32, iz: f32, iw: f32,
@@ -26,147 +28,173 @@ pub const Matrix4x4 = extern struct {
// zig fmt: on
) Matrix4x4 {
return .{
.i = .{ .vector = .{ ix, iy, iz, iw } },
.j = .{ .vector = .{ jx, jy, jz, jw } },
.k = .{ .vector = .{ kx, ky, kz, kw } },
.t = .{ .vector = .{ tx, ty, tz, tw } },
.i = .init(ix, iy, iz, iw),
.j = .init(jx, jy, jz, jw),
.k = .init(kx, ky, kz, kw),
.t = .init(tx, ty, tz, tw),
};
}
pub inline fn initVector(i: Vector4, j: Vector4, k: Vector4, t: Vector4) Matrix4x4 {
pub inline fn initArray(array: [16]f32) Matrix4x4 {
return .{
.i = .initArray(array[0..4].*),
.j = .initArray(array[4..8].*),
.k = .initArray(array[8..12].*),
.t = .initArray(array[12..16].*),
};
}
pub inline fn initVector4(i: Vector4, j: Vector4, k: Vector4, t: Vector4) Matrix4x4 {
return .{ .i = i, .j = j, .k = k, .t = t };
}
pub inline fn initTranslation(translation: Vector3) Matrix4x4 {
return .{
.i = .{ .vector = .{ 1, 0, 0, 0 } },
.j = .{ .vector = .{ 0, 1, 0, 0 } },
.k = .{ .vector = .{ 0, 0, 1, 0 } },
.t = .{ .vector = translation.vector ++ .{1} },
};
return .initVector4(
.unit_x,
.unit_y,
.unit_z,
translation.asVector4(1),
);
}
pub inline fn initRotation(rotation: Quaternion) Matrix4x4 {
const xx = rotation.getX() * rotation.getX();
const xy = rotation.getX() * rotation.getY();
const xz = rotation.getX() * rotation.getZ();
const xw = rotation.getX() * rotation.getW();
const yy = rotation.getY() * rotation.getY();
const yz = rotation.getY() * rotation.getZ();
const yw = rotation.getY() * rotation.getW();
const zz = rotation.getZ() * rotation.getZ();
const zw = rotation.getZ() * rotation.getW();
const xx = rotation.vector.getX() * rotation.vector.getX();
const xy = rotation.vector.getX() * rotation.vector.getY();
const xz = rotation.vector.getX() * rotation.vector.getZ();
const xw = rotation.vector.getX() * rotation.vector.getW();
const yy = rotation.vector.getY() * rotation.vector.getY();
const yz = rotation.vector.getY() * rotation.vector.getZ();
const yw = rotation.vector.getY() * rotation.vector.getW();
const zz = rotation.vector.getZ() * rotation.vector.getZ();
const zw = rotation.vector.getZ() * rotation.vector.getW();
return .{
.i = .{ .vector = .{ 1 - 2 * (yy + zz), 2 * (xy + zw), 2 * (xz - yw), 0 } },
.j = .{ .vector = .{ 2 * (xy - zw), 1 - 2 * (xx + zz), 2 * (yz + xw), 0 } },
.k = .{ .vector = .{ 2 * (xz + yw), 2 * (yz - xw), 1 - 2 * (xx + yy), 0 } },
.t = .{ .vector = .{ 0, 0, 0, 1 } },
};
return .init(
// zig fmt: off
1 - 2 * (yy + zz), 2 * (xy + zw), 2 * (xz - yw), 0,
2 * (xy - zw), 1 - 2 * (xx + zz), 2 * (yz + xw), 0,
2 * (xz + yw), 2 * (yz - xw), 1 - 2 * (xx + yy), 0,
0, 0, 0, 1,
// zig fmt: on
);
}
pub inline fn initScale(scale: Vector3) Matrix4x4 {
return .{
.i = .{ .vector = .{ scale.getX(), 0, 0, 0 } },
.j = .{ .vector = .{ 0, scale.getY(), 0, 0 } },
.k = .{ .vector = .{ 0, 0, scale.getZ(), 0 } },
.t = .{ .vector = .{ 0, 0, 0, 1 } },
};
return .init(
// zig fmt: off
scale.getX(), 0, 0, 0,
0, scale.getY(), 0, 0,
0, 0, scale.getZ(), 0,
0, 0, 0, 1,
// zig fmt: on
);
}
pub inline fn initTranslationRotationScale(translation: Vector3, rotation: Quaternion, scale: Vector3) Matrix4x4 {
const xx = rotation.getX() * rotation.getX();
const xy = rotation.getX() * rotation.getY();
const xz = rotation.getX() * rotation.getZ();
const xw = rotation.getX() * rotation.getW();
const yy = rotation.getY() * rotation.getY();
const yz = rotation.getY() * rotation.getZ();
const yw = rotation.getY() * rotation.getW();
const zz = rotation.getZ() * rotation.getZ();
const zw = rotation.getZ() * rotation.getW();
pub inline fn initTranslationRotationScale(
translation: Vector3,
rotation: Quaternion,
scale: Vector3,
) Matrix4x4 {
const xx = rotation.vector.getX() * rotation.vector.getX();
const xy = rotation.vector.getX() * rotation.vector.getY();
const xz = rotation.vector.getX() * rotation.vector.getZ();
const xw = rotation.vector.getX() * rotation.vector.getW();
const yy = rotation.vector.getY() * rotation.vector.getY();
const yz = rotation.vector.getY() * rotation.vector.getZ();
const yw = rotation.vector.getY() * rotation.vector.getW();
const zz = rotation.vector.getZ() * rotation.vector.getZ();
const zw = rotation.vector.getZ() * rotation.vector.getW();
const scale_x: Vector4.Vector = @splat(scale.getX());
const scale_y: Vector4.Vector = @splat(scale.getY());
const scale_z: Vector4.Vector = @splat(scale.getZ());
const rotation_i = Vector4.init((1 - 2 * (yy + zz)), 2 * (xy + zw), 2 * (xz - yw), 0);
const rotation_j = Vector4.init(2 * (xy - zw), (1 - 2 * (xx + zz)), 2 * (yz + xw), 0);
const rotation_k = Vector4.init(2 * (xz + yw), 2 * (yz - xw), (1 - 2 * (xx + yy)), 0);
const rotation_i: Vector4.Vector = .{ (1 - 2 * (yy + zz)), 2 * (xy + zw), 2 * (xz - yw), 0 };
const rotation_j: Vector4.Vector = .{ 2 * (xy - zw), (1 - 2 * (xx + zz)), 2 * (yz + xw), 0 };
const rotation_k: Vector4.Vector = .{ 2 * (xz + yw), 2 * (yz - xw), (1 - 2 * (xx + yy)), 0 };
return .{
.i = .{ .vector = scale_x * rotation_i },
.j = .{ .vector = scale_y * rotation_j },
.k = .{ .vector = scale_z * rotation_k },
.t = .{ .vector = translation.vector ++ .{1} },
};
return .initVector4(
Vector4.mulScalar(rotation_i, scale.getX()),
Vector4.mulScalar(rotation_j, scale.getY()),
Vector4.mulScalar(rotation_k, scale.getZ()),
translation.asVector4(1),
);
}
// --- CONVERSION ---
pub inline fn asArray(self: Matrix4x4) [16]f32 {
return self.i.asArray() ++ self.j.asArray() ++ self.k.asArray() ++ self.t.asArray();
}
pub inline fn asVector4(self: Matrix4x4) [4]Vector4 {
return .{ self.i, self.j, self.k, self.t };
}
// --- COMPONENT-WISE ---
pub inline fn add(self: Matrix4x4, other: Matrix4x4) Matrix4x4 {
return .{
.i = .{ .vector = self.i.vector + other.i.vector },
.j = .{ .vector = self.j.vector + other.j.vector },
.k = .{ .vector = self.k.vector + other.k.vector },
.t = .{ .vector = self.t.vector + other.t.vector },
};
return .initVector4(
Vector4.add(self.i, other.i),
Vector4.add(self.j, other.j),
Vector4.add(self.k, other.k),
Vector4.add(self.t, other.t),
);
}
pub inline fn sub(self: Matrix4x4, other: Matrix4x4) Matrix4x4 {
return .{
.i = .{ .vector = self.i.vector - other.i.vector },
.j = .{ .vector = self.j.vector - other.j.vector },
.k = .{ .vector = self.k.vector - other.k.vector },
.t = .{ .vector = self.t.vector - other.t.vector },
};
}
pub inline fn mulScalar(self: Matrix4x4, scalar: f32) Matrix4x4 {
const scalar_vector: Vector4.Vector = @splat(scalar);
return .{
.i = .{ .vector = self.i.vector * scalar_vector },
.j = .{ .vector = self.j.vector * scalar_vector },
.k = .{ .vector = self.k.vector * scalar_vector },
.t = .{ .vector = self.t.vector * scalar_vector },
};
}
pub inline fn divScalar(self: Matrix4x4, scalar: f32) Matrix4x4 {
const inv_scalar_vector: Vector4.Vector = @splat(1 / scalar);
return .{
.i = .{ .vector = self.i * inv_scalar_vector },
.j = .{ .vector = self.j * inv_scalar_vector },
.k = .{ .vector = self.k * inv_scalar_vector },
.t = .{ .vector = self.t * inv_scalar_vector },
};
return .initVector4(
Vector4.sub(self.i, other.i),
Vector4.sub(self.j, other.j),
Vector4.sub(self.k, other.k),
Vector4.sub(self.t, other.t),
);
}
pub inline fn negate(self: Matrix4x4) Matrix4x4 {
return .{
.i = .{ .vector = -self.i.vector },
.j = .{ .vector = -self.j.vector },
.k = .{ .vector = -self.k.vector },
.t = .{ .vector = -self.t.vector },
};
return .initVector4(
Vector4.negate(self.i),
Vector4.negate(self.j),
Vector4.negate(self.k),
Vector4.negate(self.t),
);
}
pub inline fn mulScalar(self: Matrix4x4, scalar: f32) Matrix4x4 {
return .initVector4(
Vector4.mulScalar(self.i, scalar),
Vector4.mulScalar(self.j, scalar),
Vector4.mulScalar(self.k, scalar),
Vector4.mulScalar(self.t, scalar),
);
}
pub inline fn divScalar(self: Matrix4x4, scalar: f32) Matrix4x4 {
const inv_scalar = 1 / scalar;
return .initVector4(
Vector4.mulScalar(self.i, inv_scalar),
Vector4.mulScalar(self.j, inv_scalar),
Vector4.mulScalar(self.k, inv_scalar),
Vector4.mulScalar(self.t, inv_scalar),
);
}
// --- OTHER ---
pub inline fn mulMatrix(self: Matrix4x4, other: Matrix4x4) Matrix4x4 {
return .{
.i = self.i.mulScalar(other.i.getX())
return .initVector4(
self.i.mulScalar(other.i.getX())
.add(self.j.mulScalar(other.i.getY()))
.add(self.k.mulScalar(other.i.getZ()))
.add(self.t.mulScalar(other.i.getW())),
.j = self.i.mulScalar(other.j.getX())
self.i.mulScalar(other.j.getX())
.add(self.j.mulScalar(other.j.getY()))
.add(self.k.mulScalar(other.j.getZ()))
.add(self.t.mulScalar(other.j.getW())),
.k = self.i.mulScalar(other.k.getX())
self.i.mulScalar(other.k.getX())
.add(self.j.mulScalar(other.k.getY()))
.add(self.k.mulScalar(other.k.getZ()))
.add(self.t.mulScalar(other.k.getW())),
.t = self.i.mulScalar(other.t.getX())
self.i.mulScalar(other.t.getX())
.add(self.j.mulScalar(other.t.getY()))
.add(self.k.mulScalar(other.t.getZ()))
.add(self.t.mulScalar(other.t.getW())),
};
);
}
pub inline fn inverseAffine(self: Matrix4x4) Matrix4x4 {
@@ -203,12 +231,12 @@ pub const Matrix4x4 = extern struct {
.add(self.k.asVector3().mulScalar(self.t.getZ()))
.negate();
return .{
.i = .{ .vector = i ++ .{0} },
.j = .{ .vector = j ++ .{0} },
.k = .{ .vector = k ++ .{0} },
.t = .{ .vector = t ++ .{1} },
};
return .initVector4(
i.asVector4(0),
j.asVector4(0),
k.asVector4(0),
t.asVector4(1),
);
}
pub inline fn inverseTransposeAffine(self: Matrix4x4) Matrix4x4 {
@@ -245,15 +273,11 @@ pub const Matrix4x4 = extern struct {
.add(self.k.asVector3().mulScalar(self.t.getZ()))
.negate();
return .{
.i = .{ .vector = i ++ .{0} },
.j = .{ .vector = j ++ .{0} },
.k = .{ .vector = k ++ .{0} },
.t = .{ .vector = t ++ .{1} },
};
}
pub inline fn asArray(self: Matrix4x4) [16]f32 {
return @bitCast(self);
return .initVector4(
i.asVector4(0),
j.asVector4(0),
k.asVector4(0),
t.asVector4(1),
);
}
};

141
src/math/Quaternion.zig
View File

@@ -1,114 +1,155 @@
const std = @import("std");
const Vector3 = @import("Vector3.zig").Vector3;
const Vector4 = @import("Vector4.zig").Vector4;
pub const Quaternion = extern struct {
vector: Vector,
vector: Vector4,
pub const Vector = @Vector(4, f32);
pub const zero = Quaternion.init(0, 0, 0, 0);
pub const one = Quaternion.init(1, 1, 1, 1);
pub const identity = Quaternion.init(0, 0, 0, 1);
// --- INIT ---
pub inline fn init(x: f32, y: f32, z: f32, w: f32) Quaternion {
return .{ .vector = .{ x, y, z, w } };
return .{ .vector = .init(x, y, z, w) };
}
pub inline fn initArray(array: [4]f32) Quaternion {
return .{ .vector = .initArray(array) };
}
pub inline fn initVector4(vector: Vector4) Quaternion {
return .{ .vector = vector };
}
pub inline fn initRotationXY(angle_rad: f32) Quaternion {
const half_angle_rad = 0.5 * angle_rad;
return .{ .vector = .{ 0, 0, @sin(half_angle_rad), @cos(half_angle_rad) } };
const c = @cos(half_angle_rad);
const s = @sin(half_angle_rad);
return .init(0, 0, s, c);
}
pub inline fn initRotationXZ(angle_rad: f32) Quaternion {
const half_angle_rad = 0.5 * angle_rad;
return .{ .vector = .{ 0, -@sin(half_angle_rad), 0, @cos(half_angle_rad) } };
const c = @cos(half_angle_rad);
const s = @sin(half_angle_rad);
return .init(0, -s, 0, c);
}
pub inline fn initRotationYX(angle_rad: f32) Quaternion {
const half_angle_rad = 0.5 * angle_rad;
return .{ .vector = .{ 0, 0, -@sin(half_angle_rad), @cos(half_angle_rad) } };
const c = @cos(half_angle_rad);
const s = @sin(half_angle_rad);
return .init(0, 0, -s, c);
}
pub inline fn initRotationYZ(angle_rad: f32) Quaternion {
const half_angle_rad = 0.5 * angle_rad;
return .{ .vector = .{ @sin(half_angle_rad), 0, 0, @cos(half_angle_rad) } };
const c = @cos(half_angle_rad);
const s = @sin(half_angle_rad);
return .init(s, 0, 0, c);
}
pub inline fn initRotationZX(angle_rad: f32) Quaternion {
const half_angle_rad = 0.5 * angle_rad;
return .{ .vector = .{ 0, @sin(half_angle_rad), 0, @cos(half_angle_rad) } };
const c = @cos(half_angle_rad);
const s = @sin(half_angle_rad);
return .init(0, s, 0, c);
}
pub inline fn initRotationZY(angle_rad: f32) Quaternion {
const half_angle_rad = 0.5 * angle_rad;
return .{ .vector = .{ -@sin(half_angle_rad), 0, 0, @cos(half_angle_rad) } };
const c = @cos(half_angle_rad);
const s = @sin(half_angle_rad);
return .init(-s, 0, 0, c);
}
pub inline fn getX(self: Quaternion) f32 {
return self.vector[0];
// --- CONVERSION ---
pub inline fn asArray(self: Quaternion) [4]f32 {
return self.vector.vector;
}
pub inline fn getY(self: Quaternion) f32 {
return self.vector[1];
pub inline fn asVector4(self: Quaternion) Vector4 {
return self.vector;
}
pub inline fn getZ(self: Quaternion) f32 {
return self.vector[2];
// --- ACCESSORS ---
pub inline fn getVector(self: Quaternion) Vector3 {
return self.vector.asVector3();
}
pub inline fn getW(self: Quaternion) f32 {
return self.vector[3];
pub inline fn getScalar(self: Quaternion) f32 {
return self.vector.getW();
}
pub inline fn setX(self: Quaternion, x: f32) Quaternion {
const x_vector: Vector = @splat(x);
return .{ .vector = @shuffle(Vector, self, x_vector, .{ ~@as(i32, 0), 1, 2, 3 }) };
pub inline fn setVector(self: Quaternion, vector: Vector3) Quaternion {
return .{
.vector = .{
.vector = @shuffle(f32, self.vector.vector, vector.vector, .{ ~@as(i32, 0), ~@as(i32, 1), ~@as(i32, 2), 3 }),
},
};
}
pub inline fn setY(self: Quaternion, y: f32) Quaternion {
const y_vector: Vector = @splat(y);
return .{ .vector = @shuffle(Vector, self, y_vector, .{ 0, ~@as(i32, 1), 2, 3 }) };
pub inline fn setScalar(self: Quaternion, scalar: f32) Quaternion {
return .initVector4(self.vector.setW(scalar));
}
pub inline fn setZ(self: Quaternion, z: f32) Quaternion {
const z_vector: Vector = @splat(z);
return .{ .vector = @shuffle(Vector, self, z_vector, .{ 0, 1, ~@as(i32, 2), 3 }) };
}
pub inline fn setW(self: Quaternion, w: f32) Quaternion {
const w_vector: Vector = @splat(w);
return .{ .vector = @shuffle(Vector, self, w_vector, .{ 0, 1, 2, ~@as(i32, 3) }) };
}
// --- COMPONENT-WISE ---
pub inline fn add(self: Quaternion, other: Quaternion) Quaternion {
return .{ .vector = self.vector + other.vector };
return .initVector4(Vector4.add(self.vector, other.vector));
}
pub inline fn sub(self: Quaternion, other: Quaternion) Quaternion {
return .{ .vector = self.vector - other.vector };
return .initVector4(Vector4.sub(self.vector, other.vector));
}
pub inline fn mul(self: Quaternion, other: Quaternion) Quaternion {
return .{ .vector = self.vector * other.vector };
pub inline fn negate(self: Quaternion) Quaternion {
return .initVector4(Vector4.negate(self.vector));
}
pub inline fn div(self: Quaternion, other: Quaternion) Quaternion {
return .{ .vector = self.vector / other.vector };
pub inline fn conjugate(self: Quaternion) Quaternion {
return .initVector4(Vector4.mul(self.vector, Vector4.init(-1, -1, -1, 1)));
}
pub inline fn mulScalar(self: Quaternion, scalar: f32) Quaternion {
const scalar_vector: Vector = @splat(scalar);
return .{ .vector = self.vector * scalar_vector };
return .initVector4(Vector4.mulScalar(self.vector, scalar));
}
pub inline fn divScalar(self: Quaternion, scalar: f32) Quaternion {
const scalar_vector: Vector = @splat(scalar);
return .{ .vector = self.vector / scalar_vector };
return .initVector4(Vector4.divScalar(self.vector, scalar));
}
// --- OTHER ---
pub inline fn len(self: Quaternion) f32 {
return self.vector.len();
}
pub inline fn lenSquared(self: Quaternion) f32 {
return self.vector.lenSquared();
}
pub inline fn normalize(self: Quaternion) Quaternion {
return .initVector4(Vector4.normalize(self.vector));
}
pub inline fn dot(self: Quaternion, other: Quaternion) f32 {
return Vector4.dot(self.vector, other.vector);
}
pub inline fn lerp(self: Quaternion, other: Quaternion, t: f32) Quaternion {
const s = 1.0 - t;
const t_vector: Vector = @splat(t);
const s_vector: Vector = @splat(s);
return .{ .vector = self * t_vector + other * s_vector };
return .initVector4(Vector4.lerp(self.vector, other.vector, t));
}
pub inline fn mulQuaternion(self: Quaternion, other: Quaternion) Quaternion {
const x1, const y1, const z1, const w1 = self.vector.vector;
const x2, const y2, const z2, const w2 = other.vector.vector;
return .init(
w1 * x2 + x1 * w2 + y1 * z2 - z1 * y2,
w1 * y2 - x1 * z2 + y1 * w2 + z1 * x2,
w1 * z2 + x1 * y2 - y1 * x2 + z1 * w2,
w1 * w2 - x1 * x2 - y1 * y2 - z1 * z2,
);
}
};

146
src/math/Vector2.zig Normal file
View File

@@ -0,0 +1,146 @@
const Vector3 = @import("Vector3.zig").Vector3;
const Vector4 = @import("Vector3.zig").Vector4;
pub const Vector2 = extern struct {
vector: Vector,
pub const Vector = @Vector(2, f32);
pub const Mask = enum(i32) { x = 0, y = 1 };
pub const zero = Vector2.init(0, 0);
pub const one = Vector2.init(1, 1);
pub const unit_x = Vector2.init(1, 0);
pub const unit_y = Vector2.init(0, 1);
// --- INIT ---
pub inline fn init(x: f32, y: f32) Vector2 {
return .{ .vector = .{ x, y } };
}
pub inline fn initArray(array: [2]f32) Vector2 {
return .{ .vector = array };
}
// --- CONVERSION ---
pub inline fn asArray(self: Vector2) [2]f32 {
return self.vector;
}
pub inline fn asVector3(self: Vector2, z: f32) Vector3 {
const z_vector: @Vector(3, f32) = .{ undefined, undefined, z };
return .{ .vector = @shuffle(f32, self.vector, z_vector, .{ 0, 1, ~@as(i32, -2) }) };
}
pub inline fn asVector4(self: Vector4, z: f32, w: f32) Vector4 {
const zw_vector: @Vector(4, f32) = .{ undefined, undefined, z, w };
return .{ .vector = @shuffle(f32, self.vector, zw_vector, .{ 0, 1, ~@as(i32, -2), ~@as(i32, -3) }) };
}
// --- ACCESSORS ---
pub inline fn getX(self: Vector2) f32 {
return self.vector[0];
}
pub inline fn getY(self: Vector2) f32 {
return self.vector[1];
}
pub inline fn setX(self: Vector2, x: f32) Vector2 {
const x_vector: Vector = @splat(x);
return .{ .vector = @shuffle(f32, self, x_vector, .{ ~@as(i32, 0), 1 }) };
}
pub inline fn setY(self: Vector2, y: f32) Vector2 {
const y_vector: Vector = @splat(y);
return .{ .vector = @shuffle(f32, self, y_vector, .{ 0, ~@as(i32, 1) }) };
}
// --- COMPONENT-WISE ---
pub inline fn add(self: Vector2, other: Vector2) Vector2 {
return .{ .vector = self.vector + other.vector };
}
pub inline fn sub(self: Vector2, other: Vector2) Vector2 {
return .{ .vector = self.vector - other.vector };
}
pub inline fn mul(self: Vector2, other: Vector2) Vector2 {
return .{ .vector = self.vector * other.vector };
}
pub inline fn div(self: Vector2, other: Vector2) Vector2 {
return .{ .vector = self.vector / other.vector };
}
pub inline fn negate(self: Vector2) Vector2 {
return .{ .vector = -self.vector };
}
pub inline fn mulScalar(self: Vector2, scalar: f32) Vector2 {
const scalar_vector: Vector = @splat(scalar);
return .{ .vector = self.vector * scalar_vector };
}
pub inline fn divScalar(self: Vector2, scalar: f32) Vector2 {
const scalar_vector: Vector = @splat(scalar);
return .{ .vector = self.vector / scalar_vector };
}
// --- SWIZZLE ---
pub inline fn swizzle2(self: Vector2, comptime mask: [2]Mask) Vector2 {
return .{ .vector = @shuffle(f32, self.vector, undefined, @as([2]i32, @bitCast(mask))) };
}
pub inline fn swizzle3(self: Vector2, comptime mask: [3]Mask) Vector3 {
return .{ .vector = @shuffle(f32, self.vector, undefined, @as([3]i32, @bitCast(mask))) };
}
pub inline fn swizzle4(self: Vector2, comptime mask: [4]Mask) Vector4 {
return .{ .vector = @shuffle(f32, self.vector, undefined, @as([4]i32, @bitCast(mask))) };
}
// --- OTHER ---
pub inline fn len(self: Vector2) f32 {
return @sqrt(@reduce(.Add, self.vector * self.vector));
}
pub inline fn lenSquared(self: Vector2) f32 {
return @reduce(.Add, self.vector * self.vector);
}
pub inline fn normalize(self: Vector2) Vector2 {
return .{ .vector = self.vector / @sqrt(@reduce(.Add, self.vector * self.vector)) };
}
pub inline fn dot(self: Vector2, other: Vector2) f32 {
return @reduce(.Add, self.vector * other.vector);
}
pub inline fn cross(self: Vector2, other: Vector2) f32 {
return self.getX() * other.getY() - self.getY() * other.getX();
}
pub inline fn lerp(self: Vector2, other: Vector2, t: f32) Vector2 {
const s = 1.0 - t;
const t_vector: Vector = @splat(t);
const s_vector: Vector = @splat(s);
return .{ .vector = self * t_vector + other * s_vector };
}
pub inline fn rotate(self: Vector2, angle_rad: f32) Vector2 {
const c = @cos(angle_rad);
const s = @sin(angle_rad);
return .{
.vector = .{
self.x * c - self.y * s,
self.x * s + self.x * c,
},
};
}
};

102
src/math/Vector3.zig
View File

@@ -1,9 +1,12 @@
const Quaternion = @import("Quaternion.zig").Quaternion;
const Vector2 = @import("Vector2.zig").Vector2;
const Vector4 = @import("Vector4.zig").Vector4;
pub const Vector3 = extern struct {
vector: Vector,
pub const Vector = @Vector(3, f32);
pub const Mask = enum(i32) { x = 0, y = 1, z = 2 };
pub const zero = Vector3.init(0, 0, 0);
pub const one = Vector3.init(1, 1, 1);
@@ -11,10 +14,33 @@ pub const Vector3 = extern struct {
pub const unit_y = Vector3.init(0, 1, 0);
pub const unit_z = Vector3.init(0, 0, 1);
// --- INIT ---
pub inline fn init(x: f32, y: f32, z: f32) Vector3 {
return .{ .vector = .{ x, y, z } };
}
pub inline fn initArray(array: [3]f32) Vector3 {
return .{ .vector = array };
}
// --- CONVERSION ---
pub inline fn asArray(self: Vector3) [3]f32 {
return self.vector;
}
pub inline fn asVector2(self: Vector3) Vector2 {
return .{ .vector = @shuffle(f32, self.vector, undefined, .{ 0, 1 }) };
}
pub inline fn asVector4(self: Vector3, w: f32) Vector4 {
const w_vector: @Vector(4, f32) = .{ undefined, undefined, undefined, w };
return .{ .vector = @shuffle(f32, self.vector, w_vector, .{ 0, 1, 2, ~@as(i32, -3) }) };
}
// --- ACCESSORS ---
pub inline fn getX(self: Vector3) f32 {
return self.vector[0];
}
@@ -29,19 +55,21 @@ pub const Vector3 = extern struct {
pub inline fn setX(self: Vector3, x: f32) Vector3 {
const x_vector: Vector = @splat(x);
return .{ .vector = @shuffle(Vector, self, x_vector, .{ ~@as(i32, 0), 1, 2 }) };
return .{ .vector = @shuffle(f32, self, x_vector, .{ ~@as(i32, 0), 1, 2 }) };
}
pub inline fn setY(self: Vector3, y: f32) Vector3 {
const y_vector: Vector = @splat(y);
return .{ .vector = @shuffle(Vector, self, y_vector, .{ 0, ~@as(i32, 1), 2 }) };
return .{ .vector = @shuffle(f32, self, y_vector, .{ 0, ~@as(i32, 1), 2 }) };
}
pub inline fn setZ(self: Vector3, z: f32) Vector3 {
const z_vector: Vector = @splat(z);
return .{ .vector = @shuffle(Vector, self, z_vector, .{ 0, 1, ~@as(i32, 2) }) };
return .{ .vector = @shuffle(f32, self, z_vector, .{ 0, 1, ~@as(i32, 2) }) };
}
// --- COMPONENT-WISE ---
pub inline fn add(self: Vector3, other: Vector3) Vector3 {
return .{ .vector = self.vector + other.vector };
}
@@ -58,6 +86,10 @@ pub const Vector3 = extern struct {
return .{ .vector = self.vector / other.vector };
}
pub inline fn negate(self: Vector3) Vector3 {
return .{ .vector = -self.vector };
}
pub inline fn mulScalar(self: Vector3, scalar: f32) Vector3 {
const scalar_vector: Vector = @splat(scalar);
return .{ .vector = self.vector * scalar_vector };
@@ -68,8 +100,46 @@ pub const Vector3 = extern struct {
return .{ .vector = self.vector / scalar_vector };
}
pub inline fn negate(self: Vector3) Vector3 {
return .{ .vector = -self.vector };
// --- SWIZZLE ---
pub inline fn swizzle2(self: Vector3, comptime mask: [2]Mask) Vector2 {
return .{ .vector = @shuffle(f32, self.vector, undefined, @as([2]i32, @bitCast(mask))) };
}
pub inline fn swizzle3(self: Vector3, comptime mask: [3]Mask) Vector3 {
return .{ .vector = @shuffle(f32, self.vector, undefined, @as([3]i32, @bitCast(mask))) };
}
pub inline fn swizzle4(self: Vector3, comptime mask: [4]Mask) Vector4 {
return .{ .vector = @shuffle(f32, self.vector, undefined, @as([4]i32, @bitCast(mask))) };
}
// --- OTHER ---
pub inline fn len(self: Vector3) f32 {
return @sqrt(@reduce(.Add, self.vector * self.vector));
}
pub inline fn lenSquared(self: Vector3) f32 {
return @reduce(.Add, self.vector * self.vector);
}
pub inline fn normalize(self: Vector3) Vector3 {
return .{ .vector = self.vector / @sqrt(@reduce(.Add, self.vector * self.vector)) };
}
pub inline fn dot(self: Vector3, other: Vector3) f32 {
return @reduce(.Add, self.vector * other.vector);
}
pub inline fn cross(self: Vector3, other: Vector3) Vector3 {
return .{
.vector = .{
self.getY() * other.getZ() - self.getZ() * other.getY(),
self.getZ() * other.getX() - self.getX() * other.getZ(),
self.getX() * other.getY() - self.getY() * other.getX(),
},
};
}
pub inline fn lerp(self: Vector3, other: Vector3, t: f32) Vector3 {
@@ -79,15 +149,19 @@ pub const Vector3 = extern struct {
return .{ .vector = self * t_vector + other * s_vector };
}
pub inline fn swizzle3(self: Vector3, comptime mask: @Vector(3, i32)) Vector3 {
return .{ .vector = @shuffle(Vector, self, undefined, mask) };
}
pub inline fn rotate(self: Vector3, quaternion: Quaternion) Vector2 {
const quaternion_scalar = quaternion.getScalar();
const quaternion_vector = quaternion.getVector();
pub inline fn swizzle4(self: Vector3, comptime mask: @Vector(4, i32)) Vector4 {
return .{ .vector = @shuffle(Vector4.Vector, self, undefined, mask) };
}
pub inline fn asArray(self: Vector3) [3]f32 {
return self.vector;
return Vector3.add(
self,
Vector3.cross(
Vector3.add(quaternion_vector, quaternion_vector),
Vector3.add(
Vector3.cross(quaternion_vector, self),
Vector3.mulScalar(self, quaternion_scalar),
),
),
);
}
};

86
src/math/Vector4.zig
View File

@@ -1,9 +1,11 @@
const Vector2 = @import("Vector2.zig").Vector2;
const Vector3 = @import("Vector3.zig").Vector3;
pub const Vector4 = extern struct {
vector: Vector,
pub const Vector = @Vector(4, f32);
pub const Mask = enum(i32) { x = 0, y = 1, z = 2, w = 3 };
pub const zero = Vector4.init(0, 0, 0, 0);
pub const one = Vector4.init(1, 1, 1, 1);
@@ -12,10 +14,32 @@ pub const Vector4 = extern struct {
pub const unit_z = Vector4.init(0, 0, 1, 0);
pub const unit_w = Vector4.init(0, 0, 0, 1);
// --- INIT ---
pub inline fn init(x: f32, y: f32, z: f32, w: f32) Vector4 {
return .{ .vector = .{ x, y, z, w } };
}
pub inline fn initArray(array: [4]f32) Vector4 {
return .{ .vector = array };
}
// --- CONVERSION ---
pub inline fn asArray(self: Vector4) [4]f32 {
return self.vector;
}
pub inline fn asVector2(self: Vector4) Vector2 {
return .{ .vector = @shuffle(f32, self.vector, undefined, .{ 0, 1 }) };
}
pub inline fn asVector3(self: Vector4) Vector3 {
return .{ .vector = @shuffle(f32, self.vector, undefined, .{ 0, 1, 2 }) };
}
// --- ACCESSORS ---
pub inline fn getX(self: Vector4) f32 {
return self.vector[0];
}
@@ -34,24 +58,26 @@ pub const Vector4 = extern struct {
pub inline fn setX(self: Vector4, x: f32) Vector4 {
const x_vector: Vector = @splat(x);
return .{ .vector = @shuffle(Vector, self, x_vector, .{ ~@as(i32, 0), 1, 2, 3 }) };
return .{ .vector = @shuffle(f32, self, x_vector, .{ ~@as(i32, 0), 1, 2, 3 }) };
}
pub inline fn setY(self: Vector4, y: f32) Vector4 {
const y_vector: Vector = @splat(y);
return .{ .vector = @shuffle(Vector, self, y_vector, .{ 0, ~@as(i32, 1), 2, 3 }) };
return .{ .vector = @shuffle(f32, self, y_vector, .{ 0, ~@as(i32, 1), 2, 3 }) };
}
pub inline fn setZ(self: Vector4, z: f32) Vector4 {
const z_vector: Vector = @splat(z);
return .{ .vector = @shuffle(Vector, self, z_vector, .{ 0, 1, ~@as(i32, 2), 3 }) };
return .{ .vector = @shuffle(f32, self, z_vector, .{ 0, 1, ~@as(i32, 2), 3 }) };
}
pub inline fn setW(self: Vector4, w: f32) Vector4 {
const w_vector: Vector = @splat(w);
return .{ .vector = @shuffle(Vector, self, w_vector, .{ 0, 1, 2, ~@as(i32, 3) }) };
return .{ .vector = @shuffle(f32, self, w_vector, .{ 0, 1, 2, ~@as(i32, 3) }) };
}
// --- COMPONENT-WISE ---
pub inline fn add(self: Vector4, other: Vector4) Vector4 {
return .{ .vector = self.vector + other.vector };
}
@@ -68,6 +94,10 @@ pub const Vector4 = extern struct {
return .{ .vector = self.vector / other.vector };
}
pub inline fn negate(self: Vector4) Vector4 {
return .{ .vector = -self.vector };
}
pub inline fn mulScalar(self: Vector4, scalar: f32) Vector4 {
const scalar_vector: Vector = @splat(scalar);
return .{ .vector = self.vector * scalar_vector };
@@ -78,8 +108,36 @@ pub const Vector4 = extern struct {
return .{ .vector = self.vector / scalar_vector };
}
pub inline fn negate(self: Vector4) Vector4 {
return .{ .vector = -self.vector };
// --- SWIZZLE ---
pub inline fn swizzle2(self: Vector4, comptime mask: [2]Mask) Vector2 {
return .{ .vector = @shuffle(f32, self.vector, undefined, @as([2]i32, @bitCast(mask))) };
}
pub inline fn swizzle3(self: Vector4, comptime mask: [3]Mask) Vector3 {
return .{ .vector = @shuffle(f32, self.vector, undefined, @as([3]i32, @bitCast(mask))) };
}
pub inline fn swizzle4(self: Vector4, comptime mask: [4]Mask) Vector4 {
return .{ .vector = @shuffle(f32, self.vector, undefined, @as([4]i32, @bitCast(mask))) };
}
// --- OTHER ---
pub inline fn len(self: Vector4) f32 {
return @sqrt(@reduce(.Add, self.vector * self.vector));
}
pub inline fn lenSquared(self: Vector4) f32 {
return @reduce(.Add, self.vector * self.vector);
}
pub inline fn normalize(self: Vector4) Vector4 {
return .{ .vector = self.vector / @sqrt(@reduce(.Add, self.vector * self.vector)) };
}
pub inline fn dot(self: Vector4, other: Vector4) f32 {
return @reduce(.Add, self.vector * other.vector);
}
pub inline fn lerp(self: Vector4, other: Vector4, t: f32) Vector4 {
@@ -88,20 +146,4 @@ pub const Vector4 = extern struct {
const s_vector: Vector = @splat(s);
return .{ .vector = self * t_vector + other * s_vector };
}
pub inline fn asVector3(self: Vector4) Vector3 {
return .{ .vector = @shuffle(Vector3.Vector, self.vector, undefined, .{ 0, 1, 2 }) };
}
pub inline fn swizzle3(self: Vector4, comptime mask: @Vector(3, i32)) Vector3 {
return .{ .vector = @shuffle(Vector3.Vector, self.vector, undefined, mask) };
}
pub inline fn swizzle4(self: Vector4, comptime mask: @Vector(4, i32)) Vector4 {
return .{ .vector = @shuffle(Vector, self.vector, undefined, mask) };
}
pub inline fn asArray(self: Vector4) [4]f32 {
return self.vector;
}
};