Implemented transformations
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Lorenzo Torres
parent
00d51fc970
commit
6b948f6718
6 changed files with 250 additions and 30 deletions
218
src/math.zig
218
src/math.zig
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@ -3,23 +3,60 @@ pub const tan = std.math.tan;
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pub const cos = std.math.cos;
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pub const sin = std.math.sin;
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pub const rad = std.math.degreesToRadians;
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pub const sqrt = std.math.sqrt;
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pub const Axis = struct {
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pub const x: [3]f32 = .{1.0, 0.0, 0.0};
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pub const y: [3]f32 = .{0.0, 1.0, 0.0};
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pub const z: [3]f32 = .{0.0, 0.0, 1.0};
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};
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pub const Transform = struct {
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translation: Matrix,
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scale: Matrix,
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rotation: Quaternion,
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pub fn init(position: [3]f32, scale: [3]f32, rotation: [3]f32) Transform {
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var translation = Matrix.identity();
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translation.translate(position);
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return .{
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.translation = translation,
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.rotation = Quaternion.fromEulerAngles(rotation),
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.scale = Matrix.scale(scale),
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};
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}
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pub fn translate(self: *Transform, delta: [3]f32) void {
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self.translation.translate(delta);
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}
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pub fn rotate(self: *Transform, angle: f32, axis: [3]f32) void {
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const delta = Quaternion.fromAxisAngle(axis, angle);
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self.rotation = self.rotation.mul(delta);
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self.rotation = self.rotation.normalize();
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}
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};
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pub const Matrix = struct {
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rows: [4]@Vector(4, f32),
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rows: [4][4]f32,
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pub fn lookAt(eye: @Vector(3, f32), target: @Vector(3, f32), arbitrary_up: @Vector(3, f32)) Matrix {
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const forward = normalize(target - eye);
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const right = normalize(cross(forward, arbitrary_up));
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pub fn lookAt(eye: [3]f32, target: [3]f32, arbitrary_up: [3]f32) Matrix {
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const t: @Vector(3, f32) = target;
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const e: @Vector(3, f32) = eye;
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const u: @Vector(3, f32) = arbitrary_up;
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const forward = normalize(t - e);
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const right = normalize(cross(forward, u));
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const up = cross(right, forward);
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const view = [_]@Vector(4, f32){
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@Vector(4, f32){ right[0], up[0], -forward[0], 0.0 },
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@Vector(4, f32){ right[1], up[1], -forward[1], 0.0 },
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@Vector(4, f32){ right[2], up[2], -forward[2], 0.0 },
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@Vector(4, f32){ -dot(eye, right), -dot(eye, up), -dot(eye, forward), 1.0 },
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const view = [4][4]f32{
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[4]f32{ right[0], up[0], -forward[0], 0.0 },
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[4]f32{ right[1], up[1], -forward[1], 0.0 },
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[4]f32{ right[2], up[2], -forward[2], 0.0 },
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[4]f32{ -dot(e, right), -dot(e, up), -dot(e, forward), 1.0 },
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};
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return Matrix{
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return .{
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.rows = view,
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};
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}
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@ -31,28 +68,161 @@ pub const Matrix = struct {
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const a = near / (far - near);
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const b = far * a;
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const projection = [_]@Vector(4, f32){
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@Vector(4, f32){ x, 0.0, 0.0, 0.0 },
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@Vector(4, f32){ 0.0, y, 0.0, 0.0 },
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@Vector(4, f32){ 0.0, 0.0, a, b },
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@Vector(4, f32){ 0.0, 0.0, 1.0, 0.0 },
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const projection = [4][4]f32{
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[4]f32{ x, 0.0, 0.0, 0.0 },
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[4]f32{ 0.0, y, 0.0, 0.0 },
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[4]f32{ 0.0, 0.0, a, b },
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[4]f32{ 0.0, 0.0, 1.0, 0.0 },
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};
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return Matrix{
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return .{
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.rows = projection,
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};
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}
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pub fn identity() Matrix {
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const view = [_]@Vector(4, f32){
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@Vector(4, f32){ 1.0, 0.0, 0.0, 0.0 },
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@Vector(4, f32){ 0.0, 1.0, 0.0, 0.0 },
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@Vector(4, f32){ 0.0, 0.0, 1.0, 0.0 },
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@Vector(4, f32){ 0.0, 0.0, 0.0, 1.0 },
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pub inline fn identity() Matrix {
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return .{
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.rows = .{
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[4]f32{ 1.0, 0.0, 0.0, 0.0 },
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[4]f32{ 0.0, 1.0, 0.0, 0.0 },
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[4]f32{ 0.0, 0.0, 1.0, 0.0 },
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[4]f32{ 0.0, 0.0, 0.0, 1.0 },
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},
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};
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}
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pub fn mul(a: Matrix, b: Matrix) Matrix {
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var result = [4][4]f32{
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[4]f32{ 0.0, 0.0, 0.0, 0.0 },
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[4]f32{ 0.0, 0.0, 0.0, 0.0 },
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[4]f32{ 0.0, 0.0, 0.0, 0.0 },
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[4]f32{ 0.0, 0.0, 0.0, 0.0 },
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};
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return Matrix{
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.rows = view,
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for (0..4) |i| {
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for (0..4) |j| {
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for (0..4) |k| {
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result[i][j] += a.rows[i][k] * b.rows[k][j];
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}
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}
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}
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return .{
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.rows = result,
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};
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}
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pub inline fn translate(a: *Matrix, pos: [3]f32) void {
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a.rows[3][0] += pos[0];
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a.rows[3][1] += pos[1];
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a.rows[3][2] += pos[2];
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}
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pub inline fn scale(s: [3]f32) Matrix {
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return .{
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.rows = [4][4]f32{
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[4]f32{ s[0], 0.0, 0.0, 0.0 },
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[4]f32{ 0.0, s[1], 0.0, 0.0 },
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[4]f32{ 0.0, 0.0, s[2], 0.0 },
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[4]f32{ 0.0, 0.0, 0.0, 1.0 },
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},
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};
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}
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pub fn transform(pos: [3]f32, s: [3]f32) Matrix {
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var translation = Matrix.identity();
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translation.translate(pos);
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return translation.mul(Matrix.scale(s));
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}
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};
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const Quaternion = struct {
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w: f32,
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x: f32,
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y: f32,
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z: f32,
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pub const identity: Quaternion = .{ .w = 1.0, .x = 0.0, .y = 0.0, .z = 0.0 };
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pub fn fromAxisAngle(axis: [3]f32, angle: f32) Quaternion {
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const half_angle = angle / 2.0;
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const s = sin(half_angle);
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return .{
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.w = cos(half_angle),
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.x = axis[0] * s,
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.y = axis[1] * s,
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.z = axis[3] * s,
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};
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}
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fn fromEulerAngles(rotation: [3]f32) Quaternion {
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const pitch = rotation[0];
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const yaw = rotation[1];
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const roll = rotation[2];
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const half_pitch = pitch / 2.0;
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const half_yaw = yaw / 2.0;
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const half_roll = roll / 2.0;
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const sin_pitch = sin(half_pitch);
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const cos_pitch = cos(half_pitch);
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const sin_yaw = sin(half_yaw);
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const cos_yaw = cos(half_yaw);
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const sin_roll = sin(half_roll);
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const cos_roll = cos(half_roll);
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return .{
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.w = cos_yaw * cos_pitch * cos_roll + sin_yaw * sin_pitch * sin_roll,
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.x = cos_yaw * sin_pitch * cos_roll + sin_yaw * cos_pitch * sin_roll,
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.y = sin_yaw * cos_pitch * cos_roll - cos_yaw * sin_pitch * sin_roll,
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.z = cos_yaw * cos_pitch * sin_roll - sin_yaw * sin_pitch * cos_roll,
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};
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}
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inline fn mul(a: Quaternion, b: Quaternion) Quaternion {
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return .{
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.w = a.w * b.w - a.x * b.x - a.y * b.y - a.z * b.z,
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.x = a.w * b.x + a.x * b.w + a.y * b.z - a.z * b.y,
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.y = a.w * b.y - a.x * b.z + a.y * b.w + a.z * b.x,
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.z = a.w * b.z + a.x * b.y - a.y * b.x + a.z * b.w,
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};
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}
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fn normalize(q: Quaternion) Quaternion {
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const mag = sqrt(q.w*q.w + q.x*q.x + q.y*q.y + q.z*q.z);
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return Quaternion{
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.w = q.w / mag,
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.x = q.x / mag,
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.y = q.y / mag,
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.z = q.z / mag,
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};
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}
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fn matrix(q: Quaternion) Matrix {
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const x2 = q.x + q.x;
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const y2 = q.y + q.y;
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const z2 = q.z + q.z;
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const xx = q.x * x2;
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const yy = q.y * y2;
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const zz = q.z * z2;
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const xy = q.x * y2;
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const xz = q.x * z2;
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const yz = q.y * z2;
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const wx = q.w * x2;
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const wy = q.w * y2;
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const wz = q.w * z2;
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return .{
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.rows = .{
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.{ 1.0 - (yy + zz), xy - wz, xz + wy, 0.0 },
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.{ xy + wz, 1.0 - (xx + zz), yz - wx, 0.0 },
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.{ xz - wy, yz + wx, 1.0 - (xx + yy), 0.0 },
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.{ 0.0, 0.0, 0.0, 1.0 },
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}
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};
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}
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};
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