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-//------------------------------------------------------------------------------
-// math.zig
-//
-// minimal vector math helper functions, just the stuff needed for
-// the sokol-samples
-//
-// Ported from HandmadeMath.h
-//------------------------------------------------------------------------------
-const assert = @import("std").debug.assert;
-const math = @import("std").math;
-
-fn radians(deg: f32) f32 {
- return deg * (math.pi / 180.0);
-}
-
-pub const Vec2 = extern struct {
- x: f32,
- y: f32,
-
- pub fn zero() Vec2 {
- return Vec2{ .x = 0.0, .y = 0.0 };
- }
-
- pub fn new(x: f32, y: f32) Vec2 {
- return Vec2{ .x = x, .y = y };
- }
-};
-
-pub const Vec3 = extern struct {
- x: f32,
- y: f32,
- z: f32,
-
- pub fn zero() Vec3 {
- return Vec3{ .x = 0.0, .y = 0.0, .z = 0.0 };
- }
-
- pub fn new(x: f32, y: f32, z: f32) Vec3 {
- return Vec3{ .x = x, .y = y, .z = z };
- }
-
- pub fn up() Vec3 {
- return Vec3{ .x = 0.0, .y = 1.0, .z = 0.0 };
- }
-
- pub fn len(v: Vec3) f32 {
- return math.sqrt(Vec3.dot(v, v));
- }
-
- pub fn add(left: Vec3, right: Vec3) Vec3 {
- return Vec3{ .x = left.x + right.x, .y = left.y + right.y, .z = left.z + right.z };
- }
-
- pub fn sub(left: Vec3, right: Vec3) Vec3 {
- return Vec3{ .x = left.x - right.x, .y = left.y - right.y, .z = left.z - right.z };
- }
-
- pub fn mul(v: Vec3, s: f32) Vec3 {
- return Vec3{ .x = v.x * s, .y = v.y * s, .z = v.z * s };
- }
-
- pub fn norm(v: Vec3) Vec3 {
- const l = Vec3.len(v);
- if (l != 0.0) {
- return Vec3{ .x = v.x / l, .y = v.y / l, .z = v.z / l };
- } else {
- return Vec3.zero();
- }
- }
-
- pub fn cross(v0: Vec3, v1: Vec3) Vec3 {
- return Vec3{ .x = (v0.y * v1.z) - (v0.z * v1.y), .y = (v0.z * v1.x) - (v0.x * v1.z), .z = (v0.x * v1.y) - (v0.y * v1.x) };
- }
-
- pub fn dot(v0: Vec3, v1: Vec3) f32 {
- return v0.x * v1.x + v0.y * v1.y + v0.z * v1.z;
- }
-};
-
-pub const Mat4 = extern struct {
- m: [4][4]f32,
-
- pub fn identity() Mat4 {
- return Mat4{
- .m = [_][4]f32{ .{ 1.0, 0.0, 0.0, 0.0 }, .{ 0.0, 1.0, 0.0, 0.0 }, .{ 0.0, 0.0, 1.0, 0.0 }, .{ 0.0, 0.0, 0.0, 1.0 } },
- };
- }
-
- pub fn zero() Mat4 {
- return Mat4{
- .m = [_][4]f32{ .{ 0.0, 0.0, 0.0, 0.0 }, .{ 0.0, 0.0, 0.0, 0.0 }, .{ 0.0, 0.0, 0.0, 0.0 }, .{ 0.0, 0.0, 0.0, 0.0 } },
- };
- }
-
- pub fn mul(left: Mat4, right: Mat4) Mat4 {
- var res = Mat4.zero();
- for (0..4) |col| {
- for (0..4) |row| {
- res.m[col][row] = left.m[0][row] * right.m[col][0] +
- left.m[1][row] * right.m[col][1] +
- left.m[2][row] * right.m[col][2] +
- left.m[3][row] * right.m[col][3];
- }
- }
- return res;
- }
-
- pub fn persp(fov: f32, aspect: f32, near: f32, far: f32) Mat4 {
- var res = Mat4.identity();
- const t = math.tan(fov * (math.pi / 360.0));
- res.m[0][0] = 1.0 / t;
- res.m[1][1] = aspect / t;
- res.m[2][3] = -1.0;
- res.m[2][2] = (near + far) / (near - far);
- res.m[3][2] = (2.0 * near * far) / (near - far);
- res.m[3][3] = 0.0;
- return res;
- }
-
- pub fn lookat(eye: Vec3, center: Vec3, up: Vec3) Mat4 {
- var res = Mat4.zero();
-
- const f = Vec3.norm(Vec3.sub(center, eye));
- const s = Vec3.norm(Vec3.cross(f, up));
- const u = Vec3.cross(s, f);
-
- res.m[0][0] = s.x;
- res.m[0][1] = u.x;
- res.m[0][2] = -f.x;
-
- res.m[1][0] = s.y;
- res.m[1][1] = u.y;
- res.m[1][2] = -f.y;
-
- res.m[2][0] = s.z;
- res.m[2][1] = u.z;
- res.m[2][2] = -f.z;
-
- res.m[3][0] = -Vec3.dot(s, eye);
- res.m[3][1] = -Vec3.dot(u, eye);
- res.m[3][2] = Vec3.dot(f, eye);
- res.m[3][3] = 1.0;
-
- return res;
- }
-
- pub fn rotate(angle: f32, axis_unorm: Vec3) Mat4 {
- var res = Mat4.identity();
-
- const axis = Vec3.norm(axis_unorm);
- const sin_theta = math.sin(radians(angle));
- const cos_theta = math.cos(radians(angle));
- const cos_value = 1.0 - cos_theta;
-
- res.m[0][0] = (axis.x * axis.x * cos_value) + cos_theta;
- res.m[0][1] = (axis.x * axis.y * cos_value) + (axis.z * sin_theta);
- res.m[0][2] = (axis.x * axis.z * cos_value) - (axis.y * sin_theta);
- res.m[1][0] = (axis.y * axis.x * cos_value) - (axis.z * sin_theta);
- res.m[1][1] = (axis.y * axis.y * cos_value) + cos_theta;
- res.m[1][2] = (axis.y * axis.z * cos_value) + (axis.x * sin_theta);
- res.m[2][0] = (axis.z * axis.x * cos_value) + (axis.y * sin_theta);
- res.m[2][1] = (axis.z * axis.y * cos_value) - (axis.x * sin_theta);
- res.m[2][2] = (axis.z * axis.z * cos_value) + cos_theta;
-
- return res;
- }
-
- pub fn translate(translation: Vec3) Mat4 {
- var res = Mat4.identity();
- res.m[3][0] = translation.x;
- res.m[3][1] = translation.y;
- res.m[3][2] = translation.z;
- return res;
- }
-};
-
-test "Vec3.zero" {
- const v = Vec3.zero();
- assert(v.x == 0.0 and v.y == 0.0 and v.z == 0.0);
-}
-
-test "Vec3.new" {
- const v = Vec3.new(1.0, 2.0, 3.0);
- assert(v.x == 1.0 and v.y == 2.0 and v.z == 3.0);
-}
-
-test "Mat4.ident" {
- const m = Mat4.identity();
- for (m.m, 0..) |row, y| {
- for (row, 0..) |val, x| {
- if (x == y) {
- assert(val == 1.0);
- } else {
- assert(val == 0.0);
- }
- }
- }
-}
-
-test "Mat4.mul" {
- const l = Mat4.identity();
- const r = Mat4.identity();
- const m = Mat4.mul(l, r);
- for (m.m, 0..) |row, y| {
- for (row, 0..) |val, x| {
- if (x == y) {
- assert(val == 1.0);
- } else {
- assert(val == 0.0);
- }
- }
- }
-}
-
-fn eq(val: f32, cmp: f32) bool {
- const delta: f32 = 0.00001;
- return (val > (cmp - delta)) and (val < (cmp + delta));
-}
-
-test "Mat4.persp" {
- const m = Mat4.persp(60.0, 1.33333337, 0.01, 10.0);
-
- assert(eq(m.m[0][0], 1.73205));
- assert(eq(m.m[0][1], 0.0));
- assert(eq(m.m[0][2], 0.0));
- assert(eq(m.m[0][3], 0.0));
-
- assert(eq(m.m[1][0], 0.0));
- assert(eq(m.m[1][1], 2.30940));
- assert(eq(m.m[1][2], 0.0));
- assert(eq(m.m[1][3], 0.0));
-
- assert(eq(m.m[2][0], 0.0));
- assert(eq(m.m[2][1], 0.0));
- assert(eq(m.m[2][2], -1.00200));
- assert(eq(m.m[2][3], -1.0));
-
- assert(eq(m.m[3][0], 0.0));
- assert(eq(m.m[3][1], 0.0));
- assert(eq(m.m[3][2], -0.02002));
- assert(eq(m.m[3][3], 0.0));
-}
-
-test "Mat4.lookat" {
- const m = Mat4.lookat(.{ .x = 0.0, .y = 1.5, .z = 6.0 }, Vec3.zero(), Vec3.up());
-
- assert(eq(m.m[0][0], 1.0));
- assert(eq(m.m[0][1], 0.0));
- assert(eq(m.m[0][2], 0.0));
- assert(eq(m.m[0][3], 0.0));
-
- assert(eq(m.m[1][0], 0.0));
- assert(eq(m.m[1][1], 0.97014));
- assert(eq(m.m[1][2], 0.24253));
- assert(eq(m.m[1][3], 0.0));
-
- assert(eq(m.m[2][0], 0.0));
- assert(eq(m.m[2][1], -0.24253));
- assert(eq(m.m[2][2], 0.97014));
- assert(eq(m.m[2][3], 0.0));
-
- assert(eq(m.m[3][0], 0.0));
- assert(eq(m.m[3][1], 0.0));
- assert(eq(m.m[3][2], -6.18465));
- assert(eq(m.m[3][3], 1.0));
-}
-
-test "Mat4.rotate" {
- const m = Mat4.rotate(2.0, .{ .x = 0.0, .y = 1.0, .z = 0.0 });
-
- assert(eq(m.m[0][0], 0.99939));
- assert(eq(m.m[0][1], 0.0));
- assert(eq(m.m[0][2], -0.03489));
- assert(eq(m.m[0][3], 0.0));
-
- assert(eq(m.m[1][0], 0.0));
- assert(eq(m.m[1][1], 1.0));
- assert(eq(m.m[1][2], 0.0));
- assert(eq(m.m[1][3], 0.0));
-
- assert(eq(m.m[2][0], 0.03489));
- assert(eq(m.m[2][1], 0.0));
- assert(eq(m.m[2][2], 0.99939));
- assert(eq(m.m[2][3], 0.0));
-
- assert(eq(m.m[3][0], 0.0));
- assert(eq(m.m[3][1], 0.0));
- assert(eq(m.m[3][2], 0.0));
- assert(eq(m.m[3][3], 1.0));
-}
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