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#[allow(unused)]
pub mod calculus {
use rand::Rng;
#[derive(Copy, Clone, Debug)]
pub struct Vec3 {
pub x: f32,
pub y: f32,
pub z: f32,
// cached: Vec3Cache,
}
pub type Point3 = Vec3;
impl Vec3 {
pub fn new(x: f32, y: f32, z: f32) -> Self {
Self { x, y, z }
}
fn random() -> Self {
let mut rng = rand::rng();
Self::new(
rng.random(),
rng.random(),
rng.random(),
)
}
fn random_range(min: f32, max: f32) -> Self {
let mut rng = rand::rng();
Self::new(
rng.random_range(min..max),
rng.random_range(min..max),
rng.random_range(min..max),
)
}
pub fn random_unit() -> Vec3 {
loop {
let p = Self::random_range(-1.0, 1.0);
let lensq = p.mag_sqr();
if f32::EPSILON < lensq && lensq <= 1.0 {
return p.scalar_mul(1.0 / lensq.sqrt())
}
}
}
pub fn random_on_hemisphere(normal: &Vec3) -> Vec3 {
let on_unit_sphere = Self::random_unit();
if on_unit_sphere.dot_prod(normal) > 0.0 {
on_unit_sphere
} else {
on_unit_sphere.scalar_mul(-1.0)
}
}
pub fn add(&self, other: &Self) -> Self {
Self {
x: self.x + other.x,
y: self.y + other.y,
z: self.z + other.z
}
}
pub fn sub(&self, other: &Self) -> Self {
Self {
x: self.x - other.x,
y: self.y - other.y,
z: self.z - other.z
}
}
pub fn scalar_mul(&self, multiplier: f32) -> Self {
Self {
x: self.x * multiplier,
y: self.y * multiplier,
z: self.z * multiplier,
}
}
pub fn mag_sqr(&self) -> f32 {
self.x * self.x + self.y * self.y + self.z * self.z
}
pub fn mag(&self) -> f32 {
self.mag_sqr().sqrt()
}
pub fn dot_prod(&self, other: &Self) -> f32 {
self.x * other.x + self.y * other.y + self.z * other.z
}
pub fn cross_prod(&self, other: &Self) -> Self {
Self {
x: self.y * other.z - self.z * other.y,
y: self.z * other.x - self.x * other.z,
z: self.x * other.y - self.y * other.x,
}
}
pub fn unit(&self) -> Self {
let mag = self.mag();
Self {
x: self.x / mag,
y: self.y / mag,
z: self.z / mag,
}
}
pub fn is_near_zero(&self) -> bool {
self.x.abs() < f32::EPSILON &&
self.y.abs() < f32::EPSILON &&
self.z.abs() < f32::EPSILON
}
pub fn reflect(&self, normal: &Self) -> Self {
self.sub(
&normal.scalar_mul(
2.0 * self.dot_prod(&normal)
)
)
}
pub fn refract(&self, normal: &Self, etai_over_etat: f32) -> Self {
let cos_theta = f32::min(
1.0,
self.scalar_mul(-1.0).dot_prod(&normal)
);
let r_out_perp = self
.add(&normal.scalar_mul(cos_theta))
.scalar_mul(etai_over_etat);
let f = (1.0 - r_out_perp.mag_sqr()).abs().sqrt();
let r_out_parallel = normal.scalar_mul(-1.0 * f);
r_out_perp.add(&r_out_parallel)
}
pub fn random_in_unit_disk() -> Self {
let mut rng = rand::rng();
loop {
let p = Vec3::new(
rng.random_range(-1.0..1.0),
rng.random_range(-1.0..1.0),
0.0
);
if p.mag_sqr() < 1.0 {
return p;
}
}
}
}
pub struct Ray {
pub origin: Point3,
pub direction: Vec3,
}
impl Ray {
pub fn at(&self, t: f32) -> Point3 {
// Get parametric location
self.origin.add(&self.direction.scalar_mul(t))
}
pub fn reflect(&self, normal: &Vec3) -> Vec3 {
// return unit direction vector
self.direction.reflect(&normal).unit()
}
pub fn refract(&self, normal: &Vec3, etai_over_etat: f32) -> Vec3 {
// return unit direction vector
self.direction.unit().refract(&normal, etai_over_etat)
}
}
pub fn deg2rad(deg: f32) -> f32 {
deg * std::f32::consts::PI / 180.0
}
pub fn sample_square() -> Vec3 {
// Returns the vector to a random point in the [-.5,-.5]-[+.5,+.5] unit square.
let mut rng = rand::rng();
Vec3::new(
rng.random_range(0.0..1.0) - 0.5,
rng.random_range(0.0..1.0) - 0.5,
0.0)
}
}
pub struct Interval {
pub min: f32,
pub max: f32,
}
#[allow(unused)]
impl Interval {
pub fn new(min: f32, max: f32) -> Self {
Self { min, max }
}
pub fn size(&self) -> f32 {
self.max - self.min
}
pub fn contains(&self, x: f32) -> bool {
self.min <= x && x <= self.max
}
pub fn surrounds(&self, x: f32) -> bool {
self.min < x && x < self.max
}
pub fn clamp(&self, x: f32) -> f32 {
if x < self.min { return self.min }
if x > self.max { return self.max }
x
}
}
impl Default for Interval {
fn default() -> Self {
Self {
min: f32::NEG_INFINITY,
max: f32::INFINITY
}
}
}
#[allow(unused)]
pub const INTERVAL_EMPTY: Interval = Interval {
min: f32::INFINITY,
max: f32::NEG_INFINITY
};
#[allow(unused)]
pub const INTERVAL_UNIVERSE: Interval = Interval {
min: f32::NEG_INFINITY,
max: f32::INFINITY
};
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